Characteristics of a supersonic laminar boundary layer over a rough wall
by Joseph Michael DSa
A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE
in Mechanical Engineering
Montana State University
© Copyright by Joseph Michael DSa (1982)
Abstract:
The characteristics of a supersonic laminar boundary layer over a rough wall were investigated. The
boundary layer was produced by, a slender body of revolution at Mach 3 and the roughness consisted
of random distributed and two dimensional periodic overlays. Results reported here cover mean flow
profiles needed to validate and characterize the flow and detect changes in the profile caused by
roughness. The critical roughness needed to cause profile distortions is based on the Reynolds number
defined by local properties rather than free stream properties. The height of the distributed roughness
needed to cause profile distortions caused great difficulty in interpreting the profile data. The two
dimensional periodic overlay with a roughness height greater than the critical roughness height caused
an upstream movement of transition. The two dimensional overlay also caused an outward
displacement of the boundary layer edge with a simultaneous decrease in the boundary layer thickness
causing a distinct distortion of the boundary layer profile and an increase in the surface skin friction. STATEMENT OF PERMISSION TO COPY
In presenting this thesis in partial fulfillment of
the requirements for an advanced degree at Montana State
University, I agree that the Library shall make it freely
available for inspection.
I further agree that permission
for extensive copying of this thesis for scholarly purposes
may be granted by my major professor, or, in his absence,
by the Director of Libraries.
It is understood that any
copying or publication of this thesis for financial gain
shall not be allowed without my written permission.
CHARACTERISTICS OF A SUPERSONIC LAMINAR
BOUNDARY LAYER OVER A ROUGH WALL
by
JOSEPH MICHAEL D 1SA
A thesis submitted in partial fulfillment
of the requirements for the degree
of
MASTER OF SCIENCE
in
Mechanical Engineering
Approved:
Chairperson, Graduate Committee
/9 -
Head, Major Department
— ___
Graduate Dean
MONTANA STATE UNIVERSITY
Bozeman, Montana
July, 1982
ACKNOWLEDGEMENT
The author offers his sincere appreciation to the
following for their contribution to this investigation.
His advisor, Anthony Demetriades, for his guidance and
support throughout this investigation.
Bill Martindale and Bob Warrington for serving as
committee members and reviewing this thesis.
Gordon
Williamson
for
helpful
assistance
in
constructing the models for the experiment.
John
Rompel
for
his
expertise
and
assistance
in
putting together the electronic system for the experiment.
Glenn McCullough and Mel Roush for their assistance
during the course of the experiment.
The Mechanical Engineering Department of Montana State
University and Air Force Office of Scientific Research for
financial assistance and funding for this investigation.
Roberta Coppock for typing this thesis.
And last but not the least, his wife, Ela, for her
never-ending encouragement and understanding during this
investigation.
TABLE OF CONTENTS
Chapter
P&gfi.
VITA . . .
............
. . . . . . . . . . . . . . . .
ii
ACKNOWLEDGEMENT.................. .. . .................ill
LIST OF FIGURES. .......................................
vi
NOMENCLATURE ..............................
X
ABSTRACT.............. ............ .................. xi I
I.
INTRODUCTION '............ .....................
I
II.
DESIGN OF THE EXPERIMENT........................
4
III.
DESCRIPTION OF THE MODEL AND WIND TUNNEL
6
IV.
INSTRUMENTATION..........................
12
V.
DESCRIPTION OF MEASUREMENTS . . .............. .
15
Transition Measurement
15
....
....................
Test M a t r i x ................
Measurement of Surface Static Pressure
17
........
20
Reynolds Number Corrections to the Pitot
Probe . . . . . . . . . . . ....................
22
Measurement of the Location of the Roughened
Surfaces . . . . . . . . . . . . . . . . . . . .
23
Data Acquisition Procedures . . . . . . . . . . .
24
VI.
SUMMARY ON THE RANDOM SURFACE ROUGHNESS MODEL . .
30
VII.
COMPARISON OF SMOOTH AND SCREW MODEL. . . . . . .
32
VIII.
CONCLUSIONS . . . . . . . . . . . . . . . . . . . .
79
BIBLIOGRAPHY ......................
81
V
Page
APPENDICES ......................... .................. . 83
APPENDIX I .............. .. .............
84
APPENDIX II. . ...................................
89
APPENDIX I I I ...................................... .. . 92
APPENDIX IV. . . . . .
.........................
.103
Vl
LIST OF FIGURES
Fiqure
I.
Placement of the Model and Probe in the Test
Section (to scale) .....................
7
2.
Tops Exploded View of Model and Roughness
Afterbodies. Bottoms Wind-Tunnel Installation .
8
Views of the Model in the Tunnel. Note Microscope
for Probe-Tip Observation ............ . . . . .
9
3.
Details of Probe-Tip and Measuring Circuit. . . . .
13
5.
Microphotographs of Roughness Profiles for ScrewType Model (top) and 60-Grit or k = 0.004" Model
.
(below) ...................... ..
19
6.
Static Pressure and Mach Number (From Static and
Pitot Pressure) Results for Smooth Model. . . . .
«3CO
7.
Static Pressure and Mach Number (From Static and
Pitot Pressure) Results for Screw Model . . . . .
.
35
8.
Static Pressure Surveys . . . . . . . . . . . . .
.
36
9.
Mach Number Results (From Static Pressure and
Supply Pressure)
............................... .
37
10.
Velocity Profile on Smooth Wall, x = 6",
P0 = 600 milimeters Hg (Mercury). . . . . . . . .
CO
CO
11.
Velocity Profile on Smooth Wall, x = 4",
P0 = 400 mm. Hg ................................
.
39
Velocity Profile on Smooth Wall, x = 4,
P0 = 500 mm. Hg ................................
.
40
Velocity Profile on Smooth Wall, x = 4™,
Pq — 600 mm # Hy
. . .41
M
to
4.
13.
Linearity of Velocity Variation Near Wall for
Smooth Model, x = 6", Pq = 400 mm. Hg . . . . . .
CM
14.
vi i
Figure
Page
15.
Linearity of Velocity Variation Near Wall for
Smooth Model, x = 6", P0 = 500 mm. H g ............ 43
16.
Velocity Profile on Screw Model, x = 5",
P0 = 400 mm. Hg (Note Pitot Probe)................ 45
17.
Velocity Profile on Screw Model, x =4",
P0 = 400 mm. H g ..................................
46
Velocity Profile on Screw Model, x = 7",
P0 = 500 mm. H g ............................ ..
47
Velocity Profile on Screw Model, x = 6",
P0 = 500 mm. Hg
..........
48
Velocity Profile on Screw Model, x = 6",
P0 = 400 mm. H g .............................. .. .
49
Pitot Pressure Profile on Screw Model, x = 4",
P0 = 600 mm. H g ............................ ..
51
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
Comparison Between Smooth and Screw Velocity
Profiles, x = 6", P0 = 400 mm. Hg . . . . . . . .
.
52
Comparison Between Smooth and Screw Velocity
Profiles, x ~ 681, P0 = 500 mm. Hg . . . . . . . . .
53
Comparison Between Smooth and Screw Velocity
Profiles, x = 6", P0 = 600 mm. H g ................
54
Comparison Between Smooth and Screw Velocity
Profiles, x = 7”, P0 = 600 mm. H g ........ ..
55
Comparison Between Smooth and Screw Velocity
Profiles, x = 7", P0 = 400 mm. H g ........ ..
56
Temperature Profile on Smooth Model, x = 4",
p = 500 mm. Hg. Note Surface Datum (Square
on Axis)............................ .............
57
Temperature Profile on Smooth Model for x = 4",
P0 = 600 mm. Hg. Note Datum (Square on Axis) . . .
58
'/
viii
Figure
29.
a.
b.
30.
(
Page
Determination of "Virtual Origin" for Smooth
Model (62 vs. x)........ ..
. . . . . . . .
.
Determination of "Virtual Origin” for Smooth
Model
vs. x) . . . . .
61
a.
