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Lectures bdquoPumps and pumpingldquo Prof T Koppel Department of Mechanics Tallinn Technical University Contents 1 Pump Types and Definitions 11 Pump Types 12 Operating Variables of the Pumps 13 Pumping Head 14 Pump Power and Efficiency 15 Pump Suction Head 2 Impeller Pumps 21 Centrifugal Pumps 211 Single-Stage Centrifugal Pump 212 Forces on Impeller 213 Main Types of Centrifugal Pumps 22 Axial Flow Pumps 23 Regenerative Pumps 24 Shaft Seals of the Impeller Pump 3 Theory of Impeller Pumps 31 Turbomachine Equation 32 Similarity of Pumps 33 Specific Speed of Pump 34 Pump Characteristics 4 Application of Pumps 41 System Curve 42 Operating Point 43 Operation of Pumps in Parallel 44 Operation of Pumps in Series 45 Energy Savings with Variable-Speed Centrifugal Pump Drive 46 Effect of Liquid Viscosity on Performance of a Pump 47 Cavitation 5 Positive-Displacement Pumps 6 Selection of Pump Literature
1 R W Fox A T McDonald Introduction to Fluid Mechanics John Wiley amp Sons 1994 781 pp
2 R Neumaier Hermetic Pumps Gulf Publishing Company 1997 593 pp 3 A Maastik H Haldre T Koppel L Paal Huumldraulika ja pumbad Greif 1995 467 lk 4 Bergius Blomsted Hedenfalk Jonsson Kempe Nilsson Pegert Ullgren
Wennstroumlm Pumpputekniikka Nesteiden pumppaus Insinoumloumlrilehdet OY 1978 s199
1 1 Pump Types and Definitions 11 Pump Types Machines that add energy to a fluid stream are called pumps when the flow is liquid or slurry and fans blowers or compressors for gas or vapor handling units depending on pressure rise Fluid machines may be broadly classified as either positive displacement or dynamic A centrifugal pump is a kinetic machine convecting mechanical energy into hydraulic energy through centrifugal activity 12 Operating Variables of the Pumps
- pump capacity (rate of flow) Q m3s m3h ls lmin ndash pumpun tilavuusvirta
- pumping head discharge head H m ndash pumpun nostokorkeus
- power P kW - tehon tarve
- pump efficiency η ndash hyoumltysuhde
- net positive suction head NPSH m NPSHA (available) and NPSHR (required) ndash NPSH ndash arvo
- rotation speed n ndash pyoumlrimisnopeus
13 Pumping Head Hst ndash static or geodetic head m H = Hst + ht ndash total dynamic pumping head m ht ndash head loss in suction and pressure pipe m Total dynamic head H = Ep ndash Es (11)
Es = hs + g
ps
ρ+
gvs
2
2
hs ndash static head on the suction side m ps ndash absolute pressure on the suction side Pa vs ndash inflow velocity ms
gps
ρ=
gpatm
ρ- V - Zv
2
Figure 1 Installation scheme of the pump [3] V ndash vacuum m patm ndash atmospheric pressure Pa and
Es = hs + g
patm
ρ- V - Zv +
gvs
2
2
Ep = hs + g
pp
ρ+
gvp
2
2
pp ndash absolute pressure on the pressure side Pa vp ndash velocity on the pressure side ms Specific energy at the pump pressure port
gpp
ρ=
gpatm
ρ+ M + Zm
3 M ndash gauge head m and
Ep = hs + g
patm
ρ+ M + Zm +
gvp
2
2
Pumping head is equal
H = M + V + Zm + Zv + gvv sp
2
22 minus
14 Pump Power and Efficiency Pump output power Pw is the power imparted to the liquid by the pump
1000gQHPw
ρ= kW
where ρ kgm3 Q m3s and H m Pump input power Pp is the power delivered to the pump shaft at the driver to pump coupling
Pp gt Pw
Pump efficiency p
wp P
P=η and
mhvp ηηηη =
ndash volumetric efficiency qQ
Qv +=η
- hydraulic efficiency thtp
h HH
hHH
=+
=η
- mechanical efficiency p
hm P
P=η where
- hydraulic power 1000
)( thh
HqQgP +=ρ
kW
4
mhvp ηηηη = = p
w
p
th
th PP
PHqQg
HH
qQQ
=+
sdotsdot+ 1000
)(ρ
Drive efficiency motor
pmotor P
P=η
15 Pump Suction Head Static suction lift ndash hs (Fig 1) Head losses in suction pipe ndash hts
tsss
satm h
gv
gph
gp
+++=2
2
ρρ
To avoid cavitation the absolute pressure everywhere in the machine is kept above the vapor pressure of the operating liquid The NPSHA is the net total head provided by the system at the inlet cross section (reference cross section) of the pump (not of the impeller) at the centre of the suction connection It consists of the absolute pressure ps predominating at this point less the vapor pressure of the fluid in the inlet cross section plus the total head from the mean flow velocity in the reference cross section NPSHA can be defined as follows on the basis of the measurements on a running pump
Avss NPSHhg
vg
p+=+
2
2
ρ
NPSHA ndash the NPSH produced by the system NPSHR ndash the NPSH required for the pump relative to the permitted degree of cavitation ∆NPSH ndash excess of NPSHA over NPSHR (safety allowance) The duty point Qopt can be taken as
NPSHR = (03hellip05) n Q
with n in s-1 and Q in m3s or
NPSHR = σH
with σ = k 34
qn and 43
H
Qnns = when n = min-1 Q = m3s and k asymp 00014
5
Suction lift of the pump hs
)( Rtsvatm
s NPSHhhg
ph ++minus=ρ
Measures for the avoidance of cavitation
i) Measures by the operator - Reduction of geodetic suction lift or increase in suction head - Short suction line with largest possible cross section - Valves bends curves avoided where possible or the maximum radii used - The temperature of the fluid to be kept to a minimum - Application of a gas pressure to the surface of the liquid in closed suction or supply
vessels
ii) Measures by pump manufacturers - Impellers with double curvature blades drawn well forward into the suction orifice - Avoidance of short deflection radii at the blade cover - Reduction of the thickness of the impeller blades - Use of a smaller blade inlet angle - Reduction in speed - Fitting an inducer - Aligning the flow to the impeller by fitting a guide vane in the inlet connection
It must be mentioned that there are no materials which are resistant to cavitation damage
Figure 2 Cavitation erosion on the impeller of a centrifugal pump
6
2 Impeller Pumps 21 Centrifugal Pumps 211 Single-Stage Centrifugal Pump Centifugal pumps are machines in which fluids are conveyed in rotors (impellers) fitted with one or more blades by a moment so that pressure is gained in a continuous flow
Figure 3 Single stage centrifugal pump
1- impeller 2- impeller blade (vane) 3- volute or scroll 4- suction pipe 5- foot valve 6- suction strainer 7- diffuser 8- valve 9- pressure pipe 10- filling opening 11- water pipe for the seal 12- shaft seal
Impellers could be enclosed (Fig 3) semiopen (Fig 4) or open (vane wheel) (Fig 5)
Figure 4 Semiopen impeller for sewage pump
Figure 5 Open impeller
7
a) good b) poor Figure 6 Air lock in suction pipe 212 Forces on Impeller
Figure 7 Impeller unbalanced to the axial pressure
4
21
1
dpF s
π=
⎟⎠
⎞⎜⎝
⎛minus=
44
221
2
ddpF p
ππ
8
After simplifing ( )4
21dppF sp
πminus=
Figure 8 Balancing of axial pressure
Figure 9 Wear ring collars (a- low- b- mean- and c- high pressure pumps) 1- pump casing 2- wear ring 3- impeller 4- clearance
Figure 10 Impeller unbalanced to the radial pressure when flow rate is smaller from the pump design flow rate (a) and radial pressure in double ndashvolute pump (b) The radial force occurs on pumps with volute casings due to the uneven pressure distribution on the circumference of the impeller Radial force increases considerably in the partial flow rates and overload ranges as the changes in cross-section of the volute guide (eg with
9 circular cross-section) change quadratically via φ whereas the increase or decrease of the transport flow is linear 213 Main Types of Centrifugal Pumps
i) Single-Stage Pumps ii) Double-Suction Pump iii) Multistage Pumps
Figure 11 Multistage pump
Figure 12 Inducer postioned before the impeller [2]
- Submersible Pumps - Process Pumps - Pumps for Turbid Water - Portable Submersible Pumps (Flygt in 1948) - Sewage Pumps (Fig 13 - Swirl Type Impeller Pump and Super ndash Vortex Pump)
10
Figure 13 Impellers of swirl type pump 22 Axial Flow Pumps Scheme of the axial flow pump is given in the Fig 14 (1- vane 2-hub 3- vane of the guide apparatus) Vanes of the impeller are fixed or reversible
Figure 14 Axial flow pump
Figure 15 Impeller of the axial flow pump
11
23 Regenerative Pumps Special type of impeller pumps An impeller with several blades which are always radial and mounted on one or both sides rotates between two plane - parallel housing surfaces The energy of the fluid which is imparted to the particular liquid particles by impulse exchange steadily increases from the inlet into the impeller blades until its exit at the interrupter High pressure low flow rate
Figure 16 Water path in the impeller of the regenerative pump 2 4 Shaft Seals of Impeller pump
- Staffing box packing - Single mechanical seal - Double mechanical seals - Dynamic seal (Ahlstroumlm)
3 Theory of Impeller Pumps 31 Turbomachine Equation The flow processes in the impeller which lead to formation of the H(Q) line can be mathematically determined by the theoretical assumption that the impeller has an infinite number of infinitely thin blades The flow consists in this case from equal stream filaments The energy conversion can be arrived at with the aid of the moment of momentum principle The change of moment of momentum in time at the inlet (position 1) and at the oulet (position 2) is equal to the moment of forces to this liquid mass The loss-free flow is considered (ideal fluid) Pump Power (W= Nms) thgQHP ρ=
12
Figure 17 Flow velocities at impeller [3] is equal to the force moment to the shaft (Nm) multiplied with the impeller angular velocity ω (rads)
P =M ω
Theoretical pump head (m)
gQMHth ρω
=
In one second through the pump is flowing liquid mass m = ρQ (31) Moment of momentum at the position 1 and 2
M1 = mc1l1 and M2 = mc2l2
and changes of the moment of momentum
M = M2 - M1 =m(c2l2 - c1l1)
When we consider that l =R cos α and for mass (31)
M = ρQ (c2R2cos α2 ndash c1R1cos α1 )
As ωR1=u1 and ωR2=u2 then
g
ucucH th
)coscos( 111222 αα minus= (32)
13 This formula is Eulerrsquos equation for centrifugal pumps It represents a theoretical relationship between the individual values where there is an ideal uniform distribution of all liquid particles in the particular flow cross-sections However it also states bdquoThe theoretical head of a centrifugal pump is independent of the density and the physical properties of the fluid flowing through itldquo
Figure 18 Inlet and outlet triangles on radial impeller [2] Modern centrifugal pumps are constructed in this way that inflow has radial direction This means α = 90deg and cos α = 0
g
ucH th
222 cosα= (33)
The vortex torque component
cu = c cos α
and Hth = gcu u22
where cu2 is the vortex component of the absolute flow at the impeller outlet
Figure 19 Flow at the impeller of centrifugal pump ( a- real b- theoretical c- vortex) [3] ns rpm 40 50 75 100 125 150 175 200 250 k 078 080 081 082 0805 077 0715 0675 055
14
The specific speed ns of a pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The theoretical head Hth is reduced by the losses which occur due to
- volumetric internal leakage losses at the radial clearance between the impeller and casing
- friction losses in the blade channels - energy conversion losses (velocity in pressure due to changes in direction and cross-
section) - shock losses where the angle of the approach flow to the impeller blades is not
vertical Hydraulic efficiency is the real and theoretical pump head ratio
222 cosα
ηukc
gHHH
thh ==
Finally the turbomachine equation takes form
g
ukcH h 222 cosαη
= (34)
Figure 20 Different shapes of the impeller [3] The energy transfer begins at the inlet to the cascade and ends on departure from the blade channels The pressure and velocity of the pumped liquid is increased on this path The pressure increase is due to the centrifugal forces and deceleration in the relative velocity w in the impeller channels between the channel inlet and outlet The strong increase in the absolute velocity c of the fluid during the flow through the impeller channels is partly converted to pressure energy in a diffuser volute guide or stator after leaving the impeller A distinction is to be made between movement processes of the absolute velocity c and relative velocity w Absolute velocity c is that which liquid particles exibit compared with a static environment The relative velocity w is the velocity of a liquid particle compared with the rotating blades when flowing through the blade channel The peripheral velocity u of the rotating blades at the particular distance from the axis of rotation is also important The pressure path in the impeller is parabolic corresponding to the laws of dynamics To
15 determine the flow processes mathematically however all that is required is the recording of the velocities at the blade inlet and outlet Real head of the pump is smaller than theoretical In reality impeller has up to 12 blades The flow is different from theoretical between blades In the convex part of blade the velocity is smaller than in concave part The energy used for keeping vortex is decreasing the developed head by pump The head given for an infinite number of blades Hth is reduced due to the incomplete flow guidance where there is a finite number (mainly 7) of blades A comparison of the velocity diagrams for the actual and fictitious flow shows vortex components The decrease of the head is considered with the coefficient k which depends from the construction of the pump k is characterized by the specific speed ns of the pump Theoretically it is impossible to calulate hydraulic efficiency ηh It depends from many factors Theory is giving qualitative recommendations to get higher efficiency
- to avioid sudden changes of velocities in pump - to avoid decrease of velocity on the impeller perimeter - to give simple shape to the impeller blades - to avoid sharp corners in the pump
In Fig 20 are given three different shapes of blades
If ω = const and Q = const for β2 = 90deg g
uH th
22= for β2 lt 90deg
guHth
22lt for β2 gt 90deg
guHth
22gt
For increasing the pump head the blades should be directed to the direction of rotation This will increase c2 and in diffuser we have to convert high kinetic energy to the potential energy and we lost in principal much energy The angle β2 lt 90deg is preferred for the pumps and β2 gt 90deg for ventilators 32 Similarity of Pumps Theoretical considerations are giving only qualitative results The more realistic results is possible to get by making pump or pump model tests especially in designing a new pump From the test results the pump similarity rules are used for calculating parameters of the pump under construction The theory of similarity is based on the rules of hydraulic modelling Geometric similitude ndash measures and shape of the model and pump should be in scale Kinematic similitude ndash velocities should be in scale
mmm cc
ww
uu
== etc
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
1 1 Pump Types and Definitions 11 Pump Types Machines that add energy to a fluid stream are called pumps when the flow is liquid or slurry and fans blowers or compressors for gas or vapor handling units depending on pressure rise Fluid machines may be broadly classified as either positive displacement or dynamic A centrifugal pump is a kinetic machine convecting mechanical energy into hydraulic energy through centrifugal activity 12 Operating Variables of the Pumps
- pump capacity (rate of flow) Q m3s m3h ls lmin ndash pumpun tilavuusvirta
- pumping head discharge head H m ndash pumpun nostokorkeus
- power P kW - tehon tarve
- pump efficiency η ndash hyoumltysuhde
- net positive suction head NPSH m NPSHA (available) and NPSHR (required) ndash NPSH ndash arvo
- rotation speed n ndash pyoumlrimisnopeus
13 Pumping Head Hst ndash static or geodetic head m H = Hst + ht ndash total dynamic pumping head m ht ndash head loss in suction and pressure pipe m Total dynamic head H = Ep ndash Es (11)
Es = hs + g
ps
ρ+
gvs
2
2
hs ndash static head on the suction side m ps ndash absolute pressure on the suction side Pa vs ndash inflow velocity ms
gps
ρ=
gpatm
ρ- V - Zv
2
Figure 1 Installation scheme of the pump [3] V ndash vacuum m patm ndash atmospheric pressure Pa and
Es = hs + g
patm
ρ- V - Zv +
gvs
2
2
Ep = hs + g
pp
ρ+
gvp
2
2
pp ndash absolute pressure on the pressure side Pa vp ndash velocity on the pressure side ms Specific energy at the pump pressure port
gpp
ρ=
gpatm
ρ+ M + Zm
3 M ndash gauge head m and
Ep = hs + g
patm
ρ+ M + Zm +
gvp
2
2
Pumping head is equal
H = M + V + Zm + Zv + gvv sp
2
22 minus
14 Pump Power and Efficiency Pump output power Pw is the power imparted to the liquid by the pump
1000gQHPw
ρ= kW
where ρ kgm3 Q m3s and H m Pump input power Pp is the power delivered to the pump shaft at the driver to pump coupling
Pp gt Pw
Pump efficiency p
wp P
P=η and
mhvp ηηηη =
ndash volumetric efficiency qQ
Qv +=η
- hydraulic efficiency thtp
h HH
hHH
=+
=η
- mechanical efficiency p
hm P
P=η where
- hydraulic power 1000
)( thh
HqQgP +=ρ
kW
4
mhvp ηηηη = = p
w
p
th
th PP
PHqQg
HH
qQQ
=+
sdotsdot+ 1000
)(ρ
Drive efficiency motor
pmotor P
P=η
15 Pump Suction Head Static suction lift ndash hs (Fig 1) Head losses in suction pipe ndash hts
tsss
satm h
gv
gph
gp
+++=2
2
ρρ
To avoid cavitation the absolute pressure everywhere in the machine is kept above the vapor pressure of the operating liquid The NPSHA is the net total head provided by the system at the inlet cross section (reference cross section) of the pump (not of the impeller) at the centre of the suction connection It consists of the absolute pressure ps predominating at this point less the vapor pressure of the fluid in the inlet cross section plus the total head from the mean flow velocity in the reference cross section NPSHA can be defined as follows on the basis of the measurements on a running pump
Avss NPSHhg
vg
p+=+
2
2
ρ
NPSHA ndash the NPSH produced by the system NPSHR ndash the NPSH required for the pump relative to the permitted degree of cavitation ∆NPSH ndash excess of NPSHA over NPSHR (safety allowance) The duty point Qopt can be taken as
NPSHR = (03hellip05) n Q
with n in s-1 and Q in m3s or
NPSHR = σH
with σ = k 34
qn and 43
H
Qnns = when n = min-1 Q = m3s and k asymp 00014
5
Suction lift of the pump hs
)( Rtsvatm
s NPSHhhg
ph ++minus=ρ
Measures for the avoidance of cavitation
i) Measures by the operator - Reduction of geodetic suction lift or increase in suction head - Short suction line with largest possible cross section - Valves bends curves avoided where possible or the maximum radii used - The temperature of the fluid to be kept to a minimum - Application of a gas pressure to the surface of the liquid in closed suction or supply
vessels
ii) Measures by pump manufacturers - Impellers with double curvature blades drawn well forward into the suction orifice - Avoidance of short deflection radii at the blade cover - Reduction of the thickness of the impeller blades - Use of a smaller blade inlet angle - Reduction in speed - Fitting an inducer - Aligning the flow to the impeller by fitting a guide vane in the inlet connection
It must be mentioned that there are no materials which are resistant to cavitation damage
Figure 2 Cavitation erosion on the impeller of a centrifugal pump
6
2 Impeller Pumps 21 Centrifugal Pumps 211 Single-Stage Centrifugal Pump Centifugal pumps are machines in which fluids are conveyed in rotors (impellers) fitted with one or more blades by a moment so that pressure is gained in a continuous flow
Figure 3 Single stage centrifugal pump
1- impeller 2- impeller blade (vane) 3- volute or scroll 4- suction pipe 5- foot valve 6- suction strainer 7- diffuser 8- valve 9- pressure pipe 10- filling opening 11- water pipe for the seal 12- shaft seal
Impellers could be enclosed (Fig 3) semiopen (Fig 4) or open (vane wheel) (Fig 5)
Figure 4 Semiopen impeller for sewage pump
Figure 5 Open impeller
7
