Cavitation in hydraulic machinery

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1

Cavitation in hydraulic machinery

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2

Cavitation in hydraulic machinery

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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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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

22

4 2 12A v s

cNPSH H h z z

g

z4

4

9 9

9

z4

4

2 223 32

2 2 3 3 3

2 22 23 32 2

2 2 4 4 3 4 4

22

2 4 4 2

2 2 2

2 2 2 2

12

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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10

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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11

NPSHNet Pressure Suction Head

z

4

4

g

czzhHNPSH

g

czzhhh

g

czzhhh

svA

sv

sv

21

21

21

22

24

22

244

22

244

Atmospheric pressure: HA = h4

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12

Suction Head

g

czzhHNPSH svA

2

122

24

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 [ - ]

221

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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17

Critical Cavitation CoefficientE

ffic

ienc

y,

[ -

]

Thoma’s Cavitation Coefficient, Critical

= 3 %