Determination of "Virtual Origin" for Screw
Model (S1^ vs. x)................................. 62
b.
Determination of "Virtual Origin" for Screw
Model
vs. x) . . . . . . ....................... 63
31.
Form Factor for <Smooth and Screw Model............ 64
32.
a.
Momentum Thickness and Unit Reynolds Number
Results for Smooth Model . . . . . ..........
65
Momentum Reynolds Number Results for Smooth
Model ...................................
66
Boundary Layer Thickness Results for Smooth
Model
..........................
67
Momentum Thickness and Unit Reynolds Number
Results for Screw Model . . . . . . . . . . . .
68
Momentum Reynolds Number Results for Screw
Model
.
69
.
b.
c.
33.
60
a.
b.
.................................
c.
Boundary Layer Thickness Results for Screw
Model
e
e
e
e
e
o
e
.
e
e
e
e
e
e
e
e
e
e
e
e
e
®
70
Schlieren Photograph of Screw Model (P0
600
mm. Hg)
Note Onset of Transition
............
72
35.
Skin Friction Results for Smooth Model
73
36.
Third Degree Polynomial Fit of Velocity Variation
Near Effective Screw Surface, x
4", P0 =
400 mm. Hg.
......... ..
75
Third Degree Polynomial Curve Fit of Velocity
Variation Near Effective Screw Surface, x = 4 "
Pq = 500 mm. Hg . . . . . . .......... ..
76
34.
-
.
.
.
...........................
=
.
37.
.
IX
Figure
Page
38.
Third Degree Polynomial Curve Fit of Velocity
Variation Near Effective Screw Surface, x = Sei
Pq ” 600 mm . H g . . . . .
39.
Skin Friction Results for Screw Model .............78
X
NOMENCLATURE
Symbol
cfl
:
Friction coefficient (wall viscosity)
cf2
!
Friction coefficient (stream viscosity)
k
:
Roughness height
kI
:
Critical height for destabilization/transition
M
:
Mach number
P
Pressure
Pt
:
Pitot pressure reading
R
:
Gas constant
Re'
:
Unit Reynolds number
Re0
:
Momentum Reynolds number
Ree,Ts
Critical Reynolds number for destabilization
(based on roughness height and stream proper­
ties)
Rek' :
Critical Reynolds number for destabilization
(based on roughness height and conditions at
that height)
T
Temperature
Local stagnation temperature at pitot tube
Top
u
:
:
x
:
Axial Coordinate (measured from trailing edge
forward)
Y
*
Coordinate normal to the surface
Velocity
■
y
:
Transformed coordinate normal to the surface
;
Symbol
Description
Y
Specific heat ratio
6
Boundary layer thickness
6*
S
Displacement thickness
0
Momentum thickness
y
Viscosity
V
Kinematic Viscosity
p
Density
( )O
Stagnation (supply) conditions
( )e
Boundary-Layer edge conditions
( >k
Conditions at roughness height
( )w
Conditions on wall surface
xii
ABSTRACT
The characteristics of a supersonic laminar boundary
layer over a rough wall were investigated. The boundary
layer was,produced by, a slender body of revolution at Mach
3 and the roughness consisted of random distributed and two
dimensional periodic overlays. Results reported here cover
mean flow profiles needed to validate and characterize the
flow and detect changes in the profile caused by roughness.
The critical roughness needed to cause profile distortions
is based on the Reynolds number defined by local properties
rather than free stream properties.
The height of the
distributed roughness needed to cause profile distortions
caused great difficulty in interpreting the profile data.
The two dimensional, periodic overlay with a roughness
height greater than the critical roughness height caused an
upstream movement of transition.
The two dimensional
overlay also caused an outward displacement of the boundary
layer edge with a simultaneous decrease in the boundary
layer thickness causing a distinct distortion of the
boundary layer profile and an increase in the surface skin
friction.
CHAPTER I
INTRODUCTION
The
purpose
determine
of
the
present
the characteristics
investigation
was
to
of a supersonic laminar
boundary layer over a rough wall.
There
gradient,
are a number
of factors
surface heat transfer,
roughness
that
could
affect
laminar boundary layer.
such as pressure
bluntness,
the
curvature and
characteristics
of a
The question of how roughness
affects transition of a laminar boundary layer has been
addressed by many researchers in the past.
van Driest with McCauley
For instance,
(I) and later with Blumer
(2)
investigated the effects of three dimensional roughness on
transition of supersonic laminar boundary layers, while
Whitfield and Iannuzzi (3) investigated similar effects up
to a Mach number of 12 to verify the hypersonic extensions
of these effects proposed by Potter and Whitfield (4).
Roughness,
spheres
for all the above researchers,
glued to a smooth
surface
consisted of
in an array.
Only
recently, Reshotko and Leventhal (5) and Kendall (6) worked
with distributed random roughness
disturbances
(sandpaper) to study
caused by roughness in laminar low speed
boundary layers.
The question of how random distributed or
two dimensional periodic roughness affects characteristics
2
of a supersonic laminar boundary layer has been given
little attention in the past.
There were three questions which were of considerable
importance to the present investigation.
First of all, it
was necessary to determine the critical size of roughness
that
would
show
profile
distortions
compared
profiles of the smooth (no roughness) surface.
to
the
Second, how
does roughness (above the critical size) affect the point
of transition?
And third, why does surface skin friction
have to be greater for a rough (roughness above critical
value) surface
compared to a smooth surface?
The question concerning the critical size of roughness
has been addressed
in the past for low speed flows.
According
(7),
to Fiendt
the critical Reynolds number
necessary to show profile distortions is defined by free
stream properties, as
On the other hand, Reshotko (5) and Kendall (6) motivated
by Smith and Clutter (8) state that the critical Reynolds
number is defined by local properties as
Rek - -TT- = 100,.
Thus
it was
Reynolds
necessary
numbers
to determine
is applicable
which
for laminar
of
the
two
supersonic
3
flows.
The question of why skin friction increases for a
rough (roughness greater than the critical value) surface
compared
to
a smooth
surface
in a supersonic laminar
boundary layer has been given little attention in the past.
Although results bn how roughness affects the point of
transition for three dimensional
roughness
in laminar
supersonic boundary layers have been reported (I),
have
been
reported
for
random
distributed
or
none
two
dimensional periodic roughness for similar boundary layers.
CHAPTER II
DESIGN OF THE EXPERIMENT
The criteria to be met in designing this experiment
were as follows:
a)
The external condition had to be uniform and the ratio
of the roughness height k to the boundary layer thick­
ness
be constant
(or nearly so)
over
the measured
length of the model so that the profile distortion be
constant,
b)
The range of the Reynolds number Re0 had to lie below
the transition
value
(thought to be 400-800)
and
yet be high enough to detect profile distortions,
c)
The ratio of k/S had to be large enough to detect pro­
file distortions compared to the smooth wall case.
The test model was a sharp nosed body of revolution.
In this w a y y the cylindrical
surface,
surface,
unlike a flat
would be void of side wall interference.
The
sharp nose would suppress any bluntness phenomena (e.g.
entropy gradients) and the small ogive angle would not
allow a large pressure drop across the weak shock from the
nose.
Calculations
show
that a model
like
the one
mentioned when placed in the test section of the wind
tunnel would have a boundary layer thick enough to avoid
resolution problems with miniaturized sensors and yet thin
5
enough to avoid phenomena peculiar to axisymmetric boundary
layers (9).
CHAPTER III
DESCRIPTION OF MODEL AND WIND-TUNNEL
The wind-tunnel and model are pictured on Figures I
through 3.
The MSU Supersonic Wind Tunnel (MSU/SWT) is
configured to operate continuously with Mach 3.0 nozzle
discharging into a 3.1" x 3.2" (7.87 cm. x 8.13 cm.) test
section.
The stream unit Reynolds number Re' range varies
from about 20,000 to 60,000 per cm.
The
model
consisted
of
a sharp
ogive-cylinder
combination with an overall length of 12.6" (32.0 cm).