a) good b) poor Figure 6 Air lock in suction pipe 212 Forces on Impeller
Figure 7 Impeller unbalanced to the axial pressure
4
21
1
dpF s
π=
⎟⎠
⎞⎜⎝
⎛minus=
44
221
2
ddpF p
ππ
8
After simplifing ( )4
21dppF sp
πminus=
Figure 8 Balancing of axial pressure
Figure 9 Wear ring collars (a- low- b- mean- and c- high pressure pumps) 1- pump casing 2- wear ring 3- impeller 4- clearance
Figure 10 Impeller unbalanced to the radial pressure when flow rate is smaller from the pump design flow rate (a) and radial pressure in double ndashvolute pump (b) The radial force occurs on pumps with volute casings due to the uneven pressure distribution on the circumference of the impeller Radial force increases considerably in the partial flow rates and overload ranges as the changes in cross-section of the volute guide (eg with
9 circular cross-section) change quadratically via φ whereas the increase or decrease of the transport flow is linear 213 Main Types of Centrifugal Pumps
i) Single-Stage Pumps ii) Double-Suction Pump iii) Multistage Pumps
Figure 11 Multistage pump
Figure 12 Inducer postioned before the impeller [2]
- Submersible Pumps - Process Pumps - Pumps for Turbid Water - Portable Submersible Pumps (Flygt in 1948) - Sewage Pumps (Fig 13 - Swirl Type Impeller Pump and Super ndash Vortex Pump)
10
Figure 13 Impellers of swirl type pump 22 Axial Flow Pumps Scheme of the axial flow pump is given in the Fig 14 (1- vane 2-hub 3- vane of the guide apparatus) Vanes of the impeller are fixed or reversible
Figure 14 Axial flow pump
Figure 15 Impeller of the axial flow pump
11
23 Regenerative Pumps Special type of impeller pumps An impeller with several blades which are always radial and mounted on one or both sides rotates between two plane - parallel housing surfaces The energy of the fluid which is imparted to the particular liquid particles by impulse exchange steadily increases from the inlet into the impeller blades until its exit at the interrupter High pressure low flow rate
Figure 16 Water path in the impeller of the regenerative pump 2 4 Shaft Seals of Impeller pump
- Staffing box packing - Single mechanical seal - Double mechanical seals - Dynamic seal (Ahlstroumlm)
3 Theory of Impeller Pumps 31 Turbomachine Equation The flow processes in the impeller which lead to formation of the H(Q) line can be mathematically determined by the theoretical assumption that the impeller has an infinite number of infinitely thin blades The flow consists in this case from equal stream filaments The energy conversion can be arrived at with the aid of the moment of momentum principle The change of moment of momentum in time at the inlet (position 1) and at the oulet (position 2) is equal to the moment of forces to this liquid mass The loss-free flow is considered (ideal fluid) Pump Power (W= Nms) thgQHP ρ=
12
Figure 17 Flow velocities at impeller [3] is equal to the force moment to the shaft (Nm) multiplied with the impeller angular velocity ω (rads)
P =M ω
Theoretical pump head (m)
gQMHth ρω
=
In one second through the pump is flowing liquid mass m = ρQ (31) Moment of momentum at the position 1 and 2
M1 = mc1l1 and M2 = mc2l2
and changes of the moment of momentum
M = M2 - M1 =m(c2l2 - c1l1)
When we consider that l =R cos α and for mass (31)
M = ρQ (c2R2cos α2 ndash c1R1cos α1 )
As ωR1=u1 and ωR2=u2 then
g
ucucH th
)coscos( 111222 αα minus= (32)
13 This formula is Eulerrsquos equation for centrifugal pumps It represents a theoretical relationship between the individual values where there is an ideal uniform distribution of all liquid particles in the particular flow cross-sections However it also states bdquoThe theoretical head of a centrifugal pump is independent of the density and the physical properties of the fluid flowing through itldquo
Figure 18 Inlet and outlet triangles on radial impeller [2] Modern centrifugal pumps are constructed in this way that inflow has radial direction This means α = 90deg and cos α = 0
g
ucH th
222 cosα= (33)
The vortex torque component
cu = c cos α
and Hth = gcu u22
where cu2 is the vortex component of the absolute flow at the impeller outlet
Figure 19 Flow at the impeller of centrifugal pump ( a- real b- theoretical c- vortex) [3] ns rpm 40 50 75 100 125 150 175 200 250 k 078 080 081 082 0805 077 0715 0675 055
14
The specific speed ns of a pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The theoretical head Hth is reduced by the losses which occur due to
- volumetric internal leakage losses at the radial clearance between the impeller and casing
- friction losses in the blade channels - energy conversion losses (velocity in pressure due to changes in direction and cross-
section) - shock losses where the angle of the approach flow to the impeller blades is not
vertical Hydraulic efficiency is the real and theoretical pump head ratio
222 cosα
ηukc
gHHH
thh ==
Finally the turbomachine equation takes form
g
ukcH h 222 cosαη
= (34)
Figure 20 Different shapes of the impeller [3] The energy transfer begins at the inlet to the cascade and ends on departure from the blade channels The pressure and velocity of the pumped liquid is increased on this path The pressure increase is due to the centrifugal forces and deceleration in the relative velocity w in the impeller channels between the channel inlet and outlet The strong increase in the absolute velocity c of the fluid during the flow through the impeller channels is partly converted to pressure energy in a diffuser volute guide or stator after leaving the impeller A distinction is to be made between movement processes of the absolute velocity c and relative velocity w Absolute velocity c is that which liquid particles exibit compared with a static environment The relative velocity w is the velocity of a liquid particle compared with the rotating blades when flowing through the blade channel The peripheral velocity u of the rotating blades at the particular distance from the axis of rotation is also important The pressure path in the impeller is parabolic corresponding to the laws of dynamics To
15 determine the flow processes mathematically however all that is required is the recording of the velocities at the blade inlet and outlet Real head of the pump is smaller than theoretical In reality impeller has up to 12 blades The flow is different from theoretical between blades In the convex part of blade the velocity is smaller than in concave part The energy used for keeping vortex is decreasing the developed head by pump The head given for an infinite number of blades Hth is reduced due to the incomplete flow guidance where there is a finite number (mainly 7) of blades A comparison of the velocity diagrams for the actual and fictitious flow shows vortex components The decrease of the head is considered with the coefficient k which depends from the construction of the pump k is characterized by the specific speed ns of the pump Theoretically it is impossible to calulate hydraulic efficiency ηh It depends from many factors Theory is giving qualitative recommendations to get higher efficiency
- to avioid sudden changes of velocities in pump - to avoid decrease of velocity on the impeller perimeter - to give simple shape to the impeller blades - to avoid sharp corners in the pump
In Fig 20 are given three different shapes of blades
If ω = const and Q = const for β2 = 90deg g
uH th
22= for β2 lt 90deg
guHth
22lt for β2 gt 90deg
guHth
22gt
For increasing the pump head the blades should be directed to the direction of rotation This will increase c2 and in diffuser we have to convert high kinetic energy to the potential energy and we lost in principal much energy The angle β2 lt 90deg is preferred for the pumps and β2 gt 90deg for ventilators 32 Similarity of Pumps Theoretical considerations are giving only qualitative results The more realistic results is possible to get by making pump or pump model tests especially in designing a new pump From the test results the pump similarity rules are used for calculating parameters of the pump under construction The theory of similarity is based on the rules of hydraulic modelling Geometric similitude ndash measures and shape of the model and pump should be in scale Kinematic similitude ndash velocities should be in scale
mmm cc
ww
uu
== etc
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
2
Figure 1 Installation scheme of the pump [3] V ndash vacuum m patm ndash atmospheric pressure Pa and
Es = hs + g
patm
ρ- V - Zv +
gvs
2
2
Ep = hs + g
pp
ρ+
gvp
2
2
pp ndash absolute pressure on the pressure side Pa vp ndash velocity on the pressure side ms Specific energy at the pump pressure port
gpp
ρ=
gpatm
ρ+ M + Zm
3 M ndash gauge head m and
Ep = hs + g
patm
ρ+ M + Zm +
gvp
2
2
Pumping head is equal
H = M + V + Zm + Zv + gvv sp
2
22 minus
14 Pump Power and Efficiency Pump output power Pw is the power imparted to the liquid by the pump
1000gQHPw
ρ= kW
where ρ kgm3 Q m3s and H m Pump input power Pp is the power delivered to the pump shaft at the driver to pump coupling
Pp gt Pw
Pump efficiency p
wp P
P=η and
mhvp ηηηη =
ndash volumetric efficiency qQ
Qv +=η
- hydraulic efficiency thtp
h HH
hHH
=+
=η
- mechanical efficiency p
hm P
P=η where
- hydraulic power 1000
)( thh
HqQgP +=ρ
kW
4
mhvp ηηηη = = p
w
p
th
th PP
PHqQg
HH
qQQ
=+
sdotsdot+ 1000
)(ρ
Drive efficiency motor
pmotor P
P=η
15 Pump Suction Head Static suction lift ndash hs (Fig 1) Head losses in suction pipe ndash hts
tsss
satm h
gv
gph
gp
+++=2
2
ρρ
To avoid cavitation the absolute pressure everywhere in the machine is kept above the vapor pressure of the operating liquid The NPSHA is the net total head provided by the system at the inlet cross section (reference cross section) of the pump (not of the impeller) at the centre of the suction connection It consists of the absolute pressure ps predominating at this point less the vapor pressure of the fluid in the inlet cross section plus the total head from the mean flow velocity in the reference cross section NPSHA can be defined as follows on the basis of the measurements on a running pump
Avss NPSHhg
vg
p+=+
2
2
ρ
NPSHA ndash the NPSH produced by the system NPSHR ndash the NPSH required for the pump relative to the permitted degree of cavitation ∆NPSH ndash excess of NPSHA over NPSHR (safety allowance) The duty point Qopt can be taken as
NPSHR = (03hellip05) n Q
with n in s-1 and Q in m3s or
NPSHR = σH
with σ = k 34
qn and 43
H
Qnns = when n = min-1 Q = m3s and k asymp 00014
5
Suction lift of the pump hs
)( Rtsvatm
s NPSHhhg
ph ++minus=ρ
Measures for the avoidance of cavitation
i) Measures by the operator - Reduction of geodetic suction lift or increase in suction head - Short suction line with largest possible cross section - Valves bends curves avoided where possible or the maximum radii used - The temperature of the fluid to be kept to a minimum - Application of a gas pressure to the surface of the liquid in closed suction or supply
vessels
ii) Measures by pump manufacturers - Impellers with double curvature blades drawn well forward into the suction orifice - Avoidance of short deflection radii at the blade cover - Reduction of the thickness of the impeller blades - Use of a smaller blade inlet angle - Reduction in speed - Fitting an inducer - Aligning the flow to the impeller by fitting a guide vane in the inlet connection
It must be mentioned that there are no materials which are resistant to cavitation damage
Figure 2 Cavitation erosion on the impeller of a centrifugal pump
6
2 Impeller Pumps 21 Centrifugal Pumps 211 Single-Stage Centrifugal Pump Centifugal pumps are machines in which fluids are conveyed in rotors (impellers) fitted with one or more blades by a moment so that pressure is gained in a continuous flow
Figure 3 Single stage centrifugal pump
1- impeller 2- impeller blade (vane) 3- volute or scroll 4- suction pipe 5- foot valve 6- suction strainer 7- diffuser 8- valve 9- pressure pipe 10- filling opening 11- water pipe for the seal 12- shaft seal
Impellers could be enclosed (Fig 3) semiopen (Fig 4) or open (vane wheel) (Fig 5)
Figure 4 Semiopen impeller for sewage pump
Figure 5 Open impeller
7
a) good b) poor Figure 6 Air lock in suction pipe 212 Forces on Impeller
Figure 7 Impeller unbalanced to the axial pressure
4
21
1
dpF s
π=
⎟⎠
⎞⎜⎝
⎛minus=
44
221
2
ddpF p
ππ
8
After simplifing ( )4
21dppF sp
πminus=
Figure 8 Balancing of axial pressure
Figure 9 Wear ring collars (a- low- b- mean- and c- high pressure pumps) 1- pump casing 2- wear ring 3- impeller 4- clearance
Figure 10 Impeller unbalanced to the radial pressure when flow rate is smaller from the pump design flow rate (a) and radial pressure in double ndashvolute pump (b) The radial force occurs on pumps with volute casings due to the uneven pressure distribution on the circumference of the impeller Radial force increases considerably in the partial flow rates and overload ranges as the changes in cross-section of the volute guide (eg with
9 circular cross-section) change quadratically via φ whereas the increase or decrease of the transport flow is linear 213 Main Types of Centrifugal Pumps
i) Single-Stage Pumps ii) Double-Suction Pump iii) Multistage Pumps
Figure 11 Multistage pump
Figure 12 Inducer postioned before the impeller [2]
- Submersible Pumps - Process Pumps - Pumps for Turbid Water - Portable Submersible Pumps (Flygt in 1948) - Sewage Pumps (Fig 13 - Swirl Type Impeller Pump and Super ndash Vortex Pump)
10
Figure 13 Impellers of swirl type pump 22 Axial Flow Pumps Scheme of the axial flow pump is given in the Fig 14 (1- vane 2-hub 3- vane of the guide apparatus) Vanes of the impeller are fixed or reversible
Figure 14 Axial flow pump
Figure 15 Impeller of the axial flow pump
11
23 Regenerative Pumps Special type of impeller pumps An impeller with several blades which are always radial and mounted on one or both sides rotates between two plane - parallel housing surfaces The energy of the fluid which is imparted to the particular liquid particles by impulse exchange steadily increases from the inlet into the impeller blades until its exit at the interrupter High pressure low flow rate
Figure 16 Water path in the impeller of the regenerative pump 2 4 Shaft Seals of Impeller pump
- Staffing box packing - Single mechanical seal - Double mechanical seals - Dynamic seal (Ahlstroumlm)
3 Theory of Impeller Pumps 31 Turbomachine Equation The flow processes in the impeller which lead to formation of the H(Q) line can be mathematically determined by the theoretical assumption that the impeller has an infinite number of infinitely thin blades The flow consists in this case from equal stream filaments The energy conversion can be arrived at with the aid of the moment of momentum principle The change of moment of momentum in time at the inlet (position 1) and at the oulet (position 2) is equal to the moment of forces to this liquid mass The loss-free flow is considered (ideal fluid) Pump Power (W= Nms) thgQHP ρ=
12
Figure 17 Flow velocities at impeller [3] is equal to the force moment to the shaft (Nm) multiplied with the impeller angular velocity ω (rads)
P =M ω
Theoretical pump head (m)
gQMHth ρω
=
In one second through the pump is flowing liquid mass m = ρQ (31) Moment of momentum at the position 1 and 2
M1 = mc1l1 and M2 = mc2l2
and changes of the moment of momentum
M = M2 - M1 =m(c2l2 - c1l1)
When we consider that l =R cos α and for mass (31)
M = ρQ (c2R2cos α2 ndash c1R1cos α1 )
As ωR1=u1 and ωR2=u2 then
g
ucucH th
)coscos( 111222 αα minus= (32)
13 This formula is Eulerrsquos equation for centrifugal pumps It represents a theoretical relationship between the individual values where there is an ideal uniform distribution of all liquid particles in the particular flow cross-sections However it also states bdquoThe theoretical head of a centrifugal pump is independent of the density and the physical properties of the fluid flowing through itldquo
Figure 18 Inlet and outlet triangles on radial impeller [2] Modern centrifugal pumps are constructed in this way that inflow has radial direction This means α = 90deg and cos α = 0
g
ucH th
222 cosα= (33)
The vortex torque component
cu = c cos α
and Hth = gcu u22
where cu2 is the vortex component of the absolute flow at the impeller outlet
Figure 19 Flow at the impeller of centrifugal pump ( a- real b- theoretical c- vortex) [3] ns rpm 40 50 75 100 125 150 175 200 250 k 078 080 081 082 0805 077 0715 0675 055
14
The specific speed ns of a pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The theoretical head Hth is reduced by the losses which occur due to
- volumetric internal leakage losses at the radial clearance between the impeller and casing
- friction losses in the blade channels - energy conversion losses (velocity in pressure due to changes in direction and cross-
section) - shock losses where the angle of the approach flow to the impeller blades is not
vertical Hydraulic efficiency is the real and theoretical pump head ratio
222 cosα
ηukc
gHHH
thh ==
Finally the turbomachine equation takes form
g
ukcH h 222 cosαη
= (34)
Figure 20 Different shapes of the impeller [3] The energy transfer begins at the inlet to the cascade and ends on departure from the blade channels The pressure and velocity of the pumped liquid is increased on this path The pressure increase is due to the centrifugal forces and deceleration in the relative velocity w in the impeller channels between the channel inlet and outlet The strong increase in the absolute velocity c of the fluid during the flow through the impeller channels is partly converted to pressure energy in a diffuser volute guide or stator after leaving the impeller A distinction is to be made between movement processes of the absolute velocity c and relative velocity w Absolute velocity c is that which liquid particles exibit compared with a static environment The relative velocity w is the velocity of a liquid particle compared with the rotating blades when flowing through the blade channel The peripheral velocity u of the rotating blades at the particular distance from the axis of rotation is also important The pressure path in the impeller is parabolic corresponding to the laws of dynamics To
15 determine the flow processes mathematically however all that is required is the recording of the velocities at the blade inlet and outlet Real head of the pump is smaller than theoretical In reality impeller has up to 12 blades The flow is different from theoretical between blades In the convex part of blade the velocity is smaller than in concave part The energy used for keeping vortex is decreasing the developed head by pump The head given for an infinite number of blades Hth is reduced due to the incomplete flow guidance where there is a finite number (mainly 7) of blades A comparison of the velocity diagrams for the actual and fictitious flow shows vortex components The decrease of the head is considered with the coefficient k which depends from the construction of the pump k is characterized by the specific speed ns of the pump Theoretically it is impossible to calulate hydraulic efficiency ηh It depends from many factors Theory is giving qualitative recommendations to get higher efficiency
- to avioid sudden changes of velocities in pump - to avoid decrease of velocity on the impeller perimeter - to give simple shape to the impeller blades - to avoid sharp corners in the pump
In Fig 20 are given three different shapes of blades
If ω = const and Q = const for β2 = 90deg g
uH th
22= for β2 lt 90deg
guHth
22lt for β2 gt 90deg
guHth
22gt
