Cavitation tests on Hydrofoil of Simple Form Report 4: Difference in performance between experiments with water temperatures of 8 and 20 degrees C

Lrtt'j ci T3chIoy

vrS Lbratorj

LIrr

Mekelweg 2- 228 CD DeIft

The Netherlands

Cavitation Tests on Hydrofoils of

Simp°ÎM

Fx3l 15781336

(Difference in Performance between Experiments with

\'ater Temperatures of 8 and 20 deg. C)

F. NUMACHI 2,

K. TSUNODA7 and I. CHIDA4

Synopsis

Cavitation tests on simple formed hydrofoil profiles have been carried out at

the water temperature 7-.9 deg. C, and the performance obtained are compared

with those at the temperature 20 deg. C which were stated in Report i

(ijj.

1.

Introduction

The effect of differences in water temperature on cavitation performance has

already been treated in the Report 2 [2) of the present series, but a further study

on larger differences in temperature has been carried out,

which forms the subject

of the present report.

2.

Experimental Method and Test Specimens

The experimental method has already been fully reported [3), and will not

be repeated here.

The specimens tested were 07, 0, 0', 0

and 0 the outline

forms of which are shown in Fig. 1. The procedure 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.

The temperatures explored this time were 7

9 deg. C (averaging 8 deg.).

Natural seasonal fluctuations of indoor water temperature in Sendai City ranges

from 5 deg. C in winter to about 20 deg. C in summer. The present

experiments

were carried out at natural room temperature at a period

immediately preceding

the height of winter. The degree of dissolved air content a/ag was therefore near

unity (precise values noted in Fig. 2 and etc.).

Rep. No. 84 (in Europiañ language) of the Institute of High Speed Mechanics, Töhoku

University. Read at the 26th General Meeting of the Japan Society of Mechanical

Engineers held on April 5, 1949.

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

of High Speed Mechanics.

Technical Official of the Institute.

Assistant of the Institute.

50

Rep. Inst. High Sp. Mech., Japan,

Vol. 9 (1958), No. 84

01

f)!

UI

U7

/75

U7

Fig. 1.

Outlines of Profiles

Table 1.

Dimensional Proportions for Drawing Profiles with Annexed

Key Diagramme

Trailing Edge

Profiles

L

t

n ¿ R1 R0 R3 R4 R5 w1 w2 ¿ 1 t1 t. t.3

100 7.00 50. 00 189.53 R1 =

0.145 0.145

0.2\ 0.29

70 4.90 35.00 132.67 R1 =

0.1 0.1 0.2

N

loo 7.00 50.00 245.63 189.53 199.64

1.71 0.145 25.00

0.29"\ 0.29

70 4.90 35.00 171.94 132.67 l39.75,'.

1.2 0.1 17.5 0.2 0.2 Ola

100 7.00 50.00 217.90 189.53 123.50

1.05 0.145 15.00 0.29 0.29

70 4.90 35.00 152.53 132.67

86.45 0.74 0.1 10.5

0.2 \.

0.2

100 7.00 50.00 245.63 217.90 l92.86 123.5O'...

1.71 1.06 24.57

15.00 0.29"\ 0.29

70 4.90 35.00 171.94 152.53 135.00

86.45 1.2 0.74 17.2 10.50 0.2 0.2

100 7.00 50.00 252.50 217.90 103.57

61.57 28.57 1.71 1.06 17.10 10.57 0.29 0.57 0.29

o;

--70 4.90 35.00 176.75 152.53 72.50

43.10 20.O 1.2

0.74 12.00 7.40 0.2 0.4 0.2

F. NUMACHI, K. TSTJNODA and I. CHIDA:

Cavitation Tests on Hydrofoils / 4

51

Table 2. Dimensional Proportion of Profiles

3.

Results

Performance curves.

The comparison between the results obtained from the present tests at 7

9

deg. C and those from the previois ones at 20-22 deg. C (1) is given in Figs. 2

-5 (for the profile 07) and Figs. 6-9 (for the 0). Various values of cavitation

coefficient k

[1 ; 3) have been examined (13 values between 1.8 and 0.25 for the

07, and 15 values between 1.8 and 0.15 for the O).