The
ogive
the
tip formed a cone 5.2°
in half angle,
with
purpose of avoiding significant shock waves reflecting on
the model surface by sidewall reflection.
The ogive was
4.6" (11.68 cm.) long and was detachable from the 8" (20.32
cm.) long cylindrical afterbody.
Several afterbodies had
been built, and the design allowed for rapid disassembly
and reinstallation of the desired afterbody in the SWT
without removing the entire model.
The ogive-afterbody
junction
for
choice.
was
designed
to be
flush
each afterbody
The entire model was suspended by two vertical
actuator struts, while two additional struts supported the
sensor probe in use.
The model-probe arrangement could be
moved vertically in unison (for example, when starting the
tunnel, they were moved to the tunnel ceiling to prevent
AFTERBODY
OGIVE
PROBE
TRANSDUCE R
HOUSING
(INCH)
Figure I
Placement of the Model and Probe in the Test Section (to scale
8
Sr.VR
'enTrfic
Figure 2
Top:
Exploded View of Model and Roughness Afterbodies.
Bottom: Wind-Tunnel Installation
9
Figure 3
Views of the Model in the Tunnel.
Tip Observation
Note Microscope for Probe
10
initial choking) or the model could remain fixed and the
probe moved independently.
Alignment of the model
uniform
is critical.
In infinite,
streams the zero-angle of attack alignment is
sometimes done by pitching or yawing a model to symmetrize
surface pressures measured at selected points on the model.
The choice of equipping the present model with static
pressure orifices was available, and in fact, the initial
tests employed two surface pressure readings for that
purpose.
The results were useful, but it was also clear
that slight pressure gradients would exist on the model
surface due to its proximity to the sidewalls.
After
confirming that mechanically aligning the model along the
precise
tunnel axis was
as accurate
achieved with surface static tubes,
as the
alignment
it was decided to
discard the latter. The method of measuring the wall static
pressure will be discussed later.
Surface
sandpaper
roughness was generated by wrapping
around
the
cylindrical
afterbody.
shop
Several
afterbodies, each clad with its own permanent roughness
overlay
were
afterbody.
kept
on hand,
including a smooth-wall
Each overlay began at the upstream end of its
afterbody; the diameter of the latter was machined so that
11
the surface of the
overlay
blended
smoothly
with
the
trailing edge of the ogive.nose-tip. Although a slight
"step" existed for the larger roughnesses, it was not clear
that this step changed the flow in any way, but for reasons
mentioned later (Chapter VI), this problem was overlooked.
In the low-speed experiments of (5, 6) the roughness
height k of the sandpaper was taken to be equal to the
particle size quoted by the sandpaper manufacturer.
In the
present experiment k was determined by measurement, using
profilometer
records obtained for each size roughness.
This roughness height measurement was done for, and is
reported in, (9).
CHAPTER IV
INSTRUMENTATION
A brief
description
diagnostic tools used for
will
be
given
here
of
the
mean flow measurements.
The mean-flow instrumentation consisted mainly of the
pitot tube,
which is presented on Figure 4 in outline,
together with its recording equipment.
The tube itself
consisted of a 0.006" (0.015 cm.) O.D. steel tube which was
sharpened
by
etching
diameter opening.
to
a 0.004"
(0.01 cm.)
frontal
The tube was about 0,1" (0.25 cm.) long
and was
telescoped into progressively larger diameter
tubing,
which was in turn attached to a bullet shaped
housing
containing
the
pressure
transducer.
This
encapsulated transducer (Kulite Semi-conductor Corp., Model
VQH-250-10A), lay in the tunnel flow during the run.
The
bullet-shaped housing was held at the front of the probe
strut and could be remotely actuated along and vertically
to the model surface.
Thus the probe tip could be moved to
any desired position of measurement while the tunnel was
running.
The electrical leads of the transducer were channeled
to the outside of the tunnel and were connected to the
recording equipment shown, in block-diagram form, on Figure
4.
The transducer output was energized by 15.0 volts d.c.,
13
P R O B E
.004
TIP
.006
t /C A P S U L E
TRANSDUCER
r
P O W E R
&
SUPPLY
CONDITIONER
AMPLIFIER
D A M P E R
A/D
I
•I
CONVERTER
DIGITAL
Figure 4
STORAGE
Details of Probe-Tip and Measuring Circuit
14
amplified and connected to a Spectral Dynamic Corp.. Model
SD 133 8-channel A/D converter, from which it emerged in
digital form for storage on cassette by means of a Texas
Instruments ASR-700 computer terminal.
Thus a mean-flow
boundary layer survey consisted of traversing the probe in
steps outwards from the model surface,
wall.
In the process,
a trigger
starting at the
wheel
geared to the
vertical actuator produced electrical pulses spaced 0.001”
(one mil) of probe travel apart.
These pulses were sent to
the A/D converter, signaling the latter to read and record
the pitot probe output at each pulse only after the output
had stabilized
over a period of time. Thus a series of
pitot pressures were recorded, spaced one mil apart, and
stored in the ASR-700.
The transducer was calibrated frequently before and
after each series of measurements.
then' least-squares
The calibration was
fitted by a computer
program
to a
straight line:
(mm Hg.) = Ax(counts) + B
where A, B were constants,
so that the stored digital
reading (in counts) could be later converted to a pressure.
The data-reduction computer program will be discussed
later.
CHAPTER V
DESCRIPTION OF MEASUREMENTS
.
1
Transition Measurement
In order
to
find
the
roughness
height
for
which
transitional changes could be observed, initial transition
measurements
were
done
by
Demetriades
(10)
with
distributed roughness heights ranging from k = 0" t o k =
0.004".
The range of stagnation pressure Pq was 400 - 600
mm. Hg (Re' = 45,000 to 67,000 per cm.) and the sensor
covered positions on the model from x = I" (2.54 cm.) to 7"
(17.5 cm.)
where x was measured from the base
of the
model. It was found that for smaller roughnesses (k = 0 to
3.38 mils.) the fluctuation content (10) of the layer for
each k and P q was identical,
and for most of the model
surface the layer was laminar with trends in transition
onset towards the base of the model.
According
to
Feindt
(7)
the
minimum
effective
roughness height is based on stream conditions and has a
value of about
ue k
Ree,T - I T
= 120
For a laminar incompressible boundary layer with a linear
velocity profile, a momentum Reynolds number of 500 and a
thickness .6 of order 0.1" (conditions expected in the
16
present experiment)
roughness height
this critical Ree^T yields a critical
of order
n Re -ikI = 5 (6) Ri^ ^ 2 mils.
On
the
motivated
other
by
hand,
Smith
Reshotko
(5) and Kendall
arid Clutter (8) , indicate
(6),
that
the
critical Reynolds number is based on the flow speed at the
roughness height, with an approximate value of
UkK
100
from which the critical roughness in the present experiment
would be as follows
uK
Rek = ue
g-
ue6
S
ve .e
tc
6
(Linear velocity profile)
R=k ■ 46'
> 2 (Ree>
''"0 l|>
0
(100
500
I )V2
15
o.l - 10 mils,
However, this critical height would further increase in the
present instance because of the variation of the kinematic
viscosity across the layer.
It was
found
that an effect
of the
roughness
transition just began to appear for the 60-grit paper
on
for
17
which it was found that
k = 0.004"
Ree,T
Rek
(9)
~ 500
-
23
Comparing this result with Feindt's criterion made it clear
that the latter's criterion had been considerably exceeded,
and that the Reynolds number based on stream properties was
not the appropriate one.
Test Matrix
During
transition
measurements done by
and
preliminary
fluctuation
Demetriades (10), it appeared that
even for the highest P q attainable (600 mm. Hg), for a
sufficiently large distance the flow on the. smooth surface
was laminar and thus useful to this study.
Also, although
changes in the fluctuation data (10) could be seen only for
the 60-grit model (k = 0.004"), yet these changes it was
thought, were hot appreciable enough to show very distinct
profile distortions.
Hence, even roughnesses higher than k
= 0.004" were necessary for investigation.
