Experimental investigation on propeller exciting forces

3 SE?.

98k

ARCH

s.

SYMPOSIUM ON

"HYDRODYNAMICS OF SHIP AND OFFSHORE PROPULSION SYSTEMS"

HØVIK OUTSIDE OSLO, MARCH 20. - 25., 1977

"EXPERIMENTAL INVESTIGATION ON PROPELLER

EXCITING FORCES"

By M. Yamaguchi Ship Strength Dept.

Research Institute

Ishikawajima-Harima Heavy Industries Co., Ltd. Yokohama, Japan

SPONSOR: DET NORSKE VERITAS

Ref.: PAPER 12/4 - SESSION 3

(7)

Lab.

y. Scheepsou'krch

Technische Hocho1

EXPERIMENTAL INVESTIGATION ON PROPELLER EXCITING FORCES

by M. Yamaguchi Ship Strength Dept. Research Institute

Ishikawajima-Harinia Heavy Industries Co., Ltd.

Ab st rac t

Results of the model tests performed for investigation of

propeller exciting forces at the cavitation tunnel and the towing tank

of the Research Institute of IHI are described. At the cavitation

tunnel pressure fluctuation induced on hull, thrust variation induced on propeller and fluctuating forces induced on rudder were investIgated

in cavitating condition. For the test at the towing tank, a new testing

instrument which was devised by the author was used and bearing force was measured.

Followings are obtained from the eYperiments:

For both amplitude and phase, pressure fluctuations at the surface of hull above propeller are affected by cavitation.

Generally obseing, influence of cavitation on thrust

variation is disregarded.

Fluctuating forces induced on rudder are affected by

cavia t ion.

For measurement of bearing force, the new device is useful.

Empirical expressions are obtained on the base of model test.

1. Introduction

Propeller exciting forces consist of surface force which is transferred from propeller to hull surface through water in the

form of pressure fluctuation and bearing force which is transmitted

to the hull through shaft bearing.

It has already been tried to obtained pressure fluctuation

induced on the surface of after-body by propeller by means of

theoretical calculations, and the theoretical calculation has been developed to such an extent that pressure fluctuation induced on

hull surface can be estimated [for example, l-41. However, it has

also been found that cavitation on propeller blade affects increase

of amplitude of pressure fluctuation [5, -11]. Thus, it has become

further difficult to treat the matter of pressure fluctuation theoretically, though calculation examples have been reported for this problem [8].

Under the circumstance like this, the author carried out the model tests at the cavitation tunnel to investigate pressure fluctuation ori surface of hull, thrust variation and fluctuating forces induced ori rudder.

Experimental studies on bearing force have been developed by the use of special measuring instrument and special measuring method [12, -15].

The author devised on entirely new measuring instrument, and with this device he investigated bearing force of a model of a large size tanker at the towing tank.

In this paper, the author reports the results of the above-mentioned model tests and tries to obtain the empirical expressions for estimations of surface force and bearing force.

2. Experiments at Cavitation Tunnel

An after-body model of container carrier was built in the

cavitation tunnel as shown in Fig. 1. It was so arranged that

wake distribution at the propeller position would be the same as that of a 6 meter long model at the towing tank by mesh placed in

front of the model. Fig. 2 shows wake distribution. Pressure

fluctuation was measured by the use of a semi-conductor type

transducer. The measuring range and natural frequency of which

are respectively ±1 kg/sq.cxn and 10 kHz or more.

Data for freely selected four to eight turns were taken out from the data recorded on a magnetic tape without using filter, and the taken out data were analysed to obtain amplitude and phase at the fundamental blade frequency (number of revolutions x number of blades).

-2-2.1 Pressure fluctuation

Table i shows particulars of the model propeller. Rudder

was not fitted. One of the transducers is buried into the hull

on the center line above the propeller. Fig. 3 shows the

relationship between cavitation number Cn and non-dimensional

pressure amplitude Kp, based on the pressure fluctuation measured

by this transducer.

