Theoretical Analysis on HydrodynamicPerformance of Troost-Series Marine Propeller

著者 Sheng Huang, Himeno Yoji, Tanaka Norio引用 Bulletin of University of Osaka Prefecture.

Series A, Engineering and natural sciences.1982, 31(1), p.85-93

URL http://doi.org/10.24729/00008613

85

Theoretical Analysis on Hydrodynamic Performance

of Troost-Series Marine Propeller

Sheng HuANG," Yoji HIMENo,"" and Norio TANAKA**

(R.eceived May 2i, l982)

A theoretical analysis using a lifting surface theory is made for predicting the

hydrodynamic performaRce of the Troost-series propeller in open-water condition.

After the discussions on the empirical coeMcients for the lift-slope modification and

the drag coethcient due to fluid viscosity, and the optimum coilogation-point number,

the numerical comptitations by Sugai's method are carried out for the Troost and

MAU-type single-screw marine propellers.

The results of the calculation show similar tendency to the experimental values in

the case of Troost-type propeller, although suMcient numerical agreement is not

achieved. In the case of MAU-type propeller, however, Sugai's method is found to give

a good prediction for the practical design of the propeller performance.

It is also found from the calculation of the pressure and Iift distributions as well

as the open-water characteristics that the MAU-type propeller has generally better

perfbrmances than the Troost type.

1. Introduction

According to the recent change of marchant ship form, the propeller geometry

has been changed from the usual data basis. The propeller design condition has

also varied and sometimes gone out beyond the applicability limit of the usual series-

propeller design method. Computational methods in Japan, on the other hand,

have recenly reached the level of practical use fbr the design and the perfbrmance

prediction of marine propellers.

Among those theoretical methods, Sugai's one') is known as one of the most

reliable methods for the analysis of the propeller open-water performance using

lifting surface theory. It gives good predictions for the AU and MAU-type pro-

pellers in the normal range of design condition and load factor.

However, even in the lifting surface theory, some simplifications and empirical

modifications have to be made so that it is necessary to examine the applicability of

the theory to the wide range of cases. Sugai's method has so far been applied only

to the AU and MAU series developed by the Ship Research Institute, Japan.

Therefore it seems worth-while to apply the method to the Troost-series propeller

which is widely used in the world. The present report thus concerns with the analysis

of the Troost-series propeller as well as the MAU series. Discussions on the em-

pirical coeMcients of the viscous modification will also be made in the fbllowing

chapters.

' Research Student, Department of Naval Architecture, College of Engineering (Visting

from The Department of Naval Architecture, Harbin Institute of Shipbuilding, People's

Repubiic of China).

** Department of Naval Architecture, Collego of Engineering.

86 Sheng HuANG, Yoji HiMENo and Norio TANAKA

2. BasicEquations

Following Sugai's lifting surface theory,2' the integral equation for determining

the distribution of the circulatign density g over the propeller surface is written in

terms ofa spiral coordinate system (C, e) as in the form,

u(c, e) -f.O J;.JL,o-(e")g(c*, e*)k(e,; ,et, ,et')d(:*de* (i)

where the kernel function k takes the forms.

K(e,; pt, k')=".S,if:, ["pt'+cos(eft;2nM/N.)

' - R3, {pte"-pt' sin (e"+2rrMINp)} {pt'e"-" sin (e"+'2nMIN.)}de" (2)

' ' R2 == e"2+pt2+pt'2-2ptpt' cos (e"+2nM/Np) (3) 'In Eqs. (1) to (3), C and e are the axes in the directions of the chord and the radius

for a single propeller blade. The term u in the left-hand side of Eq. (1) represents

the down-wash velocity and the phase angle e is subjected to the cylindrical co-

ordinates of the propeller race, so that a"=e'-e and e'=(er-eL)/2, where the

suMces T and L stand for the trailing edge and the leading edge of the propeller

blade. The term pt is defined as "== rlh, where r and h represent the radial coordinate

and the hydrodynamic pitch ratio, respectively. The superscripts ""' and "'"

correspond respectively to the geometric spiral surface and the hydrodynamic pitch

surface of the propeller blade.