The polar diagrammes for the three temperatures 7-9 deg. C, 13-16 deg. C

[2) and 20-22 deg. C [1) are compared in Figs. 10-13 (0), 14-17 (0), and 18

-21 (0).

From the above, it is seen that the shifting of the polar diagramme with

temperature differs somewhat according to the profile form and the cavitation

coefficient.

Tables 3 - 7 give detailed values.

Mode of Cavitation Occurrence.

By the procedure already reported in detail (3), the cavitation coefficient at

cavitation inception and the size of incipient cavitation were measured, and the

results compared wìth previous data.

Though we refrain from reproducing

de-tailed comparative diagrammes, it has been ascertained that the domains of erosion

danger and of violent vibrations (represented on the a-kd diagramme) do not

show appreciable susceptibility to temperature differences of the present order.

Reynolds Number.

It is well known that performance curves differ more or less according to the

Reynolds number.

It is a question whether the Reynolds number R or the

cavi-tation coefficient kr

is the dominant in their effect on peiformance.

Profile 07

Profile

X

0

Profile 0"

X

Profile 0

Profile 0

X Y0 _Y Y0 _Y

IÇ

X

Y0 Y

X

Y0 Y, 0 0 0 0 0 21.43

4.83 0.00

7.14

3.23 0.81

7.86 2.67 0.00 11.71 7.14 35.71

6.46 0.00

14.29 4.39' 0.30 15.00

4.19 0.00

24.57

5.69 0.00

17.14

4.86 0.00

50.00

7.00 0.00

25.00

5.71 0.00

32.14 &27 0.00

37.14

6.66 0.00

27.14

5.96 0.00

64.29

6.46 0.00

35.71

6.59 0.00

50.00 7.00 0.00 50.00

7.00 0.00

38.57

6.74 0.00

78.57

4.83 0.00

50.00

7.00 0.00

64.29

6.46 0.00

61.43

6.70 0.00

50.00

7.00 0.00

100.00 64.29

6.46 0.00

78.57 4.83 0.00 72.86

5.30 0.00

62.86

6.61 0.00

78.57

4.83 0.00

92.86 2.09' 0.00

85.00 4.17 0.00

75.71

5.49 0.00

92.86

2.09 0.00

100.00 92.14 89.43 100.00 100.00 100.00

52

Rep. Inst. High Sp. Mech., Japan,

Vol. 9 (1958), No. 84

û

0,8

49

0,2

8

o

-

Profile 07

tw

8

8°C--I

a/a89

20,O-22,0°CI 50

50

5o/

Ca

)'À.t'

41 L_ «of

í0

_J

I

cx30h.uJ JJ 30.

2°á4

'2'

4'

2

t°Fk/8,dfçl/f2

-8o°

û

ICw

Cw Cz,1 Cui Ca

s, RUR!! .

:

-

I

r

:°4R

Profile 07

-'/td=o24

_]7'td=48

a/a509

-t

7O98°C

II

80.

R

ooj

W

'_±i

1

R R

tw24û22,û°(

-j°;.

8

482

û« 482

8,8« 61,82 48« 11,86 8,88

Fig. 3.

Ditto with Fig. 2 (Profile 0, k0

=

1.0, 0.9, 0.8)

402

0

402

O 482

0

8,82 o;g«

Fig.

2.

Comparison of Polar Diagrams at 8 deg. and 20 deg. C

Water Temperature (Profile 07, k0=1.8, 1.4, 1.2, 1.1)

a

0,5

a

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

4

53

+

I

k=

o4

ìa=t

u -'° '°iu

-"-U

¿?02 ¿?0« ¿82 ¿?U ¿?L72

ee«

8ô

Fig. 4.

Ditto with Fig. 2 (Profile 07, kd=0.7, 0.6, 0.5)

O

Prof//c Oq

r 60

28,0-22,8 -

_{- I__}

j

°

Y

60 I

Kl

'fa='í«

¡rd=O3 30:

u.

Lil +.

t

uu.

0

UU

402 ¿?83 82 ¿?83 4'835 4'83 Q835

Fig. 5.