Pressure fluctuation at the balde frequency is written as follows:

=

Kp.4Pn2D2KQ

cos (O-n)

Cavitation number is defined as follows:

Po-e

jfl2D2

where, p : density of water

n number of propeller revolutions

D : diameter of propeller

KQ: torque coefficient

O : angle shown in Fig. 4

phase angle shown in Fig. 4

Po: static pressure at the axial center of the

prope lier

e : vapor pressure of water

According to Fig. 3, non-dimensional pressure amplitude Kp reduces slowly as cavitation number reduces, and thereafter, when

cavitation number reduces to less than 6, ¡(p rapidly increases. As for the phases, in rion-cavitating condition, when one blade of the propeller turns 180/N degree from its top position, the pressure fluctuation at the center line position above propeller

indicates the maximum positive value. N is number of blades.

In other words, pressure fluctuation indicates the maximum negative value when one of the baldes is directed to the transducer position.

In cavitating condition, however, phase angle changes with

cavita-tion number. Pressure fluctuation in the developed cavitating

-condition indicates the maximum positive value when one of the

blades is directed to the transducer position. The trend of

these experimental results seems to be similar to that of

Reference (10]. It is supposed that these phenomena are due to

the influence of tip vortex and tip vortex cavitation in addition to the influence of cavitation on blade.

2.2 Thrust variation

Fig. 5 shows the layout for measurement of thrust variation. Thrust variation was obtained from strain of the thin tube of

the measuring instrument unit indicated in Fig. 5. The wake

distribution and propeller are the same as those described in 2.1 above.

Fig. 6 shows non-dimensional thrust variation at the f

unda-mental blade frequency. Observing generally, influence of

cavita-tion phenomenon on thrust variacavita-tion may be disregarded. Thus,

the result of test at the towing tank in non-cavitating condition can be used for bearing force estimation in place of that in cavitating condition.

2.3 Fluctuating forces induced on rudder

Fluctuating forces induced on rudder were obtained by the

use of strain gauges on the rudder post shown in Fig. 7. The

wake distribution and propeller are the same as those shown in

2.1 above. The dimensions of rudders are shown in Table 2.

The symbols are defined in Fig. 8. Rudder angle was changed to

each side at every 5 degree.

Fig. 9 shows the test results at the fundamental blade

frequency. Fig. 10 and Fig. li indicate influences of rudder

angle and çavitation number. Non-dimensional coefficients and

are defined as follows:

Fn

1

--PVA2ARKQ

+PVA2ARKQ

where, : amplitvde of fluctuating rudder force

as shom in Fig. 8 at the blade frequency

VA : advance speed of propeller

AR area of rudder

3. Tests at Towing Tank

3.1 Measuring device for bearing force

The new measuring device made by the author has the following features:

The five components of bearing force except torque variation can be measured.

Moment and force induced on propeller are obtained from strain of leaf springs and inner tube which supports the propeller, though the other researchers have obtained them from strain of propeller shaft or propeller blade [12-151.

The measuring instrument unit does not turn with the propeller.

Thrust variation and moment fluctuation are measured separately

from fluctuating force. Further, fluctuating force is divided

into vertical and horizontal directions on recording its

signal.

Fig. 12 shows the structure of the measuring device. Fluctuating

force induced hydrodynamically on propeller is transferred to the

inner tube. The two components, one for vertical direction and the

other for horizontal direction, are separately measured by four

strain gauges located around the inner tube. Thrust and moment

induced ori the propeller are transferred to four terminals from the propeller boss, and measured by the strain gauges on the leaf

spring. Product of distance between the axial center of propeller

shaft and the terminal and difference between two forces within the vertical plane which goes through the propeller shaft represents

the moment around the horizontal axis. Moment around the vertical

axis is obtained from the remaining two forces by the similar

method. The summation of four forces gives thrust.

Natural frequencies of the inner tube and the leaf spring

were respectively 450 and 160 Hz. When the propeller was Installed,

however, another natural frequency was recognized at approximately

32 Hz. It was assumed that this phonomenon occurred due to an oscillation phenomenon of the propeller as the propeller was

supported at a single point on the inner tube. As for the

experi-mental results in which each component of bearing force showed the tendency of increase in the r.nge of about 25 to 60 Hz regardless of the natural frequency, and did not indicate a peak of resonance, however, the author recognized that these results were available.

