Investigation into propeller cavitation in oblique flow

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A

MITSUBISH I TECHNICAL

BULLETIN MTB 010045

MITsuffisHI TECHNICAL BULLETIN No. 45

March 1967

Investigation into the Propeller

Cavitation in Oblique Flow

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Investigation into the Propeller Cavitation in Oblique Flow

Introduction

There have been carried out many cavitation tests in order to provide propeller design data and to serve performance

prediction of high-speed vessels. It should be noted, however. that most of the propellers of high-speed vessels are operated

in oblique flow conditions. In the case of non-cavitating propellers, the effect of oblique flow on the performance of propeller has been studied by several investigators treating the problem theoretica1ly' and experimentally23, while in the case of cavitating propellers there are at present no published data or available informations on this effect. It is

highly desirable, therefore, to carry out propeller cavitation tests in oblique flow condition and to study the effect of

oblique flow on the performance of propeller, from which we

should be able to get a more reliable model-ship correlation of high-speed vessels and to predict better the cavitation pattern relating to the cavitation erosion on the propeller blades.

In 1963 Mitsubishi Experimental Tank (Nagasaki) started

the study on the propeller cavitation in oblique flow condition

under the sponsorship of the Office of Naval Research'3. The principal part of the study is to be described in this

report.

Firstly an attempt was made to develop a method to

calculate the performance of propeller in oblique flow

condi-tion from the propeller characteristics in axial flow condicondi-tion by the use of quasi-steady approach.

Then, in order to confirm the validity of the method of calculation, a series of supercavitating propellers including the variation of pitch ratio and expanded area ratio were tested in the cavitation tunnel in oblique flow condition. The test results were found to be in fairly good agreement with the propeller characteristics estimated by the quasi-steady method mentioned above.

Trial data of some high-speed boats were analyzed based on these investigations. The model-ship correlations seem to be improved to some extent by the use of the propeller

characteristics in oblique flow conditions.

Quasi-steady Calculation of Propeller

Charac-teristics

The most rigorous theoretical approach to the effect of oblique flow on the propeller would be the application of a

Dr. Eng., Manager. Nagasaki Technical Institute, Technical Headcicarters Experimental Tank, Nagasaki Technical Institute. Technical lleadquarters

Kaname Taniguchi5

Hidetake Tanibayashi55

Noritane Chiba**

Abstract

In order to serve the improvement of performance prediction of high-speed vessels, theoretical and experimental investigations into the propeller cavitation in oblique flow condition have been carried out.

As a first step, a simple quasi-steady method of calculation was developed to estimate the propeller cha racter-istics in oblique flow condition from those in axial flow condition.

Titen a series of supercavitating propellers were tested in cavitating oblique flow condition to confirm the

validity of the quasi-steady method of calculation. The test results were found to be in fairly good agreement with the propeller characteristics estimated by the quasi-steady method.

non-stationary lifting surface theory of propeller. This

method, however, requires a complicated calculation,

neces-sitating the use of a big electronic computer. Furthermore the non-linearity of propeller characteristics K, K J curves

due to the cavitation increase the difficulty in the formulation

and the numerical calculation of the problem. For practical application, therefore, we might as well attempt to develop a simpler method without so much sacrifice of the accuracy of

the calculation. To this purpose a quasi-steady method was tried as the most suitable one for the first step of this study. In the case of cavitating propeller operating in non-uniform velocity field, the results of quasi-steady method have been compared with those of non-stationary method, showing good agreement of the time-average thrust and

torque'.

The fluctuating terms, on the other hand, are affected by the frequency of oscillation of flow field around the propeller. Taking for example the reduced frequency at 0.7R, which may be taken as a representative factor for the non-stationary terms

(eC07 (dR)07

k07

_2V (1)

k77 is about 0.5 for a propeller with narrow blades and is

about 1.0 for a propeller with wide blades. Certain difference

between a quasi-steady and an unsteady method, therefore, might have to be expected in the fluctuating terms.