The boundary condition for Eq. (1) is to prescribe the down-wash velocity u on

the propeller surface, which implies the unknown variable of the circulation density

g so that the equation system becomes essentially nonlinear.

3. SolutionProcedure

To solve the basic equations it is necessary to introduce several assumptions,

singularity analyses and numerical techniques. To begin with, the functional

representation for the nondimensional circulation density g(C, e) (== r(C, 6)IV) is

assumed to be a Birnbaum series satisfying the Kutta condition at the trailing edge,

' ' g(e, c)==ao cot -S-+.M2ia.(q) sip mq - (4)

'where ' e=-lt(i+eB)--lir(i-eB) cos sb ' (s)

Substituting this into the basic equation, Eq. (1), we obtain,

7;beoretical Analysis on Ilydrodynamic Pei:formanee of 7}toost-Series Mbrine Propeller 87

"(q" sP) :2.,,,,(ii･-g.) JiJ,n e'(¢') Ia,(ip') cot -{zl ,

+/S..la.(ipt) sin mq'l x K(qo(c; .¢,, ipQ'2 /r.n,ipi,lln Q' detdQ, (7)

where the kernel function k is defined as the regular part of the original kernel form

K to avoid the dipole singularity. Eq. (7) can be reduced to a set,of simultaneous

equations for the unknowns ao(gb) and a.(ip) at a certain radial station by prescribing

collocation points on the propeller blade surface. The optimum number of thecollocation point is determined by numerical test.

The other assumption is ,to introduce the lift-slope modification coeMcient CK

and the viscous drag coeMcient CDv of a blade section in order to represent the viscous

effect. Three methods of obtaining these values are employed here. Method 1 is

to use the fbrmulaS)

C.=;O, (O.1094.70t/c) ' (8)

where the term t/c is the thickness-chord ratio. The formula for Method 2 is written

as the form,4)

90 C. ' CK= z2 '"a-a,n (9) ' ' 'where ao represents zero-lift angle, and CL the lift coeMcient which is obtained from

,the data diagram for various airfoil sections. Method 3 is to use the experimental data

of NACA airfoil sections.5'･6' The drag coeMcient CDv is also expressed in the

fbrm,

C..=O.O056+O.Ol tlc+O.1 (tlc)2

+&+lkrh(C.-C,,)2 (10)where the constants Kh and Kli can be determined by use of these three methods,

O.8

O.7

O.6

O.5

O.4

O.3

O.2

O.1

o

MAU-455

(H/D==･1.0)

EXPERIMENTS------- , METHOD l- -- -- METHOD 2.--･ ---･--- METHOD 3

i2S

r,t;.

no

E v7pt7

× NNS.x NNN sN NN).. Xts Nts N ts ts

oFig. 1'

O.2 O.4 O.6 O.8 1.0 1.2Open-water performances of MAU-455.

88 Sheng HuANq Yoji HiMENo and Norio TANAKA

Method 1 to Method 3, correspondingly.

Method 3 coincides essentially with Sugai's method. Figs. 1 to 3 Show the

results of the calculation using these three methods applied to the MAU and Troost-

type propellers. For the MAU propeller, Method 2 and 3 agree well with each

other and with the experiment, while for the Troost propeller Method 1 seems better

TROOST B-33s. EXPERIMENTS --- METHOD1 (HID-l.O) ----b-METHOD2

O.8 ,.y-e'-- o.7 .f.>C'iij,{

O.6 t o.s i9tfs

o.4 yel

O.3 . -"s x :'.l ":":$i'--'--:llirlll'sNN.';.:.:s..,.

N. ON O O.2 O.4 O.6 O.8 1.0 1.2 Fig. 2 Open-water performances of Troost B-335.

O.4

r/VO.3

O.2

O.1

o

O.4

O.3

O.2

O.1

o O.4

O.3

O.2

O.I

o O.2

O.1

o

Fig. 3

MAU-455 HID=1.0 J=O.7

V////;'l:,},'k':s'･t",.

x

NZf,tt:".""kl3}Kpt

METHOD l---- METHOD 2

- -METHOD3 ×

x. pt.,x ../"xegx X. RIRo=:O.3oo1 'N`.. N

･ts

NN

-ei.F.Nts.=ts x RIR,=O.1940 -O O.2 O.4 O.6 O.8 l.O

Circulation density disuibution of MAU-455.