Ditto with Fig. 2 (Profile 0, k,=0.4, 0.3, 0.25)

o

2°

0

ITh

54

_{Rep. Inst. High Sp. Mech., Japan,}

_{Vol. 9 (1958), No. 84}

1,0

o

Ca

88

2°

¡0

a'!

-01 3o

3O4

jO

o

882 ¿7

0

8172 o o

Profile

Oq

-tw

Z8»O°C'---I

t1 ¡9/1-280°C

Fig. 6.

Comparison of Polar Diagrams at 8 deg. and 20 deg. C

Water Temperature (Profile O, k4=1.8, 1.4, 1.2, 1.1)

f

Prof//e 07

kd=88 %ûq

tw0-.0°c---I

190-280°C'-Fig. 7. Ditto with 190-280°C'-Fig. 6 (Profile, O, k= 1.0, 0.9, 0.8)

80'! 805

0

0/120

8820

802

(w

F. NUMACH!, K. TSUNQDA and I. CHIDA: Cavitation Tests on Hydrofoils / 4

55

2/'J

_,fo

-

I

k=

-_0Ï

9°

/°

¡0

a2

--À

--34.,

o

cw O

0020

&t? 0,3 0,2

a'

=«,_

Prof/e

¿2,j

-.

-4+.

_«oy

/go2o°c-127

5°

E

o

Nj

_0

-2o

f

io cul

304É0_

J- 0

E'I

I°

¡Cd=

Fig. 8.

Ditto with Fig. 6 (Profile O, k0=

0.7, 0.6, 0.5, 0.4)

Profile O

4-"M3°

_a/a=104'

-T

-H-

¡0209°CE

-E

_-f

3°

4+20

o

'

2°?

-í

/d02

fid=t?Ì5

-1° '4. -.

0°

cw

-3°

¿w

Fig. 9.

Ditto with Fig. 6 (Profile O, k0=0.3, 0.25, 0.2, 0.15)

002

082

0,8í

56

Rep. Inst. HghSp. Mech., Japan,

Vol. 9 (1958), No. 84

1,2

0,8

2°.

I

4'82 O 02

û

482 88«

48«

486 486 o

Profile

0,7/a

tu/

¡«8-160°C

1

240 -22,0°C----!!

488

4/8

Fig. 10.

_{Comparison of Polar Diagrams at 8 deg., 15 deg. and 20 deg. C}

La

Water Temperatures (Profile 07

,

kd=1.8, 1.4, 1.2)

u..

.

z

¿v= 3°

2°

1°

0°

6°

± «o

u.

R.

Profi/e

0'a

¡«0-148°c----!

240-22,8°C-21

u..

...

_R.

R.

_.

u

.

uiuuuuuu

408 0,18

-+

Fig. 11.

Ditto with Fig. 10 (Profile 0°, k4=i.1, 1.0, 0.9)

812 o

kd0

kd=4'

0°

_jO°

-1°

_t_/7

0 90 -2

.-3°

-3°

I

F. NUMACHI, K. TSUNODA and I. CHIDA: Cavitation Tests on Hydrofoils /4

57

a2

o

-ai

Fig. 13.

a2

o

o

082

08f'

aoo

008

082

Fig. 12.

Ditto with Fig. 10 (Profile O°, k=0.8, 0.7, 0.6, 0.5, 0.4)

I

Profile u

2030«0

«-j

jW

-°c---«°

«,

200-220°cI

082

083 082

Ditto with Fig. 10

o

J'

I 8°

/_

=05

Prof/le 07

tw00ûc_--I_

C 30\ W, W

288-220°CI-3°

g_il

=02 ,'

I

L7I\JÇwI

I 0t2? 082

2

Q83 082 083

(Profile O, kl=0.3, 0.25, 0.2, 0.15)

(w

aoz

o

CZ',I 082

p-Cw 082

o

58

Rep. Inst. High Sp. Mech., Japan,

Vol. 9 (1958), No. 84

o

O 882

0

&02 ¿?0« QOS t?88

0

0,82 04(

Fig. 14.

_{Comparison of Polar Diagrams at 8 deg., 15 deg. and 20 deg. C}

Water Temperatures (Profile O, kd=1.8, 1.4, 1.2)

¿'o

ao

as

¡0.f Imp'

kd=,'l

-2

_-2°

lIj;1

X «O

UW.