In the present study, however, the prediction of the time-average thrust and torque were more accentuated than the fluctuating forces and the quasi-steady method was tried. (As mentioned later in 4.2, it is to be noted that the compari-son of the cavitation pattern between a quasi-steady and an unsteady approach showed pretty good agreement:

The quasi-steady method is based on the assumption that the elemental thrust and torque of a blade element at a certain angular position can be equated with those of axial flow condition, at the same resultant inflow velocity. The

quasi-steady advance ratio of a blade element, at the radial

distance xR and the angular position 'p (Fig. 1), can be represented as

cos O

J=xtanß=J0

. . (2)

1+(J0Jirx)sin çc.sln O

and the local circumferential velocity is (neglecting the

induced velocities),

(3)

UsinO sine

Fig. i

Velocity diagram

where u0= rnD (4)

Jo= v/nD (5)

and suffix o refers to the axial flow condition

Therefore, the elemental thrust and torque developed by this blade element are

dT'/z= (pn2D4/z) . (u/u)2 .K0(J, c5)0(x)dx (6)

dQ/z = (pn2D5/z) . (u/u)2 .KQ0(J, a0) ?Jf(x)dx (7)

where 0(x) and /J(x) are the thrust and torque distribution

function respectively.

From (3)-...(5), (u/u0)2is

(u/uo)2 = 1 +2(J0/x) sin ÇD.siflO + (Jt/1rx)2Sifl2ç.sin2 ¿I 8)

and

o= o,(a/u)2

19) Hence, using the equations (6)-.(9), we can calculate the thrust and torque developed by a blade (at the angular posi-tion ç) of a propeller operating in the oblique flow from the characteristics in axial flow condition, if we know the distri-bution functions 0(x), and V(x).

For simplicity, however, if we take the 0.7R section as

repre-sentative, the thrust and torque of one blade are given by

the following equations.

T'/z= (pfl2Dl/Z).(ze/uo)2.Krn(J o) (10)

Q/z=(pn2D°/z).(u/u0)2.K0o(J, a0) (11)

K0 and K00 corresponding to [J10, ço). a0(O, so)] can be read for each angular position of the blade from the charac-teristics in the axial flow condition. The circumferential

nO 2 uO ₎ 2

mean values of KTOk ' _{and Keo1} _' will be

u0 u0

taken as K' in the direction of propeller shaft) and K0 in

oblique flow condition respectively, viz.

KT' f2KTOJ. a5).(u/u0)2.dçt (12)

(13)

Thrust T in the direction of general flow is obtained by assuming the side force is equal to sin p,

K = K' cos O - 2Lf K00(J, a) sin O. SIflÇD(u/u)'dç

(14)

2

Fig. 2 Propeller P. 1329

Table i Propeller particulars

3. Test Scheine

3. 1 Propeller models

Five propeller models with Tulin's supercavitating blade section were tested in the present study. As described schematically in the diagram below, the particulars of the

propellers were varied systematically on the basis of P. 1329, which is a scale-model of the propellers of a high-speed boat.

p 1.286 Ae/Ad- 0.514 P. 1372 D=230 mm p= 1.286 Ae/Ad= 0.411 E.A.R. Series D=23O.Orn P = 2 05 .7 P=1 .286

P. 1369, P. 1329 and P. 1370 constitute a series of pitch

ratio, while P. 1329, P. 1371 and P. 1372 constitute a series of

expanded area ratio.

The particulars of the propeller models are presented in Table 1, and the drawing of P. 1329 is shown in Fig. 2.

3.2 Kinds of test (a) Cavitation tests

Cavitation tests in oblique flow condition were carried out with a special attachment as shown in Fig. 3. A propeller 1329 1369 1370 1371 1372 Diameter (mm) 230.00 230.00 230.90 230.00 230.00 Pitch (0.7 R) (mm) 295.71 230.00 368.00 295.71 295.71 Pitch ratio (0.7 R) 1.2857 1.0000 i 1.6000 1.2857 1.2857 Disc area (m2) 0.04155 0.04155 0.04155 0.04155 0.04155 Expanded area (m2) 0.02572 0.02572 0.02572 0.02136 0.01708

