Cavitation tunnel tests of series 2 propellers

ARCHIEF

-,

-APPENDIX 2

CAVITATION TUNNEL -TESTS OF SERIES 2. PROPELLERS BY

,H.W. LERBS

" INTERNATIONAL CONFERENCE Of .HIP HYDRODYNAMICS 1954'

- SUBJECT 3.

COMPARATIVE CAVITATION TESTS -OF" PROPELLERS

Lab.

v. Scheepsboti'wkunde

Technische Hog eschool

Delft

Introduction

The parent of the Series 2 propeller models is a

3-bladed propeller of which the developed blade area ratio

equals

0.655.

The pitch diameter ratio is constant and equals

1.333.

All sections are ogival sections with sharp leading edges. The design advance coefficient is J =

0.925.

Of this parent, models of 8, 12, 16 and 18 inches

diameter have been tested under various conditions of

water speed, cavitation nmlber and air content. Table 1

gives a synopsis of all test series which are available today and of the tunnels in which the tests have been

carried out. In each test series, a wide range of advance

coefficients has been covered for each combination of

speed, cavitation number and air content ratio. The

temperature has not been varied systematically but the tests have been carried out at random temperatures which

are indicated in the last column of Table 1.

The analysis of these test series is made difficult by the great number of independent variables involved.

Two 'ways have been attempted for an analysis, viz., using average curves and using individual test points. In the

first method, the variables are, in general, not separated

and, therefore, the conclusions may be open to question.

In the second method, the goal is to determine the effect

of individual variables on the propeller performance.

Analysis Based on Average Curves

In a first attempt to analyze the tests, averages

of KT, KQ and / relative to air content have been plotted

2

represented on Figures 1 to 3 and on Figures 5 to l7. To

obtain an impression how the results depend on air content,

plots on a basis of air content ratio have been made for

Cr = 0.75. These curves are shown for the 8 inch model on

Figure 4 and for the 18 inch model on Figure 18. The

curves indicate that a variation of air content has little effect on the Series 2 propeller model results. This

be-haviour may be expected since this series predominantly

produces sheet cavitation.

Comparing average curves which are obtained from different tunnels, systematic differences between the

tunnels become apparent. Within the test series with the

8 inch and 12 inch models, Figures a to 3 and Figures

5

to 7, respectively, the greatest values for the torque coefficient in an interval around the design advance

coefficient follow from the AEW tests. The minimum values

for KQ follow from the KMW test series for the 8 inch model and either from the MIT or from the NSP tests for the 12

Inch model (which has not been tested in the KMW tunnel).

Relative to the thrust coefficient, no indications are apparent that the greatest values of this coefficient are

consistently related to one particular tunnel. The

smallest values, however, are obtained from the KMW tunnel for the 8 inch model and from the MIT tunnel for the 12

Inch model.

For the 16 and 18 inch models, results only from

NSP and TMB are available. There are hardly any

con-clusions possible from these plots of average curves relative to systematic differences between these two

tunnels. There is a tendency for the NSP tunnel to measure greater values of thrust and torque than the Tie tunnel,

3

the differences are, however, not always in this direction.

Plotting the averages on a basis of the ratio "Area of propeller disc" to "Area of working section", indications for

the magnitude of the wall effect may be obtained when the assumption is made that the wall effect is predominant as compared to the effect of other parameters which vary when

the area ratio varies. The plots are made for three different

advance coefficients, viz., J 0.8 (Figures 19 and 20), J = 1.05

(Figures 21 and 22) and for the advance coefficients for zero

thrust (Figures

23

and

24).

Taking first the tests carried out for a water speed of 18 ft/sec (Figures 19, 21 and 23) and

keeping in mind the systematic deviations of results from

different tunnels, neither the thrust and torque curves nor

the J - curves for zero thrust indicate any methodical change when the area ratio is increased up to the greatest value

0.565.

This value corresponds to the 18 inch model in the TMB tunnel.

In addition, the plots do not indicate any systematic differences

between open-jet (MIT, TMB) and closed tunnels (KMW, AEW, NSP,

NPL). _{However, there are no measurements for closed tunnels}

available for values of the area ratio greater than 0.22. _Up

to this value methodical differences between the two types of

tunnels are not apparent. _{For greater values of the area ratio,}

no conclusions can be drawn and it is not possible to determine whether the wall effect is smaller for open-jet tunnels than

for closed tunnels as is expected from theoretical reasoning.

