Cavitation tests on Hydrofoil of Simple Form Report 3: (On four profiles of thickness ratio 3,5 percent)

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Cavitation Tests on Hydrofoil of Simple Form / Report 3

(On Four Profiles of Thikness Ratio 3.5 Per Cent)

F. NUMACHI2 K. TSUNODA arid I. CHIDA4

Synopsis

Forty hydrofoil profiles io 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 3.5 per cent among them.

1. Introduction

Hydrofoil profiles with superior cavitation performance and possessing simple forms easily reproducible were further sought with the view to contributing infor-mation for the design of axial flow turbines, pumps and ship propellors. This time a series of profiles of small thickness ratio were developed for use as blade elements

to shape the outer tips of rotor blades. Several simple forms have been obtained

which have proved upon test to possess good characteristics.

2. Experimental Method and Test Specimens

The method of experimentation used has already been fully described in

pre-vious paper [1, 2). Specimens tested were the simple formed hydrofoils O5, O

and along with the aerofoil A3.5. Their outlines are given in Fig. 1. O35 has the ogival form, O.5 is of the same basic form but with the leading edge washed back, while the O., with a similar wash-back, has the principal curve of its back

Report No. 83 (in European language) of the Institute of High Speed Mechanics,

T5hoku University. Read at the 26th General Meeting of the Japan Society of

Me-chanical Engineers, on April 5, 1949.

Professor, Faculty of Engineering, concurentiv Director of the Institute of High Speed Mechanics, Töhoku University.

Technical Official of the Institute of High Speed Mechanics. Assistant of the same.

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A35

,,1 L/35

included in the present series of experiments

showed definite advantages over the simpler forms of profile. The dimensions of

the four profiles are given in Table 2 in terms of the values of X, Y0 and Y

Table 1. Dimensional Proportions for Drawing Profiles with Annexed Key Diagramme

X Fig. 1. Specimen Profiles

side composed of two circular arcs of different diameters connected so

as to bring the point of greatest

thickness to a position 40 per cent

from the leading edge. Table i and

accessory figures indicate the method

of drawing the out lines of these

profiles except for the

A3.5 which

is more of an aerofoil. As such the A3.s's plane lower surface gives it a

fairly convenient form, but still it

can hardly be considered to be of a

particularly simple shape.

It was

to determine whether such aerofoils

Trailing Edge Leading Edge

Profiles L t n R1 R2 R3 w1 wo 1 t t3 100 3.50 50.00 390.50 R5= 0.145 0.i45_,.7 0.29 0.29 70 2.45 35.00 273.35 R1= __- 0.1 0.1 0.2 0.2 5 loo 3.50 50.00 501.24 390.50 437.86 0.86 0.145 25.00 0.29 0.29 70 2.45 35.00 350.87 273.35 306.50 0.6 0.1 17.50 0.2 0.2

o5

loo 3.50 40.00 321.24 561.60 437.86 0.86 0.145 25.00 0.29 0.29 70 2.45 28.00 224.87 393.12 306.50 0.6 0.1 17.50 0.2 0.2 A15 Table 2

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F. NUMACHI, K. TSUNODA and I. CHIDA: Cavitation Tests on Hydrofoils f 3 37

indicated in Fig. 1.

The test specimens were produced with chord and width

both of 70 mm.

Table 2. Dimensional Proportions of Profiles

J-Zone II-Zone I-Zone A0

T'

H

-a ß'-Zoae 3. Results

3.1 Mode of Cavitation Occurrence.

'rhe cavitation observed on these four profiles was in zones I to III (indicated in Fig. 2). Zone IV (pessure side towards trailing edge) was always free of cavi-tation. The mode of cavitation occurrence is shown in Figs. 2 to 5 presented in the same form as the corresponding figures in the previous reports (1).

i°i'otiÏe ¿?9.ç t,1, 2t?5-2,'°C ûtzqjer [posino onBací Si

¡Il-Zone _a/a _¡9 40 ('9/'9) ./[Ç '9an«r of [ron/on on Face Si'e

I ßegioniji of Stion, Vi'9ratÑìn

i/8'96841'920 ,

l8'\j

ir-!19 - -

(I1l7r-ir:'

f4í8-t1) o 'o o% («) /28() ¡'90gO 60 20 II-Zone _' _o

,'

t

Incipience of J-Zonethy/f

-Jncigience of II-Zone thw/.

