Cavitation tests on Hydrofoil of Simple Form Report 5: On four profiles of 11,7 percent thickness ratio

(1)

C:

Lflvr3ity

o TchflCIOY

Li

as Laboratori

LiLir'ry

Mekeweg 2 - 2628

CD Deift

The Netherlands

Phone: 31 15 7B673 - Fax 31 15 781836

Cavitation Tests on Hydrofoil of Simple Form/Report 5

(On Four Profiles of 11.7 Per Cent Thickness Ratio) i

F. NUMACH1, K. TSUNODA1 and

I. CHIDA4

Synopsis

Forty hydrofoil profiles to be used for blade elements

of

ship propellers,

axial-flow turbines and pumps were deviced and all simplified in form with a view to

facilitating their machining.

The series

of

cavitation tests have been carried out

on these hydrofoils.

The present paper forms the first report of the tests on the

hydrofoil profiles

of

thickness ratio 11.7 per cent among them.

1.

Introduction

The present report concerns a series of experiments (1] intended to provide

informational material for reference in the design of axial flow turbines and pumps

and ship propellors, by searching for blade element profiles that combine simplicity

in form with high performance under cavitation.

This time four forms with a

common thickness ratio of 11.7 per cent were taken up, some of which have proved

to be very satisfactory.

2.

Experimental Method and Test Specimens

The experimental method has already been fully reported (2j, and will not

be repeated here.

The profiles of the simple forms shown in Fig. 1,

i. e.,

011.7,

O7 and O.7 were developed.

The aerofoil profile

A11.7 was taken up for the

purpose of comparison.

The reason for adopting 11.7 per cent as the thickness

Report No. 85 (in European language) of the Institute of High Speed Mechanics,

TOhoku University.

Read at the Meeting in Sendai District of the Japan Society of

Mechanical Engineers, on December 10th, 1947.

Professor of Faculty of Engineering, concurrently Director of the Institute of High

Speed Mechanics, Trhoku University.

Technical Official of the Institute.

Assistant of the same.

(2)

the original Clark Y profile on which

_-many wind tunnel and other experi-

_0/1,7

ments have been carried out in the

past 3], the results of which could

use-o

/

fully be compared with the present

data.

The 011.7 was given the form of

a simple ogival form, the same form

$;' °

with wash-back on the leading edge

2 being the

while the

is

a

version incorporating a similar wash-

Fig. 1. Specimen Profiles

e

back but composed of two arcs

of

different diameter joined to bring the point of maximum thickness to the position

40 per cent of the chord. The A11.7 is an aerofoil resembling the Clark Y and

taken up with the view to its comparison with the simple forms. The procedures

for drawing these outlines and pertinent dimensions are given in Tables i and

2.

_{The test specimens were produced with chord and width both of 70 mm.}

Table 1.

Dimensional Proportions for Drawing Profiles

with Annexed Key Diagramme

Trailing Edge

Leading Edge

Profile

L

t

n

R1 R R3 W1 w ¡ t1 t,, 100 11.70

50.00 112.69 R1=

O O O O 70 8.19 35.00

78.88 R1=

0 0 0 o 0117 100 11.70 50.00 151.57 115.29 108.86 3.06 2.14 0.145 25.00 0.29 0.29 70 8.19 35.00 106.10 80.70 76.20 0.1 17.5 0.2 0.2

07

100 11.70 40.00 98.21 157.71 108.86 3.06 2.14 0.145 25.00 0.29 0.29 70 8.19 28.00 68.75 110.40 76.20 0.1 17.5 0.2 0.2

(3)

F. NUMACHI, K. TSUNODA and I. CHIDA: Cavitation Tests on Hydrofoils / 5

73 Table 2.

Dimensional Proportions of Profiles

3.

Results

3.1 Mode of Cavitation Occurrence.

The cavitation observed to occur on the profiles in question was in zones

I,

II and III (indicated in Figs. 2-4) only; zone IV (pressure side toward trailing

edge) was free of cavitation at all times.

