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DRAFT
Proceedings of ASME Turbo Expo 2004
Power for Land
Sea, and Air
June
14-17,
2004
Vienna
Austria
GT2004-53821
DESIGN OF SMALL CENTRIFUGAL COMPRESSORS PERFORMANCE TEST
FACILITY
Al-Sulaiman
, Fahd A.
Graduate Assistant
AI-Qutub
Amro M
Associate Professor
Mechanical
Engineering Department
King Fahd University of Petroleum
and Minerals
Dhahran, 31261, Saudi Arabia
ABSTRACT
Actual performance testing is a key element in the design
stage, development and troubleshooting of centrifugal
compressors. The present work discusses the procedure for
designing the experimental setup and the selection of drive unit
for variable centrifugal compressors sizes. It starts with setting
criteria of selection. A survey over different types of drive units
and facility setup was conducted. It was found that the electric
drive unit with the aid of transmission for stepping-up the
speeds is the most suitable type. This is due mainly to the
excellent control property of electric motors allowing for wide
range of operational speed and power. A new methodology was
developed for selecting operational power and speeds of the
drive unit for different sizes of impellers. The code, used for the
analysis, was developed by the authors. It calculates the range
of input power, input torque, and rotational speeds, as well as,
the mass flow rate, total pressure and temperature ratios for
different sizes of impellers. This will aid in selecting the proper
instrumentation for the experiments. The code was validated
with experimental results in the literature. It is expected that the
present methodology will enhance selection procedure for
designing compressor test facility.
INTRODUCTION
Improper selection of the instrumentation for a single test
rig may
lead to inaccurate reading increase
cost or even failure
in the system, such as the failure of the mass flow measurement
at the venture nozzle, Colantuoni and Colella [I]. In other
words, estimating the input power, torque, mass flow rate, rpm,
and total pressure and temperature ratios for different sizes and
configurations is essential in planning for compressor testing.
Some commercial codes are available and designed to
estimate the operating conditions of the centrifugal
compressors. However,
most
of them are for industrial
applications and used to evaluate conditions during operation
and not for the designing purposes, such as, Centrifugal
Compressor Tracking Program developed by Ronald. P.
Lapina. On the other hand, there are limited codes that can
calculate the operating conditions of the compressor for
designing purposes. An example of that is the codes developed
by PCA Engineering and Concepts Incs. However, these codes
do not show on the same figure the effect of changing impeller
size or configuration. The present work involves the
development of a code that predicts centrifugal compressor
performance at different sizes and configurations. Presentation
of results is designed such as the selection of drive unit
characteristics can be done in a very efficient manner.
Designing a flexible centrifugal compressor test facility
where different compressor configurations and sizes can be
tested with minor modifications, means reduction in cost and
time. Also, the quality of the experimental results depends on
the design of the test facility. That is the instrumentation used
for the measurement and the layout of the test rig. This raises
the need to find a methodology to satisfy these requirements.
On the other hand, one of the
main requirements in
designing the test facility
is selecting the proper type of driver
unit. For instance, in the present
study, the driver has to be
flexible to test different types of compressors with good control
system
on the rotational speed
, especially near the surge
condition.
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Based on literature survey there are three major types of
drivers
electrical motor
gas turbine and blow
-down facility
with a turbocharger
Each one of them has its advantages and
disadvantages, such as cost
size, and power requirement as
discussed below
The present work evaluates these systems as
alternatives for driving different sizes of high- speed small-size
centrifugal compressors.
NOMENCLATURE
Symbols
bImpeller wdth
CAbsolute
elocity of the impeller
coTangential
velocity of the impeller
Cr
Constant
pressure specific heat
M Mach number
m Mass flow rate
N h
Number of
the blades in the impeller
PPressure
Pr Pressure ratio
PwPower
RGas constant
r Impeller radius
r p m
Rotational speed per minute
T Temperature
U Impeller blade
velocity
WRadial relative
velocity
of the impeller
Z The reference size
Greek letters
Subscripts
Impeller angle
Density
Specific heat ratio
Slip factor
Efficiency
Flow factor
Angular velocity
act
Actual case
cr Compressor rotor
c Compressor stage
h Valueat hub
ideal Ideal case
01 Impeller inlet (compressor) stagnation condition
02 Impeller exit stagnation condition
04 Compressor exit tagnation condition
I Impeller inlet
2 Impeller exit
4 Compressor exit
PERFORMANCE
ANALYSIS
One of the main requirements of designing the centrifugal
compressor test facility is estimating the required input power
and rotational speed to select the proper drive unit. This can be
achieved through
using
the proper analysis. In addition to that,
input torque , mass flow rate, stagnation pressure and
temperature ratios can help in estimating the range of operating
conditions and selection of proper instrumentation. Based on
the analysis below a computer program was constructed to
perform the calculations for different impeller sizes and
configurations.
