An investigation of the effect of Reynolds number on velocity surveys conducted in the subsonic wind tunnel

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DEPARTMENT OF THE NAVY

NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER

WASHINGTCN, 0. C. 20034

AN INVESTIGATION OF THE EFFECT OF REYNOLDS NUMBER

ON VELOCITY SURVEYS CONDUCTED IN THE

SUBSONIC WIND TUNNEL

by

Albert L. Boyle

This document has been approved for public release and sale; its distribution

is unlimited.

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TABLE OF CONTENTS

Page

ABSTRACT 1

ADMINISTRATIVE INFORMATION 1

INTRODUCTION 1

TEST CONDITIONS AND PROCEDURES 1

PRESENTATION AND DISCUSSION OF TEST RESULTS 2

CONCLUSIONS 4

LIST OF FIGURES

Page

Figure 1 - Wake Screen and Pitot-Tube Rake Installed in

Wind Tunnel 5

Figure 2 - Circumferential Longitudinal Velocity Distribution for an Axisymmetric Body Tested at a Series of Wind

Tunnel Velocities 6

Figure 3 - Circumferential Mean Longitudinal Velocity for an Axisymmetric Model Tested at a Series of Wind

Tunnel Velocities 8

Figure 4 - Volumetric Mean Velocity for an Axisymmetric Model

Tested at a Series of Wind Velocities 8

Figure 5 - Amplitudes of Various Orders of Harmonics of Longitudinal Velocity for an Axisyinmetric Model

Tested at Different Wind Tunnel Velocities 9

Figure 6 - Phase Angles of Various Harmonics of Longitudinal Velocity for an Axisymmetric Model Tested at

Different Wind Tunnel Velocities 11

Figure 7 - Circumferential Longitudinal Velocity Distribution for a Three-Cycle Wake Screen Tested at a Series of

Wind Tunnel Velocities 14

Figure 8 - Amplitudes of Various Orders of Harmonics of

Longitudinal Velocity for a Three-Cycle Wake Screen

Tested at Different Wind Tunnel Velocities 16

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ABSTRACT

Results are presented of an investigation of the effect of Reynolds number on velocity surveys conducted in a sub-sonic wind tunnel. A series of velocity surveys was con-ducted over a wide range of wind velocities. The surveys were made behind two configurations- -an axisymmetrical body

with appendages and a three-cycle wake screen. The shape

of the velocity distribution curves was relatively unaffected by changes in wind velocity; however, the mean values of the distributions varied significantly with velocity.

ADMINISTRATIVE INFORMATION

This test program was funded under Naval Ship Systems Command

Sub-project S-Fll3 11 08, Task 10441. Completion of the analysis and

prepara-tion of the report were funded by the General Hydromechanic Research

Pro-grain, Subproject S-F009 01 01, Task 0101.

INTRODUCT ION

In recent years, it has been the practice at the Naval Ship Research

and Development Center to conduct certain kinds of ship model experiments

in the subsonic wind tunnel. While the high degree of automation in this facility greatly simplifies the acquisition of data, the physical

limi-tations of the tunnel impose a restriction on the maximum value of Reynolds number that can be attained.

Since it was desirable that the test results should agree with

similar towing-tank and full-scale measurements, generally conducted at higher Reynolds numbers, it was considered useful to determine the

Reynolds effect, if any, on the wind tunnel experiments. This investigation was accomplished by conducting a series of velocity surveys behind two

con-figurations in the wind tunnel over a range of air velocities. This report

presents and discusses the results of the tests.

TEST CONDITIONS AND PROCEDURES

The first series of velocity surveys was conducted behind an

axisymmetric body with appendages. Velocity measurements were taken at a

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The angular positions were taken at increments of 5 deg, except in the

immediate area of the appendages, where increments of 2 deg were used. The wind tunnel velocity was varied in five steps, ranging from a low of 39 fps

to the maximum tunnel velocity of 220 fps. The range of ve1ocities

corresponds to a range of Reynolds numbers from 4.4 x 106 to approximately

2.5 x 1O,7 based on overall body length. The severe restriction in the

range of attainable Reynolds numbers is due to limitations of model size and maximum air velocity. The problem becomes apparent when it is

recognized that this kind of test would normally be run in the towing tank

at a Reynolds number greater than 2.0 x l0. The corresponding full-scale

Reynolds number would be significantly larger.