In the case of O.7 a zone on the

pressure side a small distance behind the leading edge (indicated in Fig. 4) was

found to be susceptible to cavitation at very small values (0.25-0.19) of cavitation

coefficient kd when the incident angle was i -

2 deg.

This cavitation had the

peculiar form of having its head portion constituted of a series of closely packed

rows of thread-like lines, merging toward the tail into one body and thus ending

in a cavitation of orthodox form. The region of this form of cavitation was

desig-nated Zone V.

The cause of its occurrence might be the shape of the profile, which

has its point of maximum thickness occurring 40 per cent from the head (See

Figs. 2-5 illustrating the modes of cavitation observed).

3.2 Variation in Lift and Drag.

The variation in lift and drag coefficients (Ca and Ca,) according to cavitation

coefficient k

is shown in Figs. 6-9. It is seen that except for the A11.7, a point

of maximum lift coefficient in respect of kd occurs with large incident angles.

The variation in drag plotted against cavitation coefficient is shown in Figs.

10-13.

Profile

Profile O

Profile A117

X

Y0

IÇ

X

Y0 Y,,

X

Y0

Y,

X

Y0 Y, O 0 0 0 2.69 2.69 7.14 3.23 0.00 7.14 5.50 1.48 5.71 5.53 1.72 5.0 6.81 0.76 21.43 8.02 0.00 14.29 7.43 0.53 11.43 7.46 0.85 10.0 8.69 0.33 35.71 10.79 0.00 25.00 9.62 0.00 25.00 10.55 0.00 15.0 10.00 0.14 50.00 11.70 0.00 35.71 11.02 0.00 40.00 11.70 0.00 20.0 10.89 0.06 64.29 10.79 0.00 50.00 11.70 0.00 50.00 11.39 0.00 26.5 11.54 0.00 78.57 8.02 0.00 64.29 10.81 0.00 54.29 11.07 0.00 33.0 11.70 0.00 92.86 3.23 0.00 78.57 8.10 0.00 68.57 9.18 0.00 41.5 11.41

000

100.00 92.86 3.43 0.00 82.86 5.98 0.00 50.0 10.74 0.00 100.00 100.00 62.5 8.84 0.00 75.0 6.36 0.00 87.5 3.39 0.00 100.0

(4)

- ff-1Z8,98 - 'A 41° _'..1=188% A).

t',

o

0r

ir-

/ _/ /80%

III,

oa-4

410 88% /96124/888/o2?,48 f Prof//e O/I/i Profile O/,7

tf5-22.9°C R(865-8?)-h2''

/28

Fig. 2.

Position of Cavitation Head (X0) and Tail (X) of Incipient Cavitation

in Relation to Incidence Angle a; Value of kd at which Incipient

Cavitation Occurs, as well as Values of X/l for Growing Cavitation;

Ranges of Erosion and Vibration Danger

(Profile

tzo/93 2Z6°C

R

(?5985)/86

I-loro

Zflt/fli2'flce Zoc«u/?ffce

8g'rsi68ocAi'/e

of (Awt. I-Zone Cay/f.

k\\\

-

t'

i of Inc/fi/ence

V'

of I-lone Ca'8

P41U

i =1«8Z /28 /88 8068 98 28

/8

5

A

I

\,'

/ Zfiknce Paigeì' ûowgnr Beg/nnÑlf of I-Zone of Erosion of fi-osiro of.5Wrng Cowl on on

iR

Ioc/pi?nce of

___

I-Za',e

4rgt,û

Back foce .7o' 511e

J

t

/88%= \128 -Il' i ll -Zone _k» fi ___

\

-

.

o 410

'°' 80% /ì5

1,5 A-d

Fig. 3.

Ditto with Fig. 2

(Profile

28 10 5% 1-o ltd 1-f Z-Zo7e 40 6.0 41° 20 o,,

(5)

Ao

I-F. NUMACHI, K. TSUNODA and I. CHIDA:

Cavitation Tests on Hydrofoils / 5

75

o

I

1-Zilne

V-il-Zone

I / Ao

_'iI

M-Zone

U.U.