3.2 Measurement of bearing force

Influence of propeller on bearing force of a model of tanker

was investigated by the use of the above instrument. Table 4 shows

the principal particulars. Ship form and principal particulars

of the model ship are indicated in Fig. 13 and Table 3. Speed

range of the model ship is 0.10 to 0.18 in Froude number Fn. effect of blade number

Fig. 15 shows a case of Fn = 0.14 as an example. With this

figure, it may be considered that there is no remarkable difference of bearing force between the propellers with four and five blades, and that influence of draught, that is, influence of wake

dis-tribution, is rather significant. effect of skew

Fig. 16 shows a comparison of influence of skew. According

to this figure, a propeller having highly skewed blades is effective in reducing vertical fluctuating force ÉFz of bearing force although it is affected by the draught.

4. Empirical Expression

Propeller exciting forces are to be influenced by ship form, principal particulars of ship and propeller, shape of propeller,

-6-operating condition, and so on. There are many problems to be solved on the application of the model test results to ship,

because there are various differences between ship and model ship. Especially difference of wake distribution is very important for propeller exciting forces.

However, the author tries here to obtain the empirical expressions from the test results mentioned in the above.

4.1 Surface force

It can be thought by approximate consideration of pressure equation that pressure is expressed in the summation of the terms

to be in proportion to l/ri

(j

= 2, 3, 4, ), where rj is

distance between a point on the i-th blade or vortex and a field

point. The values of l/rj are different at all angular positions

of propeller blade and vortexand the pressure must be most

in-fluenced by the propeller blade and the vortex which is nearest

to the field point. In addition, the tip of the propeller blade

and tip vortex which can be nearest to the field point is also to have the most predominat influence on pressure fluctuation. Therefore pressure fluctuation mainly depends on shape and

particulars of tip of propeller blade and strength of tip vortex

of bound vortex and trailing vortex. It is easily imagined that

the tip or tip vortex which is kept nearest to the field point

yLelds one peak of the fluctuations. This indicates that the

fluctuations appear N times per one revolution in case of the N-bladed propeller or at the fundamental blade frequency.

The increase of blade number causes reduction of size of a

blade and decrease of load per a blade. Those will decrease the

amplitude of fluctuations due to reduction of size of tip, re-duction of strength of tip vortex and tip vortex cavitation and reduction of volume of cavitation on a blade.

To ease the calculation based on the experimental data, the following simplifications are accepted.

(A) When one peak of fluctuating pressure appears, the distance

ri between a point on the contributing area of propeller

-7-blade or vortex and a field point under consideration can

be replaced by the tip clearance r. It is assumed that

fluctuating pressure is in proportion to hr2 only. The

contributions of the other terms including the higher order

1fr3, l/r, ... of 1fr are disregarded.

(B) The contributing element of propeller blade and vortex must

be expressed by blade thickness and chord at the vicinity of propeller tip and length of yortex, when a peak of

fluctuating pressure appears. It is very difficult to

treat thickness and chord at the vicinity of tip and length of the tip vortex in relation with the experimental data,

especially in the case of cavitating condition. Therefore

the diameter of propeller Is used as dimension of length

for them. The error arised from this simplification is

included in the experimental coefficients.

Accordingly, as magnitude of source-sink and vortex may be supposed to be in proportion to nD, the above simplifications give the following expression.

AP nD3

-8-i

{(flVWA+f2*nD)2+f3n2D2}2 cos(O-rì)

(4)

where, f1, f2 and £3 experimental coefficients

VWA : main component of velocity due to wake

at a field point

When VWA is not forced artificially, it may be assumed that VWE is in proportion to nD. Thus, the following expression

is obtained. pn2D2

Ap = f cos(®-rì)

c*2

where, C* : tip clearance ratio (rID)

(5)

The coefficient f is decided from the test results. As the result, the expression for surface force at the fundamental blade frequency is written as follows:

S.F. = KF

pn2D

cos(0-)

(6)

¡f cos(G-)dS (7)

where, S.F. : surface force

phase angle of surface force

S : contributing area of ship surface

The non-dimensional coefficient KF is obtained from f that is, from the test results.

Some estimations of surface force have already been tried

[9, 161. The following assumptions in the manner similar to

them are made to simplify the treatment.

The contributing area S of ship surface above propeller is a square with the length of one edge D.

The amplitude of pressure fluctuation becomes to zero at boundaries x/D = ±0.5 and y/D = ±0.5.