¡9

Fig. 2. Position of Cavitation Head (X0) and Tail (X) of Incipient Cavitation

in Relation to Incidence Angle a; Value of

at which Incipient

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

Ranges of Erosion and Vibration Danger (Profile 03.5) Profile O. Profile O Profile O5 Profile A

--

y; , y; X y; y0 0 y;, O O 0 0 0.80 0.80 7.14 1.14 0.00 7.14 1.67 0.36 5.71 1.74 0.50 2.86 1.70 0.36 21.43 2.44 0.00 14.29 0.13 11.43 2.23 0.21 5.71 2.13 0.20 35.71 3.23 0.00 25.00 2.87 0.00 25.00 3.14 0.00 14.29 2.94 0.04 50.00 3.50 0.00 35.71 3.30 0.00 40.00 3.50 0.00 20.00 3.26 0.01 64.29 3.23 0.00 50.00 3.50 0.00 50.00 3.41 0.00 25.71 3.43 0.00 78.57 2.44 0.00 64.29 3.23 0.00 54.29 3.32 0.00 33.00 3.50 0.00 92.86 1.14 0.00 78.57 2.44 0.00 68.57 2.77 0.00 41.43 3.43 0.00 100.00 92.86 1.14 0.00 82.86 1.86 0.00 50.00 3.23 0.00 100.00 100.00 62.86 2.67 0.00 75.71 1.94 0.00 87.14 1.19 0.00 100.00

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00 -2" 0 ,°rofi/e O f&-21,8 °C a/af,0 R (45-f,8) .101' 2 168 198 128 /88 88 68

Daliçer of D'ion on Baûf' S7de

Dafigeroffros/on 09 Facs S,o'e

I Beginning of Strong L'iZ'ratfo/i

10 ₂₈

88 ' '80 ¡88 í2) î'uíl«o 28 /0 5%

O ¿?5 1,8 2,8

Fig. 3. Ditto with Fig. 2 (Profile

,°rof//e ¿?c tw/9,92i,5"C

t7/&5'fO R (8610)tO1'

/68 198 /28 100 88 18

09119er of fhision an &nf Si/fe

langer ofEiriion an Face Si/fe

J Beg/on/Og of StrongViOratiOn

Phoui/c ,4/5

a/ai 8 2

R (8,5-tI) 't0

--7

Danger 9fEras/on an Bud SA/e

- Danger of ErosiOnonFace Si/fe

I Beg/nniq otS/i'ngV/Oration

20 /8 11107o IOU 198 /28 180 51 5/ 9 188%,: 01-Zone /88-0 «8 88% /68!') /2X&885/8 20 18 9% ta o 43'

Fig. 5. Ditto with Fig. 2 (Profile A35)

1-2/we

i _J

2.

[-°

01-Zane

'--V-

,-

Inc-qìíencc of I-ZoneCavil.

i...

ii II//ence o ne Caw

2, \ I)-!

'. ÀA -

' _k Z-Zane

14hhi

_ff-Zon '

'.-'L

'

z'

nap/once O fil-z off-Zone oneC, k: t J cay/f fr 9010 88% 118í128(-)\\\«8 28 /8 5% 8 /088818 0,5 tO t)- 21

Fig. 4. Ditto with Fig. 2 (Profile q"

-2"

1:5 2,0

'v-- -'-

Znci3O/ence of I-Zone ¿'vll. 1nc49/ence of g-zone izv/t. I

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F. NUMACHI, K. TSUNODA and I. CHIDA: Cavitation 'l'ests on Hydrofoils

/

3 39

3.2 Variation in the Lift and Drag.

Variation of lift coefficient with cavitation coefficient [1) is shown in Figs. 6

to 9, and the same for the drag coefficient in

Figs. 10 to 11.

It is clear from

these figures that points of maximum values occur both with lift and drag,

simi-larly to the cases of

O,

O and O in the Ist report (2.