UU

t-128

'

NUN

N

60«0

'S,,'

-

-8%-'

'\

-

V-Zone

I

w1F-90 7,780% 1888060,9O,28,/8,5% 8,5 41° -2° A

i

Y

¡áo-198 /28 90 r-_-lJl-Z,ne a

Profile

0/17 /9,5-22, ?°C

(45? tOI) -/0

u

Profile

4,47

Fig. 4.

Ditto with Fig. 2

(Profile

O.7)

-S

7,

'98

88% /2?

45 Fig. 5.

Ditto with Fig. 2

to

(Profile AIL7)

t5

t'19,52/J°C

R«0,54'/,810/8'

-5-U iîoyao

100 80 60

20 /0

-"

:L-ç__.v. ,

,, -

-- -

'

-Iiìc/,wence uf I-Zone ¿zv/f.

- __I

Ix_, //

\/

-,

II%1UN //

, Jiitofiionce uf /ffZone of Ñwn'n o/i bzo{ Ie

zlznger of &usl'n on &e Sine

A -

Begineinç of 5fning Vi0ruf'on

4P

'6'YPAf'(4

/8

l'o

tif

Ii7c,ìlk'pce ¿of if-Zone ¿'wf

20

(6)

4f

û

0,5

Fig. 7.

Ditto with Fig. 6

(Profile O].7)

Fig. 6. Variation of Lift Coefficient Ca for Various Incidence Angle

a

with Changing Values of Cavitation Coefficient k

(Profile 011.7)

.Ca

.,

__

_____

p

_

I ,9'a'/i/e I I

0,.

t19,3-2I,6'C

R4f«-ûf)/ü

C

a.

M

r

M_l

___

--..1JJi

J)!

"e

'j

2,0 2,5

ai-

1,5 _2,5

(7)

F. NUMACHI, K. TsUNODA and I. CHIDA: Cavitation Tests on Hydrofoils / 5

77 0,5 o 1,0 0,5 o

Fig. 8.

Ditto with Fig. 6

(Profile O.7)

flr/e

t

1f-27,9'C

RIa5'/a8)/û6

41 vii-=---

:_____

/ "ft

-F,

ïiiuÏìrilil__Ï

_{:ItUUUlUUUUUUNU.}

18//e

R(4Ç'/8Ç)/0'

Ìf,5-21,ó

A,i

p

'C

c

a

5/roe V

g /

/27

/

/í;.g=

Irn-,/eonce of I-Zone Cavil

Inci:nience of I-Zone ('awl

ltd

¿0

1,5 2,0 2,5

Fig. 9.

Ditto with Fig. 6

(Profile A11.7)

(8)

8

o

,9'a/,!e

O,'i

Fig. 10.

Variation of Drag Coefficient C for Various Incidence Angel

a,

with Changing Values of Cavitation Coefficient k

(Profile

011.7)

,Praf,/c û,

'8f-1o5)/8'

/5-22,«'C

ì?= (45887)i86

Fig. 11.

Ditto with Fig. 10

(Profile

-0-W 1ncoieoce at 1-Zafte

¡

ûìvif 1140/OnÇt o

f J-Z

Oat C

f-Inc/at,7oc of E-Zoe Puait

liii

I IC

-: 3 7

ç

-3' w SIv9 ¿4Ora»ao

-

-0-\

_'.

--1100't

---

u

of

uiIÏu

u uuu /:

-

lu

85 ¿8 ¿5 ¿O

¿5

85

¿0

¿5 28 408 808 804' 808 406

(9)

F. NUMACHI, K. TSUNODA and I. CHIDA

Cavitation Tests on Hydrofoils / 5

79

2

/3w/i/e 0,,q

tM5-Z29'C

A' (419-.88) /86

Fig. 12.

Ditto with Fig. 10

(Profile O7)

Fig. 13.

Ditto with Fig. 10

(Profile A117)

3.3 Performance Curves.

The Ca-x and Crn-a curves representing performance has been omitted. The

numerical data are found in Table 3-6.

3.4 Comparison of the Four Profiles.

(1) The polar diagrammes: are represented in comparison to each other in

Figs. 14-18.