Fig. 17 and the other figures thereafter are based on the results of the test with a rudder (rudder angle 0) mentioned in

2-3. Coefficient KF is obtained in Fig. 17 from the test results

of a container carrier model.

Fig. 18 and Fig. 19 show the effect of blade number and cavitation number.

For example, in case that N 6, D = 7.0 m, n = 2 rps

(120 rpm), C = 0.22, and J = 0.73, the surface force is estimated

to be 18 ton at the fundamental blade frequency.

KF

1

D2

10

-4.2 Bearing force

The force induced on propeller in unsteady inhomogeneous

flow is written in a form of an infinite progression. For

example, for x-component, it is given as follows:

Fx = Fxm cos(mwt - m) (8)

m= O

In the ship vibration of view, the fundamental blade

frequency is interested. In fact, in case of the wake field with

strong steadiness, the bearing force at the fundamental blade frequency are more predominant than at the other frequencies.

The lift FL which is induced on propeller blade is written as follows:

FL = CLPVI2SO (9)

where, CL : lift coefficient

V1 : inflow velocity of water to blade

So : area of blade

The fluctuation of lift is given as,

¿FL = ¿CLPVIO2SO + 2CLOPVIOIWISO + O (LCL, ¿VI) = an2 + bn + c

(10)

where, CLO, V10 : mean value of CL and V1

CL, ¿V1 : fluctuating part of CL and V1

a, b, c : coefficients which are a function of

V/nD respectively (V: ship speed)

Therefore each component of bearing force which mainly come from lift fluctuation may be expressed in the same form with the above expression.

The analysis of the test results was performed on the assump-tion that all available data at the fundamental blade frequency

were expressed

in the

following three forms.

an2 + bn

+ C

ari + b

C

By the decision of the coefficient a, b, c in every draft and every coefficient V/nD by the least square method it was found that the second assumption provided the best result. Hence, in this paper, bearing force was analysed based on the assumption that amplitude can be expressed by the linear expres-sion of propeller revolution, for example,

Fx= (a1n+b1)

V

+an+b2

nD 2

for thrust variation.

The other fluctuating forces and moment are also obtained

from the similar expression as above presented. The coefficients

obtained from the test results of a large size tanker model are

presented in Table 5. Using these coefficients unit of bearing

force is kg or kg.m. If it is assumed that model length is

6.25 m, V/nD = 0.64, n = 9.8 rps, and that scale ratio is 54.4, thrust variation of full scale ship, for example, is estimated to be about 16 ton at full load condition.

5. Conclusions

Some of the model test researches about the propeller exciting forces performed in the Research Institute of INI were introduced

in this paper. As the conclusion, they are suuunarized as follows:

(A) Pressure fluctuation on hull surface above propeller at the

fundamental blade frequency does not increase for a time

even if cavitation number drops. Thereafter, however, it

increases rapidly with decrease of cavitation number. Phase

angle changes as cavitation number changes.

Thrust variation in cavitating condition is approximately equal to that in non-cavitating condition.

Propeller induced fluctuating forces on rudder are affected by rudder angle, cavitation number, and so on.

The new instrument was devised and was useful for bearing force measurement, though attention had to be paid to the analysis.

The empirical expressions of propeller exciting forces for prediction were obtained on the basis of the model test

results. Strictly speaking, however, propeller exciting

forces seem to be sensitively influenced by draught, that

is, wake distribution, and so on. It is desired that the

various matters to heighten the accuracy of these estimation

are more investigated.

Acknowledgement

The author wishes to express his thanks to Dr. Jinnaka, Dr. Tasaki, Mr. Mano, Mr. Nishiyama, Mr. Fujii and their staffs of the Research Institute of the IHI for their cooperation and

support.

References

BRESLIN,J.P. The Pressure Field Near a Ship Propeller.

J.Ship Res. 1 (1958); 4,pp 57-67.

BRESLIN,J.P. and TSAKONAS,S. Marine Propeller Pressure

Field Due to Loading and Thickness Effect. T.Soc.N.A.M.E.

67 (1959), pp 386-422.