For reasons
having to do with the statistical determination of the
surface (mentioned later),
60-grit was
ruled out.
use of sandpaper coarser than
Instead,
a periodic-roughness
model, called the "screw" model, was built.
This consisted
18
of the same general type of cylindrical afterbody used in
the tests except that its surface, instead of being covered
with sandpaper, was threaded like a screw.
threads per unit length was high,
The number of
so that the surface
appeared to the flow as having two-dimensional roughness.
A cross-section of the surface appears on Figure 5, and was
designed to provide the next big jump in k (in this case k
= 0.014") beyond the 60-grit paper.
In addition to answering questions posed earlier in
the introduction, the mean-flow profile measurements serve
three other functions:
and, hopefully,
"normal"?
demonstrate that the boundary-layer is
second,
measurements
first, they characterize the flow,
they
(along
with
the
hot-film
(10)) determine the turbulent vs. laminar
conditions and thus the Pof k and x bounds within which
laminar stability data would be taken? third, they provide
the distorted velocity profiles so that instability can be
theoretically predicted and compared
measurements.
with
stability
In view of the remarks of the. previous
paragraphs, the conditions for the profile measurements
were:
- type of surface:
smooth, 60-grit random, "screw".
- stagnation pressure:
600, 500, 400 mm. Hg.
19
Figure 5 Microphoto graphs of Roughness Profiles for Screw-Type Model
(top) and 60-Grit or k = 0.004" Model (below)
20
- profile positions;
x = I, 2 , 3 , 4 , 5, 6 and 7 inches
from the trailing edge.
Thus, 3 x 3 x 7 = 63 profiles were to be measured.
Measurement of Surface Static Pressure
Three
issues
regarding
the
profile
measurements
deserve brief discussion because of their importance in
finding
the
flow
properties
solutions employed.
and
the
novelty
of their
One of these was the measurement of
surface pressure on the smooth model, which was used to
determine the flow properties across the boundary layer.
.In this experiment,
this pressure was determined for
each profile by extrapolating
Specifically,
the pitot probe data.
it is safe to assume that very near the wall
(say y/ 6 - 0.1)
(a)
the
flow
is subsonic
and nearly
incompressible and (b) the velocity variation is linear.
Thus,
Pt = Pw .+ 1/2
u2
u = Cy, C is constant
Thus it follows that
Pt = Pw '+ (1/2)C2y2
and therefore Pw was determined from the intercept of a
plot of measured P t V s. y2.
There were
two main
reasons for following this
21
procedure.
First, slight Pw variations were expected from
the fact that the model was rather bulky for the size of
the test section, and the bow compression fan reflected on
the sidewalls and back onto the model.
One could drill and
instrument a large series of static taps on the model
surface, but this woiild'demand some raa priori™ knowledge of
the spots where pressure gradients were significant.
More
importantly, however, this would greatly increase the cost
and complexity of fabricating and installing the model and
would also make the measurement very tedious.
The second reason was even more forbidding:
static
pressures
were
measured
separately
sensor,
then its accuracy had to be
surface
with
happens
in such cases
that
of
the pitot
by another
"matched™
sensor.
if the
What
is that when combined
on the
usually
into the
Rayleigh relation, these two different pressure systems
give a finite, non-zero velocity on the wall.
The key lies
in the wide dynamic range needed for the pitot sensor in
supersonic flows.
For example, a non-zero surface velocity
could be detected in the present experiment if the pitot
system was off by 0.5 mm. Hg in accuracy within a required
dynamic range of about 300 mm. Hg, even without considering
the accuracy of the static-pressure system.
22
Reynolds Number Corrections to the Pitot Probe
For the first two or three points measured nearest the
wall,
the
Reynolds
number
(based
on
subsequently computed were of order 10-50=
probe
height)
In such cases,
the measurement is known to overestimate the actual pitot
reading (11).
numbers
program.
was
Initially, a correction for low Reynolds
therefore
included
in the
This correction was iterative;
data
reduction
The wall pressure
(computed as just outlined) was first used to convert all
data points to velocity, temperature, etc., and thus also
probe Reynolds number.
Using a “correction curve" such as
given in (11), p. 117, the actual pitot pressure was then
computed; the wall pressure was found anew and the process
repeated.
This procedure
was
found to be intractable.
The
correction decreased the pitot reading and therefore also
the Reynolds number, with a very small decrease in the
magnitude of the correction in the next loop.
extremely
This caused
slow convergence of the iteration.
A re­
examination of this scheme decreased confidence in the
correction itself,
experimental
which originally was a curve-fit of
points from various
sources.
Although a
Reynolds number correction was apparently necessary, its
23
magnitude
because
and algebraic
of
scatter
form
in the
are apparently
experimental
in
doubt
data.
The
correction was therefore removed from the data-reduction
loop,
resulting in probable errors in the first two or
three points closest to the wall for each profile.
As we
shall see later, this problem was not prohibitive as the
number of points needing correction was very small compared
to the total number of points used to interpret the data.
Measurement of the Location of the Roughened Surfaces
As already
mentioned,
the apparent
resistance
of
supersonic flows to destabilization by roughness, caused
this investigation to resort to large roughness heights k
(of
order
5/7).
The
definition
of
the
"surface",
therefore, became an important question when k/5 was no
longer much smaller than unity.
the surface
This is especially so when
is randomly rough.
Several alternative
definitions were considered, including the one described by
Leventhal (5) in which y = o corresponds to the peak of the
largest roughness element near the point of measurement.
This was not thought satisfactory since an extension of the
definition
of "near"
to the
upstream
or
downstream
direction could uncover an even larger roughness particle.
One can easily see that the bottom of the grit particles
24
(the valley floors) could not be used as the y = o surface.
It is evident,
in fact,
that no completely defensible
definition of the surface could be found which could remain
the same from one "x" station to the next.
The
following
scheme
was
finally
adopted.
A
microscope was set up and focused on the rough surface of
the m o d e l , centered at the point where the vertical
trajectory of the probe-tip would intercept the surface.
photograph of the surface was taken;
A
due to the model
I
surface
curvature
and
the
focusing
properties
of Ithe
' i ■
microscope, the particles on the surface lying directly in
I
the vertical plane of the probe-tip could be seen, as shown
. I
in Figure 5.
The surface was defined as the mean of |the
•'
I
curve formed by the particle outline. Thus, some particle
peaks lay above the surface, while some valleys lay below
it.
This average line is called the “surface” or "wall": in
I
I
the rough-body tests.
I
Data Acquisition procedures
During the measurements the model was axially centered
in the test section of the wind tunnel and the horizontal
pitot
tube
support
was
parallel to the model.
adjusted
until
it was axijally
The pitot tube was then moved until
I
the tip of the tube was I" away from the trailing edge of
•■ ■
'' I
■I
25
the model.
The arrangement for recording the pressure (Pt)
and the probe displacement (y) is shown in Figure 4.
The
output of the transducer (excitation voltage = 15 volts)
was amplified (gain = 50) and sent to the analog to digital
(A/D) converter (Spectra Dynamic Corp. Model SD133) from
which the digital counts were recorded on cassettes via the
ASR-700 terminal.
The actuator operated a potentiometer, the output of
which was amplified (gain = 50) and sent to the analog-todigital converter.
digital counts.
The latter output the corresponding
In order that both Pt an^ Y be measured at
the same time and at equally spaced intervals, the actuator
operated
thousandth
a switch
in
the
A/D
converter
once
of an inch traversed by the actuator.
every
The
profile surveys began by raising the pitot tube until it
touched the "surface” of the model.
("Surface" here is the
actual surface for the smooth model but is the surface of
the "peak™ of the teeth for the screw model).
To eliminate
backlash in the actuator system, the readings were taken
only after the probe had lifted from the surface.
At every
point, the reading was taken after allowing the pressure
output to stabilize over a period of time.
Away from the
surface a constant pressure output indicated the boundary
26
layer edge.
After taking about 20 readings in the free
stream, the actuator was stopped and the pitot tube moved
forward and raised to touch the surface 2" away from the
trailing edge.