For increasing the pump head the blades should be directed to the direction of rotation This will increase c2 and in diffuser we have to convert high kinetic energy to the potential energy and we lost in principal much energy The angle β2 lt 90deg is preferred for the pumps and β2 gt 90deg for ventilators 32 Similarity of Pumps Theoretical considerations are giving only qualitative results The more realistic results is possible to get by making pump or pump model tests especially in designing a new pump From the test results the pump similarity rules are used for calculating parameters of the pump under construction The theory of similarity is based on the rules of hydraulic modelling Geometric similitude ndash measures and shape of the model and pump should be in scale Kinematic similitude ndash velocities should be in scale
mmm cc
ww
uu
== etc
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
3 M ndash gauge head m and
Ep = hs + g
patm
ρ+ M + Zm +
gvp
2
2
Pumping head is equal
H = M + V + Zm + Zv + gvv sp
2
22 minus
14 Pump Power and Efficiency Pump output power Pw is the power imparted to the liquid by the pump
1000gQHPw
ρ= kW
where ρ kgm3 Q m3s and H m Pump input power Pp is the power delivered to the pump shaft at the driver to pump coupling
Pp gt Pw
Pump efficiency p
wp P
P=η and
mhvp ηηηη =
ndash volumetric efficiency qQ
Qv +=η
- hydraulic efficiency thtp
h HH
hHH
=+
=η
- mechanical efficiency p
hm P
P=η where
- hydraulic power 1000
)( thh
HqQgP +=ρ
kW
4
mhvp ηηηη = = p
w
p
th
th PP
PHqQg
HH
qQQ
=+
sdotsdot+ 1000
)(ρ
Drive efficiency motor
pmotor P
P=η
15 Pump Suction Head Static suction lift ndash hs (Fig 1) Head losses in suction pipe ndash hts
tsss
satm h
gv
gph
gp
+++=2
2
ρρ
To avoid cavitation the absolute pressure everywhere in the machine is kept above the vapor pressure of the operating liquid The NPSHA is the net total head provided by the system at the inlet cross section (reference cross section) of the pump (not of the impeller) at the centre of the suction connection It consists of the absolute pressure ps predominating at this point less the vapor pressure of the fluid in the inlet cross section plus the total head from the mean flow velocity in the reference cross section NPSHA can be defined as follows on the basis of the measurements on a running pump
Avss NPSHhg
vg
p+=+
2
2
ρ
NPSHA ndash the NPSH produced by the system NPSHR ndash the NPSH required for the pump relative to the permitted degree of cavitation ∆NPSH ndash excess of NPSHA over NPSHR (safety allowance) The duty point Qopt can be taken as
NPSHR = (03hellip05) n Q
with n in s-1 and Q in m3s or
NPSHR = σH
with σ = k 34
qn and 43
H
Qnns = when n = min-1 Q = m3s and k asymp 00014
5
Suction lift of the pump hs
)( Rtsvatm
s NPSHhhg
ph ++minus=ρ
Measures for the avoidance of cavitation
i) Measures by the operator - Reduction of geodetic suction lift or increase in suction head - Short suction line with largest possible cross section - Valves bends curves avoided where possible or the maximum radii used - The temperature of the fluid to be kept to a minimum - Application of a gas pressure to the surface of the liquid in closed suction or supply
vessels
ii) Measures by pump manufacturers - Impellers with double curvature blades drawn well forward into the suction orifice - Avoidance of short deflection radii at the blade cover - Reduction of the thickness of the impeller blades - Use of a smaller blade inlet angle - Reduction in speed - Fitting an inducer - Aligning the flow to the impeller by fitting a guide vane in the inlet connection
It must be mentioned that there are no materials which are resistant to cavitation damage
Figure 2 Cavitation erosion on the impeller of a centrifugal pump
6
2 Impeller Pumps 21 Centrifugal Pumps 211 Single-Stage Centrifugal Pump Centifugal pumps are machines in which fluids are conveyed in rotors (impellers) fitted with one or more blades by a moment so that pressure is gained in a continuous flow
Figure 3 Single stage centrifugal pump
1- impeller 2- impeller blade (vane) 3- volute or scroll 4- suction pipe 5- foot valve 6- suction strainer 7- diffuser 8- valve 9- pressure pipe 10- filling opening 11- water pipe for the seal 12- shaft seal
Impellers could be enclosed (Fig 3) semiopen (Fig 4) or open (vane wheel) (Fig 5)
Figure 4 Semiopen impeller for sewage pump
Figure 5 Open impeller
7
a) good b) poor Figure 6 Air lock in suction pipe 212 Forces on Impeller
Figure 7 Impeller unbalanced to the axial pressure
4
21
1
dpF s
π=
⎟⎠
⎞⎜⎝
⎛minus=
44
221
2
ddpF p
ππ
8
After simplifing ( )4
21dppF sp
πminus=
Figure 8 Balancing of axial pressure
Figure 9 Wear ring collars (a- low- b- mean- and c- high pressure pumps) 1- pump casing 2- wear ring 3- impeller 4- clearance
Figure 10 Impeller unbalanced to the radial pressure when flow rate is smaller from the pump design flow rate (a) and radial pressure in double ndashvolute pump (b) The radial force occurs on pumps with volute casings due to the uneven pressure distribution on the circumference of the impeller Radial force increases considerably in the partial flow rates and overload ranges as the changes in cross-section of the volute guide (eg with
9 circular cross-section) change quadratically via φ whereas the increase or decrease of the transport flow is linear 213 Main Types of Centrifugal Pumps
i) Single-Stage Pumps ii) Double-Suction Pump iii) Multistage Pumps
Figure 11 Multistage pump
Figure 12 Inducer postioned before the impeller [2]
- Submersible Pumps - Process Pumps - Pumps for Turbid Water - Portable Submersible Pumps (Flygt in 1948) - Sewage Pumps (Fig 13 - Swirl Type Impeller Pump and Super ndash Vortex Pump)
10
Figure 13 Impellers of swirl type pump 22 Axial Flow Pumps Scheme of the axial flow pump is given in the Fig 14 (1- vane 2-hub 3- vane of the guide apparatus) Vanes of the impeller are fixed or reversible
Figure 14 Axial flow pump
Figure 15 Impeller of the axial flow pump
11
23 Regenerative Pumps Special type of impeller pumps An impeller with several blades which are always radial and mounted on one or both sides rotates between two plane - parallel housing surfaces The energy of the fluid which is imparted to the particular liquid particles by impulse exchange steadily increases from the inlet into the impeller blades until its exit at the interrupter High pressure low flow rate
Figure 16 Water path in the impeller of the regenerative pump 2 4 Shaft Seals of Impeller pump
- Staffing box packing - Single mechanical seal - Double mechanical seals - Dynamic seal (Ahlstroumlm)
3 Theory of Impeller Pumps 31 Turbomachine Equation The flow processes in the impeller which lead to formation of the H(Q) line can be mathematically determined by the theoretical assumption that the impeller has an infinite number of infinitely thin blades The flow consists in this case from equal stream filaments The energy conversion can be arrived at with the aid of the moment of momentum principle The change of moment of momentum in time at the inlet (position 1) and at the oulet (position 2) is equal to the moment of forces to this liquid mass The loss-free flow is considered (ideal fluid) Pump Power (W= Nms) thgQHP ρ=
12
Figure 17 Flow velocities at impeller [3] is equal to the force moment to the shaft (Nm) multiplied with the impeller angular velocity ω (rads)
P =M ω
Theoretical pump head (m)
gQMHth ρω
=
In one second through the pump is flowing liquid mass m = ρQ (31) Moment of momentum at the position 1 and 2
M1 = mc1l1 and M2 = mc2l2
and changes of the moment of momentum
M = M2 - M1 =m(c2l2 - c1l1)
When we consider that l =R cos α and for mass (31)
M = ρQ (c2R2cos α2 ndash c1R1cos α1 )
As ωR1=u1 and ωR2=u2 then
g
ucucH th
)coscos( 111222 αα minus= (32)
13 This formula is Eulerrsquos equation for centrifugal pumps It represents a theoretical relationship between the individual values where there is an ideal uniform distribution of all liquid particles in the particular flow cross-sections However it also states bdquoThe theoretical head of a centrifugal pump is independent of the density and the physical properties of the fluid flowing through itldquo
Figure 18 Inlet and outlet triangles on radial impeller [2] Modern centrifugal pumps are constructed in this way that inflow has radial direction This means α = 90deg and cos α = 0
g
ucH th
222 cosα= (33)
The vortex torque component
cu = c cos α
and Hth = gcu u22
where cu2 is the vortex component of the absolute flow at the impeller outlet
Figure 19 Flow at the impeller of centrifugal pump ( a- real b- theoretical c- vortex) [3] ns rpm 40 50 75 100 125 150 175 200 250 k 078 080 081 082 0805 077 0715 0675 055
14
The specific speed ns of a pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The theoretical head Hth is reduced by the losses which occur due to
- volumetric internal leakage losses at the radial clearance between the impeller and casing
- friction losses in the blade channels - energy conversion losses (velocity in pressure due to changes in direction and cross-
section) - shock losses where the angle of the approach flow to the impeller blades is not
vertical Hydraulic efficiency is the real and theoretical pump head ratio
222 cosα
ηukc
gHHH
thh ==
Finally the turbomachine equation takes form
g
ukcH h 222 cosαη
= (34)
Figure 20 Different shapes of the impeller [3] The energy transfer begins at the inlet to the cascade and ends on departure from the blade channels The pressure and velocity of the pumped liquid is increased on this path The pressure increase is due to the centrifugal forces and deceleration in the relative velocity w in the impeller channels between the channel inlet and outlet The strong increase in the absolute velocity c of the fluid during the flow through the impeller channels is partly converted to pressure energy in a diffuser volute guide or stator after leaving the impeller A distinction is to be made between movement processes of the absolute velocity c and relative velocity w Absolute velocity c is that which liquid particles exibit compared with a static environment The relative velocity w is the velocity of a liquid particle compared with the rotating blades when flowing through the blade channel The peripheral velocity u of the rotating blades at the particular distance from the axis of rotation is also important The pressure path in the impeller is parabolic corresponding to the laws of dynamics To
15 determine the flow processes mathematically however all that is required is the recording of the velocities at the blade inlet and outlet Real head of the pump is smaller than theoretical In reality impeller has up to 12 blades The flow is different from theoretical between blades In the convex part of blade the velocity is smaller than in concave part The energy used for keeping vortex is decreasing the developed head by pump The head given for an infinite number of blades Hth is reduced due to the incomplete flow guidance where there is a finite number (mainly 7) of blades A comparison of the velocity diagrams for the actual and fictitious flow shows vortex components The decrease of the head is considered with the coefficient k which depends from the construction of the pump k is characterized by the specific speed ns of the pump Theoretically it is impossible to calulate hydraulic efficiency ηh It depends from many factors Theory is giving qualitative recommendations to get higher efficiency
- to avioid sudden changes of velocities in pump - to avoid decrease of velocity on the impeller perimeter - to give simple shape to the impeller blades - to avoid sharp corners in the pump
In Fig 20 are given three different shapes of blades
If ω = const and Q = const for β2 = 90deg g
uH th
22= for β2 lt 90deg
guHth
22lt for β2 gt 90deg
guHth
22gt
For increasing the pump head the blades should be directed to the direction of rotation This will increase c2 and in diffuser we have to convert high kinetic energy to the potential energy and we lost in principal much energy The angle β2 lt 90deg is preferred for the pumps and β2 gt 90deg for ventilators 32 Similarity of Pumps Theoretical considerations are giving only qualitative results The more realistic results is possible to get by making pump or pump model tests especially in designing a new pump From the test results the pump similarity rules are used for calculating parameters of the pump under construction The theory of similarity is based on the rules of hydraulic modelling Geometric similitude ndash measures and shape of the model and pump should be in scale Kinematic similitude ndash velocities should be in scale
mmm cc
ww
uu
== etc
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
4
mhvp ηηηη = = p
w
p
th
th PP
PHqQg
HH
qQQ
=+
sdotsdot+ 1000
)(ρ
Drive efficiency motor
pmotor P
P=η
15 Pump Suction Head Static suction lift ndash hs (Fig 1) Head losses in suction pipe ndash hts
tsss
satm h
gv
gph
gp
+++=2
2
ρρ
To avoid cavitation the absolute pressure everywhere in the machine is kept above the vapor pressure of the operating liquid The NPSHA is the net total head provided by the system at the inlet cross section (reference cross section) of the pump (not of the impeller) at the centre of the suction connection It consists of the absolute pressure ps predominating at this point less the vapor pressure of the fluid in the inlet cross section plus the total head from the mean flow velocity in the reference cross section NPSHA can be defined as follows on the basis of the measurements on a running pump
Avss NPSHhg
vg
p+=+
2
2
ρ
NPSHA ndash the NPSH produced by the system NPSHR ndash the NPSH required for the pump relative to the permitted degree of cavitation ∆NPSH ndash excess of NPSHA over NPSHR (safety allowance) The duty point Qopt can be taken as
NPSHR = (03hellip05) n Q
with n in s-1 and Q in m3s or
NPSHR = σH
with σ = k 34
qn and 43
H
Qnns = when n = min-1 Q = m3s and k asymp 00014
5
Suction lift of the pump hs
)( Rtsvatm
s NPSHhhg
ph ++minus=ρ
Measures for the avoidance of cavitation
i) Measures by the operator - Reduction of geodetic suction lift or increase in suction head - Short suction line with largest possible cross section - Valves bends curves avoided where possible or the maximum radii used - The temperature of the fluid to be kept to a minimum - Application of a gas pressure to the surface of the liquid in closed suction or supply
vessels
ii) Measures by pump manufacturers - Impellers with double curvature blades drawn well forward into the suction orifice - Avoidance of short deflection radii at the blade cover - Reduction of the thickness of the impeller blades - Use of a smaller blade inlet angle - Reduction in speed - Fitting an inducer - Aligning the flow to the impeller by fitting a guide vane in the inlet connection
It must be mentioned that there are no materials which are resistant to cavitation damage
Figure 2 Cavitation erosion on the impeller of a centrifugal pump
6
2 Impeller Pumps 21 Centrifugal Pumps 211 Single-Stage Centrifugal Pump Centifugal pumps are machines in which fluids are conveyed in rotors (impellers) fitted with one or more blades by a moment so that pressure is gained in a continuous flow
Figure 3 Single stage centrifugal pump
1- impeller 2- impeller blade (vane) 3- volute or scroll 4- suction pipe 5- foot valve 6- suction strainer 7- diffuser 8- valve 9- pressure pipe 10- filling opening 11- water pipe for the seal 12- shaft seal
Impellers could be enclosed (Fig 3) semiopen (Fig 4) or open (vane wheel) (Fig 5)
Figure 4 Semiopen impeller for sewage pump
Figure 5 Open impeller
7
a) good b) poor Figure 6 Air lock in suction pipe 212 Forces on Impeller
Figure 7 Impeller unbalanced to the axial pressure
4
21
1
dpF s
π=
⎟⎠
⎞⎜⎝
⎛minus=
44
221
2
ddpF p
ππ
8
After simplifing ( )4
21dppF sp
πminus=
Figure 8 Balancing of axial pressure
Figure 9 Wear ring collars (a- low- b- mean- and c- high pressure pumps) 1- pump casing 2- wear ring 3- impeller 4- clearance
Figure 10 Impeller unbalanced to the radial pressure when flow rate is smaller from the pump design flow rate (a) and radial pressure in double ndashvolute pump (b) The radial force occurs on pumps with volute casings due to the uneven pressure distribution on the circumference of the impeller Radial force increases considerably in the partial flow rates and overload ranges as the changes in cross-section of the volute guide (eg with
9 circular cross-section) change quadratically via φ whereas the increase or decrease of the transport flow is linear 213 Main Types of Centrifugal Pumps
i) Single-Stage Pumps ii) Double-Suction Pump iii) Multistage Pumps
Figure 11 Multistage pump
Figure 12 Inducer postioned before the impeller [2]
- Submersible Pumps - Process Pumps - Pumps for Turbid Water - Portable Submersible Pumps (Flygt in 1948) - Sewage Pumps (Fig 13 - Swirl Type Impeller Pump and Super ndash Vortex Pump)
10
Figure 13 Impellers of swirl type pump 22 Axial Flow Pumps Scheme of the axial flow pump is given in the Fig 14 (1- vane 2-hub 3- vane of the guide apparatus) Vanes of the impeller are fixed or reversible
Figure 14 Axial flow pump
Figure 15 Impeller of the axial flow pump
11
23 Regenerative Pumps Special type of impeller pumps An impeller with several blades which are always radial and mounted on one or both sides rotates between two plane - parallel housing surfaces The energy of the fluid which is imparted to the particular liquid particles by impulse exchange steadily increases from the inlet into the impeller blades until its exit at the interrupter High pressure low flow rate
Figure 16 Water path in the impeller of the regenerative pump 2 4 Shaft Seals of Impeller pump
- Staffing box packing - Single mechanical seal - Double mechanical seals - Dynamic seal (Ahlstroumlm)
3 Theory of Impeller Pumps 31 Turbomachine Equation The flow processes in the impeller which lead to formation of the H(Q) line can be mathematically determined by the theoretical assumption that the impeller has an infinite number of infinitely thin blades The flow consists in this case from equal stream filaments The energy conversion can be arrived at with the aid of the moment of momentum principle The change of moment of momentum in time at the inlet (position 1) and at the oulet (position 2) is equal to the moment of forces to this liquid mass The loss-free flow is considered (ideal fluid) Pump Power (W= Nms) thgQHP ρ=
12
Figure 17 Flow velocities at impeller [3] is equal to the force moment to the shaft (Nm) multiplied with the impeller angular velocity ω (rads)
P =M ω
Theoretical pump head (m)
gQMHth ρω
=
In one second through the pump is flowing liquid mass m = ρQ (31) Moment of momentum at the position 1 and 2
M1 = mc1l1 and M2 = mc2l2
and changes of the moment of momentum
M = M2 - M1 =m(c2l2 - c1l1)
When we consider that l =R cos α and for mass (31)
M = ρQ (c2R2cos α2 ndash c1R1cos α1 )
As ωR1=u1 and ωR2=u2 then
g
ucucH th
)coscos( 111222 αα minus= (32)
13 This formula is Eulerrsquos equation for centrifugal pumps It represents a theoretical relationship between the individual values where there is an ideal uniform distribution of all liquid particles in the particular flow cross-sections However it also states bdquoThe theoretical head of a centrifugal pump is independent of the density and the physical properties of the fluid flowing through itldquo
Figure 18 Inlet and outlet triangles on radial impeller [2] Modern centrifugal pumps are constructed in this way that inflow has radial direction This means α = 90deg and cos α = 0
g
ucH th
222 cosα= (33)
The vortex torque component
cu = c cos α
and Hth = gcu u22
where cu2 is the vortex component of the absolute flow at the impeller outlet