JACOBS,W.R., MERCIER,J. AND TSAKONAS,S. _{Theory and Measurements}

of the Propeller-Induced Vibratory Pressure Field. J.Ship

Res.16 (1972); 2, _{pp 124-139.}

-ISHIDA,S. On an Approximate Calculas of the Propeller-Induced

Surface Force. J.Soc. N.A.Japan (1975); 138 pp 111-123.

TAKAHASHI,H., and UEDA,T. An Experimental Inve8tigation into

the Effect Cavitation of Fluctuating Pressure around a Marine

Propeller. Proc. 12th ITTC 1969.

VAN MANEN,J.D. The Effect of Cavitation on the Investigation

between Propeller and Ship's Hull. Int.S.Prog. 19(1972);

209, pp 3-20.

HUSE,E. Propeller Hull Vortex Cavitation. Int.S.Prog.

19(1972); 212, pp 111-125.

JOHNSSON,C.A., and SONTVEDT,T. Propeller Excitation and

Response of 230,000 TDW Tankers. DNV Publication (1972); 79

TAKAHASHI,H. On Propeller Vibratory Forces of the Container

Ship. Papers of Ship R.Inst. (1973); 44, pp 1-27.

VAN OOSSANEN,P., and VAN DER KOOY,J. Vibratory Hull Forces

Induced by Cavitating Propeller. J.Royal I.N.A. (1973); 2 pp

111-144.

DYNE,G. A Study of Scale Effect on Wake, Propeller Cavitation

and Vibratory Pressure at Hull of Two Tanker Models. T.Soc.N.A.M.E. 82 (1974), pp 162-185.

TSAKONAS,S., BRESLIN,J., and MILLER,M. Correlation and

application of an Unsteady Flow Theory for Propeller Forces. T.Soc.N.A.M.E. 75 (1967), pp 158-193.

WERELDSMA,R. Some Aspects of the Research into Propeller

Induced Vibration. Int.S.Prog. 14 (1967); 154 pp 246-264

KUMAI,T., TAMAKI,I., KISHI,J., YUNOTO,H., and SAKURADA,Y. On a Method of Measurement of Propeller Bearing Force

Exciting Hull Vibrations. J.Soc.N.A.Japan (1970); 128 pp

277-281.

-HUSE,E. An Experimental Investigation of the Dynamic Forces

and Moments on One Blade of a Ship Propeller. Nor. Ship

Model Ex. Tank Publication (1967); 99.

TAKAHASHI,H., A Consideration on the Effect of the Propeller

Cavitation upon the Surface Force. T.West-Japan Soc.N.A.

(1974); 49 pp 255-285.

-Fig. 1 Arrangement of the Model Corresponding to After Body of

Ship in the Cavitation Tunnel

Fig. 2 Results of Axial Velocity Measurements in the Propeller

Disc

Fig. 3 Fluctuating Pressure and Phase at the Fundamental Blade

Frequency (6-bladed propeller)

Fig. 4 Definition of Symbols

Fig. 5 Arrangement in the Cavitation Tunnel for the Thrust

Variation Measurement

Fig. 6 Results of the Thrust Variation in the Cavitation Tunnel

Fig. 7 Arrangement in the Cavitation Tunnel for the Induced

Rudder Force Measurement

Fig. 8 Definition of Symbols for Dimensions and Fluctuating

Forces of Rudder

Fig. 9 Fluctuating Rudder Forces at the Fundamental Blade

Frequency

Fig. 10 Effect of the Rudder Angle on the Fluctuating Rudder

Forces (J = 0.4 - 0.6)

Fig. 11 Effect of the Cavitation Number on the Fluctuating Rudder

Forces (J = 0.4 - 0.6)

Fig. 12 Structure of the Instrument for Bearing Force

Fig. 13 After Body Profile of Ship Used in the Towing Tank Test

Fig. 14 Components of the Bearing Force

Fig. 15 Example of the Effect of Blade Number at the Fundamental

Blade Frequency (Fn = 0.14)

Fig. 16 Example of the Effect of the Skewed Propeller at the

Fundamental Blade Frequency (Fn = 0.14)

Fig. 17 Non-dimensional Coefficient KF at the Fundamental Blade

Frequency (an = 2.1, 6-bladed propeller, C* = 0.22)

-Fig. 18 Relation between the Fluctuating Pressure and Blade

Number (J 0.4 - 0.6)

Fig. 19 Relation between the Fluctuating Pressure and Cavitation

Number (J = 0.4 - 0.6)

Table i Model Propellers Used in the Cavitation Tunnel

Table 2 Rudder's Particulars

Table 3 Ship's Particulars and Test Conditions

Table 4 Model Propellers Usid in the Towing Tank for the

Bearing Force Measurement

Table 5 Coefficients for the Estimation of the Bearing Force

at the Fundamental Blade Frequency (5-bladed propeller)

-t ri C) Fi 1A h ti u LI LI

ti

t!