Expanded area / disc area 0.6190 0.6190 0.6190 0.5141 0.4110

Bossratio 0.1819 0.1819 0.1819 0.1819 0.1819

Thick-chord ratio at

0.7 R (%) 6.118 6.118 6.118 6.516 7.088

a e sec i°fl

BI d t S.C._typeS.C._typeS.C._typeS.C._typeS.C._type

Number of blades 3 3 3 3 3 P. 1369 P. 1329 P. 1370 D=230 mm ,=1.0Oo Ae/.4d= 0.619 D=-230mm p.= 1.286 Ae/Ad= 0.619 D=230 mm p=1.600 Ae/Ad==0.619 PitchSeries P. 1371 D=230 mm General flow Direction of rotation u

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'I

I

Handle for changing shaft inclination

Universal joints

Observation window

shaft ç900mm long and 38mm in diameter) was connected to the ordinary propeller shaft by means of a couple of universal joints, and the downstream end of the shaft was supported by a vertical strut, which enabled the variation of

the inclination of the shaft.

The test conditions were as follows; Inclination of the shaft: O

O=0, 4° and 8 Advance ratio: J=v/nD

J=0.7l.l

for P. 1329, P. 1371 and P. 1372

1=0.5-0.9 for P. 1369 J=0.9-1.5 for P. 1370

each covering the range 10-45% in slip ratio. Cavitation number: r

a,,=0.3-1.0 and atmospheric condition

for P. 1329, P. 1369, P. 1371 and P. 1372

011=0.5-1.5 and atmospheric condition

for P. 1370

Thrust and torque were measured by the

propeller

dynamometer for ordinary Cavitation tests so that the

measured thrust was in the direction of general flow.

(b) Open.water tests

In order to obtain a reasonable method of Correction for the tunnel wall effect and for the rotational wake of the rotating propeller shaft upstream of propeller, open.water tests in oblique flow condition were carried out on all the models. A special propeller dynamometer of a strain gauge type was developed and it was so arranged that the propeller shaft could be inclined in the vertical plane. It should be borne in mind that the thrust measured by this dynamometer is in the direction of the propeller shaft, while in the cavita tion tunnel it is in the direction of general flow.

4. Test Results

4. 1 Correction to the measured results in tunnel

The thrust T and torque Q measured in tunnel were

Comparison of the test results in tunnel in non.cavitating conditions with those in open-water showed that it was not

necessary to correct the results for tunnel wall effect in terms

of the equivalent inflow velocitythe water speed was

measured by a pitot tube as shown in Fig. 4, but it was

Attachment shaft

Fig. 3 Sketch of special attachment shaft

Static pressure hole Direcflonof flow

Tunnel wall

Observation window

Total pressure tube

Static pressure hole

Total pressure tube

Fig. 4 Pitot tube

observed that the rotational wake of the rotating propeller shaft upstream of propeller had a significant effect on the propeller characteristics5. The correction for the rotational wake was applied on the basis of the assumption that KQ J curves in tunnel under atmospheric condition and in open. water should agree with each other at the same Reynolds

number. In other words the correction factor in/n for the

rotational speed was obtained in such a way that KQJ

curve in tunnel should coincide with KQ*_J* curve (after the correction for Reynolds number) satisfying the relations

.

(18)

1* =iv(i+)

(19)

Using this correction factor, we obtain the corrected propeller

characteiistics as (20) Miß 010045 MARCH 1967 o o Observation window 3

reduced to the non-dimensional coefficients K1° and K0°,

KrT/pn2Dl

(15)

KQ0=QJpnODS (16)

J0v/nD

(17)

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4 0.20 Q 0.15 0.10 0.05 0 0.15 U1 Q o u-b 0.10 0.05 O 0.25 e 0.20 0.25 0.15 0.20 0.10 0.15 0.05 0.10 0.15 o 0.10 0.05 . O 0 0.05 0.15 Q u-b 0.10 0.05 07 8 4 8 Marks 08 P. 1329

Cavitation test results ir, oblique flow

09

J-1 'ID

Fig. 5 P. 1329 Kr-I curves 10

Kr J

11 12

by the variation of local cavitation number and they are nearly linear with respect to advance coefficient J. In such

a case, the quasi-steady calculation can be simplified and we

obtain, as shown in Appendix,

KT' = KTO+ [--- 70J+ - a,0 (J/O.Th)2O2

KQ = K55+ [--- JP-J+--ano (J/O.71v)2]02 (26)

or referring to (23) and (24)

1 dK0

1

Aeai=

--B0i --

SKQ0J1U/07)2

(28)

where a,0 and a5, show KTO and K50, respectively, as extra-polated linearly to J=O.