¿7 O 3 Profile O3,3 a/a3 70 t31' 24527«"C '46-tû)/86' £"/27D/ V/árzth?fl

i'c4/i"noe ûfl-Zgne &,X

¿75/075

2,5

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

with Changing Values of Cavitation Coefficient k (Profile

Fig. 7. Ditto with Fig. 6

(Profile O)

2,5 ¿75

UUUPUN

Th2111e ¿/ /98-24rC %i = 8 R p e»

4UUUUUUU__

_{'wuuuuuuUUUUU}

7°

Xr3Ofl

__

-r

4

Jaqûi?nc° * 3f I-Zo, ¿'it Iftt,3kXt 3f -Zane ' -45 Profile Oq

%i

/0 R (46-/8)/8 ca 2°-30 -. of 1-Zojie ûzvit. 20 Ad

___________

"A 0,2 llT-Z8ae

A

45 î:o

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02

'w SYiw7 V,írJion

2 10 ?/flteof if-Zae vit Jnc,p,?nce of Z-Zone

au« 006 Profile 43.5 Profile of t,,, I98-2i8°C t,,,, = 20,4'-22,2°C Inei1z&nce of 1-Zoco C

-- a

= focoìence f T-Zone (»lt

-.---it ncenfif-Zonwt.

u

u.

a'/a's"fO

R6-1j.-186

0,"-f" - ¿0 ¿5

Fig. 10. Variation of Drag Coefficient G for Various Incidence Angle with Changing Values of Cavitation Coefficient k,r (Profile 03.5 and 0,5)

, a/ai =¿0 i (05/,o- .106

C0___

lnc,o/eoce of Z-Zone i"

4 L,

st v,»

---

-

---____

o Inciolonce nf1-Zone (s'

p

-2 Profile 0j-a'/&5'=fO ti,, tp;q -21,5°C

mu

R

=9°

-u- ---

-2"

'---

Zoinpience ofI-Zone ¿iv8

---

_-1-Zone 1ncí,?nce of if-Zone Cavif

IIiI

0,"-/° /,°-2°

- Profile ,435

%0

. ti,, 209-22,2°C R (06 /8)f8 Ü

U

U 4rAhU..

u

Incipience of Z-Zone

inc/p/once of if-2one C'ro'.

05 ¿8 ¿5 2,0

Fig. 9. Ditto with Fig. 6 (Profile A3.5)

,4ouilc

t28-2«C

a/os'8

R (0,6-f

as ¿o ¿'5 2,0 z-a ¿0

Fig. 11. Ditto with Fig. 10 (Profile 0'5 and A3,5) 082

û

089

002

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F. NUMACHJ, K. TSUNODA and L CHIDA: Cavitation Tests on Hydrofoils_/3 41

3.3 Performance Curves.

The manner in which the drag-lift ratioincident angle relationship changes

with cavitation coefficient is clear from the Figs. 12 to 15. A similar relationship

o

0 781 8.82 781 782 781 8,82 781 8.82 8,83 o«

Fig. 12. Comparison on Polar Diagrams of Profiles at Various Values of Cavitation Coefficient (ka=2.0, 1.4, 1.2, 1.0)

u_Nul_u u

l

I..« /435

-"2

4'°,ç 1435

0 4

«° 2

I.

035 Ca

304Ï

O /

._

l_VI.

O3, , a/ai

urguuuu,'

_2° -20

d'

-l'I

ik12

DI:'

-

_' _°

k d'

I

uiiiuwuuuiuuuu

L

=oJlEIUU1lllUUl

_{o III}

I

10 _{Oj- -p,} 03,5 0( Oj,ç

4cIJ

oj 135 Ojç 4

_1-2°'l

-2°

a-2°

llCzv

Ul

'

_

oJ- N

U

17«

«o

IUIUN

>-Ca /4

uuvu N

'

uuuu

u

urau uruuui

130

' + ,

N

_2/

J uaciu

i/d=9

1°

ri

Iç.=48 1° . kd=47₁ 00

I

-+

III

-°

11111

035 Á-1035 09

i

___I

20. _, 44

t-°

O _70/ 4112 4'i2,' 482 8,01 '712 48/ 482 483 ,48« 48f

Fig. 13. Ditto with Fig. 12 (ka=0.9, 0.8, 0.7, 0.6) 4? 8,6 as 7« 73 0,2 21 o 77 aif 8,5 7« 73 72

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03 0,2

ai

o

a'

020 0,2 -4185 2°, 2

Iv,

0-y V35 04cl W11 035

j

A-o,5

h=«

II. Uil

_10 ..4. _i _,0.î+

H-0

0--2&4. _20_

III. _RU

..