As already stated the comparative merits of the profiles differ

ac-cording to the qualities demanded of them, but in view of the fact that the present

-ç

w

i

!-Zone

uuiu..uu

UIi

UNU

-

a

1ULIU UU

fi-Z

-fi7C«oce of/I-boo ûZ&/

k.d

U

Boflooìng of 5/roog ,8r2//8o,. /1w/i/e

E=/45-2Z5'C

A11,7 (454L.../49)./g6

,--/

-2' 41'

3'

t

Ø-Za'e

-.,

--_

VISUUL

-.-

s

--

_{_}

p1.-.

¡íìc,o!eocc f-/Ieeeof(iovit Iûci«icûce;f I 8-Zoco /Iovi/

-Id

45

20

25 15 2O

¿1

488 486 48« 402

û

4/8 488 aDs 1,82 o

(10)

0.25 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0

_30

Ca = -0.100

-0.110

-0.130

0.030 0.240 0.312 0.336 0.345 0.347 0.347 0.347 0.347 0.340 0.340

C=

0.0425 0.0545 0.0683 0.0505 0.0355 0.0265 0.0245 0.0245 0.0245 0,0250 0.0255 0.0260 0.0265 0.0270

- 2°

-0.100

-0.110

-0.130

0.080 0.313 0.405 0.422 0.430 0.430 0.433 0.433 0.433 0.433 0.433 0.0425 0.0535 0.0593 0.0480 0.0350 0.0220 0.0210 0.0210 0.0210 0.0215 0.0220 0.0220 0.0225 0.0230

-1"

-0.090

0.0425

-0.098

0.0505

-0.110

0.0505 0.200 0.0440 0.384 0.0340 0.495 0.0220 0.523 0.0195 0.523 0.0185 0.523 0.0185 0.523 0.0195 0.523 0.0200 0.523 0.0200 0.523 0.0200 0.523 0.0202 0°

-0.073

-0.090

-0.015

0.240 0.423 0.560 0.610 0.612 0.612 0.612 0.612 0.612 0.612 0.612 0.0420 0.0450 0.0460 0.0460 0.0350 0.0210 0.0185 0.0180 0.0180 0.0175 0.0183 0.0185 0.0192 0.0200 1°

-0.072

-0.090

0.075 0.280 0.428 0.570 0.672 0.700 0.703 0.708 0.718 0.725 0.730 0.730 0.0365 0.0375 0.0425 0.0455 0.0385 0.0225 0.0180 0.0175 0.0175 0.0170 0.0175 0.0178 0.0182 0.0187 20

-0.040

0.003 0.165 0.335 0.455 0.615 0.712 0.735 0.735 0.740 0.753 0.753 0.762 0.765 0.0333 0.0380 0.0435 0.0460 0.0425 0.0280 0.0195 0.0185 0.0190 0.0185 0.0190 0.0195 0.0195 0.0215 3°

-0.010

0.095 0.237 0.380 0.515 0.640 0.738 0.755 0.750 0.750 0.750 0.755 0.767 0.770 0.0330 0.0405 0.0470 0.0495 0.0475 0.0375 0.0240 0.0225 0.0225 0.0225 0.0235 0.0240 0.0245 0.0255 4° 0.060 0.135 0.276 0.405 0.537 0.657 0.755 0.790 0.798 0,785 0.785 0.785 0.790 0.790 0.0350 0.0430 0.0510 0.0545 0.0545 0.0500 0.0365 0.0325 0.0270 0.0270 0.0270 0.0275 0.0275 0.0285 5° 0.115 0.0390 0.173 0.0455 0.300 0.0550 0.423 0.0595 0.547 0.0630 0.670 0.0630 0.765 0,0560 0.825 0.0530 0.877 0.0320 0.830 0.0295 0.830 0.0297 0.830 0.0300 0.830 0.0300 0.827 0.0300 6° 0.168 0.217 0.315 0.435 0,550 0.680 0.770 0.847 0.925 0.863 0.863 0.863 0.863 0.853 0.0445 0.0480 0.0590 0.0660 0.0725 0.0755 0.0785 0.0880 0.0365 0.0325 0.0325 0.0325 0.0325 0.0310

Table 3.