The tests for a water speed of 36 ft/sec (Figures _{20, 22, and}

24) could be conducted only in the NSP and Tie tunnels. The

variations of KT and Ktli for constant _{cr are, with one exception,}

of the same order as those obtained for the _{case of 18 ft/sec}

and do not indicate a definite trend when the _{area ratio}

varies.

-Analysis Based on Individual Variables

To analyze the test results on a rational basis the

parameters which. govern the similitude of cavitation per-formance of propellers must be known. In accordance with present knowledge, the parameters are as follows:

Advance coefficient, J. Cavitation number,

cr

Reynolds number, R.

(+) Froude number, 1%

Weber number, W. Air content ratio,

A number which is related to the time necessary

for a bubble to travel geometrically similar

distances.-From recent tests carried out at the California Institute of Technology, it appears that this number or its components, viz., speed and scale ascertain the inception of cavitation.

A number which determines the wall effect of the

tunnel. This number is taken as the ratio "Area of propeller

disc" to Area of working section".

Brief remarks on air content ratio and on the cavitation number may be added.

The air .content is measured in these test series by the

Winkler method or, in one of the series, by a volumetric method, both of which give the total air content of the

water. The question arises whether this total air content defines a parameter which is significant for cavitation

similitude. For the inception of cavitation, there are strong indications that not the total air content but the content of entrained air, i.e., the nuclei content determines the

significant number. However, means of measuring the nuclei

content are still in a state of development.

The cavitation number is based on the vapor pressure of the water. When cavitation develops there may be doubt whether the vapor pressure is the proper physical quantity

in the cavitation number. There are reasons which indicate

that the vapor pressure should be replaced by the pressure within the cavity which, for steady-state cavities, is

greater than the vapor pressure.

The great number of independent variables prohibits, in general, conducting cavitation tests on propellers

under conditions of true similitude. Consequently, it is,

in general, impossible to obtain the effect of only one of

the parameters on the propeller characteristics. The goal

of the comparative cavitation tests is to yield information on the effects of tunnel wall interference, Reynolds

number and air content on the propeller model performance. When attempting to analyze the test series relative to one

of these parameters a clear separation from other parameters involved can not be generally achieved,for the

afore-mentioned reason. In spite of this limitation some conclusions may be drawn.

As mentioned before, the Figures 19 to 24 do not clearly represent the tunnel wall effect because they

in-clude effects from additional parameters. By selecting

individual test points the tunnel wall °nterference can be separated from all the rest of the parameters in the

following way. Taking, for instance, the test series with the 12 inch model, the Froude number can be made constant by selecting the tests which have been conducted at an

equal water speedr, Comparing results at an equal advance

6

both Reynolds number and Weber number may be considered as

constants since the changes of temperature are small.

Choosing an equal cavitation number and an equal air content ratio for the comparison (the latter makes interpolation necessary) any variation of the propeller coefficients

must be attributed to the wall effect. Figure 24 shows

this effect and the difference of results from open-jet tunnels (MIT, TMB) and from a closed tunnel (AEW). Relative

to the latter, the conclusions are the same as before, viz.',

that systematic differences between these two types of tunnels are not indicated within the range of area ratios

investigated. Relative to the effect of cavitation number one is led to the conclusion by this analysis that the

wall effect depends on cavitation number and becomes

greater when the cavitation number decreases. This

con-clusion, however, is tentative since the systematic

deviations between the results from different tunnels are

of the same general order as the indicated trend.

An attempt has been made to obtain the separated

effects of both air content and Re olds numbe by proper

choice of individual test points. However, the scatter

of the points does not permit conclusive results.

In-dividual test points for J. 0.925 and

cr

= 1.00 on a

basis of 0/ are represented on Figure 26. The Reynolds

number, which corresponds to each point, has been added. Corresponding plots have been made for different values

of both J and

cr

.

Within the accuracy of these measure-ments, the propeller does not appear susceptible to the

effect of air content. It is justifiable, therefore, to

average the figures for different air content ratios and to consider the dependence of these averages on Reynolds

The averages of KT and Kg relative to air content versus

Reynolds number are represented on Figures 27 to 30 for

= 0.925

and for values of 0- = 1000 and 0.75, respectively,

The scatter of these averages of individual test points is

great and increases when the cavitation number decreases, For _KT, the scatter amounts

to ± 7%

of the average at

cr

= 1000 and to i 11% at 0- z. 0.75. FOT KQ, there seem to

be systematic differences which define different curves

(see Figure 30), As to the influence of Reynolds number

on the propeller coefficients, there is no effect either

on KT or on Kg at 1.00

Ater

= 0.75, the general trend

of the points indicates an influence which is greater on

KQ than on Krit This would be expected for a Reynolds

number effect, However, the order of magnitude of this

effect over the rather small range of R is surprisingly great, particularly, when considering that fully developed cavitation takes place at cr=

0.75.