_U

i'

Cu' 09/ 912 08/ 30 082 0,8/ 902 0/1/

Fig. 14. Ditto with Fig. 12 (k0=0.5, 0.4, 0.3, 0.25)

L 0Lr,'

_{Lí- 035}

05

c-o

j-1

,45 /Oç

035 p035 iO + -I O o;-¿-'w Cu, 0,02 083 tw =/0 22,0 'C 035435

id41/2

-20 410/ 418/5 410/ 418/5 410/ 41815 4102

Fig. 15. Ditto with Fig. 12 (k,=0.2, 0.15, 0.12)

between drag-lift ratio and lift coefficient may be represented by curves drawn on the basis of the detailed values given in Tables 3 to 6.

Cu,

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Table 3.

Variation with Cavitation Coefficient k4 of Lift and Drag Coefficients

Ca and C (Profile 03,5)

Ö -t o o (n

Water temperature t=(20.5-21.4) deg. C,

Reynolds number R

(6-4O)1O,

Degree of air content a/a=1.0,

= Incidence angle (J) o p n 0.12 0.15 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 -2° Ca = cw= -0.03 0.0135 -0.07 -0.105 -0.16 0.0135 0.0135 0.0165 -0.09 -0.055 0.0165 0.0165 -0.045 -0.045 0.016 0.016 -0.045 0.016 -0.045 0.016 -0.045 0.016 -0.045 0,016 -0.045 -0.045 0.0165 0.0165 -0.05 0.0165 -0.05 -0.05 0.0165 0.0165 'n -1° -0.015 0.011 -0.03 0.011 -0.07 0.055 0,075 0.0105 0.0105 0.010 0.08 0.08 0.0105 0.0105 0.08 0.08 0.011 0.0115 0.08 0.0115 0.08 0.0115 0.08 0.0115 0.07 0.012 0.07 0.065 0.012 0.0125 0.06 0.013 0.06 0.055 0.013 0.0135

n

0° 0.005 0.010 0.065 0.011 0.155 0.185 0.185 0.0115 0.0105 0.0105 0.18 0.18 0.0105 0.0105 0.18 0.18 0.0105 0.011 0.18 0.011 0.18 0.011 0.18 0.0115 0.18 0.0115 0.18 0.18 0.0115 0.0115 0.18 0.0115 0.18 0.18 0.0115 0.0115 p p 1' 0.05 0.011 0.10 0,0115 0.18 0.255 0.34 0.0125 0.012 0.012 0.295 0.28 0.0105 0.011 0.275 0.275 0.0115 0.012 0.275 0.012 0.275 0.012 0.275 0.012 0.275 0.012 0.275 0.27 0.012 0.012 0.27 0,012 0.265 0.265 0.012 0.0125 C n (t'(I) (1) 2° 0.085 0.013 0.125 0.013 0.19 0.25 0.32 0.014 0.0145 0.016 0.42 0.46 0.0185 0.018 0.40 0.38 0.013 0.014 0.38 0.015 0.375 0.015 0.375 0.015 0.375 0.015 0.375 0.375 0.0155 0.016 0.375 0.016 0.375 0.375 0.016 0.0165 o n

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Table 4.