Variation with Cavitation Coefficient ka of Lift and Drag Coefficients C and

C (Profile 0,7)

Water temperature t11,=(19,5-22.4) deg. C,

Degree of air content a/a8=1.02,

Reynolds number R= (5.4-. 1O.7)1O,

¿

(11)

'['able 4.

Variation with Cavitation Coefficient ka of Lift and Drag Coefficients Ga and C10 (Profile O(,7)

Water temperature tm=(19.3'21.6) deg. C,

Degree of air content a/a0= 1.02,

Reynolds number R=(5.4-10.5)105,

= Incidence angle

Ö (D

o

p

n

0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.5 _30 Ca

-0.060 -0.070 -0.085

0.035 0.240 0.350 0.365 0.365 0.365 0.365 0.365 0.370 0,370 0.370 0.370 0.370 Cw=

0.0410 0.0425 0.0440 0.0235 0.0175 0.0140 0.0127 0.0125 0.0125 0.0125 0.0127 0.0127 0.0127 0.0127 0.0130

-0.057 -0.065 -0.075

0.145 0.315 0.410 0.425 0.435 0.435 0.435 0.440 0.440 0.440 0.445 0.445 0.445

- 2°

0.0360 0.0360 0.0363 0.0265 0.0146 0.0115 0.0110 0.0110 0.0110 0.0113 0.0114 0.0114 0.0114 0.0114 0.0120

-1°

-0.052 -0.055 -0.005

0.0300 0.0320 0.0300

0.170 0.0350 0.340 0,0283 0.470 0.0155 0.500 0.0135 0.505 0.0133 0.505 0.0130 0.510 0.0128 0.520 0.0127 0.520 0.0128 0.520 0.0129 0.525 0.0130

0525

0.0132 0.535 0.0133 0°

-0.052 -0.055

0.055 0.245 0.415 0.505 0.505 0.505 0.505 0.505 0.510 0.510 0.510 0.515 0.520 0.530

0.0263 0.0275 0.0300 0.0340 0.0325 0.0210 0.0145 0.0137 0.0135 0.0135 0.0135 0.0135 0.0135 0.0135 0.0135 0.0135

1°

-0.035 -0.015

0.100 0.270 0.390 0.490 0.565 0.555 0.555 0.555 0.550 0.550 0.555 0.555 0.555 0.560

0.0263 0.0290 0.0320 0.0380 0.0403 0.0365 0.0235 0.0190 0.0166 0.0165 0.0165 0.0165 0.0165 0.0175 0.0175

0.0178 2° 0.015 0.060 0.134 0.275 0.415 0.515 0.645 0.645 0.645 0.645 0.630 0.625 0.620 0.620 0.620 0.620

0.0267 0.0300 0.0350 0.0425 0.0477 0.0435 0.0375 0.0340 0.0223 0.0180 0.0190 0.0190 0.0190 0.0195 0.0195 0.0197

30 0.060 0.090 0.155 0.280 0.420 0.540 0.685 0.747 0.765 0.740 0.730 0,715 0.705 0.700 0.700 0.700

0.0270 0.0320 0.0365 0.0455 0.0517 0.0480 0.0485 0.0410 0.0303 0.0220 0.0230 0.0230 0.0233 0.0233 0.0233 0.0233

4° 0.070 0.115 0.175

0.0280 0.0335 0.0365

0.285 0.0490 0.420 0.0560 0.527 0.0545 0.655 0.0577 0.755 0.0525 0.805 0.0445 0.800 0.0350 0.835 0.0355 0.835 0.0295 0.805 0.0293 0.795 0.0295 0.785 0.0300 0.785 0.0300 0.080 0.130 0.190 0.300 0.420 0.500 0.605 0.700 0.785 0.837 0.955 1.000 0.923 0.905 0.885 0.885 50

0.0290 0.0353 0.0365 0.0525 0.0597 0.0635 0.0615 0.0655 0.0660 0.0605 0.0535 0.0365 0.0345 0.0372 0.0380 0.0380

6° 0.087 0.145 0.200 0.315 0.410 0.475 0.555 0.635 0.750 0.832 1.060 1.145 1.050 1.020 0.990 0.985

0.0300 0.0373 0.0365 0.0565 0.0630 0.0730 0.0740 0.0825 0.0875 0.0875 0.0690 0.0445 0.0395 0.0455 0.0465 0.0465

(12)

Table 5.