Analysis
The operating conditions for a given centrifugal
compressor can be obtained theoretically through using
reasonable assumptions
as well as available information from
the literature. Equations for input power, input torque, mass
flow rate
stagnation pressure and temperature ratios, as well as
some other related equations were derived. The main derived
equations are shown below. Most of the analysis, with
additional modifications, is based on Hill and Peterson [2]
derivation for centrifugal compressor.
Geometry
The geometry of the analyzed impeller is shown in Figs. I
and 2.
Major
Assumptions:
Ideal gas
Bulk flow,
No preswirl
at the inlet
Adiabatic flow.
Fig. 1: Impeller inlet geome try and velocity vector
I-V
Fig. 2: Impeller exit geometry and velocity vector
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Governing Equations:
Actual mass flow rate
To account for the bulk flow assumption in the analysis an
estimated coefficient for the average mass flow rate was
implemented in the code
It was chosen based on a well-
established experimental investigation in literature for smooth
pipes Schlichting
[3]. Also,
to account for the flow separation
(off design condition
)
an estimated relative flow angle, 10
relative to inducer tip as flow off design limits, was
implemented.
The flow factor is used to account for
the off-design
condition
When the relative flow is parallel to inducer tip the
flow is considered to be in ideal case
design condition);
otherw ise it is off design condition.
Using
the definition of the flow factor
the actual mass
flow rate can be written as:
Mact =
1
m
deal
In this case, the inlet axial velocity is:
tan /3,
1 )
2 )
Using the definitions of the static isentropic relation, Mach
number, total temperature and inlet axial velocity, the mass
flow can be written as a function of operating conditions and
impeller geometry such that:
m-,=P01
( 0,Qri2
Ytan 31
2
0 O
tan /31
yRTo1- )
x 7 c r , 2
2) 0,
rI) 3
as =(1-2
N b
cosf2
X(1-
M
ace tan
t 2)
m
2P2 7r2 r2 b( )
30
The slip factor is also defined as:
U
Impeller exit static density
4 . a )
4 . b )
To calculate the slip factor, the impeller exit static density
needs to be found first. The general procedure to derive the
required equation to find the density was done by Hill and
Peterson [2]. Some improvements were done by taking into
account actual inlet and exit mach number, as well as off design
condition as shown below. This procedure includes the
following assumptions:
Neglect the thickness of the vanes,
Neglect the boundary layer displacement thickness,
Assume the isentropic efficiency of the rotor
: 7 er x 1 277, , 17
,
is the stage isentropic efficiency.
Using the
isentropic relation the static
density ratio can be
written as:
P2 Po2
P Poi
[1 M
1+Y] M
L2
Y - l
5 )
In the case
of no preswirl condition
the stagnation pressure
ratio can be written in terms
of the blade velocity at the
impeller tip and
the absolute tangential velocity at the impeller
exit. This can be achieved by using the isentropic
relation and
the definition of the power,
as will as the rotor efficiency.
c
There are some formulas that can be used to calculate the
P 02
141 77,
U2
Fez
1 r-I
The oneli factor which was discussed by Wiesner [4] and
6
modified by Hill and Peterson [
2], is a representative formula
Poi
2
r
RTo
U2
since it has been validated experimentally. It takes into
consideration number
of the impeller blades and the exit
condition and configuration. Using their formula and
introducing the definition of the exit radial relative velocity
yields:
The rotor efficiency
is modeled from the experimental
results done by Krain et al
. [5]. These
results were selected
since they are close to the operating conditions
of the desired
test facility of the compressor Also, because Krain et al. [5]
study
was chosen as a reference to validate
four different
advanced codes which indicates the confident in their results
see Eisenlohr et al. [6 ]. The chosen eff iciency
model for
validation was:
77,. = 0.8545*exp -IE-06*rpm)
C e2
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This efficiency
equation will be introduced in the code to
account for the stage loses
so the total stage pressure and
temperature ratios can be obtained
.