Il

Profile

07«

lU

t10

8_0a

__

a.

i

aal...

_aaa

8/2

t

qo81

I

'_ -'8°

Ca

R1

j

ÇOJ

7oÇ

U5o

ui111iiiIiii

_WLUI

1l

,°rofiÏe 0/

12°.

?

_2;(

t0 i=18!4=/

kd=2

t,= 0-'0°C ---Z

04

₍

_{/8-f00°t'-- -I}

I

Z

Z

W-2/8°CJI

1.ff

'

ii

O

002

8

082

08«

081

088

ato

0

¿02

08«

Fig. 15.

Ditto with Fig. 14 (Profile O, k,=1.1, 1.0, 0.9)

nr 7°

a2

_to

a8

as

ato

0/2

¿2°

I

F. NUMACHI, K. TSUNODA and I. CHIDA: Cavitation Tests on Hydrofoils / 4

59

ff

T1' Z?'

j-2°

-2°

-2°.

1UUI11L.

0

¿702

0

0,82

0

-3°

¿704" ¿706 8,88

û

¿782

0

082

Fig. 16.

Ditto with Fig. 14 (Profile O, k8=0.8, 0.7, 0.6, 0.5, 0.4)

I

Prot,'/cOf

°

O7f

_a/at04

-t,'Z0-fJ°C--f

.fO/p

+f.---7-

u0.

--ff.

ltd -03

'I

Id

'dO25

'd82

Le-il

J0J03ff

2°'<". :30C,20'x

_Ku

(w

802 801

802 8,81

¿782 881 ¿782

Fig. 17.

Ditto with Fig. 14 (Profile O, k=0.3, 0.25, 0.2, 0.15)

-ff,

O o o

7°_

8°

y

ï

1,7 «O_J 7°

8

2°3/ 501'?470_g0

_.:-

;-z

i°ro fi/e 0

/i;'0-/40r----il

r

2170-21,8°CE

60

Rep. Inst. High Sp. Mech., Japan,

Vol. 9 (1958), No. 84

08

06

0«

02

0

Ca

IOIUUU

-ll

IuUuuR

_...

u

Profi/e ol

tw8-80(---I

18-i68°(----ff

1-go

0

002

¿2 ₀₈₂ 88« 086 088

0/8

0/2

û

082

08«

Fig. 18.

Comparison of Polar Diagrams at 8 deg., 15 deg. and 20 deg. C

Water Temperatures (Profile O, k=1.8, 1.4, 1.2)

082

0

Q82 08'!

088

a/O

0/2

0

082 004'

Fig. 19.

Ditto with Fig. 18 (Profile O, k=i.i, 1.0, 0.9)

¿0

08

0ff

a

02

F. NUMACHI, K. TSUNODA and I. CHIDA: Cavitation 'rests on Hydrofoils / 4

61

88

85

84'

82

83

82

a'

-ai

Prof//e

01

tu80°CZ

f fl/I

/4'8-168°c----li -

o-YO

9OO;O7O

Profile

_0f

=

t= Z8-8°C---T

z

/1'8-,í8°C---ff

E_L

/O -2z'8

30

)f=82

7L

JJ-L-

dr81

/

_-i°

-3° -o [

-2°w

881 61,82 ₈₈₁ 882

883

6101 882

883 881

6182

Fig. 21.

Ditto with Fig. 18 (Profile O, k,1-0.3, 0.25, 0.2, 0.15)

4'82 6184' 6185

-82

°

'

(L,''\3[

O

882

8

882

8

0

812

8

882

Table 3. Variation with Cavitation Coefficient k of Lift and Drag Ccefficients

Ga

and G (Profile O)

Waler temperature L 79 deg. C,

Degree of air content a/ai

= Incidence angle

1.02, 0.25 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.4 1.6 1.8 2.0 2.5

_30

Ca°

_C,=

-0.080

0.0325

-0.090

0.0335

-0.095

0.0300 0.015 0.0258 0.048 0.0250 0.065 0.0250 0.071 0.0250 0.075 0.0245 0.082 0.0245 0.082 0.0245 0.082 0,0245 0.082 0.0245 0.082 0.0245 0.082 0.0245 0.082 0.0245 0.082 0.0245 2°