L

FI CN

Model of

Aft-Body

o

Pressure gauge

f

Inner Surface of Tank

Fig. i

Arrangement of the Model Corresponding to After Body

of Ship in the Cavitation Tunnel

Mesh

Direction of Flow

VA

V

1.

0.97R

0

30

60

90

120

150

180

210

240

270

Fig.

2

Results of Axial Velocity Measurements

in the Propeller Disc.

Cavitation

tunnel

- - Towing tank

300

330

360

degrees

0 L I I J I o

30

60

90

120

150

180

210

240

270

300

330

360

degrees

3.0

2.5

2.0

1.5

1.0

0.5

0

Kp

0.375

Port

9

o

0.25

0.125

Phase angle

n

J: Advance ratio

o

j = 0.5

o

0.6

9

0.7 2

0.125

0.25

y/D

Fig.

3

Fluctuating Pressure and Phase

at the Fundamental Blade Frequency

(6-bladed propeller)

O Cavitation tunnel

Towing tank

Starboard

o 4 6 8 10 12 14 16 18 Gfl

h

r

revolution of propeller

271

N:

Number of blades

Fig. 4

Definition of Symbols

0.02

0.01

p.,

Universal

o

Propeller

Support

Measuring Unit

I

Joint

Propeller Shaft

Mesh

Fig. 5

Arrangement in the Cavitation Tunnel

for the Thrust Variation Measurement

6-Bladed Jropeller

J=O .6

Fig.

6

Results of the Thrust Variation

in the Cavitation Tunnel

b

h

Fig. 7

Arrangement in the Cavitation Tunnel

for the Induced Rudder Force Measurement

Strain Gauge

Rudder

Fig.

8

Definition of Symbols for Dimensions

1.0

0.2

0.4

0.6

Fig. 9

Fluctuating Rudder Forces at the Fundamental

Blade Frequency

0.2 0.4 0.6 J an

d/D

= = =

2.1

0.46

Q0 K

1.0

150 100

50

00

50 100 15° 20°

Fig. 10

Effect of the Rudder Angle on the

Fluctuating Rudder Forces (J=0.4-0.6)

1.0

0.5

2 4 6 8 10 12

an

Fig. 11

Effect of the Cavitation Number on the

Fluctuating Rudder Forces (J=O.4-O.6)

4

T'4V

uI.-AL!

W1p1

:

Strain Gauge

for the Side Force Measurement

Stern Tube

Outer Tube

Universal Joint

B

Propeller Shaft

Termin al

Leaf Spring

Strain Gauge for Thrust and

Moments Measurement

Inner Tube

Blade

Fig. 12

Structure of the Instrument for Bearing Force

Propeller Boss

Cap

(a)

AA-Section

(b)

BB-Section

(c)

Full Load

Fig. 14

Components of the Bearing Force

AP

1/4 1/2

Fig. 13

After Body Profile of Ship Used

in the Towing Tank Test

kg

kg.rn

0.005

tFx 0,2

0.2

o û AMy AMy

V

₀₆₅

V_

-=

. AFx

-0.8

AFX

0.2

o-o 4 5

N

4

5N

4 5 N

0.005

0.005

AMy

Fig. 15

Example of the Effect of Blade Number at the

Fundamental Blade Frequency (Fn=0.14)

= 0.71

nD

0.02

0.02

0.02

o O 4 5 4 5 4 5

kg

LFy

AFy

Fy

0.02

0.02

0.02

0-o.

