1
Cavitation in hydraulic machinery
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2
Cavitation in hydraulic machinery
2 2
3
• The collapse of the bobble close to a surface will be asymmetric.
• A jet stream will be formed in the center and hits the surface with
large impulse. It has been measured pressure pulses up to 1000 bar
and velocities around 200 m/s in a collapsing bubble.
• The collapse creates local pressure oscillation with a large
amplitude.
• It is not known if it is the jet stream, pressure pulse or both that
causes the damage to the surface.
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4
Cavitation over a ving profile
Ref. Morten Kjeldsen
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5
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6
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7
Types of cavitation in hydraulic machines
Saturated water vapor pressure
versus temperature
Ref. Hydraulic Machines, Turbines and Pumps
G.I. Krivchenko
Stages of cavitation
7 7
8
NPSH
Net Pressure Suction Head
2
2
c
NPSH  H A  hv   z4  z2    s  1 
2 g
4
z4
NPSH
hv
HA
z2
z4
c2
s
Net Positive Suction Head
vapor pressure head
atmospheric pressure head
Height above ref. line at location 2
Height above ref. line at location 4
mean velocity at location 2
loss coefficient
[m]
[m]
[m]
[m]
[m]
[m/s]
[-]
8 8
9
4
z4
c32
c32
c22
 3 
 h3  z3 
h2  z2 
2 g
2 g
2 g

Losses
c32
c32
c22
c22
 h4  z4   S 
 3 
 h4  z4 
h2  z2 
2 g
2 g
2 g
2 g

c22
h2  h4   z4  z2    S  1 
2 g
9 9
10
4
z4
2
2
c
h2  h4  z4  z2    s  1 
2 g
Let us introduce the vapor pressure, hv :
h2  hv  h
2
2
c
hv  h  h4  z4  z2    s  1
2 g
10 10
11
NPSH
Net Pressure Suction Head
c22
hv  h  h4   z 4  z 2    s  1 
2 g

c22
h  h4  hv   z 4  z 2    s  1 
2 g
4
z
4

c22
NPSH  H A  hv   z 4  z 2    s  1 
2 g
Atmospheric pressure: HA = h4
11 11
12
Suction Head
4
z4
2
2
c
NPSH  H A  hv  z4  z2    s  1 
2 g
hs
12 12
13
Submergence of a turbine
2
2
c
NPSH  H A  hv  H S   s  1 
2 g
HS
NPSH
hv
HA
HS
c2
s
Net Positive Suction Head
vapor pressure head
atmospheric pressure head
Submergence
mean velocity at location 2
loss coefficient
[m]
[m]
[m]
[m]
[m/s]
[-]
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14
NPSH available and NPSH required
• NPSH available
– This is the NPSH that is given by the site
where the turbine is installed
• NPSH required
– This is the NPSH that the turbine required for
non-cavitating operation
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Law of Thoma
NPSH

H
Provided that similar hydraulic cavitating flow
remain unchanged relative to the flow canals, the
relations of hydraulic similar flow, are valid also
for flow including cavitation.
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Thoma Cavitation Coefficient
Hs=10 - Sigma x He
Thoma’s Cavitation Coefficient
0.25
Coefficient
Thoma’s CavitationSigma

0.2
0.15
0.1
0.05
0
0
0.2
0.4
0.6
0.8
Speed number 
Speed no
1
1.2
1.4
 Q
16 16
17
Efficiency, h [ - ]
Critical Cavitation Coefficient
h = 3 %
Critical
Thoma’s Cavitation Coefficient,

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