Figure 19 Flow at the impeller of centrifugal pump ( a- real b- theoretical c- vortex) [3] ns rpm 40 50 75 100 125 150 175 200 250 k 078 080 081 082 0805 077 0715 0675 055
14
The specific speed ns of a pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The theoretical head Hth is reduced by the losses which occur due to
- volumetric internal leakage losses at the radial clearance between the impeller and casing
- friction losses in the blade channels - energy conversion losses (velocity in pressure due to changes in direction and cross-
section) - shock losses where the angle of the approach flow to the impeller blades is not
vertical Hydraulic efficiency is the real and theoretical pump head ratio
222 cosα
ηukc
gHHH
thh ==
Finally the turbomachine equation takes form
g
ukcH h 222 cosαη
= (34)
Figure 20 Different shapes of the impeller [3] The energy transfer begins at the inlet to the cascade and ends on departure from the blade channels The pressure and velocity of the pumped liquid is increased on this path The pressure increase is due to the centrifugal forces and deceleration in the relative velocity w in the impeller channels between the channel inlet and outlet The strong increase in the absolute velocity c of the fluid during the flow through the impeller channels is partly converted to pressure energy in a diffuser volute guide or stator after leaving the impeller A distinction is to be made between movement processes of the absolute velocity c and relative velocity w Absolute velocity c is that which liquid particles exibit compared with a static environment The relative velocity w is the velocity of a liquid particle compared with the rotating blades when flowing through the blade channel The peripheral velocity u of the rotating blades at the particular distance from the axis of rotation is also important The pressure path in the impeller is parabolic corresponding to the laws of dynamics To
15 determine the flow processes mathematically however all that is required is the recording of the velocities at the blade inlet and outlet Real head of the pump is smaller than theoretical In reality impeller has up to 12 blades The flow is different from theoretical between blades In the convex part of blade the velocity is smaller than in concave part The energy used for keeping vortex is decreasing the developed head by pump The head given for an infinite number of blades Hth is reduced due to the incomplete flow guidance where there is a finite number (mainly 7) of blades A comparison of the velocity diagrams for the actual and fictitious flow shows vortex components The decrease of the head is considered with the coefficient k which depends from the construction of the pump k is characterized by the specific speed ns of the pump Theoretically it is impossible to calulate hydraulic efficiency ηh It depends from many factors Theory is giving qualitative recommendations to get higher efficiency
- to avioid sudden changes of velocities in pump - to avoid decrease of velocity on the impeller perimeter - to give simple shape to the impeller blades - to avoid sharp corners in the pump
In Fig 20 are given three different shapes of blades
If ω = const and Q = const for β2 = 90deg g
uH th
22= for β2 lt 90deg
guHth
22lt for β2 gt 90deg
guHth
22gt
For increasing the pump head the blades should be directed to the direction of rotation This will increase c2 and in diffuser we have to convert high kinetic energy to the potential energy and we lost in principal much energy The angle β2 lt 90deg is preferred for the pumps and β2 gt 90deg for ventilators 32 Similarity of Pumps Theoretical considerations are giving only qualitative results The more realistic results is possible to get by making pump or pump model tests especially in designing a new pump From the test results the pump similarity rules are used for calculating parameters of the pump under construction The theory of similarity is based on the rules of hydraulic modelling Geometric similitude ndash measures and shape of the model and pump should be in scale Kinematic similitude ndash velocities should be in scale
mmm cc
ww
uu
== etc
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
5
Suction lift of the pump hs
)( Rtsvatm
s NPSHhhg
ph ++minus=ρ
Measures for the avoidance of cavitation
i) Measures by the operator - Reduction of geodetic suction lift or increase in suction head - Short suction line with largest possible cross section - Valves bends curves avoided where possible or the maximum radii used - The temperature of the fluid to be kept to a minimum - Application of a gas pressure to the surface of the liquid in closed suction or supply
vessels
ii) Measures by pump manufacturers - Impellers with double curvature blades drawn well forward into the suction orifice - Avoidance of short deflection radii at the blade cover - Reduction of the thickness of the impeller blades - Use of a smaller blade inlet angle - Reduction in speed - Fitting an inducer - Aligning the flow to the impeller by fitting a guide vane in the inlet connection
It must be mentioned that there are no materials which are resistant to cavitation damage
Figure 2 Cavitation erosion on the impeller of a centrifugal pump
6
2 Impeller Pumps 21 Centrifugal Pumps 211 Single-Stage Centrifugal Pump Centifugal pumps are machines in which fluids are conveyed in rotors (impellers) fitted with one or more blades by a moment so that pressure is gained in a continuous flow
Figure 3 Single stage centrifugal pump
1- impeller 2- impeller blade (vane) 3- volute or scroll 4- suction pipe 5- foot valve 6- suction strainer 7- diffuser 8- valve 9- pressure pipe 10- filling opening 11- water pipe for the seal 12- shaft seal
Impellers could be enclosed (Fig 3) semiopen (Fig 4) or open (vane wheel) (Fig 5)
Figure 4 Semiopen impeller for sewage pump
Figure 5 Open impeller
7
a) good b) poor Figure 6 Air lock in suction pipe 212 Forces on Impeller
Figure 7 Impeller unbalanced to the axial pressure
4
21
1
dpF s
π=
⎟⎠
⎞⎜⎝
⎛minus=
44
221
2
ddpF p
ππ
8
After simplifing ( )4
21dppF sp
πminus=
Figure 8 Balancing of axial pressure
Figure 9 Wear ring collars (a- low- b- mean- and c- high pressure pumps) 1- pump casing 2- wear ring 3- impeller 4- clearance
Figure 10 Impeller unbalanced to the radial pressure when flow rate is smaller from the pump design flow rate (a) and radial pressure in double ndashvolute pump (b) The radial force occurs on pumps with volute casings due to the uneven pressure distribution on the circumference of the impeller Radial force increases considerably in the partial flow rates and overload ranges as the changes in cross-section of the volute guide (eg with
9 circular cross-section) change quadratically via φ whereas the increase or decrease of the transport flow is linear 213 Main Types of Centrifugal Pumps
i) Single-Stage Pumps ii) Double-Suction Pump iii) Multistage Pumps
Figure 11 Multistage pump
Figure 12 Inducer postioned before the impeller [2]
- Submersible Pumps - Process Pumps - Pumps for Turbid Water - Portable Submersible Pumps (Flygt in 1948) - Sewage Pumps (Fig 13 - Swirl Type Impeller Pump and Super ndash Vortex Pump)
10
Figure 13 Impellers of swirl type pump 22 Axial Flow Pumps Scheme of the axial flow pump is given in the Fig 14 (1- vane 2-hub 3- vane of the guide apparatus) Vanes of the impeller are fixed or reversible
Figure 14 Axial flow pump
Figure 15 Impeller of the axial flow pump
11
23 Regenerative Pumps Special type of impeller pumps An impeller with several blades which are always radial and mounted on one or both sides rotates between two plane - parallel housing surfaces The energy of the fluid which is imparted to the particular liquid particles by impulse exchange steadily increases from the inlet into the impeller blades until its exit at the interrupter High pressure low flow rate
Figure 16 Water path in the impeller of the regenerative pump 2 4 Shaft Seals of Impeller pump
- Staffing box packing - Single mechanical seal - Double mechanical seals - Dynamic seal (Ahlstroumlm)
3 Theory of Impeller Pumps 31 Turbomachine Equation The flow processes in the impeller which lead to formation of the H(Q) line can be mathematically determined by the theoretical assumption that the impeller has an infinite number of infinitely thin blades The flow consists in this case from equal stream filaments The energy conversion can be arrived at with the aid of the moment of momentum principle The change of moment of momentum in time at the inlet (position 1) and at the oulet (position 2) is equal to the moment of forces to this liquid mass The loss-free flow is considered (ideal fluid) Pump Power (W= Nms) thgQHP ρ=
12
Figure 17 Flow velocities at impeller [3] is equal to the force moment to the shaft (Nm) multiplied with the impeller angular velocity ω (rads)
P =M ω
Theoretical pump head (m)
gQMHth ρω
=
In one second through the pump is flowing liquid mass m = ρQ (31) Moment of momentum at the position 1 and 2
M1 = mc1l1 and M2 = mc2l2
and changes of the moment of momentum
M = M2 - M1 =m(c2l2 - c1l1)
When we consider that l =R cos α and for mass (31)
M = ρQ (c2R2cos α2 ndash c1R1cos α1 )
As ωR1=u1 and ωR2=u2 then
g
ucucH th
)coscos( 111222 αα minus= (32)
13 This formula is Eulerrsquos equation for centrifugal pumps It represents a theoretical relationship between the individual values where there is an ideal uniform distribution of all liquid particles in the particular flow cross-sections However it also states bdquoThe theoretical head of a centrifugal pump is independent of the density and the physical properties of the fluid flowing through itldquo
Figure 18 Inlet and outlet triangles on radial impeller [2] Modern centrifugal pumps are constructed in this way that inflow has radial direction This means α = 90deg and cos α = 0
g
ucH th
222 cosα= (33)
The vortex torque component
cu = c cos α
and Hth = gcu u22
where cu2 is the vortex component of the absolute flow at the impeller outlet
Figure 19 Flow at the impeller of centrifugal pump ( a- real b- theoretical c- vortex) [3] ns rpm 40 50 75 100 125 150 175 200 250 k 078 080 081 082 0805 077 0715 0675 055
14
The specific speed ns of a pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The theoretical head Hth is reduced by the losses which occur due to
- volumetric internal leakage losses at the radial clearance between the impeller and casing
- friction losses in the blade channels - energy conversion losses (velocity in pressure due to changes in direction and cross-
section) - shock losses where the angle of the approach flow to the impeller blades is not
vertical Hydraulic efficiency is the real and theoretical pump head ratio
222 cosα
ηukc
gHHH
thh ==
Finally the turbomachine equation takes form
g
ukcH h 222 cosαη
= (34)
Figure 20 Different shapes of the impeller [3] The energy transfer begins at the inlet to the cascade and ends on departure from the blade channels The pressure and velocity of the pumped liquid is increased on this path The pressure increase is due to the centrifugal forces and deceleration in the relative velocity w in the impeller channels between the channel inlet and outlet The strong increase in the absolute velocity c of the fluid during the flow through the impeller channels is partly converted to pressure energy in a diffuser volute guide or stator after leaving the impeller A distinction is to be made between movement processes of the absolute velocity c and relative velocity w Absolute velocity c is that which liquid particles exibit compared with a static environment The relative velocity w is the velocity of a liquid particle compared with the rotating blades when flowing through the blade channel The peripheral velocity u of the rotating blades at the particular distance from the axis of rotation is also important The pressure path in the impeller is parabolic corresponding to the laws of dynamics To
15 determine the flow processes mathematically however all that is required is the recording of the velocities at the blade inlet and outlet Real head of the pump is smaller than theoretical In reality impeller has up to 12 blades The flow is different from theoretical between blades In the convex part of blade the velocity is smaller than in concave part The energy used for keeping vortex is decreasing the developed head by pump The head given for an infinite number of blades Hth is reduced due to the incomplete flow guidance where there is a finite number (mainly 7) of blades A comparison of the velocity diagrams for the actual and fictitious flow shows vortex components The decrease of the head is considered with the coefficient k which depends from the construction of the pump k is characterized by the specific speed ns of the pump Theoretically it is impossible to calulate hydraulic efficiency ηh It depends from many factors Theory is giving qualitative recommendations to get higher efficiency
- to avioid sudden changes of velocities in pump - to avoid decrease of velocity on the impeller perimeter - to give simple shape to the impeller blades - to avoid sharp corners in the pump
In Fig 20 are given three different shapes of blades
If ω = const and Q = const for β2 = 90deg g
uH th
22= for β2 lt 90deg
guHth
22lt for β2 gt 90deg
guHth
22gt
For increasing the pump head the blades should be directed to the direction of rotation This will increase c2 and in diffuser we have to convert high kinetic energy to the potential energy and we lost in principal much energy The angle β2 lt 90deg is preferred for the pumps and β2 gt 90deg for ventilators 32 Similarity of Pumps Theoretical considerations are giving only qualitative results The more realistic results is possible to get by making pump or pump model tests especially in designing a new pump From the test results the pump similarity rules are used for calculating parameters of the pump under construction The theory of similarity is based on the rules of hydraulic modelling Geometric similitude ndash measures and shape of the model and pump should be in scale Kinematic similitude ndash velocities should be in scale
mmm cc
ww
uu
== etc
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
6
2 Impeller Pumps 21 Centrifugal Pumps 211 Single-Stage Centrifugal Pump Centifugal pumps are machines in which fluids are conveyed in rotors (impellers) fitted with one or more blades by a moment so that pressure is gained in a continuous flow
Figure 3 Single stage centrifugal pump
1- impeller 2- impeller blade (vane) 3- volute or scroll 4- suction pipe 5- foot valve 6- suction strainer 7- diffuser 8- valve 9- pressure pipe 10- filling opening 11- water pipe for the seal 12- shaft seal
Impellers could be enclosed (Fig 3) semiopen (Fig 4) or open (vane wheel) (Fig 5)
Figure 4 Semiopen impeller for sewage pump
Figure 5 Open impeller
7
a) good b) poor Figure 6 Air lock in suction pipe 212 Forces on Impeller
Figure 7 Impeller unbalanced to the axial pressure
4
21
1
dpF s
π=
⎟⎠
⎞⎜⎝
⎛minus=
44
221
2
ddpF p
ππ
8
After simplifing ( )4
21dppF sp
πminus=
Figure 8 Balancing of axial pressure
Figure 9 Wear ring collars (a- low- b- mean- and c- high pressure pumps) 1- pump casing 2- wear ring 3- impeller 4- clearance
Figure 10 Impeller unbalanced to the radial pressure when flow rate is smaller from the pump design flow rate (a) and radial pressure in double ndashvolute pump (b) The radial force occurs on pumps with volute casings due to the uneven pressure distribution on the circumference of the impeller Radial force increases considerably in the partial flow rates and overload ranges as the changes in cross-section of the volute guide (eg with
9 circular cross-section) change quadratically via φ whereas the increase or decrease of the transport flow is linear 213 Main Types of Centrifugal Pumps
i) Single-Stage Pumps ii) Double-Suction Pump iii) Multistage Pumps
Figure 11 Multistage pump
Figure 12 Inducer postioned before the impeller [2]
- Submersible Pumps - Process Pumps - Pumps for Turbid Water - Portable Submersible Pumps (Flygt in 1948) - Sewage Pumps (Fig 13 - Swirl Type Impeller Pump and Super ndash Vortex Pump)
10
Figure 13 Impellers of swirl type pump 22 Axial Flow Pumps Scheme of the axial flow pump is given in the Fig 14 (1- vane 2-hub 3- vane of the guide apparatus) Vanes of the impeller are fixed or reversible
Figure 14 Axial flow pump
Figure 15 Impeller of the axial flow pump
11
23 Regenerative Pumps Special type of impeller pumps An impeller with several blades which are always radial and mounted on one or both sides rotates between two plane - parallel housing surfaces The energy of the fluid which is imparted to the particular liquid particles by impulse exchange steadily increases from the inlet into the impeller blades until its exit at the interrupter High pressure low flow rate
Figure 16 Water path in the impeller of the regenerative pump 2 4 Shaft Seals of Impeller pump
- Staffing box packing - Single mechanical seal - Double mechanical seals - Dynamic seal (Ahlstroumlm)
3 Theory of Impeller Pumps 31 Turbomachine Equation The flow processes in the impeller which lead to formation of the H(Q) line can be mathematically determined by the theoretical assumption that the impeller has an infinite number of infinitely thin blades The flow consists in this case from equal stream filaments The energy conversion can be arrived at with the aid of the moment of momentum principle The change of moment of momentum in time at the inlet (position 1) and at the oulet (position 2) is equal to the moment of forces to this liquid mass The loss-free flow is considered (ideal fluid) Pump Power (W= Nms) thgQHP ρ=
12
Figure 17 Flow velocities at impeller [3] is equal to the force moment to the shaft (Nm) multiplied with the impeller angular velocity ω (rads)
P =M ω
Theoretical pump head (m)
gQMHth ρω
=
In one second through the pump is flowing liquid mass m = ρQ (31) Moment of momentum at the position 1 and 2
M1 = mc1l1 and M2 = mc2l2
and changes of the moment of momentum
M = M2 - M1 =m(c2l2 - c1l1)
When we consider that l =R cos α and for mass (31)
M = ρQ (c2R2cos α2 ndash c1R1cos α1 )
As ωR1=u1 and ωR2=u2 then
g
ucucH th
)coscos( 111222 αα minus= (32)
13 This formula is Eulerrsquos equation for centrifugal pumps It represents a theoretical relationship between the individual values where there is an ideal uniform distribution of all liquid particles in the particular flow cross-sections However it also states bdquoThe theoretical head of a centrifugal pump is independent of the density and the physical properties of the fluid flowing through itldquo
Figure 18 Inlet and outlet triangles on radial impeller [2] Modern centrifugal pumps are constructed in this way that inflow has radial direction This means α = 90deg and cos α = 0
g
ucH th
222 cosα= (33)
The vortex torque component
cu = c cos α
and Hth = gcu u22
where cu2 is the vortex component of the absolute flow at the impeller outlet
Figure 19 Flow at the impeller of centrifugal pump ( a- real b- theoretical c- vortex) [3] ns rpm 40 50 75 100 125 150 175 200 250 k 078 080 081 082 0805 077 0715 0675 055
14
The specific speed ns of a pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The theoretical head Hth is reduced by the losses which occur due to
- volumetric internal leakage losses at the radial clearance between the impeller and casing
- friction losses in the blade channels - energy conversion losses (velocity in pressure due to changes in direction and cross-
section) - shock losses where the angle of the approach flow to the impeller blades is not
