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.
September 1970
Report 3408
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
11
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.
ADMINISTRATIVE INFORMATION
This test program was funded under Naval Ship Systems Command Subproject S-Fll3 11 08, Task 10441.
Completion of the analysis and prepara-
tion of the report were funded by the General Hydromechanic Research Prograin, 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 configurations 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
series of radial locations in, and slightly beyond, the propeller disk area.
1
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
The range of ve1ocities
to the maximum tunnel velocity of 220 fps.
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 screening.
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.
plotted as the ratio of the local velocity V
The distributions are
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.
2
The advisability of such
*
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.
longitudinal velocities.
Figures 7a through 7c show the
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).
3
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 concerned.
4
Figure 1 - Wake Screen and Pitot-Tube Rake Installed in
Wind Tunnel
5
Figure 2 - Circumferential Longitudinal Velocity Distribution for
an Axisynnetric Body Tested at a Series of Wind Tunnel Velocities
1
20
SYMBOL
o
o
TUNNEL VELOCITY (FPS)
78
120
00
160
*
0
2700
90°
220
x
180°
>. 0.80
I-
0
J
LJ
0.60
00Iø!0
0.40
.
0
0.20
-20 00
20.00
60.00
140 00
100 00
180.00
220 00
260.00
300 00
340 00
380 00
POSITION ANGLE IN DEGREES
Figure 2a
Radius Equal to O.354R
1.20
SYMBOL
TUNNEL VELOCITY (FPS)
78
120
160
220
B
1.00
*
X
0
0.80
I-
0
_.
0.60
0
I-
°
C
0
o8L°
0.40
0.20
-20.0
20.00
60 00
100 00
140 00
180 00
220 00
260 00
POSITION ANGLE IN DEGREES
Figure 2b
Radius Equal to O.575R
300 00
340 00
380.00
12
SYMBOL
--
-
TUNNEL VELOCITY (FPS)
878
120
X
220
>
I-
:°o'
0.8
L)
C
-
ic
'0
0
'
1xx'
0.6
C
-J
0.2
-20.
20
60
100
180
140
220
260
POSITION PJ1GLE IN DEGREES
Figure 2c - Radius Equal to l.018R
7
300
340
380
0.80
-
TUNNEL VELOCITY (FPS)
-C.70
x
78
120
160
220
0.60
>I.-
C-)
0
-J
Ui
-J
0.50
0
I-
- - - _<-.---_
0
-j
0.40
0.30
0.30
0.40
0.50
0.70
0 60
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
0.70
TUNNEL VELOCITY (FPS)
78
E
0.60
-120
- - - 160
- -220
-_.--- ----.
C-)
0.50
Ui
w
L)
0.30
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
8
Figure 5 - Amplitudes of Various Orders of Harmonics of Longitudinal
Velocity for an Axisymmetric Model Tested at Different Wind Tunnel
Velocities
0 .06
TUNNEL VELOCITY (FPS)
78
220
0.05
Lt)
0
0.04
0
-J
-J
0.03
I-
0
-J
L)
\
0.02
0
U-
0.01
UJ
N
-J
0
0.00
3
5
9
7
11
ORDER OF HARMONICS N
Figure 5a - Radius Equal to O.354R
9
13
15
0.11
TUNNEL VELOCITY (FPS
78
x
V)
- 220
o.io
0 .09
I>I-
0.08
L)
-J
0.07
-J
0.06
0.05
0.04
0.03
0.02
0.01
0.00
5
3
1
9
7
13
11
15
ORDER OF HARMONICS N
Figure Sb - Radius Equal to O.575R
U-,
0.03
TUNNEL VELOCITY (FPS)
>-
I-
78
220
-J
uJ
0.02
=
-J
\
\
0.01
3
9
5
ORDER OF HARMONICS N
Figure 5c - Radius Equal to l.018R
10
11
13
15
Figure 6 - Phase Angles of Various Harmonics of Longitudinal
Velocity for an Axisymmetric Model Tested at Different Wind
Tunnel Velocities
300
I
\
I
/
V
200
I
I
100
\
I
TUNNEL VELOCITY (FPS)
78
- - 220
0
3
5
7
9
ORDER OF HARMONICS N
Figure 6a - Radius Equal to O.354R
11
11
13
300
I
200
I
I
/
100
/
'7
\
\
\
\
TUNNEL VELOCITY (FPS)
78
- - 220
0
3
5
7
9
ORDER OF HARMONICS N
Figure 6b - Radius Equal to O.575R
12
11
13
/.