Conclusiica

Looking at the results from a general point of view,

one is led to the conclusion that the accuracy necessary

for definite information has not yet been obtained, In

general, the measurements are fairly consistent within test series conducted in a particular tunnel but vary for

equal conditions among the different tunnels. This may indicate that the scatter arises not so much from the

nature of the phenomenon to be investigated as from the properties of the measuring equipment used and from

differences between the testing techniques applied, It will

be the task of further international cooperation to establish conditions for obtaining more closely related results from different tunnels which will enable us to draw more specific

NSP MIT V Cav.Number ft/s Cr D = 18" TMB 18.0 1050

18.01.00

18.00.75

24.01.50

2400 1.00

24.00.75

24.00.50

36.0 1.5o 3600 1.00

36.00.75

36.00.50

8 TABLE 1

Air Content Ratio

0061 0.50 0.53 0.60 0.56 0.57 0.57 Temperature °Vats t (°C) 0.21 0.22 0.20 0.21 0.20 0.19 0.20 1800 1.50 0.44 0021

18.01.00

0.44 0.21

18.00.75

0029 0.21 0.82 23 0072 19 0.63 19 0.69 23 21 22 20 22 21 22 26 26 2g 28 28 24 28 29 29 29 27 29 29 31 25 26 28 29 27 30 29 27 29 30 28 27 1800 1.50 0.02 15

18.01.00

0.02 15

18.0

₀₀₇₅

0.03

15

3600 1.50 0061 0044 0021 0.06 16 19 23 18 3600 1000 0.62 0046 0.23 0.05 17 21 21 20 3600 ₀₀₇₅ 0063 0.45 0.22 0.06 19 13 22 21 3600 0050

0.66

0.45

0.22 0.03 21 24 15 22 D = 12" TMB 18.0 1050 0.50 0.40 0.30 0.16 30 30 30 1800 1.00 0,50 0040 0.20 30 30 26

1800

₀₀₇₅

0.30 0.16 22 27 25 25 25' 25 25 25" 3000 1.50 0.35 0.21 25 25 30.0 1000

0.35

0.21 25 25

30.0

0075

0.35

0.21

25 25

NSP

18.01.50

0.07 14 1800 1.00 0.08 14 1800 0.75 0007 14 D = 16" TMB

18.01.50

_0.55 0.30 0.14 1800 1.00 0.63 0030 0.19 18,0 0.75 0.50 0.29 0.18 3600 1.50 0.60 0.19 3600 1.00 0.61 0012 36.0 0,75 0.63 0.23 0.13 36,0 0.50 0075 0.24 0.15

il 4

9

-.0. AEW

D = 8"

TMR-- :

nr

ACK " NPL, ' :KI1W

.ft/s

18.0

18.0

18.0

,

18.0.

18.0

1800,.

18.0F

18.0

1800.

18.0

1800

18.0,

18.o

18.0

18.0

1800

18.0

.64v01711.mber Cr

1.50

1.00

0.75

'

1.50

1.00

0. 75

1.50

1.00

,-

0.75

1.50

1.00

0.75

1000

'0.75

1.50

1.00

'0075

Air Content Batio

C4 /as,

0.55

0.42

0011

0.45 0.27

0.19

0.4-5

0.26

0.16

0.50 o.40 0030

0.50

0.40

0.30

0!).1-0

0030 0,24

0,;49

0.20

0.31 0.20

0.37 0.20

0.91- 0.37

0.12

01.50

0,40

_0.14

0.36

'0,14

0.14

0.64

0.45 0.25

0.59 0.45

0.24

0.51 0.40

0.25

0.09

0.10

0.09

Temperature

t (°C)

25 24

23,

23

22

23

23

23,

22

28

26

29

30

26

28

3o

30

29

25' 25

25 25

25 25

18

20

19 18 19

19

18

14

15

11

18

22

12 19 23,, 16.

20

25

25

26

26

V

0.