vertical Hydraulic efficiency is the real and theoretical pump head ratio
222 cosα
ηukc
gHHH
thh ==
Finally the turbomachine equation takes form
g
ukcH h 222 cosαη
= (34)
Figure 20 Different shapes of the impeller [3] The energy transfer begins at the inlet to the cascade and ends on departure from the blade channels The pressure and velocity of the pumped liquid is increased on this path The pressure increase is due to the centrifugal forces and deceleration in the relative velocity w in the impeller channels between the channel inlet and outlet The strong increase in the absolute velocity c of the fluid during the flow through the impeller channels is partly converted to pressure energy in a diffuser volute guide or stator after leaving the impeller A distinction is to be made between movement processes of the absolute velocity c and relative velocity w Absolute velocity c is that which liquid particles exibit compared with a static environment The relative velocity w is the velocity of a liquid particle compared with the rotating blades when flowing through the blade channel The peripheral velocity u of the rotating blades at the particular distance from the axis of rotation is also important The pressure path in the impeller is parabolic corresponding to the laws of dynamics To
15 determine the flow processes mathematically however all that is required is the recording of the velocities at the blade inlet and outlet Real head of the pump is smaller than theoretical In reality impeller has up to 12 blades The flow is different from theoretical between blades In the convex part of blade the velocity is smaller than in concave part The energy used for keeping vortex is decreasing the developed head by pump The head given for an infinite number of blades Hth is reduced due to the incomplete flow guidance where there is a finite number (mainly 7) of blades A comparison of the velocity diagrams for the actual and fictitious flow shows vortex components The decrease of the head is considered with the coefficient k which depends from the construction of the pump k is characterized by the specific speed ns of the pump Theoretically it is impossible to calulate hydraulic efficiency ηh It depends from many factors Theory is giving qualitative recommendations to get higher efficiency
- to avioid sudden changes of velocities in pump - to avoid decrease of velocity on the impeller perimeter - to give simple shape to the impeller blades - to avoid sharp corners in the pump
In Fig 20 are given three different shapes of blades
If ω = const and Q = const for β2 = 90deg g
uH th
22= for β2 lt 90deg
guHth
22lt for β2 gt 90deg
guHth
22gt
For increasing the pump head the blades should be directed to the direction of rotation This will increase c2 and in diffuser we have to convert high kinetic energy to the potential energy and we lost in principal much energy The angle β2 lt 90deg is preferred for the pumps and β2 gt 90deg for ventilators 32 Similarity of Pumps Theoretical considerations are giving only qualitative results The more realistic results is possible to get by making pump or pump model tests especially in designing a new pump From the test results the pump similarity rules are used for calculating parameters of the pump under construction The theory of similarity is based on the rules of hydraulic modelling Geometric similitude ndash measures and shape of the model and pump should be in scale Kinematic similitude ndash velocities should be in scale
mmm cc
ww
uu
== etc
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
7
a) good b) poor Figure 6 Air lock in suction pipe 212 Forces on Impeller
Figure 7 Impeller unbalanced to the axial pressure
4
21
1
dpF s
π=
⎟⎠
⎞⎜⎝
⎛minus=
44
221
2
ddpF p
ππ
8
After simplifing ( )4
21dppF sp
πminus=
Figure 8 Balancing of axial pressure
Figure 9 Wear ring collars (a- low- b- mean- and c- high pressure pumps) 1- pump casing 2- wear ring 3- impeller 4- clearance
Figure 10 Impeller unbalanced to the radial pressure when flow rate is smaller from the pump design flow rate (a) and radial pressure in double ndashvolute pump (b) The radial force occurs on pumps with volute casings due to the uneven pressure distribution on the circumference of the impeller Radial force increases considerably in the partial flow rates and overload ranges as the changes in cross-section of the volute guide (eg with
9 circular cross-section) change quadratically via φ whereas the increase or decrease of the transport flow is linear 213 Main Types of Centrifugal Pumps
i) Single-Stage Pumps ii) Double-Suction Pump iii) Multistage Pumps
Figure 11 Multistage pump
Figure 12 Inducer postioned before the impeller [2]
- Submersible Pumps - Process Pumps - Pumps for Turbid Water - Portable Submersible Pumps (Flygt in 1948) - Sewage Pumps (Fig 13 - Swirl Type Impeller Pump and Super ndash Vortex Pump)
10
Figure 13 Impellers of swirl type pump 22 Axial Flow Pumps Scheme of the axial flow pump is given in the Fig 14 (1- vane 2-hub 3- vane of the guide apparatus) Vanes of the impeller are fixed or reversible
Figure 14 Axial flow pump
Figure 15 Impeller of the axial flow pump
11
23 Regenerative Pumps Special type of impeller pumps An impeller with several blades which are always radial and mounted on one or both sides rotates between two plane - parallel housing surfaces The energy of the fluid which is imparted to the particular liquid particles by impulse exchange steadily increases from the inlet into the impeller blades until its exit at the interrupter High pressure low flow rate
Figure 16 Water path in the impeller of the regenerative pump 2 4 Shaft Seals of Impeller pump
- Staffing box packing - Single mechanical seal - Double mechanical seals - Dynamic seal (Ahlstroumlm)
3 Theory of Impeller Pumps 31 Turbomachine Equation The flow processes in the impeller which lead to formation of the H(Q) line can be mathematically determined by the theoretical assumption that the impeller has an infinite number of infinitely thin blades The flow consists in this case from equal stream filaments The energy conversion can be arrived at with the aid of the moment of momentum principle The change of moment of momentum in time at the inlet (position 1) and at the oulet (position 2) is equal to the moment of forces to this liquid mass The loss-free flow is considered (ideal fluid) Pump Power (W= Nms) thgQHP ρ=
12
Figure 17 Flow velocities at impeller [3] is equal to the force moment to the shaft (Nm) multiplied with the impeller angular velocity ω (rads)
P =M ω
Theoretical pump head (m)
gQMHth ρω
=
In one second through the pump is flowing liquid mass m = ρQ (31) Moment of momentum at the position 1 and 2
M1 = mc1l1 and M2 = mc2l2
and changes of the moment of momentum
M = M2 - M1 =m(c2l2 - c1l1)
When we consider that l =R cos α and for mass (31)
M = ρQ (c2R2cos α2 ndash c1R1cos α1 )
As ωR1=u1 and ωR2=u2 then
g
ucucH th
)coscos( 111222 αα minus= (32)
13 This formula is Eulerrsquos equation for centrifugal pumps It represents a theoretical relationship between the individual values where there is an ideal uniform distribution of all liquid particles in the particular flow cross-sections However it also states bdquoThe theoretical head of a centrifugal pump is independent of the density and the physical properties of the fluid flowing through itldquo
Figure 18 Inlet and outlet triangles on radial impeller [2] Modern centrifugal pumps are constructed in this way that inflow has radial direction This means α = 90deg and cos α = 0
g
ucH th
222 cosα= (33)
The vortex torque component
cu = c cos α
and Hth = gcu u22
where cu2 is the vortex component of the absolute flow at the impeller outlet
Figure 19 Flow at the impeller of centrifugal pump ( a- real b- theoretical c- vortex) [3] ns rpm 40 50 75 100 125 150 175 200 250 k 078 080 081 082 0805 077 0715 0675 055
14
The specific speed ns of a pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The theoretical head Hth is reduced by the losses which occur due to
- volumetric internal leakage losses at the radial clearance between the impeller and casing
- friction losses in the blade channels - energy conversion losses (velocity in pressure due to changes in direction and cross-
section) - shock losses where the angle of the approach flow to the impeller blades is not
vertical Hydraulic efficiency is the real and theoretical pump head ratio
222 cosα
ηukc
gHHH
thh ==
Finally the turbomachine equation takes form
g
ukcH h 222 cosαη
= (34)
Figure 20 Different shapes of the impeller [3] The energy transfer begins at the inlet to the cascade and ends on departure from the blade channels The pressure and velocity of the pumped liquid is increased on this path The pressure increase is due to the centrifugal forces and deceleration in the relative velocity w in the impeller channels between the channel inlet and outlet The strong increase in the absolute velocity c of the fluid during the flow through the impeller channels is partly converted to pressure energy in a diffuser volute guide or stator after leaving the impeller A distinction is to be made between movement processes of the absolute velocity c and relative velocity w Absolute velocity c is that which liquid particles exibit compared with a static environment The relative velocity w is the velocity of a liquid particle compared with the rotating blades when flowing through the blade channel The peripheral velocity u of the rotating blades at the particular distance from the axis of rotation is also important The pressure path in the impeller is parabolic corresponding to the laws of dynamics To
15 determine the flow processes mathematically however all that is required is the recording of the velocities at the blade inlet and outlet Real head of the pump is smaller than theoretical In reality impeller has up to 12 blades The flow is different from theoretical between blades In the convex part of blade the velocity is smaller than in concave part The energy used for keeping vortex is decreasing the developed head by pump The head given for an infinite number of blades Hth is reduced due to the incomplete flow guidance where there is a finite number (mainly 7) of blades A comparison of the velocity diagrams for the actual and fictitious flow shows vortex components The decrease of the head is considered with the coefficient k which depends from the construction of the pump k is characterized by the specific speed ns of the pump Theoretically it is impossible to calulate hydraulic efficiency ηh It depends from many factors Theory is giving qualitative recommendations to get higher efficiency
- to avioid sudden changes of velocities in pump - to avoid decrease of velocity on the impeller perimeter - to give simple shape to the impeller blades - to avoid sharp corners in the pump
In Fig 20 are given three different shapes of blades
If ω = const and Q = const for β2 = 90deg g
uH th
22= for β2 lt 90deg
guHth
22lt for β2 gt 90deg
guHth
22gt
For increasing the pump head the blades should be directed to the direction of rotation This will increase c2 and in diffuser we have to convert high kinetic energy to the potential energy and we lost in principal much energy The angle β2 lt 90deg is preferred for the pumps and β2 gt 90deg for ventilators 32 Similarity of Pumps Theoretical considerations are giving only qualitative results The more realistic results is possible to get by making pump or pump model tests especially in designing a new pump From the test results the pump similarity rules are used for calculating parameters of the pump under construction The theory of similarity is based on the rules of hydraulic modelling Geometric similitude ndash measures and shape of the model and pump should be in scale Kinematic similitude ndash velocities should be in scale
mmm cc
ww
uu
== etc
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
8
After simplifing ( )4
21dppF sp
πminus=
Figure 8 Balancing of axial pressure
Figure 9 Wear ring collars (a- low- b- mean- and c- high pressure pumps) 1- pump casing 2- wear ring 3- impeller 4- clearance
Figure 10 Impeller unbalanced to the radial pressure when flow rate is smaller from the pump design flow rate (a) and radial pressure in double ndashvolute pump (b) The radial force occurs on pumps with volute casings due to the uneven pressure distribution on the circumference of the impeller Radial force increases considerably in the partial flow rates and overload ranges as the changes in cross-section of the volute guide (eg with
9 circular cross-section) change quadratically via φ whereas the increase or decrease of the transport flow is linear 213 Main Types of Centrifugal Pumps
i) Single-Stage Pumps ii) Double-Suction Pump iii) Multistage Pumps
Figure 11 Multistage pump
Figure 12 Inducer postioned before the impeller [2]
- Submersible Pumps - Process Pumps - Pumps for Turbid Water - Portable Submersible Pumps (Flygt in 1948) - Sewage Pumps (Fig 13 - Swirl Type Impeller Pump and Super ndash Vortex Pump)
10
Figure 13 Impellers of swirl type pump 22 Axial Flow Pumps Scheme of the axial flow pump is given in the Fig 14 (1- vane 2-hub 3- vane of the guide apparatus) Vanes of the impeller are fixed or reversible
Figure 14 Axial flow pump
Figure 15 Impeller of the axial flow pump
11
23 Regenerative Pumps Special type of impeller pumps An impeller with several blades which are always radial and mounted on one or both sides rotates between two plane - parallel housing surfaces The energy of the fluid which is imparted to the particular liquid particles by impulse exchange steadily increases from the inlet into the impeller blades until its exit at the interrupter High pressure low flow rate
Figure 16 Water path in the impeller of the regenerative pump 2 4 Shaft Seals of Impeller pump
- Staffing box packing - Single mechanical seal - Double mechanical seals - Dynamic seal (Ahlstroumlm)
3 Theory of Impeller Pumps 31 Turbomachine Equation The flow processes in the impeller which lead to formation of the H(Q) line can be mathematically determined by the theoretical assumption that the impeller has an infinite number of infinitely thin blades The flow consists in this case from equal stream filaments The energy conversion can be arrived at with the aid of the moment of momentum principle The change of moment of momentum in time at the inlet (position 1) and at the oulet (position 2) is equal to the moment of forces to this liquid mass The loss-free flow is considered (ideal fluid) Pump Power (W= Nms) thgQHP ρ=
12
Figure 17 Flow velocities at impeller [3] is equal to the force moment to the shaft (Nm) multiplied with the impeller angular velocity ω (rads)
P =M ω
Theoretical pump head (m)
gQMHth ρω
=
In one second through the pump is flowing liquid mass m = ρQ (31) Moment of momentum at the position 1 and 2
M1 = mc1l1 and M2 = mc2l2
and changes of the moment of momentum
M = M2 - M1 =m(c2l2 - c1l1)
When we consider that l =R cos α and for mass (31)
M = ρQ (c2R2cos α2 ndash c1R1cos α1 )
As ωR1=u1 and ωR2=u2 then
g
ucucH th
)coscos( 111222 αα minus= (32)
13 This formula is Eulerrsquos equation for centrifugal pumps It represents a theoretical relationship between the individual values where there is an ideal uniform distribution of all liquid particles in the particular flow cross-sections However it also states bdquoThe theoretical head of a centrifugal pump is independent of the density and the physical properties of the fluid flowing through itldquo
Figure 18 Inlet and outlet triangles on radial impeller [2] Modern centrifugal pumps are constructed in this way that inflow has radial direction This means α = 90deg and cos α = 0
g
ucH th
222 cosα= (33)
The vortex torque component
cu = c cos α
and Hth = gcu u22
where cu2 is the vortex component of the absolute flow at the impeller outlet
Figure 19 Flow at the impeller of centrifugal pump ( a- real b- theoretical c- vortex) [3] ns rpm 40 50 75 100 125 150 175 200 250 k 078 080 081 082 0805 077 0715 0675 055
14
The specific speed ns of a pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The theoretical head Hth is reduced by the losses which occur due to
- volumetric internal leakage losses at the radial clearance between the impeller and casing
- friction losses in the blade channels - energy conversion losses (velocity in pressure due to changes in direction and cross-
section) - shock losses where the angle of the approach flow to the impeller blades is not
vertical Hydraulic efficiency is the real and theoretical pump head ratio
222 cosα
ηukc
gHHH
thh ==
Finally the turbomachine equation takes form
g
ukcH h 222 cosαη
= (34)
Figure 20 Different shapes of the impeller [3] The energy transfer begins at the inlet to the cascade and ends on departure from the blade channels The pressure and velocity of the pumped liquid is increased on this path The pressure increase is due to the centrifugal forces and deceleration in the relative velocity w in the impeller channels between the channel inlet and outlet The strong increase in the absolute velocity c of the fluid during the flow through the impeller channels is partly converted to pressure energy in a diffuser volute guide or stator after leaving the impeller A distinction is to be made between movement processes of the absolute velocity c and relative velocity w Absolute velocity c is that which liquid particles exibit compared with a static environment The relative velocity w is the velocity of a liquid particle compared with the rotating blades when flowing through the blade channel The peripheral velocity u of the rotating blades at the particular distance from the axis of rotation is also important The pressure path in the impeller is parabolic corresponding to the laws of dynamics To
15 determine the flow processes mathematically however all that is required is the recording of the velocities at the blade inlet and outlet Real head of the pump is smaller than theoretical In reality impeller has up to 12 blades The flow is different from theoretical between blades In the convex part of blade the velocity is smaller than in concave part The energy used for keeping vortex is decreasing the developed head by pump The head given for an infinite number of blades Hth is reduced due to the incomplete flow guidance where there is a finite number (mainly 7) of blades A comparison of the velocity diagrams for the actual and fictitious flow shows vortex components The decrease of the head is considered with the coefficient k which depends from the construction of the pump k is characterized by the specific speed ns of the pump Theoretically it is impossible to calulate hydraulic efficiency ηh It depends from many factors Theory is giving qualitative recommendations to get higher efficiency
- to avioid sudden changes of velocities in pump - to avoid decrease of velocity on the impeller perimeter - to give simple shape to the impeller blades - to avoid sharp corners in the pump
In Fig 20 are given three different shapes of blades
If ω = const and Q = const for β2 = 90deg g
uH th
22= for β2 lt 90deg
guHth
22lt for β2 gt 90deg
guHth
22gt
For increasing the pump head the blades should be directed to the direction of rotation This will increase c2 and in diffuser we have to convert high kinetic energy to the potential energy and we lost in principal much energy The angle β2 lt 90deg is preferred for the pumps and β2 gt 90deg for ventilators 32 Similarity of Pumps Theoretical considerations are giving only qualitative results The more realistic results is possible to get by making pump or pump model tests especially in designing a new pump From the test results the pump similarity rules are used for calculating parameters of the pump under construction The theory of similarity is based on the rules of hydraulic modelling Geometric similitude ndash measures and shape of the model and pump should be in scale Kinematic similitude ndash velocities should be in scale
