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'