77ieoretieal Analysis on H),ch'odynamic Pet:fo rmanee of 77'oost-Series Marine Propeller 89

Table 1 Numerical check of open-water performanoe

MAU 455 HID =1.0 J== O.7'

NxM11 ×7

l3×9

KT

O.1267

O.1245

KQ

O.O179

O.O176

Vo

O.7886

O.7877

1.6

r/V

1.2

O.8

O.4

,o

-O.4

-O.8

N

x N N N N N N N N N N

TROOST B-455 HID=l.O J-O.7

M×N= 13×9.---- M×N==11×7

--N ./ xr..."t

N N s l , t' t

O.2 O.4 O.6 o.8 X

l

1

l

'

Numerical check of circulation

density.

O.8

O.4Cp o

-O.4

-O.8

-1.0

ss

M×N=13×9MxN==11×7

-- n

O.2

d

O.4

htt

O.6

-d.-..-.-V

o.

'

t-.

TROOST B-455

/ NN

1 l t , l

Fig. 5 Numerical check of pressure

distribution.

Fig. 4

'

than others. For the local quantities, like the circulation density and the pressure

distribution, the agreement among those methods seems good in general. Considering

these features the calculations will hereafter be carried out using Method 2 for the

MAU propeller and Method 3 fbr the Troost.

The optimum number of the collocation point is also examined for the Troost

propeller. Figs. 4 and 5 and Table 1 show that 11 radial points and 7 chord points

are enough fbr the calculation of the open-water characteristics and the local quantity

distribution.

4. Result of Calculation and Discussions

The results of the calculation of the propeller open-water characteristics for the

MAU and Troost series are shown in Figs. 6 and 7. For the MAU propeller, the

calculated thrust coeMcient K) value is in close agreement with the experiment,7'

and the torque coeMcient Kb and the eMciency v show only small discrepancy within

a few percent. For the Troost propeller,8' on the other hand, Kin and Kl? become

lower than the experimental values, so that the eMciency calculated is higher in about

10 percent, though the tendency of the performance curve agrees with the experiment.

It is thus found that Sugai's method is not applicable directly to the propeller

90 Sheng HuANG, Yoji HiMENo and Norio TANAKA

O.8

O.6

O.4

O.2

o

MAN--455 EXP.---- CAL.

iQS

s L

<kli;

n- L z-Z --z NNN

i2f5

.g Q6 O.6

'ti

M

!･o lo

% N ul9

1."

Vo

O.2 O.4 O.6 O.8 1.0 1.2 l.4 1.6Open-water performances of MAU-455 series.

o

Fig. 6

TROOST , B-335 EXP.- - CAL.

O.9

O.8

O.7

O.6

O.5

O.4 .

0.3

O.2

O.I

o

!.o- ..1..-7.'Oft t}ZD.,2 ....i.g.'"S'.l2t'-'

,, 1i2tte

Lo4 4ki 1 o.

'-N-NN

Ns.""'NN$NN

N'N

-`

:.N..t...$".'`

q.....

:l.NNN

oFig. 7

O.2 O.4 O.6 O.8 1.0 ･1.2 1.4Open-water performanoes of Troost 3-blade series.

performance design for the Troost series even after the modifications of the empirical

coeMcients concerning viscous eflect.

However, the results of the local quantity distribution as shown in Figs. 8 to

13 seem quite useful when we consider the propeller performance in detail. The

comparison of the results between the MAU and Troost series through the figures

leads to the fo11owing discussipns.