0.1

^

8 INCH DIAMETER

WATER SPEED 18 FEET PER

SECOND

CAVITATION NUMBER Cr = 1.50

TUNNEL, AIR CONTENT RATIO

K M W 0,64, 045, 0v25, 1009r

A E W 0.54, 0.37, 0.12

MIT

0.49, azo

.1MB

0.50, '0.40, 0:30

SCALE OF ADVANCE COEFFICIENt

.02

0

Ui Lii .04

S

.0

0

cc

0

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0.8

0.7

00 0.2

0.1

WATER SPEED 18 FEET PER SECOND

CAVITATION NUMBER cr = 1.00

SCALE OF ADVANCE COEFFICIENT J

0.02 ,w 0.04

0

UJ

0

cc 0.06 1- U-0 0.08

FIG. 2

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TUNNEL AIR CONTENT RATIO

0.59,. 0.45, 0.24, 0.10 0.14 0.50, 0.40, 0.14 0.31, 0.20 0.50, 0.40, 0.30 K M W NPL A E W

MIT

T MB I 0.8

0

u..

0 4

8 INCH DIAMETER

WATER SPEED 18 FEET PER SECOND

'CAVITATION NUMBER cr

0,75

10

0.6

08

10 112 I 4

SCALE 'OP AOVA,NGE COEFFICIENT

.08 _FIG. 3 .

I

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NPL

AEW

MIT

TMB

AIR GONYENT RATIO_

0.51, 0.40, 0.25, 0.09' 0:114 0.36

azr, 0.20

-0.40, 0.30, 024

741 0.7 = 0 0.02 0, 0.06

0

_ 0. O. 0. 0.2 0.1

WATER SPEED 18 FEET PER SECOND_

CAVITATION -NUMBER

o- .= 0.75

TESTED AT K MW

SYMBOL: Ali CONTENT RATIO

0:5

8

`. 0.40 -a) : 0.25. 0 0.09 9 0.4

₀₆

_{0.8 10 12}

SCALE OF ADVANCE COEFFICIENT, _J

1.4 -.10 .02 -z LT

5

0

w'

0

_ .06 -.w

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!get .08 , _ - cv . .9 .9.

,

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a

0.04

0

FIG. 4

0

'12" INCH DIAMETER

WATER SPEED 18 FEET PER SECOND

CAVITATION NUMBER. a ;

1.50

-TUNNEL AIR CONTENT RATIO

SCALE OF ADVANCE .COEFFICIENt.4

0.02

a

iw

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.8

10 ,11.1 .0 '0 064-po" Lu I_J .08 .10

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, . :t i0.4 .. _0.8 1.0 1.2 iI 4 'AEW 1kA 11 TIV1B NS P ; 0.55, 0.44, 0.50, 0.42, 0.2.1 0.40, o.ol 0.11 0.30, 0.16 0.05

0.8 - 0.7 >-La

5

z

.0.4

oi

ET_ u_

0

co 0.3

0

.0 0.2 0.5 .1

TUNNEL AIR CONTENT RATIO

E W 0.45,- 0.27, OA%

MIT

TMB 0.50, 0.40,, 0..30 NSP 0.05 -0.03 ., 11

It INCH DIAMETER

WATER SPEED 18 FEET PER SECOND

CAVITATION NUMBER. & 1.00 tr,

M

1111

ii

ITIE111

11/11/1111

NI IN

0.6 0.8 1.0 1.2

SCALE OF ADVANCE COEFFICIENT Al,

030

FIG. 6 i

s-T, = A 0.44, 0.21

o.

12 INCH DIAMETER

WATER SPEED 18 'FEET PER

SECOND

CAVITATION NUMBER cr =

0.75

A E W 0.45,, -0.26, 0.16

MIT 029, 0.21

T M B 0.O, 6.16

P JO. 03 - 0.02

TUNNEL .AIR. CONTENT RATIO

1

06

a8

1.0

-

11.2

SCALE OF 'ADVANCE COEFFICIENT

-1 Lb

FM. 7,

, i -1 . ,, _ , - - -"*" . , , I .. . -_ , , . , _ . . _ _ -I 1 - i

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, , .. . 1 0.6 0.4 0.2 NS J 0 0.02

a

0.04 0.08 1.40.10 , 0.1 00

0.

0.

SCALE OF ADVANCE COEFFICIENT j'

0.10 .02 'LL

8

0

cr

0

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IL-0

.0.8

FIG. 8

5 .. , ! 1 , ! . ! _ 1 , 1 IF 1 , 1 _ ____ . , ,

111.4

- 1 il , / . 1 ,

.

___

--:.-

1 _,-.-_-_./ , 1 1 . 1

-1 , , ! __----___-- __

IL.

