6.6 Interaction between a hull & a propeller

So far in the study of the resistance of a ship & its propeller the

two have been considered separately. However, in reality the

propeller has to work behind the ship & in consequence one has an

interaction upon the other. How does the hull affects the water

in which the propeller is working? (later we will also study the

effects of a propeller on the hull)

A ship affects the water near its stern in 3 aspects:

1) pressure increase at the stern;

2) boundary layer (a propeller is in the boundary layer or way

of the ship);

3) Water particle velocity induced by ship generated waves.

Wake fraction: water particle velocity near the propeller is

not the same as the ship velocity.

( : ship velocity & flow velocity at its stern)

: , thus 1

: , thus (1 )

The relationship between Froude & Tay

s A s A

s A sF A

A F

s AT A s T

s

w V V V V

V V Vw V

V w

V Vw V V w

V

Froude

Tay

wake factor

wake factorlor

lor wake factor:

or 1 1

When wake (most cases, a single screw)

When , wake (only for high speed ship)

F TT F

F T

A s

A s

w ww w

w w

V V

V V

positive

nagative

wT & wF, (wake factors) are determined by the measurements

made in a model test (near a hull’s stern) or in a real ship test.

Nominal wake: wake measured near the stern of a hull in the

absence of the propeller (using pilot tubes).

Effective wake: wake measured in the presence of propeller.

The measurements show that a propeller at a rotating speed n

behind a hull advancing at velocity, Vs, delivers thrust T. By

comparing it to the results of the same propeller in the open-water

tests, we will find that at the same revolutions n, the propeller will

develop the thrust T but at a different speed (usually lower),

known as effective speed of advance, VA. The difference between

Vs & VA is considered as the effective wake.

•Relation between nominal wake & effective wake.

Since propellers induce an inflow velocity which reduces the

positive wake to some extent, the effective wake factor usually is

0.03~0.04 lower than the corresponding nominal wake.

Wake factor of a

single screw ship

Averaged Wake Fraction

Wake factor of a

twin screw ship

• Relative Rotation EfficiencyThe efficiency of a propeller in open water is called open-water

efficiency,

where VA is the advance speed, T the thrust, n the rotation speed

(# of rotations per unit time), & Q0 is the torque measured in the

open water test when the propeller is delivering thrust T at the

rotation speed n.

In the case the same propeller behind a hull, at the same advance

speed it delivers the same thrust T at the same revolution n but

needs torque Q. In general, Q is difference from Q0. Then, the

efficiency of the propeller behind the hull,

0

02

AT V

nQ

2

AB

T V

nQ

• The ratio of behind-hull efficiency to open-water efficiency is

called the relative rotative efficiency.

The difference between Q0 and Q is due to

1. wake is not uniform over the disc area while in open water, the

advance speed is uniform.

2. model and prototype propellers have different turbulent flow.

(Remember then Reynolds number are not the same)

1.0~1.1 for single-screw ship

0.95~1.0 for twin-screw ship

00

0

, thus BR B R

Q

Q

R

• The influence of the propeller on the hull

Thrust-deduction factor (fraction)

When a hull is towed, there is an area of high pressure over the

stern, which has a resultant forward component to reduce the total

resistance. With a self-propelled hull (in the presence of the

propeller), the pressure at the stern is decreased due to the

propeller action. Therefore, there is a resistance augment due to

the presence of the propeller. If T is the trust of the propeller & RT

is the towing resistance of a hull at a given speed Vs , then in order

that the propeller propel the hull at this speed, T must be greater

than RT because of the resistant augment. The normalized

difference between T and RT, is called the thrust-deduction

Fraction, and denoted by t.

1 , thus 1

- is the "naked" hull resistance

- the thrust after subtracting the resistance of the rudder & other

stern appendages.

measured in experiments depends, not

T TT

T

T R Rt R t T

T T

R

T

t

only on the shape of the hull

& the characteristics of the propeller, but also the type of the rudder.

• Hull Efficiency

Hull Efficiency is defined as the ratio of the effective power for

a hull with appendages to the thrust power developed by

propellers.

1

1

where

- effective horsepower EHP

- "naked" hull resistance

- speed of the ship

- the work done by the propeller in delivering a thrust

- the speed of

T sEH

T A

E T s

T

s

T

A

R VP t

P T V w

P R V

R

V

P T

V

the propeller w.r.t. the ambient water.