The main purpose of
pressure ratio validation is to check whether the code can
predict the compressor performance accurately as shown later.
Mach number at the impeller inlet can be written as:
M, _
C
2(7
C, )
YR T01-2C
r
Substituting
for C,
in term of the angular velocity and the
inlet angle and then square the Mach numb er leads to:
yR
2
f .
tan /3,
z
0, Qr.
t a n 1 3
o
2C
r
Similarly, the square exit Mach number can be written as:
z
M
2
=
C2
C
YR (T02 - )
n
8 )
9 )
where
C, is the absolute velocity at
the impeller exit as
illustrated
in Fig. 2.
It can be written as:
2
C2= U2-
Wr
2
ttanQ2)_
Wr
1 0 )
The derived Eqs., 4 and 6, can be substituted into Eq. 10 to
obtain the density at the impeller exit.
2
y ) RT
o
x
1t^^
^
Input Power
Assuming there is no presw irl at the inlet, CO
, is equal to
zero so the input pow er can be written as:
Pw=
y
., 6sU22
1 2 )
Substituting into Eq. 12 for the slip factor and write blade
velocity at the impeller tip as a function of the angular velocity,
the power can be obtained as:
Pw =M'
1- cosfl2)
b
z
x 1
mom, m
tan/i2)(2r2)
2P2 n2 r2 b(0 )
IMPLEMENTATIONS
OF THE ANALYSIS
1 3 )
A computer code was developed
, using MATLAB
software
to calculate compressor performance parameters.
Figure 3 is a flow chart for the code. The input data are:
Impeller radiuses,
Impeller configuration (angles and number of blades),
Inlet conditions, total pressure and temperature, as
well as flow factor,
Gas properties ideal gas only).
Three types of output are configured to present the
compressor performance as the following:
The first type produces plots for input power, input torque.
total pressure and temperature ratios, separately vs. mass flow
rate for different rpm. This will serve in validating the code.
The second type produces plots for input power, input
torque,
total pressure and temperature ratios and mass flow rate.
separately, vs. rpm for different impeller sizes and exit
tangential
velocities. This will aid in selecting proper
instrumentation range and determine
the required power input
for a given impeller geometry.
The third type produces plots of the total pressure ratio vs.
impeller size for different input power and rpm. This output is
the distinguish one which will aid in designing compressor for
a given system, as well as aid in the design of a drive unit for
different impeller sizes and configurations. Further details are
given in the example set in results and discussion section.
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Input
geometry
, size, gas properties,
inlet stagn ation
conditions, efficiency, flow factor, rpm, bulk flow correction.
p2 = pt , as a first iteration for p2
Calculate: slip factor
, W,2. C2, C 02 ,
Power
Torque T a Mi Mt
efficiency over the flow range for a given rpm. Figure 4
illustrates
clearly the validation of the efficiency model used in
the present code for the given case. Input to the code is the
same as provided in the literature. The impeller data are shown
in Fig. 5. Figure 5 is a comparison between the experimental
results and the present code output for total pressure ratio. It is
clear that the present code predicts total pressure ratio very well
up to the running speed of 40,000 rpm with negligible error,
specifically near the maximum efficiency. At higher rpm the
present code over predicts the total pressure ratio. The
deviation increases with rpm and as operating condition
deviates from maximum efficiency point. However, the
maximum deviation
is less
than 11% at 50, 000 rpm at the
highest efficiency. Surge cannot be predicted by the present
code, which is the usual case for many codes.
K r a i n e t a l [ 6 ]
0.85
Calculate: p2rew
u
0.83
N d
V
0.81
CL m
0.79
- - - -1
U
N
0.77
0.75
25,000
35,000
rpm
, 0.07 s.-G.tt2r.-0.93
63se.
q.. -310.8
0-36 b. 010T
Fig. 4: Efficiency
modeling validation.
If U2> 6 00, break
the loop rpm loop)
Calculate final
Power
Torque
, Pa/Pui, T(Mrrn,
3
Show
the output
Fig. 3: General flow chart of the code.