Variation with Cavitation Coefficient k1 of Lift and Drag Coefficients Ga and C0 (Profile

Water temperature t=(l9.5'-.22.9) deg. C,

Degree of air content a/a0=1.02,

Reynolds number R°=(5.4-lO.8)'105,

a = Incidence angle

0.25 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0

_30

Ca =

0.075

-0.072

0.107 0.282 0.340 0.341 0.342 0.342 0.342 0,338 0.338 0.337 0.337 0.337

C,,=

0.0432 0.0457 0.0318 0.0188 0.0130 0.0129 0.0136 0.0139 0.0139 0.0138 0.0137 0.0138 0.0139 0.0142

-2°

-0.070

0.0343

-0.076

0.0364 0.195 0.0336 0.362 0.0275 0.420 0.0205 0.434 0.0149 0.429 0.0131 0.428 0.0134 0.428 0.0134 0.427 0.0134 0.426 0.0134 0.426 0.0136 0.426 0.0137 0.426 0.0137

-lo

0.068 0.0314 0.044 0.0340 0.222 0.0382 0.390 0.0340 0.481 0.0219 0.518 0.0150 0.509 0.0147 0.509 0.0147 0.509 0.0147 0.510 0.0147 0.508 0.0147 0.509 0.0149 0.509 0.0151 0.509 0.0155 00 0.002 0.098 0.263 0.428 0.540 0.572 0.563 0.563 0.564 0.565 0.563 0.565 0.581 0.589 0.0313 0.0347 0.0406 0.0340 0.0232 0.0154 0.0160 0.0160 0.0160 0.0160 0.0160 0.0162 0.0164 0.0164 10 0.037 0.118 0.292 0.466 0.577 0.615 0.615 0.611 0.610 0.610 0.610 0.614 0.621 0.628 0.0337 0.0374 0.0441 0.0430 0.0365 0.0297 0.0221 0.0191 0.0191 0.0191 0.0191 0.0193 0.0199 0.0200 2° 0.073 0.143 0.304 0.462 0.570 0.633 0.687 0.729 0.761 0.681 0.681 0.681 0.685 0.685 0.0350 0.0386 0.0481 0.0521 0.0490 0.0430 0.0350 0.0285 0.0245 0.0221 0.0220 0.0222 0.0233 0.0238 3° 0.108 0.182 0.310 0.437 0.540 0.640 0.746 0.840 0.866 0.769 0.763 0.762 0.763 0.761 0.0365 0.0413 0.0525 0.0591 0.0590 0.0555 0.0485 0.0412 0.0315 0.0252 0.0260 0.0262 0.0270 0.0279 0.137 0.209 0.318 0.435 0.540 0.647 0.765 0.857 0.895 0.858 0.875 0.858

0858

0.860 40 0.0402 0.0452 0.0573 0.0651 0.0684 0.0680 0.0640 0.0582 0.0483 0.0372 0.0327 0.0295 0.0310 0.0325 5° 0.163 0.224 0.334 0.435 0.504 0.659 0.750 0.820 0.880 0.965 1.055 0.965 0.961 0.951 0.0452 0.0503 0.0625 0.0704 0.0769 0.0800 0.0808 0.0793 0.0760 0.0610 0.0412 0.0332 0.0355 0.0380 6 0.186 0.0516 0.235 0.0562 0.350 0.0680 0.435 0.0755 0.540 0.0843 0.671 0.0915 0.711 0.0983 0.760 0.1030 0.854 0.1040 1.095 0.0891 1.285 0.0522 1.095 0.0378 1.068 0.0402 1.053 0.0440

(13)

Table 6.