The second configuration used in the test program was that of a

three-cycle wake screen. The device was constructed to generate an

essentially pure third harmonic wake by varying the density of the

screen-ing. Figure 1 shows the screen and the pitot tube rake assembly.

PRESENTATION AND DISCUSSION OF TEST RESULTS

Figures 2a through 2c show the circumferential distributions of

longitudinal velocity behind the axisymmetric body. The distributions are plotted as the ratio of the local velocity V to the free-stream velocity V for three values of nondimensional radius r/R, where the value of R used

is 2.26 in. The results are shown for four test velocities, ranging from

78 to 220 fps. An additional test was conducted at a wind velocity of 39 fps; however, the extreme scatter of data rendered it useless in this

kind of analysis. The distributions shown in Figures 2a through 2c clearly

show an increase in the general level of the longitudinal velocity ratio as

the test velocity is increased. This is also illustrated by the plot of circumferential mean velocity in Figure 3 and by the calculated volumetric

mean velocity in Figure 4. This result indicates that the use of these

values in the design of wake-adapted propellers should be accompanied by

the application of a suitable correction factor. The advisability of such

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*

a correction is discussed in Reference 1, where a similar result was

en-countered in a study of scale effect on velocity surveys.

The test velocity seems, however, to have little effect on the shape

of the distribution curves. The curves were subjected to harmonic

analysis, and the effect of wind speed on the amplitudes and phase angles

was found to be random with scatter similar to that previously encountered

in tests of this kind. The maximum scatter is shown by the plot of har-monic amplitudes for the two velocity extremes in Figures 5a through 5c.

The agreement shown here is surprisingly good, considering that a test

velocity of 78 fps produces a rough distribution curve that would normally show a rather large difference at higher harmonics. The comparison of harmonic phase angles is shown in Figures 6a through 6c. It should be

recognized that the phase angle is extremely sensitive to small changes in the distribution curve, especially where the amplitudes are small.

The velocity distributions measured behind the three-cycle wake

screen were analyzed in the same manner. Figures 7a through 7c show the

longitudinal velocities. The results are plotted for three radial

positions inside a disk having a radius R equal to 3 in. The comparisons

are made for three test velocities at 50, 100, and 150 fps.

Figure 7a shows the same relationship between the mean level of the

curves and the test velocity. That is, the general level of the curves

tends to rise as the velocity is increased. The effect is not quite so

evident in Figures 7b and 7c where the radial positions are increased to a

region of higher local velocity. Again the shape of the curves seems to

be relatively unaffected by changes in wind velocity. This is also shown

by the plots of harmonic amplitude in Figures 8a through 8c.

While the foregoing discussion was confined to the longitudinal velocity component, the radial and tangential components were also measured

and analyzed. The quantities were relatively small, and no significant

effect of Reynolds number was noted.

1. Cheng, H.M. and Hadler, J.B., "Analysis of NSMB Wake Survey on Victory Ship Models," Marine Technology, Vol. 3, No. 1 (Jan 1966).

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CONCLUSIONS

The following conclusions are drawn from the analysis.

Wind velocity used in the velocity surveys has little effect on

the shape of the circumferential distribution of longitudinal velocity;

however, it has a definite effect on its mean value. This change in the

circumferential mean velocity results in a corresponding change in the volumetric mean velocity, i.e., the higher the test velocity the higher

the value. This conclusion is similar to that reached by Cheng and Hadler in their investigation of scale effect on velocity surveys.

There is no consistent relationship between the magnitudes of

harmonic anplitude and phase angle and the test velocity. The changes in

amplitude and phase are random and of the magnitude usually encountered in

tests of this kind. It appears that the Reynolds number has little effect insofar as the relative amplitudes of various orders of harmonics are

con-cerned.