1 I1 t _ i ....,_ _ 0 6 0.8 1.0 1.2 1.

WATER SPEED 18 FEET PER SECOND

CAVITATION NUMBER a- =

,L50

,

TUNNEL AIR CONTENT RATIO'

T 0.55E 030; 0.14 S P

002

0.6 >-0.5 0.4

0

c2 0.3 M B 0.04 KT

112 0:8 0.7 10.5 z I 11 0

₀₄

84ANS...7uM

Esig

awn= smnra 11/11/1C_{NWIMMO SWIM}

_Ina

MIMI, MO= MINIM WINES SE

"

MIMS O jra:

ELJELNI:=SE...

ME

E-Imm.EPILIMEIJAM

mem

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=NM-.3E-"Erl.ERWEEMEr.aairi

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11_4

=MEM!

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5 =ME_

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4: -4w, 1.11 miiHEN 0 2

MIME

EMMEN

SMINCE

111111KME

kfi

ME

1111111ffin

11E11

16 INCH DIAMETER

WATER SPEED 18 FEET PER SECOND

CAVITATION. NUMBER a. = 11.00

1

TUNNEL AIR CONTENT RATIO

T MB

_{0.63, 0.30, 0.19}

NS P

0.6 0.8 1.0 1.2

SCALE OF ADVANCE COEFFICIENT .1

Ui 0.101 1.4., 0.02

5

0.04 u.

8

0, Ui'., 10

. 0 .

0.1 0.02

0

0.08

,FIG. 9

0.8

0.7

WATER SPEED 18 FEET PER SECOND

CAVITATION NUMBER cr = 0.75

rUNNEL AIR CONTENT RATIO

T M B 0.50, 0.29, 0.18

N S P 0.03

06 0.8 1.0

SCALE OF ADVANCE COEFFICIFNT J

1.2 0.02

a

1-z

O. 04E_ Iii cr 0.061-u_

0

LLI _J

0

to 0.08 10 FIG. 10

1111111111111111

10A

11!1111111111111

:z°Ew

1111111 11111

0

0.5

Ell

Ell

ugr MIEN 11

All MI

MI

m10.3

11/11/11 EMI

MI 1111

in

II

0.2

111111 MEM

111111111E1111

0.1

MEM 11101

111111111111111111111011111111.

°04

0. 0.7 0.6

>-0

uJ

3

Lii 0.5 La 0.4 3 LL cn cc 0.3 u_ Ui

0 0.2

0.1

16 INCH DIAMETER

WATER SPEED 36 FEET PER SECOND

CAVITATION NUMBER a- = 1.50

TUNNEL AIR CONTENT RATIO

TM B 0.60, 0.19

N SP 0.61, 0144, 0.21, 0.06

SCALE OF ADVANCE COEFFICIENT J

0 0.02 Ui O. 04.1LI: UJ

0

(.1 Lii cc 0 0.06 E-LI_ LA.1 (r) 0.08 .10

FIG. II

/'---t/

/

e i

/

, s \ / , K Q `.,.,

./'

1 I \'

\

. 1.4 0.6 0.8 10 L2 0

0

I ---,

0.8 0.7 w 0.4 IL u_ Jo cn 0.3 u_ -J

0 0.2

cr) 0.1

WATER SPEED.36 FEET PER SECOND

CAVITATION NUMBER a =

1.00

TUNNEL AIR 'CONTENT RATIO

T MB 0.61, 0.12

N S P 0.62, 0.46, 0.23, 0.05

SCALE OF ADVANCE COEFFICIENT J

0 0.02

a

0.04 kt UJ

0

0

0.061-LLI ,(/) 0.08 0.10

FIG. 12

---.., ,-, \

/

,,., KO ---_______. , , , , r 4 0.6 0.8 1.0 1.2 1.4 I

6

11

0.

o

16 INCH DIAMETER

WATER SPEED(36 FEET PER SECOND

CAVITATION NUMBER o---= 0.75

.TUNNEL AIR CONTENT; RATIO:

.TMB

_0.63, 0.23, 1113

NSP

0.63, 0.45, 0.22, 0.06

SCALE OF ADVANCE COEFFICIENT

.02 Itjj =4,

'FIG. 13

1 1 ' I 1 , i . . , t I

1111

. . - _.-1 1 1 , v .. .. I _ fr r . - . .. _, . . I I . I I

--. _1 . 1 II .. 1 . II li -

ii

. . , -__ 1 .. F 1 _ , I'l . 1 0.6 0.8 1.0

_

1.2 1.4 -O. 0. 0.3 0 -J cn 0.2 0.1 J 0 0.04

0

0

0.06 0.08 .10

0.8 0.7 0.6 C.) L.LJ 0.5 0.4 IL C.) 0.3

0 0.2

SCALE OF ADVANCE COEFFICIENT J

WATER SPEED 36 FEET PER SECOND

CAVITATION NUMBER

ser

0.50

TUNNEL AIR CONTENT. RATIO,

T MB 0.75, 0.24, .0.115 PI

NSF

066, 0.45, 0.22, 0.03

0.6 ,0.8 1.0, 1.2 0 0.02

'a

: 0.04,LT

8

a

0.06+2 0.08 Ui 0.10

FIG. 14

I . I 1 . . _. -II , . ,.. _

7

, [ , . . .. , 1 ( _ , , , 1 1

/

1' 1 Ily, 1 , Ii t I ... -. I I , I . ' I . -.. ( 4 I 1 , A : \ i _ , 0 ; 1 . . 1 i . . . I 1 .. . 1 LI. .

--, r ' - it __ _ _ - _ .,- ...-1 ss s A =

LL LLI 0.8 0.7 0.1 00

18 INCH DIAMETER

WATER SPEED 18 FEET PER SECOND

CAVITATION NUMBER a =

1.50

TUNNEL AIR CONTENT RATIO

T M B 0.61, 0.21 N S P 0.07

0.6 0.8 1.0 1.2

SCALE OF ADVANCE COEFFICIENT J

0.02

a

0.04 L.L. ILJ

0

0.06

0

0.08

FIG. 15

Mink

\

\

li

1,11

\

I

1

OM

MI

o. 0.5 I

0.8

0.7

0.1

Q0

$8.1NCH DIAMETER

WATER SPEED 118 FEET PER SECOND

CAVITATION NUMBER cr

WO

TUNNEL AIR ,CONTENT RATIO

=-.e... _Tris1B

_{0.50, azz}

NSP 0.08

SCALE OF ADVANCE COEFFICIENT J.

.02

.0

o

tL .04

0

:ce

o

.06 LL. w, 1.

0

t.n 0 '.<!J

'FIG.16,.

1 . . I, , ic 1 I ! I

L.

MM.

NI

,, 77 ., I' .1 , , 1 .. I A , , _ , _ ., , i 1 il .,. s--'--7---"---,,,1 2 - -IL,_{, _} - ---'--.1, _ --- .1 e ,-, .. , 8 _. ., I .. , , [ _, 1 ... .. , . . ,---.. hiih I 1 ,. . . . I .. :!..' . .. ''.11 . ' , . , . . '. 0.5 0.6 0.8 1.0 1.2

/

-,

0. 0.7 1--

_z

ILI 0.4 LT.. Ui 0 U") cC 0.3 Lu 00 0.2 0..1 00.

18 INCH DIAMETER

WATER SPEED 18 FEET PER SECOND

CAVITATION NUMBER Cr

= 0.75

TUNNEL AIR CONTENT RATIO

T MB 0.53, 0.20

NSP 0.07

SCALE OF ADVANCE COEFFICIENT J

0.02 LU O. 0 4 LLJ

0

0.061-Lii _J 0.08 .10 FIG. 17 ,

/

-\

\

\

r

PII.111

Ell

y '

_ - .-K T 0.6 0.8 1.0 1.2 1.4 I

r

K 0

a

0

0. 0. 0.2 0.1 _ ..

.18 INCH DIAMETER

WATER SPEED

18 FEET PER SECOND'

.

CAVITATION NUMBER a

0.75

TESTED AT TM B

SYMBOL _{AIR CONTENT' RATIO}

0.53

_ 0.20

os.

0.8

1.0_

12 SCALE OF ADVANCE COEFFICIENT' LP/

3 .10 - 11,4 o212

0

.1 ,

z

..04E

0

.0 tLI

0

.06 I.

0

lii .< c.3 .08

FIG. 18

, 1 -3 .. I , -. -, ._ , , : . -1 . ,, II , . ... ,.. 1 . 3 ri -1 , , 1 :. . . . K Q : 4 .Fl . 1 = lio - --m - 1 + - ..

-ITT

! 1: . . I . I

a&MIL.

I _

Fu

T

4 = -. ... 0.6 = 8 0

)-0

uJ Iii 0.8 0.7 0.6 0.5 IC W_.r 0.4 LL LU , ir 0.3 0 Ui 0 0.2 Cl) 0.1

COMPARISON OF PROPULSION CHARACTERISTICS

ADVANCE COEFFICIENT J = 0.8

WATER SPEED 18 FEET PER SECOND

CAVITATION NUMBER a 1.50 1.00 0.75 0.08 0.061-C.)