mmm cc
ww
uu
== etc
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
9 circular cross-section) change quadratically via φ whereas the increase or decrease of the transport flow is linear 213 Main Types of Centrifugal Pumps
i) Single-Stage Pumps ii) Double-Suction Pump iii) Multistage Pumps
Figure 11 Multistage pump
Figure 12 Inducer postioned before the impeller [2]
- Submersible Pumps - Process Pumps - Pumps for Turbid Water - Portable Submersible Pumps (Flygt in 1948) - Sewage Pumps (Fig 13 - Swirl Type Impeller Pump and Super ndash Vortex Pump)
10
Figure 13 Impellers of swirl type pump 22 Axial Flow Pumps Scheme of the axial flow pump is given in the Fig 14 (1- vane 2-hub 3- vane of the guide apparatus) Vanes of the impeller are fixed or reversible
Figure 14 Axial flow pump
Figure 15 Impeller of the axial flow pump
11
23 Regenerative Pumps Special type of impeller pumps An impeller with several blades which are always radial and mounted on one or both sides rotates between two plane - parallel housing surfaces The energy of the fluid which is imparted to the particular liquid particles by impulse exchange steadily increases from the inlet into the impeller blades until its exit at the interrupter High pressure low flow rate
Figure 16 Water path in the impeller of the regenerative pump 2 4 Shaft Seals of Impeller pump
- Staffing box packing - Single mechanical seal - Double mechanical seals - Dynamic seal (Ahlstroumlm)
3 Theory of Impeller Pumps 31 Turbomachine Equation The flow processes in the impeller which lead to formation of the H(Q) line can be mathematically determined by the theoretical assumption that the impeller has an infinite number of infinitely thin blades The flow consists in this case from equal stream filaments The energy conversion can be arrived at with the aid of the moment of momentum principle The change of moment of momentum in time at the inlet (position 1) and at the oulet (position 2) is equal to the moment of forces to this liquid mass The loss-free flow is considered (ideal fluid) Pump Power (W= Nms) thgQHP ρ=
12
Figure 17 Flow velocities at impeller [3] is equal to the force moment to the shaft (Nm) multiplied with the impeller angular velocity ω (rads)
P =M ω
Theoretical pump head (m)
gQMHth ρω
=
In one second through the pump is flowing liquid mass m = ρQ (31) Moment of momentum at the position 1 and 2
M1 = mc1l1 and M2 = mc2l2
and changes of the moment of momentum
M = M2 - M1 =m(c2l2 - c1l1)
When we consider that l =R cos α and for mass (31)
M = ρQ (c2R2cos α2 ndash c1R1cos α1 )
As ωR1=u1 and ωR2=u2 then
g
ucucH th
)coscos( 111222 αα minus= (32)
13 This formula is Eulerrsquos equation for centrifugal pumps It represents a theoretical relationship between the individual values where there is an ideal uniform distribution of all liquid particles in the particular flow cross-sections However it also states bdquoThe theoretical head of a centrifugal pump is independent of the density and the physical properties of the fluid flowing through itldquo
Figure 18 Inlet and outlet triangles on radial impeller [2] Modern centrifugal pumps are constructed in this way that inflow has radial direction This means α = 90deg and cos α = 0
g
ucH th
222 cosα= (33)
The vortex torque component
cu = c cos α
and Hth = gcu u22
where cu2 is the vortex component of the absolute flow at the impeller outlet
Figure 19 Flow at the impeller of centrifugal pump ( a- real b- theoretical c- vortex) [3] ns rpm 40 50 75 100 125 150 175 200 250 k 078 080 081 082 0805 077 0715 0675 055
14
The specific speed ns of a pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The theoretical head Hth is reduced by the losses which occur due to
- volumetric internal leakage losses at the radial clearance between the impeller and casing
- friction losses in the blade channels - energy conversion losses (velocity in pressure due to changes in direction and cross-
section) - shock losses where the angle of the approach flow to the impeller blades is not
vertical Hydraulic efficiency is the real and theoretical pump head ratio
222 cosα
ηukc
gHHH
thh ==
Finally the turbomachine equation takes form
g
ukcH h 222 cosαη
= (34)
Figure 20 Different shapes of the impeller [3] The energy transfer begins at the inlet to the cascade and ends on departure from the blade channels The pressure and velocity of the pumped liquid is increased on this path The pressure increase is due to the centrifugal forces and deceleration in the relative velocity w in the impeller channels between the channel inlet and outlet The strong increase in the absolute velocity c of the fluid during the flow through the impeller channels is partly converted to pressure energy in a diffuser volute guide or stator after leaving the impeller A distinction is to be made between movement processes of the absolute velocity c and relative velocity w Absolute velocity c is that which liquid particles exibit compared with a static environment The relative velocity w is the velocity of a liquid particle compared with the rotating blades when flowing through the blade channel The peripheral velocity u of the rotating blades at the particular distance from the axis of rotation is also important The pressure path in the impeller is parabolic corresponding to the laws of dynamics To
15 determine the flow processes mathematically however all that is required is the recording of the velocities at the blade inlet and outlet Real head of the pump is smaller than theoretical In reality impeller has up to 12 blades The flow is different from theoretical between blades In the convex part of blade the velocity is smaller than in concave part The energy used for keeping vortex is decreasing the developed head by pump The head given for an infinite number of blades Hth is reduced due to the incomplete flow guidance where there is a finite number (mainly 7) of blades A comparison of the velocity diagrams for the actual and fictitious flow shows vortex components The decrease of the head is considered with the coefficient k which depends from the construction of the pump k is characterized by the specific speed ns of the pump Theoretically it is impossible to calulate hydraulic efficiency ηh It depends from many factors Theory is giving qualitative recommendations to get higher efficiency
- to avioid sudden changes of velocities in pump - to avoid decrease of velocity on the impeller perimeter - to give simple shape to the impeller blades - to avoid sharp corners in the pump
In Fig 20 are given three different shapes of blades
If ω = const and Q = const for β2 = 90deg g
uH th
22= for β2 lt 90deg
guHth
22lt for β2 gt 90deg
guHth
22gt
For increasing the pump head the blades should be directed to the direction of rotation This will increase c2 and in diffuser we have to convert high kinetic energy to the potential energy and we lost in principal much energy The angle β2 lt 90deg is preferred for the pumps and β2 gt 90deg for ventilators 32 Similarity of Pumps Theoretical considerations are giving only qualitative results The more realistic results is possible to get by making pump or pump model tests especially in designing a new pump From the test results the pump similarity rules are used for calculating parameters of the pump under construction The theory of similarity is based on the rules of hydraulic modelling Geometric similitude ndash measures and shape of the model and pump should be in scale Kinematic similitude ndash velocities should be in scale
mmm cc
ww
uu
== etc
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
10
Figure 13 Impellers of swirl type pump 22 Axial Flow Pumps Scheme of the axial flow pump is given in the Fig 14 (1- vane 2-hub 3- vane of the guide apparatus) Vanes of the impeller are fixed or reversible
Figure 14 Axial flow pump
Figure 15 Impeller of the axial flow pump
11
23 Regenerative Pumps Special type of impeller pumps An impeller with several blades which are always radial and mounted on one or both sides rotates between two plane - parallel housing surfaces The energy of the fluid which is imparted to the particular liquid particles by impulse exchange steadily increases from the inlet into the impeller blades until its exit at the interrupter High pressure low flow rate
Figure 16 Water path in the impeller of the regenerative pump 2 4 Shaft Seals of Impeller pump
- Staffing box packing - Single mechanical seal - Double mechanical seals - Dynamic seal (Ahlstroumlm)
3 Theory of Impeller Pumps 31 Turbomachine Equation The flow processes in the impeller which lead to formation of the H(Q) line can be mathematically determined by the theoretical assumption that the impeller has an infinite number of infinitely thin blades The flow consists in this case from equal stream filaments The energy conversion can be arrived at with the aid of the moment of momentum principle The change of moment of momentum in time at the inlet (position 1) and at the oulet (position 2) is equal to the moment of forces to this liquid mass The loss-free flow is considered (ideal fluid) Pump Power (W= Nms) thgQHP ρ=
12
Figure 17 Flow velocities at impeller [3] is equal to the force moment to the shaft (Nm) multiplied with the impeller angular velocity ω (rads)
P =M ω
Theoretical pump head (m)
gQMHth ρω
=
In one second through the pump is flowing liquid mass m = ρQ (31) Moment of momentum at the position 1 and 2
M1 = mc1l1 and M2 = mc2l2
and changes of the moment of momentum
M = M2 - M1 =m(c2l2 - c1l1)
When we consider that l =R cos α and for mass (31)
M = ρQ (c2R2cos α2 ndash c1R1cos α1 )
As ωR1=u1 and ωR2=u2 then
g
ucucH th
)coscos( 111222 αα minus= (32)
13 This formula is Eulerrsquos equation for centrifugal pumps It represents a theoretical relationship between the individual values where there is an ideal uniform distribution of all liquid particles in the particular flow cross-sections However it also states bdquoThe theoretical head of a centrifugal pump is independent of the density and the physical properties of the fluid flowing through itldquo
Figure 18 Inlet and outlet triangles on radial impeller [2] Modern centrifugal pumps are constructed in this way that inflow has radial direction This means α = 90deg and cos α = 0
g
ucH th
222 cosα= (33)
The vortex torque component
cu = c cos α
and Hth = gcu u22
where cu2 is the vortex component of the absolute flow at the impeller outlet
Figure 19 Flow at the impeller of centrifugal pump ( a- real b- theoretical c- vortex) [3] ns rpm 40 50 75 100 125 150 175 200 250 k 078 080 081 082 0805 077 0715 0675 055
14
The specific speed ns of a pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The theoretical head Hth is reduced by the losses which occur due to
- volumetric internal leakage losses at the radial clearance between the impeller and casing
- friction losses in the blade channels - energy conversion losses (velocity in pressure due to changes in direction and cross-
section) - shock losses where the angle of the approach flow to the impeller blades is not
vertical Hydraulic efficiency is the real and theoretical pump head ratio
222 cosα
ηukc
gHHH
thh ==
Finally the turbomachine equation takes form
g
ukcH h 222 cosαη
= (34)
Figure 20 Different shapes of the impeller [3] The energy transfer begins at the inlet to the cascade and ends on departure from the blade channels The pressure and velocity of the pumped liquid is increased on this path The pressure increase is due to the centrifugal forces and deceleration in the relative velocity w in the impeller channels between the channel inlet and outlet The strong increase in the absolute velocity c of the fluid during the flow through the impeller channels is partly converted to pressure energy in a diffuser volute guide or stator after leaving the impeller A distinction is to be made between movement processes of the absolute velocity c and relative velocity w Absolute velocity c is that which liquid particles exibit compared with a static environment The relative velocity w is the velocity of a liquid particle compared with the rotating blades when flowing through the blade channel The peripheral velocity u of the rotating blades at the particular distance from the axis of rotation is also important The pressure path in the impeller is parabolic corresponding to the laws of dynamics To
15 determine the flow processes mathematically however all that is required is the recording of the velocities at the blade inlet and outlet Real head of the pump is smaller than theoretical In reality impeller has up to 12 blades The flow is different from theoretical between blades In the convex part of blade the velocity is smaller than in concave part The energy used for keeping vortex is decreasing the developed head by pump The head given for an infinite number of blades Hth is reduced due to the incomplete flow guidance where there is a finite number (mainly 7) of blades A comparison of the velocity diagrams for the actual and fictitious flow shows vortex components The decrease of the head is considered with the coefficient k which depends from the construction of the pump k is characterized by the specific speed ns of the pump Theoretically it is impossible to calulate hydraulic efficiency ηh It depends from many factors Theory is giving qualitative recommendations to get higher efficiency
- to avioid sudden changes of velocities in pump - to avoid decrease of velocity on the impeller perimeter - to give simple shape to the impeller blades - to avoid sharp corners in the pump
In Fig 20 are given three different shapes of blades
If ω = const and Q = const for β2 = 90deg g
uH th
22= for β2 lt 90deg
guHth
22lt for β2 gt 90deg
guHth
22gt
For increasing the pump head the blades should be directed to the direction of rotation This will increase c2 and in diffuser we have to convert high kinetic energy to the potential energy and we lost in principal much energy The angle β2 lt 90deg is preferred for the pumps and β2 gt 90deg for ventilators 32 Similarity of Pumps Theoretical considerations are giving only qualitative results The more realistic results is possible to get by making pump or pump model tests especially in designing a new pump From the test results the pump similarity rules are used for calculating parameters of the pump under construction The theory of similarity is based on the rules of hydraulic modelling Geometric similitude ndash measures and shape of the model and pump should be in scale Kinematic similitude ndash velocities should be in scale
mmm cc
ww
uu
== etc
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
11
23 Regenerative Pumps Special type of impeller pumps An impeller with several blades which are always radial and mounted on one or both sides rotates between two plane - parallel housing surfaces The energy of the fluid which is imparted to the particular liquid particles by impulse exchange steadily increases from the inlet into the impeller blades until its exit at the interrupter High pressure low flow rate
Figure 16 Water path in the impeller of the regenerative pump 2 4 Shaft Seals of Impeller pump
- Staffing box packing - Single mechanical seal - Double mechanical seals - Dynamic seal (Ahlstroumlm)
3 Theory of Impeller Pumps 31 Turbomachine Equation The flow processes in the impeller which lead to formation of the H(Q) line can be mathematically determined by the theoretical assumption that the impeller has an infinite number of infinitely thin blades The flow consists in this case from equal stream filaments The energy conversion can be arrived at with the aid of the moment of momentum principle The change of moment of momentum in time at the inlet (position 1) and at the oulet (position 2) is equal to the moment of forces to this liquid mass The loss-free flow is considered (ideal fluid) Pump Power (W= Nms) thgQHP ρ=
12
Figure 17 Flow velocities at impeller [3] is equal to the force moment to the shaft (Nm) multiplied with the impeller angular velocity ω (rads)
P =M ω
Theoretical pump head (m)
gQMHth ρω
=
In one second through the pump is flowing liquid mass m = ρQ (31) Moment of momentum at the position 1 and 2
M1 = mc1l1 and M2 = mc2l2
and changes of the moment of momentum
M = M2 - M1 =m(c2l2 - c1l1)
When we consider that l =R cos α and for mass (31)
M = ρQ (c2R2cos α2 ndash c1R1cos α1 )
As ωR1=u1 and ωR2=u2 then
g
ucucH th
)coscos( 111222 αα minus= (32)
13 This formula is Eulerrsquos equation for centrifugal pumps It represents a theoretical relationship between the individual values where there is an ideal uniform distribution of all liquid particles in the particular flow cross-sections However it also states bdquoThe theoretical head of a centrifugal pump is independent of the density and the physical properties of the fluid flowing through itldquo
Figure 18 Inlet and outlet triangles on radial impeller [2] Modern centrifugal pumps are constructed in this way that inflow has radial direction This means α = 90deg and cos α = 0
g
ucH th
222 cosα= (33)
The vortex torque component
cu = c cos α
and Hth = gcu u22
where cu2 is the vortex component of the absolute flow at the impeller outlet
Figure 19 Flow at the impeller of centrifugal pump ( a- real b- theoretical c- vortex) [3] ns rpm 40 50 75 100 125 150 175 200 250 k 078 080 081 082 0805 077 0715 0675 055
14
The specific speed ns of a pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The theoretical head Hth is reduced by the losses which occur due to
- volumetric internal leakage losses at the radial clearance between the impeller and casing
- friction losses in the blade channels - energy conversion losses (velocity in pressure due to changes in direction and cross-
section) - shock losses where the angle of the approach flow to the impeller blades is not
vertical Hydraulic efficiency is the real and theoretical pump head ratio
222 cosα
ηukc
gHHH
thh ==
Finally the turbomachine equation takes form
g
ukcH h 222 cosαη
= (34)
Figure 20 Different shapes of the impeller [3] The energy transfer begins at the inlet to the cascade and ends on departure from the blade channels The pressure and velocity of the pumped liquid is increased on this path The pressure increase is due to the centrifugal forces and deceleration in the relative velocity w in the impeller channels between the channel inlet and outlet The strong increase in the absolute velocity c of the fluid during the flow through the impeller channels is partly converted to pressure energy in a diffuser volute guide or stator after leaving the impeller A distinction is to be made between movement processes of the absolute velocity c and relative velocity w Absolute velocity c is that which liquid particles exibit compared with a static environment The relative velocity w is the velocity of a liquid particle compared with the rotating blades when flowing through the blade channel The peripheral velocity u of the rotating blades at the particular distance from the axis of rotation is also important The pressure path in the impeller is parabolic corresponding to the laws of dynamics To