--0.068

-0.043

0.143 0.165 0.178 0.187 0.187 0.187 0.187 0.187 0.187 0.187 0.0184 0.187 0.0187 0.187 0.0187 0.187 0.0187 0.187 0.0187 (J) 0.0273 0.0267 0.0185 0.0183 0.0185 0.0185 0.0185 0.0184 0.0184 0.0184 0.0184 _10 1)010 0.0250 0.110 _0.0242 0.285 0.0i60 0.287 0.0147 0.287 0.0147 0.289 _0.0147 0.289 0.0147 0.289 0.0147 0.289 0.0147 0.289 0.0147 0.289 0.0147 0.289 0.0147 0.289 0.0146 0.289 0.0146 0.289 0.0146 0.289 0.0146 Ç) P-00 0.082 _0.0243 0.197 0.0240 0.367 0.0170 0.378 0.0140 0.378 0.0135 0.388 0.0135 0.388 0.0135 0.388 0.0132 0.388 0.0132 0.388 0.0132 0.388 0.0132 0.388 0.0135 0.388 0.0135 0.388 0.0135 0.388 0.0135 0.388 0.0135 (J _'z, 0.086 0.200 0.395 0.477 0.477 0.484 0.484 0.484 0.484 0.484 0.484 0.484 0.484 0.484 0.484 0.484 (J z, 10 0.0240 0.0253 0.0226 0.0165 0.0145 0.0145 0.0145 0.0140 0.0140 0.0143 0.0143 0.0147 0.0147 0.0147 0.0147 0.0147 2° 0.132 0.0248 0.223 0.0265 0.402 0.0268 0.508 0.0205 0.567 0.0175 0.592 0.0175 0.553 0.0175 0.553 0.0170 0.553 0.0170 0.553 0.0174 0.553 0.0174 0.553 0.0175 0.553 0.0175 0.553 0.0175 0.553 0.0175 0.553 0.0175

o

0.182 0.257 0.405 0.528 0.638 0.730 0.628 0.618 0.615 0.607 0.605 0.605 0.605 0.605 0.605 0.605 30 0.0260 0.0282 0.0313 0.0268 0.0229 0.0220 0.0220 0.0218 0.0218 0.0218 0.0218 0.0219 0.0219 0.0219 0.0219 0.0219 Ql

i 'na

11 9

n ais

û

.4i

0.647 0746 0.714 0.725 0.726 0.718 0.713 0.699 0.695 0.692 0.687 0.687 40 0.0278 0.0308 0.0363 0.0355 0.0332 o.o318 0.0318 0.0298 0.0280 0.0272 0.0272 0.0275 0.0280 0.0280 0.0280 0.0280

z

9Â û i19

ûd5

ûss6

0.646 0.732 0.800 0.852 0.885 0.866 0.840 0.810 0,800 0.790 0.782 0.778

p

5° 0.0302 0.0338 0.0417 0.0463 0.0500 0.0525 0.0530 0.0478 0.0350 0.0321 0.0330 0.0341 0.0360 0.0355 0.0355 0.0355 60 0.273 0.0330 0.335 0.0375 0.460 0.0474 0.570 0.0603 0.646 0.0720 0.720 0.0770 0.890 0.0780 0.995 0.0705 1.075 0.0440 1.048 0.0375 0.970 0.0395 0.928 0.0420 0.915 0.0450 0.898 0.0440 0.878 0.0440 0.865 0.0440

co

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Table 7.