/
300
/
/
/
1
200
/
/
I
-
I
I
I
\
A
\\
\
I
100
TUNNEL VELOCITY (FPS)
78
\
3
5
7
- 220
9
ORDER OF HARMONICS N
Figure 6c - Radius Equal to 1.018R
13
11
13
Figure 7 - Circumferential Longitura1 Velocity Distribution for a
Three-Cycle Wake Screen Tested at a Series of Wind Tunnel
Velocities
1.20
U
TUNNEL VELOCITY (FPS)
SYMBOL
°
III'
2950
1.00
C
1:01IIlI'2400
0.80
C
LU
0.60
0:
0
=
C
0
040
00o.
C0
0
0 20
-20.00
,o.
20 00
60 00
100 00
0
140 00
180 00
220 00
260 00
POSITION ANGLE IN DEGREES
Figure 7a - Radius Equal to O.267R
14
300 00
340 00
380.00
1.20
TUNNEL VELOCITY (FPS)
SYMBOL
o
o
X
50
100
150
1.00
0.80
>-
L)
C
-
0
J'
0
0
0
00
0
0
0.
0.60
i
0.
-
.
I
I.o
.0
0.40
0
0.20
-20.0
20 00
100 00
60 00
140 00
0
260 00
220 00
180.00
300 00
340.00
380.00
POSITION ANGLE IN DEGREES
Figure 7b - Radius Equal to O.433R
1.20
SYMBOL
TUNNEL VELOCITY (FPS)
o
:
50
100
150
o
X
1.00
C
.. ...
..g e64
0
.
0.80
0
0.40
0.20
-20.00
20.00
60 00
100.00
140 00
180.00
220 00
260.00
POSITION ANGLE IN DEGREES
Figure 7c - Radius Equal to O.933R
15
300.00
340.00
380.00
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
TUNNEL VELOCITY (FPs)
50
- 100
- 150
0.15
0.14
0.13
ii
0.12
0.11
Ii
0.06
0.05
0.04
0.03
0.02
0.01
0.00
1
3
5
7
ORDER OF HAR?IONICS N
Figure 8a - Radius Equal to O.267R
16
9
0.26
TUNNEL VELOCITY (FPS)
50
- 100
0.24
x
150
0.22
(t)
>-
I-
0.18
(-)
0.16
-4
0.14
F-
0
-4
0
0.12
0.10
L)
0
0.08
=
Li..
0
0.06
u.j
I-4
3-
< 0.02
0.00
5
3
7
ORDER OF HARMONICS N
Figure 8b - Radius Equal to 0.433R
17
9
0 .2
TUNNEL VELOCITY (FPs)
50
100
0.26
- 150
0.24
I
X 0.22
(I,
0
>-
I-f
0
-J
0.20
/
0.18
0.16
-j
-4
=
I4-
o
-J
0
v,
L)
-4
=
0.10
0.08
!
0.02
0.00
1
5
3
7
ORDER OF HARMONICS N
Figure 8c - Radius Equal to 0.933R
18
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IJ4CLASSIFIED
DOCUMENT CONTROL DATA - R & D
Security classltication of title, body of abstract nod index.n' ,.nnotatin ruuI be entered when the overall report Is classified)
Za. REPORT SECURITY CLASSIFICATION
ORIGINATING ACTIVITY (Corporate author)
UNCLASSIFIED
Naval Ship Research and Development Center
Washington, D.C. 20034
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
Ta. TOTAL NO, OF PAGES
6. REPORT GATE
lb. NO. OF REFS
1
21
September 1970
Sn. ORIGINATOR'S REPORT NUMBERISt
S.. CONTUACT OR GRANT NO
b. POJEC T NO.
3408
S-Fll3 11 08, Task 10441
C.
S-F009 01 01, Task 0101
St'. OTHER REPORT NOISI (Any other numbers that may be assigned
this report)
d.
tO. DISTRIRUTION STATEMENT
This document has been approved for public release and sale; its distribution is
unlimited.
12. SPONSORING MILITARY ACTIVITY
II, SUPPLEMENTARY NOTES
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.
DD
FORM
I NOV 15
1473
S/N O1O1.O7.68O1
(PAGE 1)
UNCLASSIFIED
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KEY WORO
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WT
ROLE
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Effect of Reynolds Number on
Wake Surveys
DD
(PAG
FORM
I NOV 68
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1473 (BACK)
UNCLASSIFIED
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LINK C
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WI