0

cc

0

u_

0

0.02

0

FIG. 19

III

I

I

II

11111

111111111111

I

1

!NIEL

.111

MI

I

IF

Ii

I

III

x z 0 Z

z

o o 3 3 tc a la 4

1111

IIIII

III

1111

11111

Ili

-

-Pill

Pill

II

I I

111

I

0.1 0.2 0.3 0.4 0.5 0.6

SCALE OF AREA OF PROPELLER DISK AREA OF WORKING SECTION

4

I

I

0.

0.

0.1

ADVANCE COEFFICIENT J = 0.8

WATER SPEED, 36 FEET PER SECOND

CAVITATION NUMBER

.11

...

...ims _1.50

1.00

0,.75

0.50

AREA OF WORKING SECTION

-0.08

FIG. '20

I' 1 , 1 1 1 1 . -... ! 1 I L . --. I -- ----1 4:---I' . c4 .. -I 1 11 . 1 'M 'Cm) AO r,. I I 2 it . .... ... ... -,- - I K n II II , 1 [ I , _ - 1 1 IKT1 I il I. , '4. 1 I 1 . 0.1 0.2 0.3 0.4 0.5 SCALE OF _

AREA OF PROPELLER DISK

.

0.8

0.7

0.6

0.1

0

COMPARISON OF PROPULSION CHARACTERISTICS

ADVANCE COEFFICIENT J =1.05

WATER SPEED 18 FEET PER SECOND

CAVITATION NUMBER 1-50 1.00 0.75 0.08

a

0.06 1E5 U. IL 0.04 Lii

0

0

u_

0

0.02 <Co

FIG. 21

! i '

\IN

;,-\

_\

kr,

_{, A}

-

"."--1111011111hlki

NPL MIT

'MIT & NPL

II&

_ MIT. m o

z

x x,M-o 0, 0

z

n. co 40 Z i-01'w.0, xi o

i

= x

0 a

zz

_ 40 _i-a. o.. tn

z z

-.. = 0 _ N w *At

zz

40 CL 03 m .=

0 0

_z

N 03 X Z

i-= 0 =0 _ m E

z

3e La 4_ 3e zi

z

z"

CO .2 2 ₂

-

X I-03 X -

i

---

li

.---Al"...

ppm

_- .. } K N 0 0.1 0.2 0.3 0.4 0.5 0.6

SCALE OF AREA OF PROPELLER DISK AREA OF WORKING SECTION

0

0

0.2

I

i

I

I

-I -I

I I

I

& NPL

-7,1 sr 0. O. . P-. -

z

7_ O.

z

,

5 0.

8

0.3 LW -J

g:02

0.1 7 -. ADVANCE COEFFICIENT J =11.05 .

". WATER SPEED! 36, FEET PER SECOND'

CAVITATION NUMBER cy:

I . 5 1.00 0.75 40.50 mL' -=s,05 . 0.1 0.2 . 0.3 0.4 SCALE OF AREA OF PROPELLER DISK

-AREA OF WORKING SECTION

-6,-.08 0.5 1 I -. .. .. 1 I 1 - I ,

III

I -. . 1 II ..-, . 1 1 -.. , I IiI .2 I-I m

-

1 -1 I 11 , . I . ,

-,

PIM _{1111111%11111111111111} 1 I. r _ . 1 , , 1 :, , MEM I _ I 0. 0.04

0

.02

FIG. 22

0

COMPARISON OF PROPULSION CHARACTERISTICS

ADVANCE COEFEICIENT FOR ZERO THRUST

WATER SPEED 18 FEET PER SECOND

CAVITATION NUMBER a 1.00 0.75

FIG. 23

' 'NPL A A MIT NPI2 46411 & NPIL.; - --X 0

z

0 x x 0 c_, x:o le`ico;

z.z

___ oF___c.,

z

t-

L.2-x L.2-x

z

E 0 !to aw UV

Z Z

a

z

0 .N W

< Z

or 1 o

z

_ :

.