Variation with Cavitation Coefficient kd of Lift and Drag Coefficients Ga and C0 (Profile O)

Water temperature t

7

9 deg. C,

Degree of air content a/ai

= Incidence angle

1.02,

a

0.15 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.4 1.6 1.8 2.0 2.5

_30

Ca

-0.063 -0.075 -0.095 -0.170 -0.068 -0.057 -0.049 -0.038 -0,030 -0.026 -0.024 -0.024 -0.024 -0.026 -0.030 -0.035 -0.035

Cw =

0.0234 0.0265 0.026]

0.0241

0.0185 0.0173 0.0161 0.0158 0.0158 0.0159 0.0159 0.0159 0.0160 0.0162 00165 0.0165 0.0168

-2°

-0.055

0.0175

-0.056

0.0206

-0.060

0.0203

-0.049

0.0151 0.040 0.0126 0.050 0.0123 0.065 0.0125 0.066 0.0126 0.065 0.0126 0.067 0.0128 0.067 0.0130 0.067 0.0130 0.067 0.0130 0.067 0.0131 0.067 0.0132 0.065 0.0137 0.065 0.0137 0.065 0.0139

-1°

-0.038

0.0160

-0.045

0.0185 0.029 0.0173 0.130 0.0135 0.160 0.0114 0.172 0.0116 0.173 0.0115 0.169 0.0117 0.170 0.0117 0.170 0.0117 0.170 0.0118 0.170 0.0120 0.170 0.0120 0.170 0.0121 0.170 0.0121 0.170 0.0124 0.170 0.0124 0.170 0.0127 0°

-0.030

0.028 0.100 0.183 0.278 0.285 0.282 0.273 0.273 0.273 0.273 0.273 0.273 0.273 0.273 0.273 0.273 0.273

0.0149 0.0173 0.0180 0.0161 0.0120 0.0119 0.0119 0.0120 0.0120 0.0120 0.0120 0.0121

0.0121 0.0121 0.0121 0.0121 0.0124 0.0129 1°

-0.002

0.055 0.123 0.200 0.340 0.396 0.382 0.376 0.376 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370 0.370

0.0143 0.0183 0.0203 0.0209 0.0161 0.0149 0.0140 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0150 0.0151

0.0151 2° 0.026 0.086 0.142 0.210 0.345 0.447 0.490 0.499 0.499 0.490 0.468 0.468 0.468 0.468 0.465 0.465 0.465 0.465

0.0145 0.0190 0.0216 0.0235 0.0210 0.0202 0.0199 0.0197 0.0177 0.0177 0.0185 0.0185 0.0186 0.0185 0.0185 0.0185 0.0186 0.0183

0.057 0.105 0.158 0.215 0.326 0.428 0.541 0.632 0.645 0.599 0.579 0.572 0.570 0.562 0.555 0.555 0.555 0.555 30

0.0156 0.0198 0.0228 0.0248 0.0270 0.0286 0.0297 0.0271 0.0210 0.0210 0.0220 0.0229 0.0232 0.0229 0.0229 0.0229 0.0229 0.0229

4° 0.118 0.170 0.213 0.313 0.405 0.510 0.600 0.672 0.673 0.725 0.705 0.695 0.662 0.469 0.648 0.644 0.640

0.0214 0.0262 0.0290 0.0335 0.0369 0,0426 0.0390 0.0321 0.0321 0.0302 0.0300 0.0307 0.0300 0.0300 0.0300 0.0300 0.0300

5° 0.130 0.173 0.213 0.307 0.393 0.485 0.580 0.660 0.735 0.826 0.835 0.810 0.768 0.743 0.738 0.727 0.721

0.0233 0.0312 0.0335 0.0403 0.0460 0.0600 0.0543 0.0558 0.0558 0.0458 0.0416

0.0402 0.0392 0.0392 0.0392 0.0392 0.0392

6° 0.179 0.215 0.310 0.400 (1.491 0.589 0.682 0.790 0.881 -0.915 0.919 0.877 0.843 0.822 0.807 0.799

0.0343 0.0380 0.0483 0.0567 0.0744 0.0710 0.0779 0.0808 0.0671 0.0591

0.0569 0.0548 0.0526 0.0514 0.0505 0.0505

7° 0.185 0.225 0.323 0.421 0.522 0.621 0.722 0.830 0.917 0.982 1.019 0.990 0.946 0.908 0.882 0.867

0.0364 0.0427 0.0568 0.0690 0.0855 0.0885 0.0960 0.1023 0.1002 0.0950 0.0890 0.0781 0.0693 0.0655 0.0623 0.0623

8° 0.191 0.245 0.345 0.464 0.570 0.676 0.770 0.844 0.946 1.035 1.113 1.114 1.055 0.990 0.952 0.925

0.0372 0.0470 0.0660 0.0820 0.0949 0.1066 0.1121

0.0904 0.0811 0.0765 0.0765

Table 8.