The procedure was repeated for stations 2,
3, 4, 5, 6 and 7 inches from the trailing edge.
The same
was done for P0 = 500 mm. Hg and 400 mm. Hg.
The data acquired was reduced using a computer program
(Appendices I and II) as follows:
a)
The
"pressure
counts"
and
the
"displacement
counts" were converted to the corresponding physi­
cal pressure and displacement quantities using the
respective calibration constants.
b)
The boundary layer thickness was determined by in­
spection of the plot of
c)
A linear curve fit of Pt
Pt
v s
vs. y.
.
y2 gave the static
pressure at y = 0 for the smooth model.
Static
pressure for the screw model was obtained from a
static pressure survey of the screw model.
d)
The boundary layer thickness was determined at the
point corresponding to 99.9%^of P^e 1
e)
Assuming a recovery factor
of 0.95 for the
oe
temperature and knowing the boundary layer thick­
{ -J^)
ness, the local stagnation temperature was calcu­
27
lated as
Tpp = Tq [0.05 (£) + 0.95]
f)
The Mach number and the stagnation temperature
gave the static temperature
from the isentropic
relationship:
T = Top £ I +
g)
The static
(I^L)M2]"1
temperature and
the Mach number gave
the velocity at a point
u = M(y RT)V 2
h)
The static pressure and the static temperature
gave the density
i)
The viscosity was calculated as a function of the
static temperature.
j)
The viscosity,
density,
velocity and the probe
diameter of the pitot tube gave the Reynolds num­
ber of the probe diameter
k)
The boundary layer thickness was calculated again
I
.
by making it correspond to the point where the
local velocity was 99% of the free stream velocity
(the velocity calculated at 6 cm. from the sur­
28
face).
l)
Once again Top, T, N r U, P , y, and Re^ were cal­
culated using the latest obtained boundary layer
thickness.
m)
The ratio of the momentum thickness
to the boun­
dary layer thickness was given as
0
6
n)
6 pu
37:
e e
-S-Jd <£)
The ratio of the displacement thickness to the
boundary layer thickness was given as
F-S K-S^Jd
4
o)
The skin friction coefficient from the wall vis­
cosity wag givep as
PTv
yW p W
where (|y)w
was the velocity gradient on the sur­
face of the model.
A linear curve fit of U vs. y
for the first 15 points from the surface gave
for the smooth model. For the screw model,
vSy'w
the slope of a third degree polynomial curve fit
for the first 30 points from the surface at the
tooth tip gave (|y)w .
29
The skin friction coefficient based on the true
stream viscosity was given as
u (Ak)
Cf2
=
Reynolds number based on the momentum thickness
was given as
Re6 = (Ree)e
Where Ree is the unit stream Reynolds number.
r)
The external Mach number was given as Meo
s)
The transformed coordinate y was given as
A sample output of this program is given in Appen
dices III and IV.
CHAPTER VI
SUMMARY OM THE RANDOM SURFACE ROUGHNESS MODEL
Readings for the 60-grit model at a particular station
on the model were taken starting from the level of the
highest peak of. the roughness in view since it was not
possible to reach the mean surface of the roughness.
The
results were as follows.
a)
The randomness of the surface roughness made it
difficult to define an effective surface for the
model.
b)
The uncertainty of an effective surface made it
extremely difficult to calculate the momentum
thickness.
c)
The profile of the pitot pressure (Pt) at any
station showed variation in the free stream.
This
was suspected to be a consequence of shock waves
originating from the peaks of the roughness.
If
this were true, then the flow could have a compo­
nent in the direction perpendicular to the model
axis.
This was a deviation from the design of.the
experiment.
These and several other problems made it extremely
difficult to interpret the random surface roughness (60grit) model data.
Therefore, it was decided to discontinue
31
further investigations on the 60-grit model and continue
the
reduction and
interpretation
periodic roughness (screw model).
of data
for
the 2-D
CHAPTER VII
COMPARISON OF SMOOTH AND SCREW MODELS
Results
stated
here
consist
of
(a)
transition
measurements with the hot-film anemometer and (b) mean flow
surveys.
The. former has been briefly described in (10) and
were aimed towards the stability objective as much as
towards defining the transition onset.
The main finding
from these hot-film anemometer surveys was that, for a
range of k up to about 4 mils. (0.01 cm.) the stabilitytransition picture is insensitive to k and consists of
transition appearing only near the end of the model, i.e. x
= I" and possibly also x = 2" for P0 = 6 00 mm. Hg.
The aim of the mean flow surveys was to see if the
flow is "normal", when k = 0 (smooth wall) and to assemble
a coherent, quantitative picture of the profile distortion
for those values of k for which transition acceleration is
apparent.
Results
listed
in
Appendices
exemplified by Figures 6 through 39.
III
and
IV
are
Each profile is
marked by a four-digit code (e.g. 1600)? the first digit
refers to the x-position in inches from the trailing end of
the model and the remaining three digits indicate P0 in mm.
Hg.
Noteworthy points from the mean flow results are:
33
a)
The external Mach number Mg (from PTe and Pw) for
the smooth model is depressed from 3 (nominal
stream value without model) as shown in Figure 6„
This is due to
pressure
increases
towards the
trailing edge of the model as shown in Figure 6.
This in turn is caused by the compression fan from
the ogive reflecting onto the model surface after
reflecting from the side walls.
A similar
behavior
of
the Mach number Mg
from PTe and Pw) is seen for the screw model as
shown in Figure 7.
A plot of the static pressure
(measured with a static probe) shown in Figure 8,
qualitatively confirms the result mentioned
above.
b)
The velocity variation near the wall of the smooth
model is linear as shown on Figures 10 through 15
which plot the data in the physical coordinate y
as well as the transformed coordinate y/6.
Fig­
ures 14 and 15 include a straight line drawn
through the points to illustrate the latter fin­
ding.
The first two or three points near the wall
show a deviation from the straight line; this is
expected and is probably caused by the neglect of
34
\n
SMOOTH
Po =600 M M . HG.
M M . HG.
N O M I N A L
S T R E A M
= 400
00
4.00
X- (INCHES)
SMOOTH
= 400
N O M I N A L
S T R E A M
X- (INCHES)
Figure 6 Static Pressure and Mach N umber (From Static and Pitot P r e s ­
sure) Results for Smooth Model
35
SCREW
O --P0 =600 MM. HG.
□ $ =500 MM.HG.
= 400 MM.HG.
in
CU
NOMINAL
STREAM
00
4.00
X- (INCHES)
SCREW
600 MM.HG.
400 MM.HG.
N O M I N A L
S T R E A M
X- (INCHES)
Figure
7
Static Pressure and Mach Number (From Static and Pitot Pres^
sure) Results for Screw Model
Omm
EMPTY
63mm.H{
O-GRIT
SCREW
5 1Im m.Hg
SMOOTH
ANC
Figure 8
Static Pressure Surveys
37
SCREW
M M . HG.
= 5 0 0 M M . HG.
= 4 0 0 M M . HG.
O
X- (INCHES)
io
SMOOTH
=<5 O
= 6 0 0 M M . HG.
M M . HG.
M M . HG.
O
2.00
Figure
9
X- (INCHES)
Mach Number Results (From Static Pressure and Supply
Pressure)
0.80
1.00
1.20
38
0.60
V
+
+
+
+
+
+
+
+
0.40
U/UE
4+
6 6 0 0 - S M0 0 T H
+
+
+
+
+
.00
0-20
+
Sd1-OO
F i g u r e 10
o'.04
o'.08
o'. 1 2
. Y-CMS.