Comparison of the coefficients A and B as obtained by experiments and theory will be a good measure for checking the reliability of the quasi-steady calculation. In the table below, the comparison is given in terms of ratio a and b

(25)

(27)

KQ=KQ0(1+ 21)

=10(1+ An) (22)

The correction factor An/n obtained in non-cavitating con-dition was applied also for cavitating concon-ditions, because significant variation of the rotational wake is not expected

by the change of the pressure in tunnel.

Thus corrected K and K5 were plotted to the base of the corrected J. An example of the corrected results is given in Figs. 5 & 6.

4.2 Comparison with a quasi-steady calculation The variation of KT' and K5 due to the effect of oblique flow can be expressed by an even function of the shaft

inclination O. For a small angle of shaft inclination, Ky.' and K5 are approximated by

KT'KTo+AO2 (23)

KQ*KQO+BO2 (24)

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0.04 N. o

Ub

0.03 0.02 0.01 O 0.04 o o u. b 0.03 0.02 0.01 O 0.05 e o Ub 0.04 0.03 0.02 0.01 0.03 0.02 0.01 0.03 o o 0.02 0.01 07 08 8 a=Aexp/Aci (29)

bBexp/Bi

(30) where _{Aexp=(KT'K70)/02} Bexj, (KQ_KQO)/02

A5 and

were obtained from open-water test results.

It is to be noted that a and b are generally larger than unity and b increases with pitch ratio. If we compare KQ itself, however, instead of its increment due to the inclination of

OQ

O.4

P. 1329

Cavitation test results in oblique flow

K0 -J L..

OQ3

j = V/nD Fig. 6 P. 1329 KQ-J curves 0 9 1.0 1 1 1 2 MIB 010045 MARCH 1967

the shaft, the differences between the measured values and those calculated by the quasi-steady method are about 2 except for P. 1370 with the highest pitch ratio (p= 1.6), for which the difference amounts to 3-5%. Further study both on theory and on experiments will be necessary to make clear this trend.

In cavitating condition, the estimation of the propeller characteristics in oblique-flow from those in axial flow con-dition is much more difficult and complicated than in non-cavitating condition. The instantaneous K- and K53 in eqs.

ib) and (111 respectively, at each angular position of a blade are functions of local cavitation number as well as local

advance coefficient. Besides, K0 and K50 versus J curves can no longer be approximated by a linear relation due to thrust and torque breakdown caused by cavitation on the 5

P. No. p AelAd a(6=8°) 6(8=8°)

P. 1329 1.286 0.619 3.74 1.92 P. 1369 1.000 0.619 2.07 1.55 P. 1370 1.600 0.619 1.29 2.34 P. 1371 1.286 0.514 3.15 1.97 P.1372 1.286 0.411 2.28 1.92 0.03 o o

ub

0.02 0.01 o Marks o o

(7)

o Measured Calculated o=0.S P 1329 p 1.2857) or. = 04 P 1369(p=l.O

\

=0.5 K0 K0 P 1370 (p=I.6) 0.5 0.6 0.7 0.8 0 9 1,0 1.1 1.2 J V ltD

Fig. 7 Comparison between the measured values and those calculated by quasi-steady method O = 8°

blades. At present, therefore, the quasi-steady calculation as stated before in 2, will be the most useful, and may be the only available method to estimate the effect of oblique flow, although the method yields slight discrepancy from the experimental results even in the simplest condition viz, in

non-cavitating condition. In Figs. 7 & 8, the calculated KT corrected to the direction of general flow) and K6 are coni-pared with those measured at O=81. The measured K9's agree quite well with those calculated by the quasi-steady method except for P. 1370, for which the measured torque is slightly larger than that calculated. As for KT, the measured values are slightly smaller than those calculated. In general,

however, it may he said that the agreement is pretty good and is within the accuracy of measurement. The remaining discrepancies, though considerably small, may be due to the approximate analysis by means of the quasi-steady method. Better agreement will be achieved by the refinement of the measuring technique as well as the development of a more

rigorous theory.