Relation of Cavitation Coefficient kd to Reynolds Number R

07 07

0

twmean=7.8°C twmean=22.l°C

2O.8°Ctwrne

= 8.6°C twmea

22.7°C tomeapI

19.8°C ttomean= 8.2°C tumea,i= 14.7°C t.wme= 21.2°C

vm/secR. 10vm/sec R iOvm/secR 105vm/sec R. l0vm/sec R.

105vm/secR' 105vm/secR 10vm/secR. 105vm/secR

lo-.

3.0 8.00 4.03 8.00 5.8 8.02 5.7 8.03 4.04 8.02 5.9 8.02 5.5 8.01 4.03 8.04 4.9 7.98 5.7 1.8 9.57 4.82 9.54 7.0 9.60 6.8 9.60 4.83 9.60 7.1 9.60 6.6 9.58 4.82 9.62 5.8 9.52 6.8 1.4 10.33 5.20 10.34 7.6 10.35 7.3 10.37 5.22 10.35 7.7 10.37 7.2 10.35 5.21 10.38 6.3 10.30 7.4 1.2 10.80 5.44 10.81 7.9 10.82 7.6 10.84 5.46 10.82 8.0 10.81 7.5 10.81 5.46 10.85 6.6 10.77 7.7 1.1 11.05 5.56 11.05 8.1 11.07 7.8 11.09 5.58 11.06 8.2 11.06 7.6 11.07 5.57 11.11 6.8 11.02 7.9 1.0 11.33 5.71 11.30 8.3 11.36 8.0 11.37 5.73 11.34 8.4 11.35 7.8 11.34 5.71 11.27 6.9 11.29 8.1 0.9 11.62 5.85 11,59 8.5 11.66 8.2 11.66 5.87 11.65 8.6 11.64 8.0 11.64 5.86 11.67 7.1 11.58 8.3 0.8 11.95 6.02 11.92 8.7 11.97 8.5 11.98 6.03 11.98 8.9 11.95 8.2 11.96 6.02 11.98 7.3 11.90 8.5 0.7 12.29 6.19 12.27 9.0 12.31 8.7 12.33 6.21 12.34 9.1 12.28 8.5 12.31 6.20 12.31 7.5 12.24 8.7 0.6 12.67 6.37 12.65 9.3 12.68 9.0 12.70 6.39 12.71 9.4 12.67 8.7 2.68 6.38 12.69 7.7 12.60 9.0 0.5 13.07 6.58 13.05 9.5 13.08 9.2 13.10 6.60 13.14 9.7 13.08 9.0 13.08 6.59 13.11 8.0 13.00 9.3 0.4 13.51 6.80 13.50 9.9 13.54 9.6 13.55 6.82 13.58 10.1 13.53 9.3 13.52 6.80 13.56 8.2 13.45 9.6 0.3 14.00 7.05 14.03 10.3 14.05 9.9 14.04 7.07 14.07 10.4 14.04 9.7 14.02 7.06 14.08 8.6 13.97 10.0 0.25 14.27 7.18 14.30 10.5 14.31 10.1 14.32 7.21 14.34 10.6 14.31 9.9 14.28 7.19 14.36 8.7 14.23 10.2 0.2 14.55 7.32 14.62 10.7 14.62 10.3 14.60 7.35 14.63 10.8 14.60 10.1 14.57 7.33 14.65 8.9 14.53 1 1)1 0.15 14.85 7.47 14.97 10.9 14.97 10.6 14.90 7.51 14.91 10.3 14.87 7.48 14.97 9.1 14.85 10.6

'l'able 8.

(._

jill

1111 k4

o;

8.50C 1u'rneam 15.1°C 'wmeuò 20.7"C twmea, 7.9°C 15.1°C twmean= 20.4°C

um/sec R. 10vm/sec R. 10vm/secR. 105vm/sec R. 10vm/secR.