O1.1 6
3.20
V e l o c i t y P r o f i l e on S m o o t h W al l , x = 6", P q = 6 0 0 mm. Hg
39
o
0.60
4 4 0 0 - S M0 0 T H
o
.00
0.20
0.40
U/UE
0.80
I . 00
OJ
93.00
F i g u r e 11
SrToo
e'.oo
oToo
■ Y C AR/THE IA
TaToo
Ts. oo
V e l o c i t y P r o f i l e on S m o o t h Wall, x = 4", P 0 = 400 mm. Hg
KOO
I, - 20
40
0-60
0
□
□
0
0.40
U/UE
0.80
inmjgnHEDD
S
4 5 0 0 - SM0 0 TH
O
0.20
0
0
O
-s
.00
§
S d'.00
Figure 12
YToo
YToo
YToo
TFToo
Ts.oo
YCAP/THET A
V e l o c i t y P r o f i l e on S m o o t h Wal l, x = 4, P 0 = 500 mm. Hg
41
O
OJ
4 6 0 0 - SM0 0 T H
12.00
YCAP/THET A
F i g u r e 13
V e l o c i t y P r o f i l e on S m o o t h Wal l, x = 4", P0 = 600 mm. Hg
0.60
0.40
U/UE
Oi-SO
I 1-OO
I • 20
42
.00
0.20
6 4 0 0 - S M0 0 T H
20
Figure 14 Linearity of Velocity Variation Near Wall for Smooth M o d e l ,
w — C 11
D
= /IHA mm
Mn
0.60
0.40
U/UE
0.80
I 1-OO
1,-20
43
.00
0.20
6 5 0 0 - SM0 0 T H
20
Y-CMS.
Figure 15
Linearity of Velocity Variation Near Wall for Smooth M o d e l ,
x = 6", P 0 = 500 mm. Hg
44
Reynolds number effect (see Chapter V) and pos­
sible wall probe effects.
(On occasion the line
did not go through the origin and the origin was
shifted to eliminate this offset.
These shifts
are listed in Appendix III and are seen to be neg­
ligible) .
c)
In the case of the screw model, the first reading
was taken when the lower surface of the pitot tube
was in line with the surface representing the top
of the teeth (shown in Figure 16), irrespective of
whether the tip of
the
pitot tube
"valley" or the "peak" of a tooth.
Figure
16,
is
an initial
was above a
Also shown in
guess of the surface
(dotted line through tooth), taken to be at the
mean curve formed by the teeth outline.
The mean velocity profiles are shown in Fig­
ures 16 through 20.
Except for the first three or
four points, the profiles indicate that the flow
has zero velocity at the surface represented by
the top of the teeth.
This is in agreement with
Charwat, Roos, Dewey and Hitz (12), who refer to
the "cavity" between teeth (because of the length
to height ratio of the latter) as being "open"
45
5400-SCREW
tsE T o e
' 0.04
0708
0T T 2
Y-CMS.
PITOT
Figure 16
ETTe
PROBE
Velocity Profile on Screw Model, x = 5", P 0 = 400 mm. Hg
(Note Pitot Probe)
0.60
U/UE
46
4400-SCREW
0.04
Figure
17
0712
Y-CMS.
0.16
0.20
V e l o c i t y P r o f i l e on S c r e w M o d e l , x = 4", P 0 = 400 mm. Hg
47
7500-SCREW
0.04
F i g u r e 18
0.08
0 . 12
0. 16
0.20
V e l o c i t y P r o f i l e on S c r e w M o d e l , x = 7", P 0 = 500 mm. Hg
48
6500-SCREW
0 . 12
Y-CMS.
F i g u r e 19
V e l o c i t y P r o f i l e on S c r e w M o d e l , x = 6", P 0 = 500 mm. Hg
49
+H iin n m -•»•+»
6400-SCREW
0.08
Y-CMS.
F i g u r e 20
0 . 16
0.20
V e l o c i t y P r o f i l e on S c r e w M o d e l , x = 6", P 0 = 4 00 mm. Hg
50
(i.e. the flow bridges the cavity).
The identical nature of the pitot pressure
plots as shown in Figure 21 at a station above a
cavity and at a station above a tooth, further
confirms that the cavity is "open”.
\
d)
Comparison of the mean velocity profiles (shown
in Figures 22 through 26).for a particular supply
pressure and station on the model shows a distinct
change in the boundary layer profile indicating an
increase in skin friction for the screw model.
e)
The temperature profiles for the smooth model look
normal and approach the wall with zero slope, as
is proper for the adiabatic model; see Figures 27
and 28 for examples.
Note that the wall values
are denoted by square points on the axis.
These
were computed for the assumed recovery factor of
0.95 by;
Tw/T0 = 0.95 (I + 0.2 Me2)
where Me is a measured property listed, on Appendix
III.
Thus, it is proper to say that Tw / t 0 is a
measured property.
f)
At the forward end of the surveyed region, the
boundary layer is considerably thicker than it
P R E S S U R E - M M . HG
51
Fig ur e 21
P i t o t P r e s s u r e P r o f i l e on S c r e w Mod el , x = 4", P 0 = 600 mm. Hg
.
52
o
CXJ
LU to
6400
□
= SMOOTH MODEL
A
: SCREW MODEL
Y-CMS
F i g u r e 22
C o m p a r i s o n B e t w e e n S m o o t h and S c r e w V e l o c i t y P ro fi l e s , x =
6", P 0 = 4 0 0 mm. Hg
0.60
0.40
U/UE
0.80
I . 00
1.20
53
6500
A Jr1
A □
□ -.SMOOTH M O D E L
A SCREW MODEL
□
□
.00
0-20
□
cUTbo
F i g u r e 23
O'. 04
o'. 08
o'. 12
Y-CMS.
o'. I 6
0.20
C o m p a r i s o n B e t w e e n S m o o t h and S c r e w V e l o c i t y P ro fi l e s , x =
6", P 0 = 500 mm. Hg
0.60
U/UE
0.80
I - 00
I - 20
54
□
□
□
□
□
0.40
a
6600
□
Q
□
□
O :S M O O T H M O D E L
A -.SCREW M O D E L
.00
0-20
A
A
cUToo
F ig ur e 24
0.04
o'. 08
o'. 1
.2
Y-CMS.
o'. I 6
3.20
C o m p a r i s o n B e t w e e n S mo ot h and S c r e w V e l o c i t y P ro fi l e s , x =
6", P 0 = 600 mm. Hg
0-20
0.40
U/UE
0.60
0- 80
I..00
1.-20
55
.00
□ •S M O O T H M O D E L
A •S C R E W M O D E L
cUToo
F i g u r e 25
o'. 04
OrTos
0.12
Y-CMS.
GTiTs
G .20
C o m p a r i s o n B e t w e e n S m o o t h and Scr ew V e l o c i t y P ro files,
x = 7", P q = 600 mm. Hg
0.60
0-40
0.20
7 40 0
□ -.SMOOTH M O D E L
A -.SCREW M O D E L
&
.00
UZUE
0.80
I .00
I .20
56
0GToo
F i g u r e 26
OrTol
oToi
OrTTTi
Y-CMS.
o'. 1 6
o'. 2 0
C o m p a r i s o n B et w e e n S m o o t h and S cr e w V e l o c i t y P ro files,
x - 7", P 0 = 4 00 mm. Hg
57
o
o
U J OO
45 0 0 - SM 0 0 T H
0. I 2
Y-CMS.
Figure 27 Temperatur e Profile on Smooth M o d e l , x = 4", P q = 500 mm. Hg.
Note Surface Datum (Square on Axis)
X.
I • 80
A
A
A
A
A
A
A
A
A
A
A
A
1.40
T/TE
2 . 20_
2.60
3.00
58
.60
1.00
4 6 0 0- SM 0 0 T H
S d1.oo
Figure 28
o'. "04
OrTos
0TT2
Y-CMS.
o'. 16
C?.20
T emperatur e Profile on Smooth Model for x = 4", P q = 600
mm. Hg. Note Datum (Square on Axis)
59
should, be* but thereafter it decreases in size and
then begins growing again as the square root of x.
This result is shown in Figures 29 and 30,
This
initial thickening is thought to be caused by an
initial oyer-expansion of the flow near the model
shoulder, plus a smaller effect of the axial model
symmetry.
