Download - Cavitation in hydraulic machinery
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Cavitation in hydraulic machinery
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Cavitation in hydraulic machinery
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• 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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Cavitation over a ving profile
Ref. Morten Kjeldsen
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Saturated water vapor pressure versus temperature
Stages of cavitation
Types of cavitation in hydraulic machines
Ref. Hydraulic Machines, Turbines and Pumps G.I. Krivchenko
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NPSH Net Positive Suction Head [m]hv vapor pressure head [m]HA atmospheric pressure head [m]z2 Height above ref. line at location 2 [m]z4 Height above ref. line at location 4 [m]c2 mean velocity at location 2 [m/s]s loss coefficient [ - ]
NPSH Net Pressure Suction Head
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4 2 12A v s
cNPSH H h z z
g
z4
4
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z4
4
2 223 32
2 2 3 3 3
2 22 23 32 2
2 2 4 4 3 4 4
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2 4 4 2
2 2 2
2 2 2 2
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S
S
c cch z h z
g g g
c cc ch z h z h z
g g g g
ch h z z
g
Losses
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z4
4
g
czzhh s
2
122
2442
hhh v 2
Let us introduce the vapor pressure, hv :
g
czzhhh sv
2
122
244
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NPSHNet Pressure Suction Head
z
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4
g
czzhHNPSH
g
czzhhh
g
czzhhh
svA
sv
sv
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244
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244
Atmospheric pressure: HA = h4
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Suction Head
g
czzhHNPSH svA
2
122
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hs
z4
4
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Submergence of a turbine
NPSH Net Positive Suction Head [m]hv vapor pressure head [m]HA atmospheric pressure head [m]HS Submergence [m]c2 mean velocity at location 2 [m/s]s loss coefficient [ - ]
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2A v S s
cNPSH H h H
g
HS
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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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0
0.05
0.1
0.15
0.2
0.25
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Thoma Cavitation CoefficientHs=10 - Sigma x He
Sig
ma
Speed no Q
Thoma’s Cavitation Coefficient
Speed number
Tho
ma’
s C
avita
tion
Coe
ffic
ient
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Critical Cavitation CoefficientE
ffic
ienc
y,
[ -
]
Thoma’s Cavitation Coefficient, Critical
= 3 %