• Propulsive Efficiency

“Quasi-propulsion” coefficient is defined as the ratio of the

effective horsepower to the delivery horsepower.

0

0

0

2 2

- delivered horsepower 2

- efficiency of a propeller in open water,

- relative rotative efficiency,

- hull efficienc

T s T sE AD B H R H

D A

E T s

D

D R H

R

H

R V R VP TV

P nQ nQ TV

P R V

P nQ

y.

The division of the quasi-propulsive coefficient into three parts is

helpful in 1) understanding the propulsive problem & 2) in

making estimates of propulsive efficiency for design purposes.

( )

In the design, usually we let

(1 )( ) ,

where is a correlation allowance, (or load factor). It depends

principally on the hull roughness of the newly

TD

H R o H R o

D D H R o

D

R VEHPP DHP

EHPP DHP

painted ship,

foaling, weather condition & the length and type of a ship.

Finally, the ,

where is the shaft efficiency.

s

s

DHPSHP

main engine horsepower

6.7 Cavitation

A typical pressure distribution in a blade element is shown below,

Pressure (+)

Suction (-)Back VR

face

As the pressure on the back of a propeller falls lower and lower

with the increase in a propeller’s n, the absolute pressure at the

back of the propeller will eventually become low enough for the

water to vaporize and local cavities form. This phenomenon is

known as cavitation. ( , vapor pressure of water)vP

• Cavitation on a propeller will

1. lower the thrust of the propeller, & thus decrease its

efficiency,

2. cause vibration of hull & the propeller and generate

uncomfortable noise, &

3. cause erosion of the propeller blade.

• Criteria for prevention of cavitation

Mean thrust loading coefficient 21

2

c

R p

T

V A

22 2

- density of water, - Thrust,

- project blade area, 1.067 0.229 ,

- the relative velocity at 0.7 of a propeller

2 0.7

p

p

D

R

R A

T

A PA

A D

V R

V V R n

• Cavitation number

0

212

0 - presuure at some point of a blade

- vapor presuure of water

v

R

v

p p

V

p

p

The cavitation is most likely to occur at the tips of blades where

the relative velocity is the largest and the hydro-static pressure is

the lowest when blades rotate to the highest position. It can also

occur near the roots where blades join the boss of a propeller

because the attack angle is the largest.

Cavitation diagram (SNAME)

6.8 Propeller Design

Methods of Propeller Design

a. Design based upon charts (diagrams). These charts are obtained

form the results of open-water test on a series of model

propellers. (also upon software, such as NavCad).

b. Design using circulation theory and CFD (not studied here).

Methodical Series

A model propeller series is a set of propellers in which the principal

characteristics such as pitch ratio etc are changed in a systematic

manner. There are many series tested, and their results are

summarized and presented in the form of charts which can be used

in design. The most extensive model propeller series is Netherland

Ship Model Basin (NSMB) at Wageningen. This series test was run

from 1937 to 1964.

NSMB Series includeSeries A: narrow blade tips, airfoil sections, high efficiency

only for light loaded propellers (not widely used)

Series B: wider tips, airfoil section from blade root to 0.7

radius, and circular back from 0.8 radius to tip.

Scope of series B is shown

Given below is the dimensions (outline, thickness) of

B.4 blade

The B series results are presented in the form of charts of

diagrams, known as diagram .

At upper right corner, the diagram gives 4.40 B. (indicating B

type, 4 blades & AE /A0 = 0.40, t0/D = 0.0045 (blade-thickness

fraction), d/D = 0.167 (diameter ratio of the boss to the

propeller), & the Pitch, P.

At low left corner, it gives the definitions of

PB

and PB

0.5

2.5, and (notice that )

- revolutions per min, - propeller diameter (ft)

- delivered at propeller

(1- ) - speed of advance (knots)

and are

D Ap

A A

D

A s

p

n P VnDB J

V V nD

n D

P

V V w

B

horsepower

dime !nsional

diagram

Horizontal coordinate:

Vertical coordinate: ratio of the pitch to diameter P/D

Two sets of curves , and one optimal ( ) line

PB

0 &

PB

0

• Propeller Design Based on Charts-The information required for making a propeller design from

charts are:

1. Principal dimensions, & main coefficients of a ship used to

estimate wake, thrust factors, & relative rotative efficiency.