On these Figures, straight lines have
been drawn through the points
and
(x) to
find the "virtual origin" of the flow? these lines
were least-squares fitted and show that the vir­
tual origin lies near the apex of the body itself.
Figure 31
shows the form factor
from flat plate theory (13).
6/8
calculated
For most of the .
surveyed region, the theory and experiment are in
good agreement.
This is significant because it
indicates that the computer program makes a cor­
rect determination of 6 and that the flow is "nor­
mal" in that respect.
g)
Three significant points emerge from the plots of
Reg and Re' for the smooth and the screw model
shown in Figures 32 and 33.
(I)
The changes in the unit Reynolds number Re
caused by pressure changes do not seem
i-'
SMOOTH
P0 = 6 0 0 M M - HG.
500 MM-HG400 MM-HG-
OOo'
VIRTUAL
O R I G I N
X- (INCHES)
F i g u r e 29. a.
6-00
D e t e r m i n a t i o n of "Virtual O r i g i n " for S m o o t h Model («52 vs. x)
0.05
*n o"' .
0.04
0.02
0.03
O '-Po = 6 0 0 M M . HG.
□ S = 5 0 0 M M . HG.
A s. = 4 0 0 M M . HG-
0.01
0
(crn
SMOOTH
VIRTUAL
.00
O R I G I N
X- (INCHES)
F i g u r e 29. b.
6.00
D e t e r m i n a t i o n o f "Virtual O r i g i n " for S m o o t h Model (02 vs. x)
P0 = 6 0 0 M M . HG.
M M . HG.
= 400
0.03
CTt
0.02
rx>
0.01
VIRTUAL
ORIGIN
.00
S z (CM )
0.04
0.05
SCREW
4.00
5.0
X- (INCHES)
F ig ur e 30. a.
D e t e r m i n a t i o n o f “Virtual O r i g i n ' for S c r e w Model (62 vs. x)
O -P0 =600 MM. HG
□ -• =500 MM. HG
A
= 400 MM.HG
o
VIRTUAL
0.02
0.03
0-04
0.05
SCREW
.00
0.01
O R I G I N
X- (INCHES)
F i g u r e 30. b.
D e t e r m i n a t i o n of "Virtual O r i g i n " for S c r e w Model (G
21 . 0 0
64
SCREW
O
O -R0 = 6 0 0
a *• = 5 0 0
O
O
A
•-
)
O
>
O
CO
A
O
O
a
a
in_
M M . HG.
MM. HG.
= 4 0 0 M M . HG.
a
O
A
A
$
0
D
O
O
:
:
/-CO
MM. HG.
M M . HG.
M M . HG.
ED
N.
O
O
CM
Il
CO
6'. 0 0
SMOOTH O :P0 = 6 0 0
THEORY
□ =500
=400
/ M=3
@▲
O
/I » M
O
9
A
A
O
O
r>
O
O
N-
CU
O
O
O
O
3.00
4'. 0 0
X- (INCHES)
"I
O
O
ro
I
C
,
A
n .00
o
2'. 0 0
Figure 31
3.00
4'. 0 0
X- (INCHES)
S1- O O
6‘. 0 0
Form Factor for Smooth and Screw Model
A
S
/.00
65
in
<v
SMOOTH
M M . HG.
M M - HG.
= 400
X- (INCHES)
SMOOTH
(D "•Pt
NOMINAL
S T R E A M
6.00
6 0 0 M M . HG.
5 0 0 M M - HG.
4 0 0 M M . HG.
W J T O
O O
400
LU
X- (INCHES)
F ig ur e
32
a.
M o m e n t u m T h i c k n e s s and U n i t Rey no l ds N u m b e r Results for
S m o o t h Model
66
SMOOTH
o
o
Fig ur e 32. b.
O Sp0 =600 M M . H G
=500 M M . H G
□ I
A l =400 M M . H G
M o m e n t u m R ey n o l d s N u m b e r Res ul t s f or S m o o t h Model
SMOOTH
Ol
O
0.35
□
0.25
0.20
S (CMS.)
0.30
A
P0 = 6 0 0 M M . HG.
= 5 0 0 M M . HG.
= 4 0 0 M M . HG.
.10
0.15
—0
0VToo
Figure
21. O O
32. c.
3.00
4‘. 0 0
X- (INCHES)
SrToo s'.oo
T1- O O
B o u n d a r y L a y e r T h i c k n e s s Res ul t s f o r S m o o t h Model
68
in
CU
SCREW
M M . HG.
=500
= 4 0 0 M M . HG.
X- (INCHES)
SCREW
NOMINAL
STREAM
O
Sp0 = 6 0 0 MM. HG.
5 0 0 M M . HG.
600
LU
400
3.00
4.00
X- (INCHES)
F i g u r e 33. a.
M o m e n t u m T h i c k n e s s and U n i t R ey no l ds N u m b e r Res ul t s for
S c r e w Model
69
SCREW
M M . HG.
MM. H G
MM. H G
TRANSITIONAL
O oo"
X- (INCHES)
F i g u r e 33.
b.
M o m e n t u m R ey n o l d s N u m b e r R esults for S c r e w Model
70
SCREW
6 (CMS
5 0 0 M M . HG.
4 0 0 M M . HG.
3.00
4'. 0 0
X- (INCHES)
F ig u r e
33. c.
3.00
B o u n d a r y Lay er T h i c k n e s s R esults for S c r e w Model
71
significant enough to control Re0 .
(2)
The plot.of Reg for the smooth model clearly
indicates that laminar boundary layers are
attainable for Re0 beyond 700.
(3)
Downstream of the 3" station, the flow for
the screw model at P0 = 600 mm. Hg is clearly
transitional.
This, is further confirmed by a
Schlieren photograph of the flow on the model
for Pq = 600 mm. Hg (Figure 34).
h)
The friction coefficient for the smooth model
obtained using wall viscosity.and the measured
velocity slope at the wall is plotted versus Re
on Figure 35.
The theoretical expectation (13)
plotted on the same Figure lies within 20% - 50%
of the plotted data.
This disparity should pro­
bably be expected because the theory refers to
flat plates whereas some curvature effects might
be present in the experiment.
For the screw model, in order to find the
velocity slope at the wall, the first 30 points
(except
the first
4 points) were curve fitted
using a least squares polynomial fit of degree 3.
Also assurance of the
fact
that the cavity was
ro
Figure 34
Shlieren Photograph of Screw Model (P
600 mm. Hg).
Note Onset of Transition
73
CM
I
O
SMOOTH
FLAT-PLATE
T H E O R Y
Figure
35
Skin Friction Results for Smooth Model
74.
open was an instigation to force the curve through
the effective origin (u/ue = 0 ? y = 0) at the
surface of the top of the teeth, by adding about
35 points lying at the origin, to the data needed
for the curve fit.
Figures 36 through 38 show the
best polynomial curve (degree 3) through the data
points.
The plot of the surface skin friction using
wall viscosity and the measured velocity slope at
the wall versus Re^ shown in Figure 39, indicates
a definite increase in the friction coefficient
for the screw model when compared to that of the
smooth model shown in Figure 35.
4400-SCREW
.00
0.20
0.40
U/UE
0.60
0-80
1.00
1.20
75
F i g u r e 36
T h i r d D e g r e e P ol yn o mi a l Fit o f V e l o c i t y V a r i a t i o n N ear E f f e c ­
t ive S c r e w S u r f a c e , x = 6", P 0 = 400 mm. hg
0.40
U/UE
0.60
0.80
1.-00
1.20
76
.00
0-20
4500-SCREW
Y-CMS.
F i g u r e 37
T h i r d D e g r e e P olynomial C u r v e Fit of V e l o c i t y V a r i a t i o n
N e a r E f f e c t i v e S cr e w S u r f a c e , x = 4", P q = 5 00 mm. Hg
o
0.40
U/UE
0.60
0.60
I .00
<\j
.00
0-20
5600-SCREW
cD -OO
F ig ur e 38
o'.04
OrTos
o'. I 2
Y-CMS.
o'. 16
3.20
T h i r d D e g r e e Polyn o mi a l C u r v e Fit of V e l o c i t y V a r i a t i o n N ea r
E f f e c t i v e S c r e w S ur f a c e , x = 5", P 0 = 600 mm. Hg
78
SCREW
CM
O
O =P0 =600 MM. HG.