Variation with Cavitation Coefficient kd of Lift and Drag Coefficients G and C,, (Profile O.5)

a

Water temperature t,(19.9-21.8) deg. C,

R=«6-1O) 1O,

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

angle Reynolds number 0.12 0.15 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° 1° 0° 10 2° 3° 40 = C,0= -0.03 -0.035 -0.065 -0.125 -0.135 -0.035 0.011 0.0115 0.012 0.013 0.0105 0.010 -0.015 0.035 0.09 0.095 0.10 0.10 0.0095 0.010 0.0095 0.0095 0.0090 0.0095 -0.015 0.045 0.165 0.21 0.20 0.195 0.010 0.011 0.011 0.0095 0.0095 0.0095 0.07 0.10 0.165 0.25 0.325 0.385 0.011 0.0115 0.0115 0.0115 0.011 0.0105 0.08 0.11 0.165 0.225 0.285 0.42 0.011 0.0115 0.0125 0.014 0.017 0.0195 0.115 0.165 0.22 0.275 0.39 0.012 0.015 0.0185 0.0225 0.027 0.165 0.22 0.275 0.39 0.0215 0.024 0.0295 0.036 -0.03 -0.03 0.0105 0.011 0.095 0.095 0.0095 0.010 0.19 0.19 0.0095 0.010 0.31 0.30 0.0105 0.011 0.55 0.45 0.0205 0.014 0.505 0.60 0.031 0.0335 0.52 0.645 0.0435 0.050 -0.03 0.0115 0.095 0.010 0.19 0.010 0.30 0.0115 0.415 0.015 0.63 0.0295 0.735 0.0535 -0.03 0.0115 0.09 0.010 0.19 0.010 0.29 0.012 0.405 0.016 0.555 0.0235 0.755 0.0455 -0.03 0.0115 0.09 0.010 0.19 0.010 0.29 0.012 0.405 0.016 0.53 0.0235 0.0385 -0.03 0.012 0.09 0.0105 0.19 0.0105 0.285 0.0125 0.40 0.0175 0.52 0.0235 0.675 0.036 -0.035 -0.035 0.0115 0.012 0.085 0.085 0.0105 0.0105 0.185 0.185 0.0105 0.0105 0.285 0.285 0.013 0.013 0.395 0.39 0.0175 0.0175 0.505 0.495 0.0235 0.0235 0.63 0.60 0.0345 0.034 -0.035 0.012 0.085 0.0105 0.185 0.0105 0.285 0.013 0.39 0.0175 0.49 0.0235 0.59 0.034 -0.035 0.012 0.085 0.0105 0.185 0.0105 0.285 0.013 0.39 0.0175 0.49 0.024 0.59 0.034 -0.035 0.0115 0,085 0.0105 0.185 0.0105 0.285 0.013 0.39 0.0175 0.49 0.024 0.59 0.0345

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Table 5.

Variation with Cavitation Coefficient k of Lift and Drag Coefficients G0 and G, (Profile 0,5)

01

Water temperature t?O=(19.9'-21.5) deg. C,

Reynolds number R=(6-1O) 1O,

Degree of air content a/a=1.O, tr,,= Incidence angle

a0 0.12 0.15 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 -2° C0 -0.045 C,, = 0.012 -0.05 0.0115 -0.07 0.0125 -0.15 0.014 -0.08 0.0135 -0.04 -0.035 -0.035 -0.035 0.011 0.011 0.011 0.0115 -0.035 0.0115 -0.035 -0.035 -0.04 -0.04 -0.04 -0.04 -0.04 -0.04 0.0115 0.012 0.012 0.0125 0.013 0.013 0.013 0.013 -0.01 0.055 0.085 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.085 0.085 0.08 0.08 0.07 - lo 0.010 0.0105 0.0085 0.0085 0.0085 0.009 0.0095 0.0095 0.0095 0.0095 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0° 0.035 0.0095 0.105 0.011 0.19 0.0115 0.195 0.0095 0.185 0,0095 0.18 0.18 0.175 0.0095 0.010 0.010 0.175 0.010 0.175 0.010 0.175 0.175 0.175 0.175 0.175 0.175 0.175 0.010 0.010 0.010 0.010 0.010 0.010 0.010 0.175 0.0105 10 0.07 0.011 0.11 0.011 0.18 0.0125 0.25 0.0125 0.33 0.013 0.325 0.29 0.28 0.0095 0.011 0.0115 0.28 0(1115 0.28 0.0115 0.28 0.28 0.28 0.275 0.275 0.275 0.275 0.012 0.012 0.0125 0.0125 0.013 0.013 0.013 0.275 0.013 2° 0.085 0.115 0.18 0.24 0.315 0.445 0.555 0.42 0.40 0.39 0.385 0.38 0.375 0.37 0.37 0.37 0.37 0.37 0.012 0.0125 0.0135 0.017 0.0195 0.021 0.0235 0.0165 0.0145 0.0155 0.016 0.016 0.016 0,016 0.017 0.017 0.017 0.0175 3° 0.11 0.0135 0.165 0.018 0.23 0.021 0.295 0.025 0.425 0.535 0.61 0.0305 0.0345 0.0345 0.60 0.027 0.52 0.0225 0.50 0.495 0.49 0.485 0.485 0.475 0.475 0.0215 0.0225 0.0225 0.0225 0.0225 0.0225 0.0225 0.475 0.0225 0.185 0.24 0.30 0.42 0.54 0.65 0.735 0.70 0.66 0.635 0.61 0.595 0.58 0.575 0.575 0.575 40 0.0225 0.027 0.031 0.040 0.046 0.0525 0.052 0.045 0.0385 0.0355 0.0335 0.0335 0.0335 0.0335 0.034 0.034