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Figure 1 - Wake Screen and Pitot-Tube Rake Installed in Wind Tunnel

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*

0

>. 0.80

I-0

J

LJ 0.60 0.40 1.20 1.00 *

0

0.80

I-0

_. 0.60 0 I-0.40 0.20

Figure 2 - Circumferential Longitudinal Velocity Distribution for an Axisynnetric Body Tested at a Series of Wind Tunnel Velocities

1 20

0.20

100 00 140 00 180.00 220 00

POSITION ANGLE IN DEGREES

Figure 2a Radius Equal to O.354R

260.00 300 00 340 00 380 00

-20.0 20.00 60 00 100 00 140 00 180 00 220 00 260 00 300 00 340 00 380.00

Figure 2b Radius Equal to O.575R

SYMBOL TUNNEL VELOCITY (FPS)

o

78

o

120 160 x 220 00 2700 90° 180°

00Iø!0

. 0

B

12078 160

X

220 ° C

o8L°

0 -20 00 20.00 60.00

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12 > 0.8 I-L) C 0.6 C -J 0.2 7

878 120

X 220 -

--:°o'

ic -'0

'

0

1xx'

-20. 20 60 100 140 180 220 260 300 340 380

POSITION PJ1GLE IN DEGREES

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E w L) 0.80 C.70 x >- 0.60 I.-C-)

0

-J Ui -J 0.50

0 I-0

-j

0.40 0.30 0.70 0.60 C-) 0.50 Ui 0.30 TUNNEL VELOCITY (FPS) 78

-120

- - - 160

- -220

8 TUNNEL VELOCITY (FPS) 78 120 160 220

- -

-- --

-

_{_<-.---_}

-0.30 0.40 0.50 0 60 0.70 0 80 0 90 1 00 RADIUS r/R

Figure 3 _{- Circunferentia1. Mean Longitudinal Velocity for an Axisymmetric} Model Tested at a Series of Wind Tunnel Velocities

0.30 0.40 0 50 0.60 0.70 0 80 0.90 1.00

RADIUS r/R

Figure 4 - Volumetric Mean Velocity for an Axisymmetric Model Tested at Series of Wind Velocities

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Figure 5 - Amplitudes of Various Orders of Harmonics of Longitudinal Velocity for an Axisymmetric Model Tested at Different Wind Tunnel

Velocities 0 .06 0.05 Lt)

0

0.04

0

-J -J 0.03

I-0

-J 0.02 L)

0

U-0.01 UJ -J 0 0.00 3

\

5 7 9 ORDER OF HARMONICS N

Figure 5a - Radius Equal to O.354R

9 TUNNEL VELOCITY (FPS) 78 220

N

11 13 15

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U-, 0.03 >- I--J uJ 0.02 = -J 0.01 TUNNEL VELOCITY (FPS 78

- 220

TUNNEL VELOCITY (FPS) 78 220 \ 3

\

5 9 ORDER OF HARMONICS N

Figure 5c - Radius Equal to l.018R

10

11 13 15

1 3 5 7 9 11 13 15

ORDER OF HARMONICS N

Figure Sb - Radius Equal to O.575R

0.11 o.io x V) _{0 .09} I->- 0.08 I-L) -J _0.07 -J 0.06 0.05 0.04 0.03 0.02 0.01 0.00

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300

200

100

0

\

Figure 6 - Phase Angles of Various Harmonics of Longitudinal Velocity for an Axisymmetric Model Tested at Different Wind

Tunnel Velocities

I

\

V

11 /

I

I TUNNEL VELOCITY (FPS) 78

- - 220

I I 3 5 7 9 11 13 ORDER OF HARMONICS N

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300 200 100 0

/

'7

/

\

I

TUNNEL VELOCITY (FPS) 78

- - 220

12 3 5 7 9 11 13 ORDER OF HARMONICS N

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300 200 100 13

/

/.

/

1 I

/

-

I

A

\

I

\\

I

\

TUNNEL VELOCITY 78 (FPS)

- 220

3 5 7 9 11 13 ORDER OF HARMONICS N

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1.00 C 0.80 C LU 0.60 = 1.20

040

C

Figure 7 - Circumferential Longitura1 Velocity Distribution for a Three-Cycle Wake Screen Tested at a Series of Wind Tunnel

Velocities

0 20

14 SYMBOL TUNNEL VELOCITY (FPS)

°

III'

U 2950

1:01IIlI'2400

0:

,o.