Variation with Cavitation Coefficient kd of Lift and Drag Coefficients Ga and G,,, (Profile A11.7)

Water temperature t=(19.5-'21.6) deg. C,

Degree of air content a/a=1.O2,

Reynolds number R= (5.41O.4)1O,

= Incidence angle

a>

0.25 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 2.5

_30

C, =

C=

-0.020

0.0520

-0.025

0.0545 0.043 0.0516 0.217 0.0182 0.221 0.0187 0.226 0.0180 0.230 0.0183 0.231 0.0185 0.230 0.0184 0.230 0.0184 0.230 0.0182 0.230 0.0182 0.230 0.0182 0.230 0.0187 0.230 0.0187

-2°

-0.020

0.0492

-0.025

0.0503 0.155 0.0449 0.327 0.0307 0.336 0.0175 0.339 0.0160 0.341 0.0164 0.340 0.0167 0.340 0.0170 0.340 0.0171 0.340 0.0173 0.340 0.0173 0.340 0.0173 0.340 0.0181 0.340 0.0182

-1°

-0.018

0.0467

-0.015

0.0454 0.206 0.0440 0.389 0.0369 0.444 0.0235 0.444 0.0165 0.444 0.0162 0.443 0.0165 0.443 0.0168 0.443 0.0173 0.443 0.0174 0.441 0.0172 0.440 0.0172 0.440 0.0175 0.440 0.0177 0°

-0.018

0.0442 0.068 0.0427 0.228 0.0462 0.425 0.0457 0.537 0.0380 0.549 0.0209 0.549 0.0155 0.549 0.0153 0.549 0.0154 0.549 0.0158 0.549 0.0167 0.550 0.0172 0.550 0.0174 0.550 0.0175 0.550 0.0179 1° 0 0.0410 0.088 0.0429 0.265 0.0499 0.440 0.0523 0.575 0.0475 0.650 0.0330 0.655 0.0187 0.657 0.0172 0.658 0.0172 0.659 0.0167 0.659 0.0160 0.659 0.0154 0.6' 0.01 0.659 0.0152 0.659 0.0152 2° 0.055 0.0410 0.124 0.0445 0.298 0.0532 0.457 0.0575 0.597 0.0562 0.707 0.0495 0.758 0.0297 0.770 0.0198 0.760 0.0177 0.759 0.0173 0.759 0.0164 0.759 0.0165 0.759 0.0161 0.759 0.0160 0.759 0.0160 3° 0.117 0.0418 0.172 0.0460 0.319 0.0563 0.464 0.0620 0.602 0.0650 0.723 0.0620 0.818 0.0498 0.865 0.0228 0.862 0.0180 0,860 0.0185 0.859 0.0185 0.850 0.0190 0.850 0.0183 0.850 0.0185 0.850 0.0181 4° 0.118 0.0425 0.180 0.0480 0.319 0.0599 0.459 0.0670 0.594 0.0729 0.708 0.0729 0.808 0.0660 0.892 0.0420 0.931 0.0370 0.955 0.0310 0.957 0.0230 0.950 0.0210 0.940 0.0209 0.945 0.0200 0.949 0.0199 5° 0.118 0.0439 0.176 0.0499 0.304 0.0635 0.434 0.0722 0.573 0.0802 0.690 0.0830 0.789 0.0818 0.880 0.0760 0.952 0.0721 1.035 0.0518 1.051 0.0290 1.042 0.0230 1.032 0.0228 1.037 0.0221 1.041 0.0219 6° 0.118 0.0455 0.170 0.0517 0.285 0.0669 0.400 0.0779 0.542 0.0871 0.671 0.0924 0.767 0.0966 0.850 0.1067 0.960 0.1055 1.100 0.0715 1.140 0.0366 1.125 0.0266 1.120 0.0255 1.122 0.0241 1.130 0.0235

(14)

¿2

Ca

¿o

48

12 Ca

¿0

48

46 4«

42 aa

= I

I

_'

_2' t

í47

if

'/

_9/1.7

'#"

«

3

¼17

3'

2°'

2

t] /3-229°C

-4,,,,

'd

=2,

0ì

2,' 4-

-2

0/17_'tf

tr1o,,7--3° 0.

