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 HQ

nn

qs n55,51n

Affinity laws

2

1

2

1

nn

QQ

2

2

1

2

2

1

2

1

nn

uu

HH

3

2

1

2

1

nn

PP

Assumptions:Geometrical similarityVelocity triangles are the same

Exercise

sm1,1110001100Q

nnQ 3

11

22

m12110010001100H

nnH

2

1

2

1

22

kW16412310001100P

nnP

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

sm9,015,045,0Q

DDQ

nn

DD

cBDcBD

QQ

31

1

22

2

1

2

1

2m22

1m11

2

1

m811005,045,0H

DDH

2

1

2

1

22

kW901235,045,0P

DDP

3

1

3

1

22

Velocity triangles

Slip angle

Reduced cu2

Slip angle

Slip

Best efficiency point

Friction loss

Impulse loss

Power

MPWhere:

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

t

1u12u2

111222

HgQcucuQ

coscrcoscrQP

gcucuH 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

g2ww

g2cc

g2uuH

21

22

21

22

21

22

t

Euler’s pump equation

gcucuH 1u12u2

t

g2ww

g2cc

g2uuH

21

22

21

22

21

22

t

g2uu 2

122 Pressure head due to change of

peripheral velocity

g2cc 2

122

g2ww 2

122

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

cg

pzg2

cg

pH

g2ww

g2cc

g2uuH

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:

g2u

g2w

gp

g2u

g2w

gp 2

1211

22

222

Rothalpy

The rothalpy can be written as:

ttancons

g2r

g2w

gpI

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

5,01000H

Qnn 4343q

1153n55,51n qs

Specific speed:

This is a radial pump

0,1Ku

sm3,44Hg2KuHg2

uK u22

u

srad7,10460

n2

m85,02uD2

Du 22

22

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

11,0K 2m

sm87,4Hg2KcHg2

cK 2m2m2m

2m

m038,0cD

Qd

dDQ

AQc

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

dszDQ

AQc

2mu22

2u22m

We choose: s2 = 0,005 mz = 5

m013,05,22sin

005,0sin

ss o2

2u

145,0K 1m

sm4,6Hg2KcHg2

cK 1m1m1m

1m

u1

w1

c1= cm1

405,0DD

2

1

m34,0D405,0D405,0DD

212

1

m09,0cD

QddD

QAQc

1mm11

1m111m

We choose:

Dhub

m17,0D5,0D 1hub

m27,02DDD

2hub

21

m1

Without thickness

Thickness of the blade at the inlet

m015,08,19sin

005,0sin

ss o1

11u

u1

w1

Cm1=6,4 m/s

sm8,17234,07,104

2Du 1

1

1

o

1

1m1 8,19

8,174,6tana

uctana

m10,0cszD

Qd1m1um1

1

m15381,996,05,323,44

gcucuH

h

1u12u2

u2=44,3 m/s

c2w2

cm2=4,87m/s

2=22,5o

cu2

sm5,32tancuc

cuctan

2

2m22u

2u2

2m2

u2=44,3 m/s

c2w2

cm2=4,87m/s

cu2

sm3,213,44

81,996,0100u

gHcg

cuH2

h2u

h

2u2

o

2u2

2m2 9,11

3,213,4487,4tana

cuctana'

ooo2slipslip 6,109,115,22'