Centrifugal pumps. Impellers Multistage impellers

Centrifugal pumps

Impellers

Multistage impellers

Cross section of high speed water injection pump

Source: www.framo.no

Water injection unit 4 MW

Source: www.framo.no

Specific speed that is used to classify pumps

nq is the specific speed for a unit machine that

is geometric similar to a machine with the head Hq = 1 m and flow rate Q = 1 m3/s

43q H

Qnn

qs n55,51n

Affinity laws

2

1

2

1

n

n

Q

Q

2

2

1

2

2

1

2

1

n

n

u

u

H

H

3

2

1

2

1

n

n

P

P

Assumptions:Geometrical similarityVelocity triangles are the same

Exercise

sm1,111000

1100Q

n

nQ 3

11

22

m1211001000

1100H

n

nH

2

1

2

1

22

kW1641231000

1100P

n

nP

3

1

3

1

22

• Find the flow rate, head and power for a centrifugal pump that has increased its speed

• Given data:h = 80 % P1 = 123 kW

n1 = 1000 rpmH1 = 100 m

n2 = 1100 rpm Q1 = 1 m3/s

Exercise• Find the flow rate, head and power

for a centrifugal pump impeller that has reduced its diameter

• Given data:h = 80 % P1 = 123 kW

D1 = 0,5 m H1 = 100 m

D2 = 0,45 m Q1 = 1 m3/s

sm9,015,0

45,0Q

D

DQ

n

n

D

D

cBD

cBD

Q

Q

31

1

22

2

1

2

1

2m22

1m11

2

1

m811005,0

45,0H

D

DH

2

1

2

1

22

kW901235,0

45,0P

D

DP

3

1

3

1

22

Velocity triangles

Slip angle

Reduced cu2

Slip angle

Slip

Best efficiency point

Friction loss

Impulse loss

Power

MP

Where:M = torque [Nm] = angular velocity [rad/s]

t

1u12u2

111222

HgQ

cucuQ

coscrcoscrQP

g

cucuH 1u12u2

t

In order to get a better understanding of the different velocities that represent the head we rewrite the Euler’s pump equation

1u121

21111

21

21

21 cu2uccoscu2ucw

2u222

22222

22

22

22 cu2uccoscu2ucw

g2

ww

g2

cc

g2

uuH

21

22

21

22

21

22

t

Euler’s pump equation

g

cucuH 1u12u2

t

g2

ww

g2

cc

g2

uuH

21

22

21

22

21

22

t

g2

uu 21

22 Pressure head due to change of

peripheral velocity

g2

cc 21

22

g2

ww 21

22

Pressure head due to change of absolute velocity

Pressure head due to change of relative velocity

RothalpyUsing the Bernoulli’s equation upstream and downstream a pump one can express the theoretical head:

1

2

2

2

t zg2

c

g

pz

g2

c

g

pH

g2

ww

g2

cc

g2

uuH

21

22

21

22

21

22

t

The theoretical head can also be expressed as:

Setting these two expression for the theoretical head together we can rewrite the equation:

g2

u

g2

w

g

p

g2

u

g2

w

g

p 21

211

22

222

Rothalpy

The rothalpy can be written as:

ttancons

g2

r

g2

w

g

pI

22

This equation is called the Bernoulli’s equation for incompressible flow in a rotating coordinate system, or the rothalpy equation.

StepanoffWe will show how a centrifugal pump is designed using Stepanoff’s empirical coefficients.

Example: H = 100 mQ = 0,5 m3/sn = 1000 rpm2 = 22,5 o

4,22100

5,01000

H

Qnn

4343q

1153n55,51n qs

Specific speed:

This is a radial pump

0,1Ku

sm3,44Hg2KuHg2

uK u2

2u

srad7,10460

n2

m85,02u

D2

Du 2

22

2

We choose: m17,0D5,0D 1hub

11,0K 2m

sm87,4Hg2KcHg2

cK 2m2m

2m2m

m038,0cD

Qd

dD

Q

A

Qc

2m22

222m

u2

c2w2

cu2

cm2

Thickness of the blade

Until now, we have not considered the thickness of the blade. The meridonial velocity will change because of this thickness.

m039,0cszD

Qd

dszD

Q

A

Qc

2mu22

2u22m

We choose: s2 = 0,005 mz = 5

m013,05,22sin

005,0

sin

ss

o2

2u

145,0K 1m

sm4,6Hg2KcHg2

cK 1m1m

1m1m

u1

w1

c1= cm1

405,0D

D

2

1

m34,0D405,0D405,0D

D21

2

1

m09,0cD

Qd

dD

Q

A

Qc

1mm11

1m111m

We choose:

Dhub

m17,0D5,0D 1hub

m27,02

DDD

2hub

21

m1

Without thickness

Thickness of the blade at the inlet

m015,08,19sin

005,0

sin

ss

o1

11u

u1

w1

Cm1=6,4 m/s

sm8,172

34,07,104

2

Du 1

1

1

o

1

1m1 8,19

8,17

4,6tana

u

ctana

m10,0cszD

Qd

1m1um11

m15381,996,0

5,323,44

g

cucuH

h

1u12u2

u2=44,3 m/s

c2w2

cm2=4,87m/s

2=22,5o

cu2

sm5,32tan

cuc

cu

ctan

2

2m22u

2u2

2m2

u2=44,3 m/s

c2w2

cm2=4,87m/s

cu2

sm3,213,44

81,996,0100

u

gHc

g

cuH

2

h2u

h

2u2

o

2u2

2m2 9,11

3,213,44

87,4tana

cu

ctana'

ooo2slipslip 6,109,115,22'