Ship Hydrodynamics2

Propeller Cavitation

Dr. Adel Banawan

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Recall EGL and HGL for a propeller

EGL

EGL
V12
HGL 2g
HGL

p4 p1
 

z4  0
z1  0
V4 V2 V1

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Let us look at the pressure

just beind the propeller EGL
V22 V12
When propeller is in action, 2g
2g
water is accelerated HGL
V2 increases and P2 decreases
p2 p1
 

V4
V1
V2 z2  0 z1  0

4 3 2 1

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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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EGL
V12
V22
2g
2g
HGL

p2 p1
 

V4
V1
V2 z2  0 z1  0

4 3 2 1

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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

In absoulte scale: P/ (m)

P > Pvapour water is liquid +ve(gage)
When P= Pvapour vapor forms PA=98kN/m2 = 10 m H20
i.e. bubble forms Zero Gage 10.0
i.e. water boils -ve(gage) 9.0
i.e. flow cavities form 8.0

+ve PV=1.7kN/m2 = 0.174 m H20 0.17

Zero Absolute 0.0

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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 causing

Vibration
Noise
Pitting
Material damage
Loss 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

Cavitating Propeller

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Effect on propeller
efficiency
h0
Non Cavitating Propeller

Cavitating Propeller

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Propeller Cavitation Charts

At any blade section position r,
margin against cavitation is:
PA
P( r )  PA   (h  r )

PA   ( h  r )  Pv
define s as cavitation number VA
M arg in against cavitation
 (r ) 
Dynamic pressure r
h
R RPM
P   (h  r )  Pv
 (r )  A
0.5V R2
Thrust
At 0.7R blade section r
PA   (h  r )  Pv
 (0.7 R ) 
0.5V R2
0. 7 R

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Burrill cavitation diagram

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Required Blade Area

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

EAR 
(1.3  0.3Z )T k
( p A  h  pv )D 2

where
T thrust
Z number of propeller blades
PA atmosheric pressure
PV vapour pressure
h propeller centerline immersion
k constant varying from 0 (for transom stern naval vessels) to 0.2
(for high powered single screw vessels)

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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

7.5 m

RT=888.64 kN

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Estimated QPC 0.75

Wake fraction, w 0.20
Thrust deduction fraction, t 0.20
Relative rotative efficiency, hR 1.00
RPM 102
The results obtained are:

Expanded Blade Area Ratio 0.4

Value of d 95
V 19.56 feet
D  A feet
n (5.96 m)
P/D 1.26
Open water Efficiency ho 0.77

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Solution
V A  V (1  w)  10.8(1  0.2)  8.64m / s

The required thrust is

R RV PE 9592
T     1044.9kN
(1  t ) (1  t )V (1  t )V (1  0.15)10.8

The Keller area criterion for a single screw vessel gives:

EAR 
(1.3  0.3Z )T  0.2
( p A  h  pv )D 2

EAR 
(1.3  0.3 * 4)1044.9 *1000  0.2  0.633
(98 *1000  1025* 9.81* 7.5  1.72 *1000)5.962
Hence, the used blade area is not enough to avoid cavitation

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If Burril cavtitation limit is given by:

(TAb )
 0.2533  0.03892ln( 0.7 R )
2

0.5V0.7 R
2

Patm   (h  0.7 R )  Pv
 0 .7 R 
0.5V02.7 R
V02.7 R  V A  (0.7R )
2 2

V02.7 R  V A  (0.7R )
2 2

2 *  * 102
2
 
V02.7 R  8.642   0.7 * * 2.96   564.47m 2 / s 2
 60 

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Patm   (h  0.7 R )  Pv
 0.7 R 
0.5V02.7 R
98 * 1000  1025* 9.81(7.5  0.7 * 2.98)  1.72 * 1000
 0.7 R 
0.5 * 1025* 564.47
 0.7 R  0.1446
0.32 ِCavitati
(TAb )
on
 0.2533  0.03892ln( 0.7 R )
2 ِ
0.5V0.7 R
2 T AP
Limit
1
(TAb ) VR2
 0.2533  0.03892ln(0.1446)  0.0317 2
2

0.5V02.7 R 0.032 ِNo Cavitation

lim it

(TAb ) 1045* 1000 / (0.4 * 2.982 )

  0.32
0.5V02.7 R actual
0.5 * 1025* 564.47

(TAb )

(T Ab )
0.5V02.7 R 0.5V02.7 R PA   (h  0.7 R )  Pv
actual lim it
0.144  0.7 R 
Hence Cavitation will take place 1
VR2
2 0.7 R

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Bubble cavitation
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Partial sheet cavitation

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Cloud cavitation on hydrofoil

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Tip vortex cavitation

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Tip and hub vortex cavitation

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