_o-.

o 4 5 4 5 4 5

(a) Full Load

(b) Ballast Cond.(l)

(c) Ballast Cond.(2

o o O

4 5 4 5 4 5

kg.rn

AMz

AMz

AMz

0.005

0.005

0.005

o o o-o

o--.

kg

AFz 4 5 AFz 4 5 AF z 4 5

o

kg

_AFx

0.2

kg.m

0.00

kg.rn

0.00

o

kg

0.02

O

kg

0.02

O

My

Mz

O o Fz o Fy

s.

V

= 0.65

kg

Fx

4

s.

O 50 % o 0.2

kg.m

0.005

t o 50 0 kg.rrt Mz

0.005

O 50

kg

0.02

50

kg

0.02

O

AMy

O AFz 50 50 %

0.005

50 0

kg.m

AMZ

0.005

50 0

50%

kg

0.02

0.02

AFz O 50 0 50 %

kg

AFy

0.71

I

p.

50 % O O O 0 50 0 50 0

50%

(a) Full Load

(b) Ballast Cond. (1)

(c) Ballast Cand. (2

Fig. 16

Example of the Effect of the Skewed Propeller

at the Fundamental Blade Frequency (Fn=0.14)

0.80

kg 0.2 O

AFx

I

V

=

kg.m

0

AMy

o

AFy

0. 0012

0.0010

0.0008

0. 0006

0.0004

2 i O

kp(N6)

.1 C*=O .22 Ae=O .96 4 5 6 N

Number of Blade

Fig. 18

Relation Between the Fluctuating Pressure

and Blade Number (JO.4-O.6)

0.1

0.2 0.3

0.4

0.5

0.6 0.7

0.8

Fig. 17

Non-dimensional Coefficient KF

at the Fundamental Blade Frequency

1.0

0.5

10 12

Fig. 19

Relation between the Fluctuating Pressure

and Cavitation Number (J=O.4-O.6)

Table i

Model Propellers Used in the

Cavitation Tunnel

Table 2

Rudder's Particulars

B,C:

Contra Rudder

Model Propeller No.

135

Diameter

(in)

0.240

Pitch ratio

1.00

Expanded area ratio

0.96

Boss ratio

0.20

Mean Blade Width Ratio

0.33

Blade Thickness Ratio

0.059

Angle of Rake

00

Nuither of Blade

6

Skew

(%)

10.9

h/D

iu/D

tu/D

L/D

tL/D

d

A

1.1

0.88

0.14

0.88

0.14

0.46

B " " II C rl Il lt U lt

Table 3

Ship's Particulars and Test Conditions

Table 4

Model Propellers Used in the Towing Tank

for the Bearing Force Measurement

Full Load

Ballast (1)

Ballast (2)

Ship

Model

Ship

Model

Ship

Model

Lpp

(m)

340.0

6.25

340.0

6.25

340.0

6.25

B (in)

68.0

1.25

68.0

1.25

68.0

1.25

Draft at

(in)

22.6

0.42

10.9

0.20

17.7

0.33

Draft at AP (m)

22.6

0.42

13.6

0.25

17.7

0.33

Draft at FP (m)

22.6

0.42

8.3

0.15

17.7

0.33

CB

0.80

0.80

Model Propeller No.

215

216 222

Diameter

(in)

0.176

0.176

0.176

Pitch Ratio

0.71

0.67

0.71

Expanded Area Ratio

0.62

0.62

0.62

Boss Ratio

0.16

0.16

0.16

Mean Blade Width Ratio

0.29

0.23

0.23

Blade Thickness Ratio

0.056

0.056

0.056

Angle of Rake

00

0°

00

Number of

1ade

4 5 5

Table 5

Coefficients for the Estimation of the Bearing Force at the Fundamental Blade Frequency (5-bladed propeller) Full Load

Ballast (1) a1 b1 a2 b2 a1 b1 a2 b2 AFx -0.0665 0.594 0.0638 -0.491 -0.0224 0.0287 0.0228 0.0600 j AMy

xl02

0.0707 0.259 -0.0157 -0.0232 0.377 -2.818 -0.292 2.539 ANz

xl02

0.0551 0.440 -0.0320 -0.232 0.221 -1.26 -0.185 1.21 AFz

x10'

0.111 -0.420 -0.0626 0.513 0.402 -2.765 0.315 2.429 AFy

xl01

0.100 -0.680 -0.0637 0.529 0.174 -1.029 -0.134 0.887