I-, .x

o

Xo xo

_z

CO ,F. le AO

_

'4 ae

z

N AD . 12 ICO JZ II...1ai 2

2

t -- _{- A}

AMIT:

II MIT MIT' NPL.' _ _____,}1<0 _ ____._____,

a

NPL' 0.1 0.2 03 0.4 0.5 0.6

SCALE OF AREA OF PROPELLER DISK

AREA OF WORKING SECTION

I

I

11

I

I

I

11 II

_I

I

Lii

LL

0

ADVANCE COEFFICIENT FOR ZERO THRUST

WATER SPEED 36 FEET PER SECOND

CAVITATION NUMBER cir

- - -

L5 0,

100

0.75

0.50

0.1 0.2

03

04

AREA OF PROPELLER DISK

SCALE OF

AREA OF WORKING SECTION

05

FIG. 24'

I I . -1 - _ . . , '

II I

- -I i 1

-I I 1 I ll 1 1 1 1 ' 1 X ' 0 X0 I Z

0

1 ' I 0_1 2 .m. 1.D 1 -:cn 1

z

_ 1 . .. . . ...L__ 2_ 1---.t 1 ..1 . I I . . .1 ''''.77' `..'"--' I 1. _::, . ... I , -... , . . IMMERMIROXIMMIIIIIIROL* -,i , 1 , t...1.::. , . 1 . , .,. ... ...

:

' . . _.1I H..` .. , 11 ...

0.15

TUNNEL WALL EFFECT

12 INCH DIAMETER

J =0.925

V = 18 ft./sec.

R = 2.6x106

F = 3.2

a/as= 0.30 (interpolated)

D = 8" 12" 16" 18" o o-TMB NSP MIT

A EW KMW NPL

e

Eli 413I e

FIG. 25

02

0.3 0.4

SCALE OF bREA OF PROPELLER DISK AR EA OF WORKING SECTION I I -= -6

9

0.15 0.10 0.05

J = 0.925

cr = 1.00

D18"

8" 12" 16" o

o-

0 'TM e NSP MIT AEW KMW NPL

o

e

ED

FIG. 26

24-5 go

5.7

(1,--1.5 s A A_w

e

. 3. 4 . 1. 7. R=4.6

e-.4 .. . 1.5 X106 2_2 ciD 3.8_ 17

0

1.4 27

c

I.4.6 5.8

M,--0

lt,

1.5 27 iRei. 49 4

9

3.2 5.3 4,-3.4 s_i

0-0 0,1 _0.2 0.3 _{0.4 0.5 0.6 0.7}

AIR CONTENT RATIO

_a/as

.

0.15

0.10

0.05

106

AVERAGE OF KT RELATIVE TO AIR CONTENT

J = 0.925

= 1.00

D = 8" 12" 16" 18" o

6

o-

9

TMB NSP

MIT

AEW KMW NPL

0

9

(i)

o-0.122 t 7% 1.5 2 3 4 5 6 7 8 _{9 107}

LOG R (REYNOLDS NUMBER)

ere 0.15 0-05 e-r

J =0-925

0.75

-D=

8"

1 2" 16" 18"

o

6

o-

9

TMB 1NSP MIT

_{AEW :KMW' NPL}

e

411

e

e

'FIG. 28

I 1 d1 1 i . II ' 1 , 1 ,,

:

. , ., .. i (1)

eo

. I 1 14

n

T 1 :

a=

I ., 1 1 ,, 1 , I -of108 t 1E111 Vo .7 1 1 ti r 1 . , .. , ' ., ,. i ',.., ---1A 1 i I

-

. 106 1.5 2 3 4 5 6 7 8 9_ 107

LOG R (REYNOLDS NUMBER).

5

0.10

0

Cl) = 0

a

a

0.30

AVERAGE, OF

Ka,

RELATIVE TO

AIR 'CONTENT:

0.925

.t. 00 D = 8" 12" 1i6"' 113" 0 0-T MB

NSP MIt

AEW KMW NPL,

3

S .

FIG. 29,

1. 11 .. ' 'i 1 1 , 1 _., 1 G , , , il ,

o

-. its

9

.. , ... ..,,. ] 1 1 .. i, '., .1 106 1:5 2 3 4 5 6 7 8 9 107

LOG IR (REYNOLDS NUMBER).

0.25

0

0.30

106 1.5, 2 3 4 5 6

_{7 8 9 107}

LOG R (REYNOLDS NUMBER)

FIG- 30

_ , I , . , , ' , i . , I , . ! 1 , , . i 1 ri .. . 1 , . 1 ! . . J . . 1 ---1 ---....1 1. I I , I .=F , . ,. , '

It

1 1 . 1

6

1 , , III , ,., . , , . --1

,

.,. 1

II. .

= 0.925

-

= 0.75

D 112" 16" c'y O. TMB NSP

MIT AEW KMW

1NPL cp, , Elf Cc

a

J 18"

9