15 determine the flow processes mathematically however all that is required is the recording of the velocities at the blade inlet and outlet Real head of the pump is smaller than theoretical In reality impeller has up to 12 blades The flow is different from theoretical between blades In the convex part of blade the velocity is smaller than in concave part The energy used for keeping vortex is decreasing the developed head by pump The head given for an infinite number of blades Hth is reduced due to the incomplete flow guidance where there is a finite number (mainly 7) of blades A comparison of the velocity diagrams for the actual and fictitious flow shows vortex components The decrease of the head is considered with the coefficient k which depends from the construction of the pump k is characterized by the specific speed ns of the pump Theoretically it is impossible to calulate hydraulic efficiency ηh It depends from many factors Theory is giving qualitative recommendations to get higher efficiency
- to avioid sudden changes of velocities in pump - to avoid decrease of velocity on the impeller perimeter - to give simple shape to the impeller blades - to avoid sharp corners in the pump
In Fig 20 are given three different shapes of blades
If ω = const and Q = const for β2 = 90deg g
uH th
22= for β2 lt 90deg
guHth
22lt for β2 gt 90deg
guHth
22gt
For increasing the pump head the blades should be directed to the direction of rotation This will increase c2 and in diffuser we have to convert high kinetic energy to the potential energy and we lost in principal much energy The angle β2 lt 90deg is preferred for the pumps and β2 gt 90deg for ventilators 32 Similarity of Pumps Theoretical considerations are giving only qualitative results The more realistic results is possible to get by making pump or pump model tests especially in designing a new pump From the test results the pump similarity rules are used for calculating parameters of the pump under construction The theory of similarity is based on the rules of hydraulic modelling Geometric similitude ndash measures and shape of the model and pump should be in scale Kinematic similitude ndash velocities should be in scale
mmm cc
ww
uu
== etc
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
12
Figure 17 Flow velocities at impeller [3] is equal to the force moment to the shaft (Nm) multiplied with the impeller angular velocity ω (rads)
P =M ω
Theoretical pump head (m)
gQMHth ρω
=
In one second through the pump is flowing liquid mass m = ρQ (31) Moment of momentum at the position 1 and 2
M1 = mc1l1 and M2 = mc2l2
and changes of the moment of momentum
M = M2 - M1 =m(c2l2 - c1l1)
When we consider that l =R cos α and for mass (31)
M = ρQ (c2R2cos α2 ndash c1R1cos α1 )
As ωR1=u1 and ωR2=u2 then
g
ucucH th
)coscos( 111222 αα minus= (32)
13 This formula is Eulerrsquos equation for centrifugal pumps It represents a theoretical relationship between the individual values where there is an ideal uniform distribution of all liquid particles in the particular flow cross-sections However it also states bdquoThe theoretical head of a centrifugal pump is independent of the density and the physical properties of the fluid flowing through itldquo
Figure 18 Inlet and outlet triangles on radial impeller [2] Modern centrifugal pumps are constructed in this way that inflow has radial direction This means α = 90deg and cos α = 0
g
ucH th
222 cosα= (33)
The vortex torque component
cu = c cos α
and Hth = gcu u22
where cu2 is the vortex component of the absolute flow at the impeller outlet
Figure 19 Flow at the impeller of centrifugal pump ( a- real b- theoretical c- vortex) [3] ns rpm 40 50 75 100 125 150 175 200 250 k 078 080 081 082 0805 077 0715 0675 055
14
The specific speed ns of a pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The theoretical head Hth is reduced by the losses which occur due to
- volumetric internal leakage losses at the radial clearance between the impeller and casing
- friction losses in the blade channels - energy conversion losses (velocity in pressure due to changes in direction and cross-
section) - shock losses where the angle of the approach flow to the impeller blades is not
vertical Hydraulic efficiency is the real and theoretical pump head ratio
222 cosα
ηukc
gHHH
thh ==
Finally the turbomachine equation takes form
g
ukcH h 222 cosαη
= (34)
Figure 20 Different shapes of the impeller [3] The energy transfer begins at the inlet to the cascade and ends on departure from the blade channels The pressure and velocity of the pumped liquid is increased on this path The pressure increase is due to the centrifugal forces and deceleration in the relative velocity w in the impeller channels between the channel inlet and outlet The strong increase in the absolute velocity c of the fluid during the flow through the impeller channels is partly converted to pressure energy in a diffuser volute guide or stator after leaving the impeller A distinction is to be made between movement processes of the absolute velocity c and relative velocity w Absolute velocity c is that which liquid particles exibit compared with a static environment The relative velocity w is the velocity of a liquid particle compared with the rotating blades when flowing through the blade channel The peripheral velocity u of the rotating blades at the particular distance from the axis of rotation is also important The pressure path in the impeller is parabolic corresponding to the laws of dynamics To
15 determine the flow processes mathematically however all that is required is the recording of the velocities at the blade inlet and outlet Real head of the pump is smaller than theoretical In reality impeller has up to 12 blades The flow is different from theoretical between blades In the convex part of blade the velocity is smaller than in concave part The energy used for keeping vortex is decreasing the developed head by pump The head given for an infinite number of blades Hth is reduced due to the incomplete flow guidance where there is a finite number (mainly 7) of blades A comparison of the velocity diagrams for the actual and fictitious flow shows vortex components The decrease of the head is considered with the coefficient k which depends from the construction of the pump k is characterized by the specific speed ns of the pump Theoretically it is impossible to calulate hydraulic efficiency ηh It depends from many factors Theory is giving qualitative recommendations to get higher efficiency
- to avioid sudden changes of velocities in pump - to avoid decrease of velocity on the impeller perimeter - to give simple shape to the impeller blades - to avoid sharp corners in the pump
In Fig 20 are given three different shapes of blades
If ω = const and Q = const for β2 = 90deg g
uH th
22= for β2 lt 90deg
guHth
22lt for β2 gt 90deg
guHth
22gt
For increasing the pump head the blades should be directed to the direction of rotation This will increase c2 and in diffuser we have to convert high kinetic energy to the potential energy and we lost in principal much energy The angle β2 lt 90deg is preferred for the pumps and β2 gt 90deg for ventilators 32 Similarity of Pumps Theoretical considerations are giving only qualitative results The more realistic results is possible to get by making pump or pump model tests especially in designing a new pump From the test results the pump similarity rules are used for calculating parameters of the pump under construction The theory of similarity is based on the rules of hydraulic modelling Geometric similitude ndash measures and shape of the model and pump should be in scale Kinematic similitude ndash velocities should be in scale
mmm cc
ww
uu
== etc
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
13 This formula is Eulerrsquos equation for centrifugal pumps It represents a theoretical relationship between the individual values where there is an ideal uniform distribution of all liquid particles in the particular flow cross-sections However it also states bdquoThe theoretical head of a centrifugal pump is independent of the density and the physical properties of the fluid flowing through itldquo
Figure 18 Inlet and outlet triangles on radial impeller [2] Modern centrifugal pumps are constructed in this way that inflow has radial direction This means α = 90deg and cos α = 0
g
ucH th
222 cosα= (33)
The vortex torque component
cu = c cos α
and Hth = gcu u22
where cu2 is the vortex component of the absolute flow at the impeller outlet
Figure 19 Flow at the impeller of centrifugal pump ( a- real b- theoretical c- vortex) [3] ns rpm 40 50 75 100 125 150 175 200 250 k 078 080 081 082 0805 077 0715 0675 055
14
The specific speed ns of a pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The theoretical head Hth is reduced by the losses which occur due to
- volumetric internal leakage losses at the radial clearance between the impeller and casing
- friction losses in the blade channels - energy conversion losses (velocity in pressure due to changes in direction and cross-
section) - shock losses where the angle of the approach flow to the impeller blades is not
vertical Hydraulic efficiency is the real and theoretical pump head ratio
222 cosα
ηukc
gHHH
thh ==
Finally the turbomachine equation takes form
g
ukcH h 222 cosαη
= (34)
Figure 20 Different shapes of the impeller [3] The energy transfer begins at the inlet to the cascade and ends on departure from the blade channels The pressure and velocity of the pumped liquid is increased on this path The pressure increase is due to the centrifugal forces and deceleration in the relative velocity w in the impeller channels between the channel inlet and outlet The strong increase in the absolute velocity c of the fluid during the flow through the impeller channels is partly converted to pressure energy in a diffuser volute guide or stator after leaving the impeller A distinction is to be made between movement processes of the absolute velocity c and relative velocity w Absolute velocity c is that which liquid particles exibit compared with a static environment The relative velocity w is the velocity of a liquid particle compared with the rotating blades when flowing through the blade channel The peripheral velocity u of the rotating blades at the particular distance from the axis of rotation is also important The pressure path in the impeller is parabolic corresponding to the laws of dynamics To
15 determine the flow processes mathematically however all that is required is the recording of the velocities at the blade inlet and outlet Real head of the pump is smaller than theoretical In reality impeller has up to 12 blades The flow is different from theoretical between blades In the convex part of blade the velocity is smaller than in concave part The energy used for keeping vortex is decreasing the developed head by pump The head given for an infinite number of blades Hth is reduced due to the incomplete flow guidance where there is a finite number (mainly 7) of blades A comparison of the velocity diagrams for the actual and fictitious flow shows vortex components The decrease of the head is considered with the coefficient k which depends from the construction of the pump k is characterized by the specific speed ns of the pump Theoretically it is impossible to calulate hydraulic efficiency ηh It depends from many factors Theory is giving qualitative recommendations to get higher efficiency
- to avioid sudden changes of velocities in pump - to avoid decrease of velocity on the impeller perimeter - to give simple shape to the impeller blades - to avoid sharp corners in the pump
In Fig 20 are given three different shapes of blades
If ω = const and Q = const for β2 = 90deg g
uH th
22= for β2 lt 90deg
guHth
22lt for β2 gt 90deg
guHth
22gt
For increasing the pump head the blades should be directed to the direction of rotation This will increase c2 and in diffuser we have to convert high kinetic energy to the potential energy and we lost in principal much energy The angle β2 lt 90deg is preferred for the pumps and β2 gt 90deg for ventilators 32 Similarity of Pumps Theoretical considerations are giving only qualitative results The more realistic results is possible to get by making pump or pump model tests especially in designing a new pump From the test results the pump similarity rules are used for calculating parameters of the pump under construction The theory of similarity is based on the rules of hydraulic modelling Geometric similitude ndash measures and shape of the model and pump should be in scale Kinematic similitude ndash velocities should be in scale
mmm cc
ww
uu
== etc
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
14
The specific speed ns of a pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The theoretical head Hth is reduced by the losses which occur due to
- volumetric internal leakage losses at the radial clearance between the impeller and casing
- friction losses in the blade channels - energy conversion losses (velocity in pressure due to changes in direction and cross-
section) - shock losses where the angle of the approach flow to the impeller blades is not
vertical Hydraulic efficiency is the real and theoretical pump head ratio
222 cosα
ηukc
gHHH
thh ==
Finally the turbomachine equation takes form
g
ukcH h 222 cosαη
= (34)
Figure 20 Different shapes of the impeller [3] The energy transfer begins at the inlet to the cascade and ends on departure from the blade channels The pressure and velocity of the pumped liquid is increased on this path The pressure increase is due to the centrifugal forces and deceleration in the relative velocity w in the impeller channels between the channel inlet and outlet The strong increase in the absolute velocity c of the fluid during the flow through the impeller channels is partly converted to pressure energy in a diffuser volute guide or stator after leaving the impeller A distinction is to be made between movement processes of the absolute velocity c and relative velocity w Absolute velocity c is that which liquid particles exibit compared with a static environment The relative velocity w is the velocity of a liquid particle compared with the rotating blades when flowing through the blade channel The peripheral velocity u of the rotating blades at the particular distance from the axis of rotation is also important The pressure path in the impeller is parabolic corresponding to the laws of dynamics To
15 determine the flow processes mathematically however all that is required is the recording of the velocities at the blade inlet and outlet Real head of the pump is smaller than theoretical In reality impeller has up to 12 blades The flow is different from theoretical between blades In the convex part of blade the velocity is smaller than in concave part The energy used for keeping vortex is decreasing the developed head by pump The head given for an infinite number of blades Hth is reduced due to the incomplete flow guidance where there is a finite number (mainly 7) of blades A comparison of the velocity diagrams for the actual and fictitious flow shows vortex components The decrease of the head is considered with the coefficient k which depends from the construction of the pump k is characterized by the specific speed ns of the pump Theoretically it is impossible to calulate hydraulic efficiency ηh It depends from many factors Theory is giving qualitative recommendations to get higher efficiency
- to avioid sudden changes of velocities in pump - to avoid decrease of velocity on the impeller perimeter - to give simple shape to the impeller blades - to avoid sharp corners in the pump
In Fig 20 are given three different shapes of blades
If ω = const and Q = const for β2 = 90deg g
uH th
22= for β2 lt 90deg
guHth
22lt for β2 gt 90deg
guHth
22gt
For increasing the pump head the blades should be directed to the direction of rotation This will increase c2 and in diffuser we have to convert high kinetic energy to the potential energy and we lost in principal much energy The angle β2 lt 90deg is preferred for the pumps and β2 gt 90deg for ventilators 32 Similarity of Pumps Theoretical considerations are giving only qualitative results The more realistic results is possible to get by making pump or pump model tests especially in designing a new pump From the test results the pump similarity rules are used for calculating parameters of the pump under construction The theory of similarity is based on the rules of hydraulic modelling Geometric similitude ndash measures and shape of the model and pump should be in scale Kinematic similitude ndash velocities should be in scale
mmm cc
ww
uu
== etc
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
15 determine the flow processes mathematically however all that is required is the recording of the velocities at the blade inlet and outlet Real head of the pump is smaller than theoretical In reality impeller has up to 12 blades The flow is different from theoretical between blades In the convex part of blade the velocity is smaller than in concave part The energy used for keeping vortex is decreasing the developed head by pump The head given for an infinite number of blades Hth is reduced due to the incomplete flow guidance where there is a finite number (mainly 7) of blades A comparison of the velocity diagrams for the actual and fictitious flow shows vortex components The decrease of the head is considered with the coefficient k which depends from the construction of the pump k is characterized by the specific speed ns of the pump Theoretically it is impossible to calulate hydraulic efficiency ηh It depends from many factors Theory is giving qualitative recommendations to get higher efficiency
- to avioid sudden changes of velocities in pump - to avoid decrease of velocity on the impeller perimeter - to give simple shape to the impeller blades - to avoid sharp corners in the pump
In Fig 20 are given three different shapes of blades
If ω = const and Q = const for β2 = 90deg g
uH th
22= for β2 lt 90deg
guHth
22lt for β2 gt 90deg
guHth
22gt
For increasing the pump head the blades should be directed to the direction of rotation This will increase c2 and in diffuser we have to convert high kinetic energy to the potential energy and we lost in principal much energy The angle β2 lt 90deg is preferred for the pumps and β2 gt 90deg for ventilators 32 Similarity of Pumps Theoretical considerations are giving only qualitative results The more realistic results is possible to get by making pump or pump model tests especially in designing a new pump From the test results the pump similarity rules are used for calculating parameters of the pump under construction The theory of similarity is based on the rules of hydraulic modelling Geometric similitude ndash measures and shape of the model and pump should be in scale Kinematic similitude ndash velocities should be in scale
mmm cc
ww
uu
== etc
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
16
The peripheral velocity
602nDu π
=
and corresponding ratio of velocities (model and pump)
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
nDnD
uu
2
2
where ml is the length scale Theoretical flow rate of the pump 2222 sinαπ cbDQth = (35) where b2 is the width of the outflow of the impeller
Then ⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmm nnm
cbDcbD
QQ 3
2222
2222
sinsin
απαπ (36)
The pump head is calculated from (34)
2
2
222
222
coscos
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmmhm
h
m nnm
uckukc
HH
αηαη
(37)
where ηhk= ηhmkm Pump power P = ρgQH
35
⎟⎟⎠
⎞⎜⎜⎝
⎛==
ml
mmm nnm
HgQgQH
PP
ρρ
Dynamic similitude - ratio of frictional- and inertial forces and gravity- and inertial forces in the model and pump should be the same Reynolds number is characterizing the ratio of frictional and inertial forces