For a propeller blade in oblique flow condition, local advance

ratio and cavitation number change with its angular position. It is interesting to compare the cavitation pattern on the blade in oblique flow condition with that in axial flow at the corresponding J and o. Fig. 9 shows a comparison of the cavitation patterns between oblique flow and axial flow

con-ditions. The sketch in the middle of this figure represents the cavitation pattern in oblique flow conditions (O=8.

çD=900). _{The local advance ratio J(O. çs) and the local}

cavi-tation number o(O, ço) calculated by (2) and (9) are, J=0.93 and a,=O.44

Comparing this cavitation pattern with the sketches in axial flow )at the corners of this flgure, vie may say that the propeller blade operates in nearly the same condition as is

predicted by the quasi-steady calculation.

0.8 0.9 1.0 0.8 0.9 1.0 0.8 0.9 1.0

jV eD

Fig. 8 Comparison between the measured values and those calculated by quasi-steady method O = 8°

Fig. 9 Cavitation pattern in oblique flow

4. 3 Effect of pitch ratio and expanded area ratio In non-cavitating condition the effect of oblique flow can be expressed, as mentioned above, by the increase of thrust and torque which is in proportion to the square of the angle

P 1371 :L' li 0= Q, 0.514 K0 Measured Calculated A P 1372 ,4a-0 411 0.5 0.04 0.03 0.02 0.2 0j P 1329 A/Aa=O,616 S' c-. 0.5 0.04 0.03 0.02 0.2 0.1 o =0.6 K1 P 1370

(8)

of shaft inclination. From (25), (27) and (29), we obtain,

Kr(J,0)Kro_--02[aIj0J ato(J/0.7r)21

..

31)

and similarly from (26), (28) and (30)

KQ(J, 0)=Ko_02[

aJJ

aqo(J/0.72r)2] (32)

Since a propeller with large pitch ratio operates in general at large advance ratio and the factor b increases with pitch ratio as mentioned before, the increments of K7 and KQ

increase with pitch ratio.

As for expanded area ratio, there is no significant variation

3K70

of the factors a and b. and -a-,- increase slightly with expanded area ratio. In non-cavitation, therefore, the effect of oblique flow varies little with expanded area ratio.

In cavitating condition, such a simplified analysis is not suitable for the discussion on the effect of pitch ratio and expanded area ratio.

In general the increments of KQ due to shaft inclination decreases with the decrease of cavitation number, and for the range of e<O.5 and s>0.3 the design point of super-cavitating propellers usually lies in this range no appreciable variation in K is found with the angle of shaft inclination

except for P. 1370. For P. 1370, which has the highest pitch

ratio p= 1.6) among the propellers tested, K increases still at aj=O.5 with the angle of shaft inclination.

On the other hand, K)J. (measured in the direction of general

flow) decreases in oblique flow cavitating condition in con-trast with non-cavitating condition. The decrement of K7 increases slightly with pitch ratio, while expanded area ratio does not have a definite influence on the decrease of K7 due to shaft inclination.

5. Conclusions

The results of the above-mentioned theoretical and ex-perimental studies may be summarized as follows:

(a) _{Quasi-steady calculation can be used to predict the}

propeller characteristics in oblique flow in cavitating

con-dition as well as in non-cavitating concon-dition.

)b) Observation of the photographs of the cavitation

Simplification of the quasi-steady calculation in non-cavitatifig condition

In non-cavitating condition K7 and K are not affected by cavitation number and are expressed approximately by a linear function of advance ratio, viz.

K7=a,+h7J (A.1)

KQ=aQ±b4J (A.2)

As mentioned in section 2, the quasi-steady K is obtained

by u(f1,ç) 2dço (13) no J aq0+b50J(0,ça) u(0, ç,)

Substituting (2) and (8) for J(0, ç) and

respective-I u I

ly, we obtain

KQ(JQ, O)=a00+b00.J0.cos

a0

(J0/irx)' sifl2 Q --. (A. 3)

where x=0.7.