RESULTS AND DISCUSSION OF THE ANALYSIS
Code validation
The present code and analysis are to be validated through
comparison with experimental results of Krain et al. [5]. The
validation of the code is based on the comparison of the total
pressure ratio. So, efficiency model of the compressor must be
first validated with experimental results of Krain et al. [5].
Experimental results shown in Fig. 4 are based on the average
Efficiency m odel
45,000 55.000
sower;'' ,
116 . 1S2
_2S3
Anu6wr
0* )
Fig. 5: Code validation,
total pressure
r a t io vs .
flow rate for different
rotational speeds
Example
Dimensions
of the impeller given in
table I are for the
reference
size in the example
. A multiplication factor, Z, is
used to
alter the dimensions
of the reference impeller without
effecting
geometrical angles and number
of blades.
The working fluid is
air with inlet total pressure and
temperature
of 101.3 kPa and 27 C, respectively. Both high
and low mass
flow rate impellers are considered
each as a case
as shown in table
I (,(3l = 45 and 67). Figures 6 to 9 are the
first type of output for
the present
code for the basic dimension
of impeller (Z=1). This type of output is useful for code
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validation with experimental work for further development and
modification. It can also aid in the selection of instrumentation
for a given impeller, as well as predicting the required drive
power and speed range. In addition, it shows the effect of
changing impeller configuration, such as impeller inlet angle.
The second type of output is illustrated in Figs. 10-14.
Here,
mass
flow rate, the input power and torque, as well as
total temperature and pressure ratios are provided for different
impeller sizes vs. rpm on the same plot. Moreover, impellers tip
speeds are indicated. The information provided will indicate the
set of instrumentation required for the whole test rig. The first
design constrain is the available input power (say 500 kW, for
example). This will provide the limit for the impellers tip
speed. For example, if the tested impeller is of a 3Z size, this
will lead to a tip speed limit of about 530 m/s at (0, =1). The
second design constrains is the maximum output rpm for the
drive unit (say 100,000 rpm as an example). This would also
put a limit for tip speed of small impellers as shown in Fig. 10.
The third type of output is illustrated in Figs. 15. a and b.
The figures indicate the total pressure ratio vs. impeller size for
two different angles
. Iso-lines of input power and rpm provide a
useful tool not only for experimental drive unit setup but also
for selecting impeller size for a given compression system or
gas turbine engine. For example, if the power limit is 200 kW,
speed limit is 100,000 rpm and inlet impeller angle is 67, then
the maximum total pressure ratio that can be tested is 2.9 for
impeller size of (Z= 3) due to power limit. Also, the maximum
total pressure ratio for an impeller size of (Z=1) is 2.8 due to
speed limit. However, the maximum possible total pressure
ratio that can be obtained for 200 kW at 100,000 rpm is 8.2
with impeller size corresponding to (Z= 1.56). The same
outputs of the code may be obtained for any configuration of
impeller for the design purpose of a test facility.
Table 1: Impeller characteristics of the reference size Z
Impeller characteristics Value
Inlet im pe
l ler raduis r , m)
0.025
H u
p
im p
eller raduis ri, (m)
0.008
Exit impeller raduis
r2 m)
0.0381
Im el ler width
m ) 0.005
Im eller inlet an gle deg)
67,45
Im
p
eller exit angle (deg)
25
Impeller blades
number
7+ 7
a t
o
0.05... 0.1015..... 02...025 03... 035 04
A6W.1 mess Aow rep tkgfs)
Fig. 6: Input power vs. actual mass flow rate
for different rpm and a given size, Z=1.
00005 0 04602025
Acted mesa now W e tkp0 s )
i39R rt ka^
o _ _ _ _
03504
Fig. 7: Input torque vs. actual mass flow rate for
different
rpm and a given
size, Z=1.
+flrn k,afi
0 050t 0
t5 02 .._..0.25
Ac tual m.s1 flow rate l 51)
0 .3 0 . 3 5 04
Fig. 8: Stagnation temperature ratio vs. actual mass
flow rate
for different
rpm and a given
size, Z=1.
6
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1I .. 60k rpm
12
... _., .... _.,._.
00060AOti 02026. 0
6OJ6Oa
M1* maea now rue ftW
Fig. 9: Stagnation
pressure ratio
vs. actual mass flow rate
for different rpm and a given size, Z=1.
U -000.M
7 ..............., .... _...
