Ship Hydrodynamics2

Propeller Cavitation

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Recall EGL and HGL for a propeller

HGL

124 3

HGL

EGL

EGL

g

V

2

2

1

4p

1p

01 z04 z

1V2V4V

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Let us look at the pressure just beind the propellerWhen propeller is in action, water is acceleratedV2 increases and P2 decreases

2V

4V

02 z

124 3

HGL

EGL

g

V

2

2

1

1p

01 z

1V

g

V

2

2

2

2p

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Pending on V2 we have three possibilities for P2

P2/γ above the system centerline (above atmosphere +ve gage pressure)P2/ γ drops to system centerline (atmosphere zero gage pressure)P2/ γ falls below the system centerline (sub atmosphere -ve gage pressure)

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2V

4V

02 z

124 3

HGL

EGL

g

V

2

2

1

1p

01 z

1V

g

V

2

2

2

2p

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What is the limit for water to stay in a liquid state?The limit is that when the pressure is equal to the pressure at which vapor starts to form Or when the pressure is equal to the water vapor pressure

PV=1.7kN/m2 = 0.174 m H20

PA=98kN/m2 = 10 m H20

+ve(gage)

Zero Gage-ve(gage)

+ve

Zero Absolute

P/ (m)

0.17

0.0

8.09.010.0

In absoulte scale:P > Pvapour water is liquid

When P= Pvapour vapor formsi.e. bubble formsi.e. water boils i.e. flow cavities form

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Types of cavitation

Sheet Bubble Cloud Tip vortex Hub vortex

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consequences of cavitation occurrence

Bubble forms, then collapse close to the blade boundaries causingVibrationNoisePittingMaterial damageLoss of thrust,Lower propulsion efficiency

Conclusion:Cavitation should be avoided by proper design of propeller and proper operation

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Effect on thrust coefficient

KT

Non Cavitating Propeller

J

Cavitating Propeller

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Effect on propeller efficiency

h0

Non Cavitating Propeller

J

Cavitating Propeller

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Propeller Cavitation ChartsAt any blade section position r,

margin against cavitation is:

define s as cavitation number

)()( rhPrP A

vA PrhP )(

( )pressureDynamic

cavitationagainstinMr

arg

( )( )

25.0 R

vA

V

PrhPr

At 0.7R blade section

( )( )

RR

vA

V

PrhPR

7.0

25.07.0

VA

RPMR

PA

Thrust

h

r

r

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Burrill cavitation diagram

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Required Blade AreaA useful formula for obtaining a first indication as to the required expanded blade area ratio was derived by Keller (1966),

whereT thrustZ number of propeller bladesPA atmosheric pressure PV vapour pressureh propeller centerline immersionk constant varying from 0 (for transom stern naval vessels) to 0.2

(for high powered single screw vessels)

( )( )

kDphp

TZEAR

vA

2

3.03.1

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Example: The propeller in the previous example was designed using B4.40 propeller series chart. It is required to Check whether this propeller will or will not cavitate. Use :1- Keller criterion.2- Burril cavitation chart

Vs=21 knots

RT=888.64 kN

7.5 m

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The results obtained are:

Estimated QPC 0.75

Wake fraction, w 0.20

Thrust deduction fraction, t 0.20

Relative rotative efficiency, hR 1.00

RPM 102

Expanded Blade Area Ratio 0.4

Value of d 95

19.56 feet

(5.96 m)

P/D 1.26

Open water Efficiency ho 0.77

feetn

VD A

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Solution

The required thrust is

The Keller area criterion for a single screw vessel gives:

Hence, the used blade area is not enough to avoid cavitation

2/28/2010

( ) ( ) smwVVA /64.82.018.101

( ) ( ) ( ) ( )kN

Vt

P

Vt

RV

t

RT E 9.1044

8.1015.01

9592

111

( )( )

2.03.03.1

2

Dphp

TZEAR

vA

( )( )

633.02.096.51000*72.15.7*81.9*10251000*98

1000*9.10444*3.03.12

EAR

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If Burril cavtitation limit is given by:

( )( )

( )

( )22

7.0

2

7.0

7.0

2

7.02

7.0

7.0

5.0

7.0

ln03892.02533.05.0

2

RVV

V

PRhP

V

AT

AR

R

vatmR

R

R

b

( )

22

2

22

7.0

22

7.0

/47.56496.2*60

102**2*7.064.8

7.02

smV

RVV

R

AR

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( )

( )

1446.0

47.564*1025*5.0

1000*72.198.2*7.05.781.9*10251000*98

5.0

7.0

7.0

7.0

2

7.0

7.0

R

R

R

vatmR

V

PRhP

( )( )

( )( )

( ) ( )

( ) ( )

placetakewillCavitationHence

V

AT

V

AT

V

AT

V

AT

V

AT

itR

b

actualR

b

actualR

b

itR

b

R

R

b

lim

2

7.0

2

7.0

2

2

7.0

2

lim

2

7.0

2

7.02

7.0

5.05.0

32.047.564*1025*5.0

98.2*4.0/1000*1045

5.0

0317.01446.0ln03892.02533.05.0

ln03892.02533.05.0

0.144

0.32

0.032

( )

R

R

vAR

V

PRhP

7.0

27.0

2

1

7.0

2

2

1R

P

V

AT

Cِavitati

on ِ

Limit

Nِo Cavitation

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