00o. 0 0 0 C0 0 -20.00 20 00 60 00 100 00 140 00 180 00 220 00 260 00 300 00 340 00 380.00

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L) C C 1.20 1.00 >- 0.80 i 0.60 I.-0.40 0.20 1.20 : 1.00 0.80 0.40 0.20 -20.00 20.00 60 00 100.00 140 00 180.00 220 00 260.00 300.00 340.00 380.00 POSITION ANGLE IN DEGREES

Figure 7c - Radius Equal to O.933R

15 SYMBOL TUNNEL VELOCITY (FPS)

o

50

o

100

X

150 0 00 J' 0 0 0 -0 0. 0. -0 I . o 0

.0

0

o

50

o

100

X

150 0

..g e64

..

...

. 0 -20.0 20 00 60 00 100 00 140 00 180.00 220 00 260 00 300 00 340.00 380.00

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Figure 8 - Amplitudes of Various Orders of Harmonics of Longitudinal Velocity for a Three-Cycle Wake Screen

Tested at Different Wind Tunnel Velocities

0.16 0.15 0.14 0.13 0.12 0.11 0.06 0.05 0.04 0.03 0.02 0.01 0.00

ii

Ii

TUNNEL VELOCITY (FPs) 50

- 100

- 150 1 3 5 7 ORDER OF HAR?IONICS N

Figure 8a - Radius Equal to O.267R

16

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0.26

0.24

0.22 x

(t) >-

0.18

I-(-)

0.16

-4

0.14 F-0.12

0

-4

0

0.10

L)

0

0.08 =

Li..

0.06

0

u.j

I--4

3-< 0.02

0.00

17 TUNNEL VELOCITY (FPS) 50

- 100

150 3 5 7 9 ORDER OF HARMONICS N

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0 .2

0.26

0.24 X 0.22

(I,

0

0.20 >-I-

0.18 -f

0

-J

0.16 -j

-4

=

I-

4-o

-J

0

v,

0.10

L) -4

0.08 =

!

0.02

0.00

1

/

I

TUNNEL VELOCITY (FPs) 50 100

- 150

3 5 7 ORDER OF HARMONICS N

Figure 8c - Radius Equal to 0.933R

18

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IJ4CLASSIFIED

DD

FORM

1473

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I NOV 15 UNCLASSIFIED

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Security classltication of title, body of abstract nod index.n' ,.nnotatin ruuI be entered when the overall report Is classified) ORIGINATING ACTIVITY (Corporate author)

Naval Ship Research and Development Center Washington, D.C. 20034

Za. REPORT SECURITY CLASSIFICATION

UNCLASSIFIED 2b. GROUP

3. REPORT TITLE

AN INVESTIGATION OF THE EFFECT OF REYNOLDS NUMBER ON VELOCITY SURVEYS CONDUCTED IN THE SUBSONIC WIND TUNNEL

4. OESCRIPTIVE NOTES (Type of report and inclusIve aatesl

Research and Development

S AU THORISI (First name, middle initial, last name)

Albert L. Boyle

6. REPORT GATE

September 1970

Ta. TOTAL NO, OF PAGES 21 lb. NO. OF REFS 1 S.. CONTUACT OR GRANT NO b. POJEC T NO. S-Fll3 11 08, Task 10441 C. S-F009 01 01, Task 0101 d.

Sn. ORIGINATOR'S REPORT NUMBERISt

3408

St'. OTHER REPORT NOISI (Any other numbers that may be assigned

this report)

tO. DISTRIRUTION STATEMENT

This document has been approved for public release and sale; its distribution is

unlimited.

II, SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY NAVSHI PS

3. ABSTRACT

Results are presented of an investigation of the effect of Reynolds number on velocity surveys conducted in a subsonic wind

tunnel. A series of velocity surveys was conducted over a wide range of wind velocities. The surveys were made behind two

configurations--an axisymmetrical body with appendages and a three-cycle wake screen. The shape of the velocity distribution

curves was relatively unaffected by changes in wind velocity; however, the mean values of the distributions varied significantly

with velocity.

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UNCLASSIFIED Security CIassifiction

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I NOV 68FORM

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UNCLASSIFIED

KEY WORO LINK A LINK 6 LINK C

ROLE WT ROLE Wi ROLE WI

Effect of Reynolds Number on Wake Surveys