2762
:,- 32
5w
2 757
6 6 0 x , . ^ .
5
a l e _ 2 262
4 6 Q,
2 2
62
1.7
z M o .
.
%W tb
2
.7 15z
I
Fig. 10: Input power vs. rpm for different
impeller sizes
and exit tangential velocities.
120-
100.
60 .
252
GO 400 ..-1 2165 ..
2Z
a
1762
20 ti 152
Zk m wp.[.
1la.
t26Z
Z
TSZ
00O1Y6. 2
I n
Fig. 11: Input torque
vs. rpm for different
impeller sizes and
impeller exit tangential velocities.
25
10
Fig. 13: Stagnation pressure ratio vs. rpm for different impeller
sizes and impeller exit tangential velocities.
0
0611622S
151510
Fig. 14: Actual
mass
flow rate vs. rpm for different impeller
sizes and impeller exit tangential
velocities.
^,na.i.,.u.12r
Fig. 15.a: Pressure ratio versus impeller size for different
rotational speed and input power where 6, = 670.
Fig. 15.b
Pressure ratio versus im peller size for different
Fg 12: Stagnation Temperature ratiovs rpmfor different o
impeller sizes and impeller exit tangential velocities. rotational speed and input power where
,5I = 45.
7
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DRIVER UNIT SELECTION
The type of driver unit used to drive a compressor has to
satisfy many criteria. For instance, the driver has to be flexible
to test different types of compressors with good, control system
on the rotational speed, especially near the surge line. In
general, the driver has to be:
Flexible (
can accumulates
several sizes of compressor),
Reliable,
Excellent control on the rpm and torque,
Safe,
Easy to use,
Environment friendly,
Economical.
Comparison Between The Electric Motor,
The Combustion
Gas Turbine And The Blow
-
Down Facility Wth A
Turbocharger
The choice of an electric motor type depends on the
application. One of the examples of the electric motor selection
criteria was discussed by Clarkson et al. [7]. In case of selection
a motor driver for driving a high-speed centrifugal compressor,
over 30,000 rpm, usually a gearbox is used since majority of
motors in the market cannot reach a very high speed, especially
in the case of high power requirements (>250 hp). Recently,
considerable efforts are made to
overcome this problem for the
case
of the low power, Soong et al. [8] and Yuri and Smith, [9].
Most of these motors
are still under development phase, so
availability and reliability is questionable at the present. Most
of the
experimental
investigations for centrifugal compressors
with high rotational speed and power are accompany with a
gearbox, Kim et al. [101.
As a drive unit for centrifugal compressors,
gas turbines
have many drawbacks compared to electric motors. In general,
the efficiency of the gas turbine is low, except at its design
operation point. Normally, the gas turbine is affected by the
change in the ambient temperature, operation at partial loads,
filtration of inlet air and blade fouling of the compressor,
Saxena [11]. It is also difficult to control the turbine especially
if it is operating at off-design condition. Actually, the control
unit of the turbine engine alone needs speed, temperature, flame
detection and vibration inputs. These inputs are important to
control the turbine engine during startup and shutdown, steady
state operation and for the turbine protection, Boyce [12].
Moreover, gas turbines require a number of auxiliaries, such as,
the electrical starter, the main oil pump and the fuel pump. All
of these auxiliaries require control. These supplementary
devices increase the maintenance difficulty and price, as well as
complexity of control system. The flexibility to test many
different sizes of compressors is also reduced due to
performance characteristics of gas turbines. In addition, special
type of fuel and filtration need to be used to decrease air
pollution. Gas turbines are also considered to be unsafe
machine. Sometimes the available turbine needs some
development before it can be used to drive the centrifugal
compressor for the purpose of testing; see Turner et al. [13] as
an example. In their case, any considerable change in
compressor size and characteristics may require some
modifications, such as, a special gearbox. This means this type
of drive is not suitable for testing wide range of compressors
sizes and configurations.
The third possible driver is the cold air turbine, such as in
turbochargers. Blow-down facility is usually required to
provide compressed air to the turbocharger to rotate the radial
turbine that is coupled directly with the centrifugal compressor
through a common shaft. This type of experiment is not
expensive especially if the blow-down facility is available.