10um/sec R. 10

3.0 8.03 4.04 8.00 4.9 8.00 5.6 8Á3 4.04 8.00 4.9 8.00 5.6 1.8 9.60 4.83 9.61 5.9 9.58 6.8 9.60 4.83 9.61 5.9 9.56 6.7 1.4 10.37 5.22 10.37 6.4 10.34 7.3 10.38 5.23 10.35 6.3 10.34 7.2 1.2 10.84 5.46 10.82 6.6 10.82 7.6 10.84 5.46 10.82 6.6 10.79 7.6 1.1 11.09 5.58 11.06 6.8 11.06 7.8 11.10 5.59 11.07 6.8 11.05 7.7 1.0 11.37 5.73 11.35 7.0 11.33 8.0 11.37 5.73 11.35 7.0 11.33 7.9 0.9 11.66 5.87 11.65 7.1 11.62 8.2 11.67 5.88 11.64 7.1 11.62 8.1 0.8 11.98 6.03 11.97 7.3 11.97 8.4 11.99 6.04 11.98 7.3 11.93 8.3 0.7 12.33 6.21 12.31 7.5 12.31 8.7 12.34 6.21 12.32 7.6 12.26 8.6 0.6 12.70 6.39 12.69 7.8 12.68 8.9 12.71 6.40 12.70 7.8 12.64 8.9 0.5 13.10 6.60 13.09 8.0 13.07 9.2 13.11 6.60 13.09 8.0 13.05 9.1 0.4 13.55 6.82 13.54 8.3 13.52 9.5 13.55 6.83 13.55 8.3 13.50 9.5 0.3 14.04 7.07 14.06 8.6 14.04 9.9 14.05 7.08 14.07 8.6 14.02 9.8 0.25 14.32 7.21 14.34 8.8 14.30 10.1 14.32 7.21 14.35 8.8 14.30 IOU 0.2 14.60 7.35 14.62 9.0 14.60 10.3 14.60 7.35 14.63 9.0 14.60 10.2 0.15 14.90 7,51 14.95 9.2 14.92 10.5 14.90 7.51 14.94 9.2 14.90 10.1

F. NUMACHI, K. TSUNODA and I. CHIDA: Cavitation Tests on Hydrofoils / 4

69

In the present series of tests the Reynolds number R (R = vi/ii,

y :

flow

velocity, i: chord length) varies with velocity and with temperature.

If, as in the

case of wind tunnel experiments, the performance is chiefly determined by R, the

lift and drag should change with water temperature. Upon drawing the GaR and

C,0R curves we have found that the effect on performance of changes in R

dependent on water temperature was extremely small within the range examined,

in contrast to the overwhelming influence yielded by differences in cavitation

coefficient.

(The Ca - R and C -. R curves have not been reproduced here, but

the relevant values are found

in Tables 3

7,

while Table 8 gives the kgR

relationship).

4.

Conclusion

The results obtained from the present study is as follows:

(1) The effect of differences in water temperature (range: 8, 15 and 21 deg. C)

on cavitation performance, especially lift and drag, were clarified.

( 2 )

It was determined that the effect of differences

in Reynolds number

on cavitation perfomance was small, in contrast to the determining factor

consti-tuted by the cavitation coefficient.

In conclusion, acknowledgement is due to Mr. S. Nakayama, technical officer of

the ex-Japanese Navy for his valuable collaboration in developing the profiles and

in preparing the specimens. The able assistance in the experiments provided by

Mr. K. Izumi is also

appreciated.

Bibliography

i i

F. Numachi, K. Ysunoda and I. Chida,

Cavitation Tests on Hydrofoils of

Simple Form/Rep. i (On Five Profiles of 7 Per Cent Thickness Ratio),

Rep. Inst. High Sp. Mech., Japan, Vol. 8 (1957), p. 67.

(2)

F. Numachi, K. Tsunoda and

I. Chida,

Cavitation Tests on Hydrofoils

of Simple Form / Rep. 2 (Difference in Performance between

Experi-ments with Water Temperatures of 20 and 15 deg. C), Rep. Inst. High

Sp. Mech., Japan, Vol. 8 (1957), p. 89.

3

F. Numachi, Kraftmessungen an vier Fliigelprofilen bei Hohlsog, Forsch.