The lift distribution of the MAU propeller seems fiat and close to the elliptic

distribution compared to the Troost propeller as shown in Figs. 8 and 9. A sort

of hollow is recognized at 60% chord in the circulation density distribution of the

Troost type, which makes the pressure distribution worse than the MAU type in

Figs. 10 and 11. Figure 12 shows that the circulation G per unit spanwise length

increases with the propeller load as well as the pitch ratio. The mean hydrodynamic

camber line in Fig. 13 also increases with the propeller load. It is realized that for

T;heoretical Analysis on H>,cb'odynamic Pet:rbrman'ce of' 7>'oost-Series Marine Propeller 91

r!V

O.4

O.2

o

O.2

o

O.4

O.2

oO.4

O.2

o

O.2

o

HtD=. t.O J=O,9'

RIRo=O.8799

RIRo=O,6961

RIRo=O,4839

RIRo#O.3ool

RtRo=O.1940

O.4

O.2

oO.4

O.2

oO,6

O.4

O.2

oO.4

O.2

oO.4

O.2

o

HID-l.OJ,.-O.7

RtRo==-,-O.8799

RIRo=O,6961

R/Rot-O.4839

R/Ro==O,3co1

RIR,=O,1940

Circulation density distributions

of MAU-455.

rlV

O.8

O.6

O.4

O.2

o

O.6

O.4

O.2

o

O.4

O.2

o-O.2 O.2

o

Fig. 8

HID==1.0J==O.9 HID==l,OJ=O.7

RIRo=O;7918

RIR,=O.583S

R/Ro=O,7918

1.0

O.8

O.6

O.4

e.2

oO.6O.4O.2oO.4O.2o

RIRe#O,5835

RIR,=:=O.2890

RIRo==O,18t2

O.4

O.2

o

RfRo=O.2890

RIRo==O,l812

Fig. 9 Circulation density distributions

of Troost B-455.

qO.4

o-O.4

O.4

o-O.4

O.4

o-O.4

O.4

o

-O.4

HID=1.0J=e:7

FACE･----- BACK

RIRo==O.8799

--.tsx-.f---'

RIRe==O.6961'

.-N.....J-

RIR,==O.3850

tltt

tslNJR/Ro=O.1940

sttzN/Nt~--t

O.4

o

-O.4

O.4

o

-O.4

O.4

o

-O.4 O.4

o-O.4

H/D= 1.0 J=O.9

FACE----- BACK

R/Ro=O.8799

N---.----

RtRo=O.6961

N ..,t -b-..-..

R/Ro =O.3850 -

s

Nt-NNtt'--

RIRe==O.1940

-NtN/ v-17

Cp

O.4

o

-O.4

O.4

o-O.4

O.4

o-O.4

O.4

o-O.4

HID=l.oJz:o.7

RIR,=:O.8,780

'1rN.-v.-vltRfRo=O.6913I

lt

r-J!S.-/it

S<R/Ro=O.37531t

'tt-'t-t-t/tR/Re==O.18l2

i/tN-x--

O.4

o

-O.4

O.4

o-O.4

O.4

o-O.4

O.4

o-;O.4

H/D= 1 .0 J=O.9

'RIRo=-O.87so

t

[yt'`×--..-.vl

RIRo=O.6913

vt-~----N-1'

''

R!Ro=O,3753 /

x

N -t×..-t

-

R/Re:±O.1812 /

N

N--''

''

Fig. 10 Pressure distributions of

MAU-455.

Fig. 11 Pressure distributions of Troost

B-455.

the MAU type the hydrodynamic attack angle becomes nearly zero at the design

condition and then the lift is created almost only by camber, while for the Troost type

the'lift depends much on attack angle.

Figure 14 shows a comparison of the geometry between the MAU and Troost

G

92 Sheng HuANG, Yoji HiMENo and Norio TANAKA

MAU--455(HID=1.0) TROOSTB-455(H/D=t.O) TROOSTB-335(J=O.7)

J= 9/;-5.-･s..

i'i,,if.il;t:{,z"5N,i

J=O.5o.os/"x

O,ou

,,

H/D=1.2

.06-･.'xZN.!' H/D==i.oN

O.04!.--.XN x'N.!///o.o2/.ll/H/D=O.sxNht'

o O.2O.4O.6O.81.0O.2O.4O.6O.81.0O.2O.4O.6O.81.RfRo

Fig. 12 Circulation distributions along radial Iine.

o.ou

o

-o.ou

o.ou

o-o.ou

o.pa

o

-o.ou

o.ou

o-o.ou

J==O.9MAU-455-J==O.7

(H/D=l.O)----J==O.5

'---'-'---.----- N--..--..N..-..RIRe=O.6961

----.-.--..---s.