νcD
=Re and Re = Rem
In case we have the same liquid in model and in pump ν = νm then cD = const From the experimental research has been appeared that influence of the Re number is not important when Re ge 5 104 Different roughness of the pump and model impellers will cause difference in efficiency Efficiencies are connected by the formula
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
17 a
m
m DD
⎟⎠⎞
⎜⎝⎛=
minusminusηη
11 where a = 0 when the roughness is modelled and a = 02 when the
roughnesses are equal Froude number is characterizing the ratio of gravity- and inertial forces
Fr = gDc 2
Fr = Frm
A special case is ml = 1 Pump characteristics depend from the pump speed
2
1
2
1
nn
uu
=
2
1
2
1
nn
=
2
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
HH
and 3
2
1
2
1⎟⎟⎠
⎞⎜⎜⎝
⎛=
nn
PP
or
3
2
1
2
1
2
1
2
1
PP
HH
nn
===
The rate of pump flow where the operating conditions are equal is therefore proportional to its speed the heads behave as the square of its speeds the requared motor power output changes with the cube of its speed In case the pump speed is increasing 2 times the flow rate is increasing 2 times head 4 times and necessary power 8 times The hydraulic efficiencies are equal the pump efficiencies reduce slightly with speed
33 Specific Speed of Pump Definition The specific speed ns of a centrifugal pump is the required speed of one of the present pumps which are geometrically similar in all parts which delivers a flow rate of 1 m3s at a head of 1 m The term is used for comparing numerically different centrifugal pumps This is a variable obtained from the service data which has great practical significance for the design and choice of pumps For the working parameters of the model pump we can use index s From the equations (36) and (37) we have next expressions
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
18
sl
s nnm
QQ 3=
22
⎟⎟⎠
⎞⎜⎜⎝
⎛=
sl
s nnm
HH
giving us ml and ns
sss
sl n
nHH
nQQn
m == 3
4321
⎟⎠⎞
⎜⎝⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HH
QQnn s
ss
Considering that Q = 1m3s and H = 1 m
43
21
HQnns =
From the last equation the specific speed increases with n and Q and decreases with H The value of the specific speed is determined at the highest efficiency working condition of the pump and its value is valid for one impeller The specific speed is characterizing the construction of the pump The value of the height c2sinα2 could be calculated from u2 and angles α2 and β2 (Fig 21)
Figure 21 Velocity diagram
( )22
22222 sin
sinsinsinβαβα
α+
= uc
and
( )22
222 sin
sinβαβ+
=uc (38)
The expression (38) will be placed to the centrifugal pump equation (33) Then pump head
( )22
2222
sinsincosβαβα
+=
guH
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
19 or
( )
2
22222
sinsincos
ββαα
gcH +
= (39)
and velocities
( )HAgHu =
+=
22
222 sincos
sinβαβα
and
( ) HBgHc =+
=222
22 sincos
sinβαα
β
Quantities A and B are constants the values depends from the impeller construction (angles α2 and β2)
Rotation speed D
unπ60
2= (310)
Specific speed ns = n if H = 1 m The expressions (310) and (39) are giving
( )
22
22
sincossin60
βαβα
π+
=g
Dns (311)
The specific speed depends from the impeller construction ndash from diameter D and from angles α2 and β2
Figure 22 Impeller of the mixed-flow pump Dependent from the specific speed and construction the dynamic pumps could be low- normal- and high-speed centrifugal pumps mixed-flow pumps and axial flow pumps The pumps with small specific speed have low flow rate but high head pumps with high specific speed large flow rate and small head (Fig 23)
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
20
Figure 23 Impeller shapes and specific speed
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
21 34 Pump Characteristics Next parameters as a function from flow rate are used for the pump characteristics H(Q) P(Q) η(Q) and NPSH(Q) The characteristics are used for a constant rotation speed of pump (n = const) and for the fixed density and viscosity of he liquid The theoretical head curve Hth(Qth) could be derived from the pump equation (33) and from the expression of theoretical flow rate (35) From Fig 17 (velocity diagram) ( ) 222222 tancossin βαα cuc minus= (312)
Substituting in (312) c2sinα2 =22bD
Qth
π from (33) and
222 )cos
ugH
c th=α from(35) the
result will be next
22
222
tan βπ ⎟⎟
⎠
⎞⎜⎜⎝
⎛minus=
ugH
ubD
Q thth
and the theoretical pump head
thth QbDg
ug
uH
22
2
2
22
tan1
πβminus=
Dependent from the angle β2 we have three straight lines If β2 = 90deg horizontal line for β2 lt 90deg declining line and for β2 gt 90deg rising line (centrifugal ventilators) When the flow rate is equal to 2222 tan βπ bDuQ = theoretically the head is zero Line 3 is for the ideal fluid flowing in the impeller with the infinite number of thin blades With the correction k (34) we have line 4 for finite number of blades After reducing the friction losses in pump we have the characteristic 5 In case we have different flow rate from the design value the inflow direction is different from the radial direction and we have the characteristic 6 (supplementary head losses) Part of the flow is circulating in the pump (ηv lt 1) the final result is curve 7 In reality it is much more complicated and the real characteristics of the pump are evaluated experimentally The shape of the characteristics depends from the specific speed of the pump ns Different pump manufacturers form the characteristis in a different way Many conclusions for application of pumps could be done on the basis of characteristic curves The starting of the pump should be done when it needs from the motor low power For centrifugal pumps it is on zero flow rate this means with closed valve on pressure pipe The pumps with high specific speed have minimum power on high flow
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
22
rate These pumps should be started with open valve on pressure pipe It is quite common that axial flow pumps do not have valve on pressure pipe
Figure 24 The H(Q) curve (constant speed characteristic curve)
Figure 25 The H(Q) curve The impeller pumps before starting should be filled with the liquid The axial pumps are big and as the foot valves have a high local losses the foot valves are not installed normally It is impossible to fill the suction pipe in this case We have to install the pump under the water level surface in suction side It is constructive way to have pump filled before the starting
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
23
Figure 26 Pump MENBLOC 65-40-200 L85 2 (n =2960 rmin) curve
Figure 27 Ahlstroumlm closed impeller pump APP 22-65 (n =2950 rmin) curves
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
24
Figure 28 Axial flow pump curves
Figure 29 Regenerative pump curves There is possible to use many impellers in one casing of pump (Fig 27) The multistage pump has many impellers The impeller diameters could be reduced by turning (cut off in some limits) This way of reducing the impeller diameter has been used quite offenly in the past The best or recommended working area of the pump is usually indicated on H(Q) curve Roughly saying the pump could work in the area 05 Qdesign le Q le 12 Qdesign where design discharge will correspond to the maximum efficiency ηmax
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
25
Figure 30 Sarlin submersible sewage pump with SuperVortex impeller
Figure 31 H(Q) curves relative to speed (shell diagram) [2] The pump could be characterized by the shell diagram where the same value curves of efficiency are drawn In Fig 28 the shell digram for the axial flow pump is given The H(Q) lines are for five different angle of blades efficiency curves (full lines) and NPSH curves (stripe lines) The efficiency of this pump is quite high up to 84 High is also NPSH value from 85m to 15 m in the upper part of diagram The recommendable working area is indicated with the bold line In starting of the pump the head could not rise over the level of line I
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
26
Regenerative pump curves are in Fig 29 When we compare the curves with the same powerful centrifugal pump curves the regenerative pump has low flow rate but high head The H(Q) curve is concave and the P(Q) curve is declining The Sarlin company SuperVortex swirl type impeller pump curves are in Fig 30 The characteristic curves are different from the centrifugal pump curves This should be considered in case the pump is working in parallel with some other type of pump 4 Application of Pumps 41 System Curve The pump characteristic curves indicate the capability of the pump Before we are starting to select a pump we have to calculate the system requirements For this the system head curve should be calculated The task of the pump as a machine is to impart energy to a fluid In steady state the head H of the pump is equal to the head Hs of a system The necessary head is equal to
H = Hst + ht
where Hst ndashstatic or geodetic head m and ht is the head loss in suction and pressure pipe m The head loss in pipes consists from friction and minor (local) head losses
The mean velocity is calculated from the continuity equation
v=AQ
As the flow rate is not changing on the pipe length then
gA
Qdlht 2
2
2⎟⎠⎞
⎜⎝⎛ += sum sumζλ (41)
or 2kQht =
where k is expressing the flow resistance The system head curve could be expressed by the next way 2kQHH st += (42)
This is parabola starting from the point H = Hst +kQ2 (Fig 32)
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
27
42 Operating Point The operating point of the centrifugal pump is the intersection point of the pump characteristic curve and system head curve (Fig 32 and Fig 34) A corresponding variable for the power input efficiency of the pump and NPSHR value is assigned to each duty point In the design of the operating data of a centrifugal pump care should be taken to ensure that the pump works as close as possible to the point of best efficiency (Fig 33)
Figure 32 System and pump head curves [1]
Figure 33 Best efficiency operating point [1] For changing the operating point of the pump we have to change system head curve or pump head curve In Fig 35 the change in rate of flow with a fluctuating static head are given The flat pump curves produce relatively large flow rate fluctuations and those for steeper ones are smaller The system head curve is possible to change by throttling control (Fig 36) If the pump does not deliver the required service flow rate then throttling control (gate valve or orifice) must be used to set
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
28
Figure 34 System and pump curves [2]
Figure 35 Change of the flow rate with a fluctuating static head duty point B at flow rate Q This means an additional pipe friction loss dynH∆ The additional pipe friction loss dynH∆ may however be created only in the pipeline because throttling control on the inlet side poses the danger of cavitation Allowance must of course be made for a deterioration in efficiency because the drop in head is converted to heat in the throttling device For this reason pumps with a flat H(Q) curve should be used where possible for throttling control
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
29
Figure 36 Throttling control pump characteristics [2] The pump characteristic is possible to change by speed control or by reducing mechanically the impeller diameter The semiconductor frequency converters are used mainly The pump similarity rules are used to calculate a new speed n2 that the pump curve intersects the system head curve at duty point B2
( ) 21212 nnHH = ( )1212 nnQQ = ( )31212 nnPP = etc
Figure 37 Variable speed control [2]
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
30
The duty points of equal shock states which lie on the affinity parabolas passing through the co-ordinates data have the approximately equal efficiency It is particularly important that the affinity law is valid only if it does not lie within the range of cavitation The shell diagram of a centrifugal pump clearly shows the possible applications of this pump (Fig 31) If the impeller characteristic curve does not agree with the required flow characteristics for the actual operating conditions this can be corrected by changing the impeller outlet conditions The reduction of the impeller diameter depends from the specific speed of the pump
1200750
min
1 snDD
+=⎟⎠⎞
⎜⎝⎛
where D is the nominal diameter of the impeller and D1 reduced diameter mm Axial flow and mixed-flow pump impeller diameters is not possible to reduce The new pump characteristic is calculated by next expressions
DDQQ 11 = ( )211 DDHH = ( )311 DDPP =
43 Operation of Pumps in Parallel
Figure 38 Parallel operation using two centrifugal pumps with the same characteristic curves Centrifugal pumps in pumping stations frequently pump through a common pressure pipe with the pumped liquid being drawn mainly through separate suction pipes Where there is an
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
31
Figure 39 Parallel operation of two centrifugal pumps with unequal charactersitic curves
Figure 40 Three pumps operating parallel
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
32
increased demand one or more pumps are switched in either automatically or manually thus producing parallel operations With the parallel operation the rate of flow is less than the total of the rates of flow of centrifugal pumps operating singly and parallel operation leads to a reduction of the efficiency of the pumps under certain circumstances
IIIIIIIII
III
IIIIII
III QQQHgQHgQ
HgQ+
+
+=
+=
ηηηη
ηρηρρ
η
Figure 41 Optimum parallel operation domain of the centrifugal pumps with frequency converters 44 Operation of Pumps in Series Pumps operating in series are used for the increase of pressure
IIIIII HHH +=+ The efficiency
IIIIIIIII
III
IIIIII
III HHHgQHgQH
gQH+
+
+=
+=
ηηηη
ηρηρρ
η
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
33
45 Energy Savings with Variable-Speed Centrifugal Pump Drive
Figure 42 Example of energy saving on centrifugal pumps using variable speed control (Danfoss-GmbH) [2] The speed of three-phase induction motors for pump drives can be changed using static frequency converters These devices change a constant power supply with its associated frequency into a converted voltage and frequency Fig 42 shows example of possible power savings on centrifugal pumps Although frequency converters still represent a considerable investment cost they are becoming cheaper If the cost of the converter is set against the annual saving in energy cost the is recovered very quickly particularly for pumps with a long service life
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
34 46 Effect of Liquid Viscosity on Performance of a Pump An increase in the viscosity of the pumped fluid changes the characteristic curves of the pump Flow rate and head reduce accompanied by an increase in power input ie efficiency is lowered (Fig 43) The characteristic curves for pumping viscous fluid can only be accurately determined by trial The correction values kQ kH and kη relative to the flow rate head and efficiency are given in Fig 44 dependent from Reynolds number
wQz QkQ = wHz HkH = wz k ηη η=
Figure 43 Reduction in performance when handling viscous liquids [2]
Figure 44 Correction factors for pumping viscous fluids [3]
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
35
47 Cavitation
Figure 45 NPSHA safety margin with respect to NPSHR in the H(Q) diagram [2]
Figure 46 Cavitation [2] Cavitation can occur in any machine handling liquid whenever the local static pressure falls below the vapor pressure of the liquid When this occurs the liquid can flash to vapor locally forming a vapor cavity and changing the flow pattern from the non-cavitating condition The vapor cavity changes the effective shape of the flow passage thus altering the local pressure field Since the size and shape of the vapor cavity are influenced by the local pressure field the flow may become unsteady The unsteadiness may cause the entire flow to oscillate and the machine to vibrate As cavitation commences the effect is to reduce the performance of a pump rapidly Thus cavitation
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
37
characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
40
6 Selection of Pump
36
must be avoided to maintain stable and efficient operation In addition local surface pressures may become high when the vapor cavity collapses causing erosion damage or surface pitting The damage may be severe enough to destroy a machine made from a brittle low-strength material Obviously cavitation must be avoided to assure long machine life
Figure 47 NPSHA and NPSHR in the H(Q) diagram [2]
Figure 48 Regenerative impeller with a radial impeller mounted in front [2] Common regenerative pumps have quite frequently unsatisfactory NPSHR values A design such shown in Fig 48 is based on a radial impeller with good normal flow
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characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
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Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
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Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
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6 Selection of Pump
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characteristics being positioned before the regenerative impeller as a booster pump In this way the comparatively good NPSHR values for this type of impeller can be used and combined at the same time with the advantages which the regenerative impeller has in achieving large pressures at low capacity coefficients
Figure 49 NPSHR values of a centrifugal pump specified according to various criteria [2] Table 1 Criteria for (NPSHA) of centrifugal pumps [2]
In addition to increase in pressure before the first impeller of the pump the inducer also performs a further task that it ensures the inlet conditions to the cascade are such that positive pre-rotation conditions are produced thus improving the NPSHR
38
Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
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6 Selection of Pump
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Figure 50 Impact of an inducer on NPSHR [2]
Figure 51 NPSHR curve of inducer and impeller [2] Due to the severely throttled delivery recirculation flows out of and into the impeller occur at the impeller inlet and outlet in the partial load range and severe pre-rotation occurs (Fig 52) This produces shear layers between the normal and reverse flow thus forming vortices and these in turn form vapor bubbles which implode at the pressure side of the impeller blade
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
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6 Selection of Pump
39
Figure 52 Pre-rotation and recirculation in an impeller operating in the partial load range [2] 5 Positive-Displacement Pumps Main types of positive-displacement pumps are - piston pumps - single-acting piston pump - double-acting piston pump - differential piston pump
- diaphragm pump - wing pump - rotary pump - gear pump - screw pump - vane pump - rotary-piston pump - peristaltic pump (hose pump) - liquid ring pump - pumping devices (water wheel Archimedian screw etc)
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6 Selection of Pump
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6 Selection of Pump