2. Speed of a ship

3. EHP (from model tests or estimated from other available data)

4. engine power (SHP) & rpm.

5. restrictions on the maximum diameter of propeller.

0.5

0.5

D

-Design Procedures

( )1. Calculating , (assuming , for computing )

From the chart to find , pitch ratio that give the best efficiency.

(From , & pitch ratio )

D Ep D D

A

n P PB P

V

D P

2. This will give a best propeller in open water. Since the

propeller works behind the hull, it is usually to reduce by

5%~8%, for single-screw ship, 4% for twin screw ship.

3.With the same value p

D

B

0

a smaller value ( ), use

the chart again to find efficiency and pitch ratio ( / ).

4. In the same way, we may use different chart & different

to see the effects (no. of blades, blade area r

A

nD

V

P D

n

0

0

0

atio) on .

5. After determining , we calculate (propulsive coeff).

1 where . Then we re-calculate ( ) .

1

D

ED R H H D

D

PtP

w

6. If the newly computed, , is very close to the previous

assumed one, then we continue to examining the cavitation

of the propeller. If not, we use the newly computed to

repeat the above 1-5 ste

D

D

P

P

ps again.

7. Examining the condition of cavitation for the propellers.

If the condition is not satisfied, choose a propeller with larger

, or make other adjustments (such as reducing , & using

mul

EA n

tiple screws).

Examples

Example a, Using the B4.40 chart to design a propeller suitable for

the following conditions. Also determine SHP. (knowing EHP, Vs to

determine , P, D)

Vs = 16 knots Taylor wake factor w = 0.3075

EHP = 5000 Hp thrust deduction t = 0.186

Allowance for appendage 6% Shaft loss = 3%

Allowance for weather 15% reduction in δ = 7%

n = 120 r/min relative rotative effi. 1.0R

0

0.5 0.5

2.52.5

: EHP(1 ) EHP(1 0.06 0.15) 6050 hp

Assuming 0.65, (DHP) EHP / 9308 hp

Advance velocity 1 11.08 knots

120 9308Taylor propeller coeff., 28.33

11.08

D D D

A s

D

p

A

P

V w V

n PB

V

Solution

0

Checking B4.40 chart, 213, 213(1 0.07) 198,

1 0.8140.597, 0.597 0.597 0.705.

1 0.6925

The previous is assumed to low. New iteration starts.

Let 0.71, EHP / 8521 hp,

opt

o D H R

D

D D D p

t

w

P B

0

27.1,

From B4.40 chart, 209, 209(1 0.07) 194.4,

0.8140.602, 0.602 0.708 0.71

0.6925

This time the assumed is very close to the comupted one.

194.4 11.08, 17.9 ft

120

opt

o D H R

D

A

A

VnDD

V n

, 0.85,

DHP 85210.85 17.9 15.2 ft, SHP 8784 hp

1 0.03s

P

D

P

Example b. Give D (due to the restriction of draft) & using

B.4.40 chart to find the optimum n, P/D, and

A cargo Ship

L = 86 m Vs = 9 knots

B = 13 m EHP = 515 hp

T = 5.66 m w = 0.184

= 4500 m3 t = 0.125

= 1.0 = 0.97

D = 4m = 13.14 ft χ = 0.218 (load factor or allowance)

R s

D

1. 1 9 1 0.184 7.34 knots,

2. Assuming 0.69,

1 EHP3. (DHP) 909 hp,

A s

D

D

D

V V w

P

Solution :

4. Try a range of rotation velocities, n

0.5

2.5

( )Dp

A

N PB

V

A

ND

V

1

1D o R

t

w

No. Name Unit Value

1 n rpm 90 95 100 105 110

2 18.6 19.6 20.7 21.7 22.7

3 161 170 179 188 197

4 % 64.5 64.6 64.7 64.3 63.8

P/D 0.95 0.875 0.79 0.75 0.70

5 P = P/D*D m 3.8 3.5 3.16 3 2.8

6 0.691 0.692 0.693 0.69 0.688

0 From the chart

Based on the results shown in the table, it is found that

the highest value is 0.693 when 100,

and it is also closest to the assumed .

Thus, 100 is the optimal rotation speed.

Pitch. = 3.16

D

D

n

n

P

m = 10.37',

(DHP) 909SHP 937 hp.

0.97

D

s

P

A different problem: given the rotation velocity, n, to determine

the optimal diameter of the propeller.