Expanding (A. 3) into the series of 0, we obtain KQ(JO, 0) =a00+ hqoJo+ [_ _hq0J0+ J0/0.7 7)2]02

patterns on the blades suggests that the propeller blades in oblique flow condition operate in nearly the same manner as is estimated by means of a quasi-steady calculation from the behaviour in axial flow condition.

(c) In non-cavitating condition, the increments of K7 and KQ due to shaft inclination increase with pitch ratio, but little with expanded area ratio. In cavitating condition,

the effect of shaft inclination is not in such a simple relation with the geometry of a propeller. In general it was observed that the increment of KQ decreases with the decrease of cavitation number and that K7 decreases

in oblique flow in contrast with non-cavitating condition.

As an application of these investigations, the trial data of some high-speed crafts were analyzed based on the propeller characteristics which were estimated for the oblique flow conditions using the present method. The model-ship cor-relations seem to be improved to some extent by such

treat-ment.

6. Acknowledgements

This investigation has been carried out under the sponsor-ship of the Office of Naval Research, Department of the

Navy, Contract No. Nonr 5002)00).

The authors wish to express their gratitude to all the members of Mitsubishi Experimental Tank (Nagasaki) who cooperated in carrying out this investigation.

References

R. Yamazaki: On the Theory of Screw Propellers in Non-Uniform

Flows, Memoirs of the Faculty of Engineering, Kyushu University, XXV, 2, (1966)

K. Taniguchi and K. Watanabe: An Experimental Study on Propeller Characteristics in Oblique Flow, Journal of Seibu Zosen

Kyokai, 8, (Aug. 1951)

F. Gutsche: Untersuchung von Schiffschrauben in schräger

Anströmung, Schiffbauforschung, 3, (3/4/1961

K. Taniguchi and N. Chiba: Investigation into the Propeller Cavitation in Oblique Flow (ist report), Mitsubishi Experimental

Tank, Report 1800, May 1964)

K. Taniguchi, H. Tanibayashi and N. Chiba: Investigation into

the Propeller Cavitation in Oblique Flow 2nd report Mitsu-bishi Experimental Tank, Rep3rt 2221, (May 1966)

Appendix

MIB 010045 MARCH 1967

Referring to (A. 2), we can write

KQ(J0, 0)=KQO+[--- 1°j0+ OO(J/O7 r)2]02 -.. (A.4)

Similar discussion holds also for K7', and

K7'(J0, 0) = K70+ [- - aK.0+ ---U0/0.7 7)2102 -- - (A. 5)

List of Symbols

Ag/Ad Expanded area ratio

A, B Coefficient of increment of thrust coefficient and

torque coefficient

b= B051,/Brai

C07 Chord length at 0.7 R

D Diameter of propeller dT, dQ Thrust and torque element

J

Advance coefficient

k07 Reduced frequency at 0.7 R

K7 Thrust coefficient in the direction of general flow K7' Thrust coefficient in the direction of propeller axis

KQ Torque coefficient

n Number of revolution of propeller

(9)

8

p Density of fluid

pse

_{Cavitation number based on the rotational}

p(nD)2

speed of propeller

Angular position of blade (QO at the top)

Thrust distribution function Torque distribution function

w Frequency of oscillation of the velocity relative to

propeller

u (Subscript refers to the quantities in axial flow condition. o (Superscript refers

to the quantities as measured in

cavitation tunnel in oblique flow condition.

* refers to the open-water propeller characteristics.

Reprntin or reproduction without written permission prohibited.

We would appreciate receiving technicol literature published by you.

An/n Correction factor for the rotational wake of the

upstream shaft

p Pitch ratio of propeller

Q Torque

R Radius of propeller

T Thrust in the direction of general flow T, Thrust in the direction of propeller axis

u Circumferential velocity relative to propeller blade

without induced velocity

V Resultant inflow velocity to propeller V Advance speed of propeller

X Non-dimensional radius of propeller z Number of blades

Hydrodynamic pitch angle without the correction

for the induced velocity