However, it needs some auxiliaries for the purpose of control,
which leads to larger size and more complexity in construction
and maintenance compared to the electric motor. The facility is
considered to be safe, has no negative effect on the
environment but its major drawback is the limited flexibility for
the purpose of testing different sizes of compressors.
The main objective of this study is to develop a test
facility that can be used to test different compressor sizes with a
good controlling system up to a speed limit of 100,000 rpm.
Table 2 compares the characteristics of the three driver units
discussed. From this table the selection of the electrical motor
as a driver unit is the best choice. The main reasons of that are
the simplicity of control and flexibility to test different
compressor sizes. In addition, it is easier to maintain and the
overall system is smaller compared to the other two drive
systems.
Comparison
Between
Two Electrical Motors,
With And
Without Vacuum System
There are two methods commonly used to satisfy dynamic
similarity when testing centrifugal compressors driven by
electric motors. First method includes a vacuum environment
system and the second one is without vacuum. By using the
vacuum system almost all practical conditions can be tested and
this is done mainly by simulating the pressure to match the
Reynolds and Mach numbers while maintaining low rpm.
However, this type of driving system is relatively complex. It
requires an advanced sealing system; a closed loop that needs a
heat exchanger to cool the output air from the compressor; and
flow straightener and equalizer to improve the flow quality at
the compressor inlet, Shirley [14]. Also, the test section of the
vacuumed type is more difficult to move, maintain, control
(inlet conditions) and has larger size compared to non-vacuum
one. However, it has lower power requirement for the motor
due to low rpm and vacuum. On the other hand, driving the
impeller without the vacuum system is relatively simple
compared to the vacuum assisted system. It does not need a
closed loop or advanced sealing system but requires higher
power and rpm drive unit, which might require a gearbox in
some cases Table 2 shows the characteristics of the two type of
electrical system.
To sum up, the non-vacuumed type is the most suitable to
meet the objectives of the present design. However, future
developments can be made by adding a vacuum loop to
broaden the test condition, Re and Mach numbers. The
suggested drive unit will be composed of electric motor,
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gearbox and variable speed torque converter to meet variation
of impeller size, see Fig. 16.
Table 2: Characteristics of the electric motor gas turbine and
bow down facility with a turbocharger as centrifugal
compressor driver units.
Drive
Motor no Motor
with Blow-down
vacuum
a v acu u m Gas Turb ine
facility with
Characte r is t ics
Sys.)
system
turbocharger
Cost
Expe nsive
Ex pen sive V ex pe nsive Medium
Size
Medium Medium
Medium La r ge
Specification
Isolated -La rg er E xtra
Blow-down
base - Isolated
vent i l a t ion facility
requirement
Al loca t ion
Diff icul t difficult Possible
Possible
flexibili
Energy High
Relatively
Fuel
Compressed air
re q
uirement
low
Technology S p e c i a l
Advanced
V . h i g h
V . h i g h
gearbox
scal ing S y
s
Excellent
Contro l
Difficult
at
Diff icu l t a t
rpm, power
Excellent
Difficult
flow
surge
surge
conditions)
Ma in te n a n c e
Easy
Difficult Difficult
Medium
Environmenta l
Excellent
Excellent
Poor Excellent
issue
Bi-directional
OK
OK
Special
No
g e a rbox
S a f e
t y
H i
gh
High Low High
Flexibility of
V. good
Excel lent Low
Low
compressors
sizes
C
I- Centrifugal compressor, 2- Gearbox
3- Torque converter, 4- Electric motor
Fig. 16: General facility layout of the centrifugal compressor,
CONCLUSION
A performance analysis for centrifugal Compressors of
high-pressure ratio was developed and incorporated into a
numerical code. The analysis was validated with experimental
results. A special output configuration was made for
compressor perfomance in which total pressure ratio was
plotted against both power requirements and operating speeds
for different impeller sizes. This proved to be vital tool on the
selection process of the drive unit for testing varies impeller
sizes. Moreover, the results of the analysis will guide the
selection of the instrumentation
range
. Further improvement of
the code is needed in terms of efficiency prediction.
Alternatives of drive units were studied carefully. As a result,
eclectic motor in combination with a variable speed torque
converter and a gearbox was selected to meet present
requirements. In addition a vacuum loop can be integrated with
the facility to broaden test conditions.
ACKNOWLEDGMENTS
The authors would like to acknowledge KFUPM for the
support in the preparation
of this
research.
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