_-r

-3'

I l4/I,7

a,7

-3, 4,,

/

f.

?tx I

Ip

/d

=8

'd

A111

9f/7

j'

/(

«,f'

5Jtt-9J

3'

íjt

0 /

t1 M.3-229°C

I «7

\Ç)'Çct6

'

3'c

X--'17

41

0

/d

'V

.

"id ='2

i

i-7e

4 -/

_.p

_-ì

iz

7Ç21û,9

_-2

_j

0iI

2'

Ij

¿77

-t

U//7,72.A

(4,7

A

2-j.

i.

nf/

,,

'j'/17'

C, 1V17 9

c-w

','.'

i I ¿I,L0 ¿W!

48«

8

¿7,82 48« 486 O

₄

48« 481 &

Fig. 15.

Ditto with Fig. 14 (k1.4, 1.2,

[.0)

cw

488 ¿j

0 - '' ao«

è! - '' 48«

4'Ó72 4'8« 492

Fig. 14.

Comparison on Polar Diagrams of Profiles at Various Values

of Cavitation Coefficient (k=3.0, 2.5, 2.0, 1.8, 1.6)

(15)

F. NUMACHI, K. TSUNODA and I. CHIDA: Cavitation Tests on Hydrofoils / 5

85

C-0,8

2"-'

_«

a

42

48

41

42

A,,7

=t7

CL' 4'81

I

Fig. 16.

Ditto with Fig. 14 (k,=0.9, 0.8, 0.7)

O 0,82

ao«

486

487 a« 481 488 411/

'q

Fig. 17.

Ditto with Fig. 14 (kd=0.6, 0.5, 0.4)

0,83 48« 485 401 8,82 8x23 88« 485

Fig. 18.

Ditto with Fig. 14. (k4=0.3, 0.25)

Cu,

(16)

first requisite, and if therefore low drag-lift ratio at high lift, and high maximum

lift coefficient are used as criteria, the sequence of superiority would be somewhat

as follows:

the condition where the incidence angle a

6 deg, and the sequence is

re-versed when a < 6 deg)

From the above it may be said that:

Even in the case of such thick profiles, the simpler forms surpass the aerofoil

forms at high speeds, though this does not hold at lower speeds.

The simple ogival form 011.7 does the most poorly at high and low speeds,

but comes out next to the A11,7 at medium speeds.

The best performance is yielded at high speeds, not by the modified ogival

01.7, as might be expected, but by the O1.7, which has its point of maximum

thickness shifted forward.

(2)

Susceptibility to cavitation occurrence:

are indicated in Fig. 19.

The

sequence in the order of lateness of cavitation inception is somewhat as follows:

8 (N. B.

The apparent superiority of 011,7 over A11,7

Fig. 19.

Comparison of Profiles with Regard to Manner

of Cavitation Occurrence

for k4 < 0.3 only applies to

a

1/11% (I1)

11)

¡nc//ence

fU

Z8ncCÌV4UUU__

u.

of ll-Zcne Com

---.-

OiO,q Iflüfilence /88%(LI)

Il

k4 = 3.0-1.4

A7

0,7

oL.,

011,7

k4 = 1.2

11,7

0,7

0,.,

011,7

k4 = 0.9-0.7

A11.7 011.7

0,,

01.7 k4 = 0.6-0,4

k4 = 0.3--0.25:

01.7

A11,,

01.7 0,,

A,

011.7 011,7 2 ¿1

-r

û

_'ç

(17)

F. NUMACHI, K. TSUNODA and I. CHIDA: Cavitation Tests on Hydrofoils / 5

87

7 Ç

-7

In Zone I

In Zone II

In Zone III

A117 Ofl.7

0.7

01.7

07

A11.7

01

0

A117

(3) Incident angle for minimum drag-lift ratio: Its variation with cavitation

is compared in Fig. 20.

The order according to imperturbability of the angle is:

0.7,

017,

A11.7,