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Table 6.

Variation with Cavitation Coefficient k

of Lift and Drag Coefficients Ca and C,,, (Profile A3.5)

Water temperature t,,(2O.4-.22.2) deg. C,

Reynolds number R=(6-1O) iOu,

Degree of air content a/a,1.0,

x°,=Incidence angle

k 0.12 0.15 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

.-(5°, -2° Ca cw = 0 0.011 -0.02 0.012 -0.095 0.0125 -0.175 0.0145 -0.075 0.0115 -0,06 -0.055 0.0115 0.011 -0.05 0.011 -0.05 0.0115 -0.05 0.011 -0.05 0.011 -0.045 0.011 -0.045 0.011 -0.045 0.0115 -0.045 0.0115 -0.045 -0.045 0.0115 0.012 0.005 -0.005 0.01 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055 0.055

-lo 0.0115 0.011 0.009 0.009 0.0085 0.009 0.009 0.0095 0.0095 0.0095 0.0095 0.0095 0.0095 0.0095 0.0095 0.0095 0.0095 0.010 0° 0.005 0.075 0.010 0.011 0.045 0.09 0.19 0.011 0.165 0.165 0.0095 0.23 0.165 0.0095 0.305 0.165 0.010 0.305 0.16 0.16 0.010 0.010 0.29 0.265 0.16 0.010 _0.265 0.16 0.010 _0.265 0.16 0.010 0.265 0.16 0.010 0.265 0.16 0.010 0.265 0.16 0.010 0.265 0.16 0.010 0.265 0.16 0.010 0.265 0.16 0.16 0.010 0.010 0.265 0.265 0.011 0.0115 0.013 0.0135 0.014 0.011 0.0085 0.0095 0.010 0.010 0.010 0.010 0.010 0.010 0.0105 0.0105 0.0105 0.011 2° 0.04 0.085 0.0125 0.0125 0.135 0.0145 0.20 0.017 0.26 0.019 0.39 0.0215 0.515 0.415 0.0245 0.015 0.38 0.013 0.365 0.013 0.365 0.0135 0.365 0.014 0.36 0.014 0.36 0.014 0.36 0.0145 0.36 0.0145 0.36 0.355 0.0145 0.015 0.095 0.16 0.215 0.28 0.415 0.55 0.645 0.54 0.495 0.48 0.475 0.465 0.465 0.46 0.45 0.45 0.45 30 0.015 0.019 0.0215 0.025 0.032 0.037 0.0375 0.029 0.021 0.0195 0.019 0.019 0.019 0.020 0.020 0.020 0.020 0.155 0,215 0.28 0.405 0.535 0.66 0.715 0.685 0.625 0.60 0.575 0.57 0.56 0.56 0.56 0.555 0.022 0.0265 0.031 0.040 0.0485 0.056 0.057 0.051 0.040 0.0335 0.030 0.0295 0.0295 0.029 0.029 0.0295

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F. NUMACHI, K. TSUNODA and I. CHIDA: Cavitation Tests on Hydrofoils / 3 47

3.4 Comparison of the Four Profiles.

1. Performance curves:

Figs. 12 to 15 represent the polar diagrammes of

the four profiles for 15 values of cavitation coefficient k4 between 2.0 and 0.12.