N.NNN.

N.N.Nt

RIRo=O.4839

t------.--'N's.N.N x

N.N.N,RIRo==O.3oo1

------.--..s-...

N.-h.-..

R/Re=O.1940

JiO,9TROOSTB-455-----J=O.7

(H/D-=1,O)---･-J=O,5

'xN---..×.'-NsN

~.NNXN'N'xN'XN

R/Re=6.6913XN-N

X,ksxx.×N.×XN,N

xNN-×R/Re='O.4757×･

xr"'･･-s.x.×x.×NN'N.N

XJN.x.R/Ro==O.2890X.

-----N.-..s-N.--.--..

N,R/Ro=O.1812N,

TROOST PROPELLER

MAU PROPELLER

777 O.7R

-- ttt------

O.2 R

L.E.

Fig. 13

T.E.

Hydrodynamic camber line.

Fig. 14 Comparison of blade sections.

types. The Troost propeller has a wash-back at trailing edge from the boss to the

O.65 R radius and a larger wash-back at the leading edge than the MAU type. The

nose radius and the leading-edge wash-back of the MAU type is designed to satisfy

the shock free condition. The position of the maximum thickness lies at the 35%

7;rieoretieal Analysis on Hydeoclynamic Pei:formance qf' 77oost-Series Mbrine Propeller 93

chord length for the Troost,

fications fbr the MAU type

cavitation.

while

have

30% fbr MAU. It can be said that these modi-

led to the improved performance on propleler

5. Conclusions

Through the present analysis of the open-water perfbrmance of the two marine-

propeller types, using Sugai's method, the following conclusions can be made.

i) Although satisfactory numerical agreements between the calculation and

the experiment are not obtained for the Troost-type propeller, the calculation gives

at least similar tendency to the experiment, so that it can be used for improving the

performance of an original propeller or for developing a new propeller series.

ii) For the MAU propeller, the lift-slope modification coeMcient CK and the

viscous drag coeMcient CDv can be obtained by Method 2 in the present analysis.

For the Troost propeller, those values obtained by' Method 1 give better results.

iii) The optimum number of the collocation point is examined and confirmed

to be 7 for the chord Iength and 1 1 radially for the Troost type as it is for the MAU

type.

iv) Summing up, the MAU type has better perfbrmances of propeller load and

cavitation than the Troost type.

Closing the present report, the authors express their appreciation to Dr. Sugai

at Ship Research Inst., Japan for offering his original computer program, which has

been revised and modified to an appropriate form by the authors. The computer

system ACOS-7oo at the University of Osaka Prefecture has been used fbr the

computatlon.

References

1) K. Sugai, Proc. 2nd Symposium on Marine Propellers, Soc. Naval Architects of Japan (1971)

(in Japanese)

2) K. Sugai, Jour. Soc. Naval Arghitects of Japan, Vol. 128 (1971) (in Japanese)

3) The Kansai Soc. Naval Architects, Japan, Shipbuilding Design Handbook (1976) (in Japanese)

4) Zh. B. Sheng, Propulsion of Ships, Bekin, China (1962) (in Chinese)

5) F. W. Riegels, Aerofoil Sections, Butterworth (1961)

6) I. H. Abbot and A. E. van Doenhoff; Theory of'Wing Sections, McGrawhill (1949)

7) K. Yokoo and A. Yazaki, Marine Propeller Design Method for Medium and Small Vessels

and Design Diagrams, Seizan Shodo Book Inc. (1963) (jn Japanese)

8) W. P. A. van Lammeren, L. Troost, and J. G. Koning, Resistance and Steering of Ships

(1948)