An assessment of the relative merits of the four profiles on the basis of this

comparison results in a sequence of superiority not always consistent when cavi-tation coefficient is varied and depending also on the qualities demanded of the

profiles.

For the range k4 = 2.0 0.9: A3.5 and O surpass the others with high

lift and small drag-lift ratio.

For k4 = 0.8 - 0.7: A35 and O are still superior.

For k4 = 0.6 - 0.5: results of comparison vary with incident angle.

2 2

For k4 = 0.4: O35 and 035 excel.

(y)

For k4=0.3 and below: O

and O

are relatively good though

per-formance deteriorates appreciably in all models at such speeds. The 03.5 sets up

violent vibrations when the incident angle is larger than 2 deg. (rendering

measure-ment difficult) and is defective in this respect, but

it should be noted that the

lift coefficient at 2 deg. is higher in absolute value than the maximum values (at 3.4 deg.) of any of the other models.

2. Conditions of cavitation occurrence: Comparatively represented in Fig. 16,

from which it may be said generally that for promptness to cavitation ocurrence

the sequence would be:

o o

RI

U

a4, /3/1,2 1, /7 U35 3/35 V35 ;j- 11!(IOO -2° o 0035O35O3; a,c A95 05 05 tj/,» IO' J (fØ9O'/0

-:

1nc47/e/ice of IJT-Zaoe

i'

22,O0C

a/a5o

6'-O) /06 035 f3/ 1,2 c r Jnc4s?ûce of J-Zû,e /Lv,t Jncp/ence ofF&70e ¿rh

U

u

UIl

UkdR

¿5 Z8

Fig. 16. Comparison of Profiles with Regard to Manner of Cavitation

Occurrence As regards occurrence in zone I

As regards occurrence in zone II

As regards occurrence in zone III: £r,0>0:

A3.5, A,5, 035 , 03,5, 03.5, A,5

0.5,

05

A3.5

(14)

3. Incident angles for minimum drag-lift ratio: Relative insusceptibility of

this value to changes in cavitation coefficient is judged from Fig. 17 to be in the

following order: 03.5, A3.5,

tI9022.0"C

a/a to

3° 20

00

2,0

Fig. 17. Variation with Changing Cavitation Coefficient ka of Incidence Angle for Minimum Drag-Lift Ratio

4. Conclusions

Conditions of cavitation inception and the sizes of incipient cavitation were determined for hydrofoil profiles of 3.5 per cent thickness-chord ratio of

simple form, namely, 03.5, and O

and for the aerofoil A.

Performance curves of the same profiles were obtained for the lift and drag under cavitation occurrence.

The superiority of the O series profiles and in particular that of the

0

and the O

were demonstrated: at high speeds they proved to surpass the

aerofoil A3.5 in performance with their high maximum lift, though at low speeds

they were not equal to the A3.5.

The 03.5 showed a further advantage in the small susceptibility of the

incident angle giving maximum lift, to changes in cavitation coefficient.

In conclusion the authors wish to acknowledge the valuable collaboration

contributed by Mr. S. Nakayama, technical officer of the ex-Japanese Navy. Their

appreciation for the assistance given by Mr. K. Izuini in the experimental work

must also be recorded.

Bibliography

(1)

F. Numachi, Kraftmessungen an vier Fhigeiprofilen bei Hohisog, Forsch.

Ing.-Wes., Bd. 11(1940), S. 303.

(2

F. Numachi, K. Tsunoda and I. Chida, _{Cavitation Tests on Hydrofoil} Profile of Simple Form / Report 1 (On Five Profiles of 7 Per Cent Thick-ness Ratio), Rep. Inst. High Sp. Mech., Japan, Vol. 8 (1957), p. 67.

£ /Oc,O7c