□ « =500 MM.HG.
A i =400 MM.HG.
TRANSITIONAL
o
FLAT-PLATE
T H E O R Y
4
I 0
Figure 39
Skin Friction Results for Screw Model
CHAPTER VIII
CONCLUSIONS .
1)
There is no change in the transition picture for random
u,k
surface roughness where Rejc =
Iess than 23
confirming the
statements
of Reshotko and Kendall
rather than conclusions of Feindt.
2)
The height of the random surface roughness needed to
disturb the laminar supersonic boundary layer causes
great difficulty in the interpretation of the profile
data.
3)
The use of a periodic 2-D roughness (screw) of Re^ =
greater
than
the
critical value
uuk
and of height to
spacing ratio such that the cavity remains "open" pro­
duces an upstream movement of transition, compared to
the smooth model.
4)
The 2-D overlay causes an outward displacement of the
boundary layer edge smaller than the rise of the
effective
layer.
surface,
resulting
in a thinner boundary
This decrease in the boundary layer thickness
causes a distinct distortion in the boundary layer pro­
file and an increase in the surface skin friction.
BIBLIOGRAPHY
BIBLIOGRAPHY
1.
Van Driest, E. R= and McCauley, W. D., The Effect of
Controlled Three-Dimensional Roughness on BoundaryLayer Transition at Supersonic Speeds, Journal of the
Aerospace Sciences. Vol. 27, No, 4, pp, 261-271,
December, 1957.
2.
Van Driest, E. R. and Blumer, C. B., Boundary-Layer
Transition at Supersonic Speeds--Three-Dimensional
Roughness Effects (Spheres), Journal of the Aerospace
Sciences. Vol. 29, No. 8, pp. 909-916, August, 1962.
3.
Whitfield, J. D. and Iannuzzi, F. A., Experiments on
Roughness Effects on Cone Boundary-Layer Transition Up
to Mach 16, AIAA Journal. Vol. 7, No. 3, pp. 465470, March, 1969.
'
4.
Potter, J. L. and Whitfield, J. D., Effects of Unit
Reynolds Number, Nose Bluntness, and Roughness on Boun­
dary Layer Transition, Rept. 256, 1960, AGARD.
5.
Reshotko, E, and Leventhal, L., Disturbances in a Lami­
nar Boundary-Layer Due to Distributed Surface Rough­
ness, AIAA Paper 81-1224, Palo Alto, California, June,
1981.
6.
Kendall, J. M., Jr., Laminar Boundary Layer Velocity
Distortion by Surface Roughness? Effect Upon Stabil­
ity, AIAA Paper No. 81-0195, St. Louis, Missouri,
January, 1981.
7.
Feindt, E. G., Untersuchangen uber die Abhangigkeit des
Umschlages Laminar-Turbulent Von Der Oberflachenrauhigkeit und der Druckverteilung, Jahrbuch 1956 der Schiffbautechnischeh Gesellschaff. Vol. 50, 1957, pp. 180203.
8.
Smith, A. M. 0. and Clutter, D. W., The Smallest Height
of Roughness Capable of Affecting Boundary^Layer
Transition, Journal of the Aerospace Sciences. Vol 26,
pp. 229-245, April, 1959.
9.
Demetriades, A., Roughness Effects on Boundary-Layer
Transition in a Nozzle Throat, AIAA Journal. Vol. 19,
No. 3, pp. 282-289, March, 1981.
82
10o
Demetriades, A . , and D 1Sa, J., The Stability of a
Supersonic Laminar Boundary Layer Over a Rough Wall,
Private Communication, November, 1981.
11.
Chambre, P. L. and Schaaf, S. A., The Impact Tube, Phy­
sical Measurements in Gas Dynamics and Combustion (R.
W. Ladenburg, Ed.), Princeton University, Princeton,
New Jersey, 1954, pp. 111-112.
12.
Gharwat, A. P., Roos, I. N., Dewey, F . C., Jr., and
Hitz, J. A., An Investigation of Separated Flows Part I: The Pressure Field, Journal of Aerospace Sci­
ences. Vol. 28, June, 1961.
13.
Low, G. M., Simplified Method for Calculation of Com­
pressible Laminar Boundary Layer With Arbitrary FreeStream Pressure Gradient, NACA Technical Report No.
2531, 1951.
APPENDICES
APPENDIX I
DATA REDUCTION PROGRAM FOR SUMMARY OF PROFILES
I O D E M . * » . » » . *
D A T A R E D U C T I O N P R O G R A M F O R S M O O T H
A N D S C R E W M O D E L
P O D I M P M 300> , P < 300> , P * < 300) , Y ( J O O ) , M ( 300) , T E ( 303) , T M 300) , T ( 300) , T E (
S O D I M T l ( 300) , U E ( 300) , D ( S O O ) , R E ( S O O ) , U ( J O O )
'.0 D I M V S ( J O O ) , T N ( J O O ) , S ( S O O ) , Y C A P ( J O O ) , D E ( S O O )
50 R E M * . * * * *
R E A D
D A T A F I L E
40 I N P U T F S
70 O P E N F J T O ! , I N P U T
S O I N P U T * I , G , X , P 0, C , K K , 0M . T S , A 1, A Z , A J
90 I N P U T * 1, A C , E , N , P Z
T O O A Z = O M Z Z
I 10 F O R
I = I T O N
I ZO I N P U T * I , Y ( I ) , P A ( I )
I J U N E X T
I
H O
C L O S E ( I )
I 50 R E M * . . . * . . .
C O N V E R T D I S P L A C E M E N T
( Y ) A N D P R E S S U R E
( P A ) C O U N T S
I 60 F O R
1*1 T O N
I 70 Y l ( I ) * A 1• ( Y d ) - Y ( I ) ) * A Z
I S O
Y l ( E ) = A I » ( Y ( 1) - Y ( E ) ) * A Z
’90 Y Z ( I ) = ( Y K I ) Z Y l ( E ) )
Z C O P M I > * ( A 3* P A ( I ) ) A A A
Z I O N E X T
I
Z Z O
I F C >0 T H E N A S O
Z J O R P M * . * * C A L C U L A T I O N O F S T A T I C P R E S S U R E
( P Z ) U S I N G
Z A O R E M . * * «
A L I N E A R E X T R A P O L A T I O N OF P I T O T P R E S S U R E
( P A )
Z S O R E M * . * .
A N D S O U A T E O f T H E D I S T A N C E
( T l )
F R O M T H E
S U R F A C E
Z D O
R E M . . . .
( O N L Y
F O R S M O O T H M O D E L )
Z 70 C l = C Z = C S = C A = C S = C D = C
Z S O
F O R
I = I T O 10
Z 90 C l = C I H
S O O C Z = C Z A Y I ( I ) * * Z
J I O C J = C Z
J Z O C A = C A A Y I ( I > * *A
J J O C S = C S A P J ( I )
J A O C 6= C 6* ( Y I ( I ) * * Z ) * P J ( I )
S S O N E X T
I
S D O P Z = ( ( C S * C A ) - ( C D * C S ) ) Z ( ( C 1* C A ) - < C Z ‘ C S ) )
370 R E M * S E C O N D E V A L U A T I O N O f D E L T A ( T K E ) ) ( O N L T F O R S M O O T H M O D E L )
580 P E A = O
390 F O R I = E T O N
A O O P E A = P E A A P S ( I )
A l Q N E X T
I
A Z O P r = P E A Z ( N - E A l )
A s o F O R
I = D O
T O N
A A O
I F P S ( I ) S = . 999. P T A N D P 3( I X = I . O O I 1 P T G O T O A D O
A S O N E X T
I
A D O E = I
A 70 F = I
A S O N C = O
A 93 F O R
I= I
T O N
500 I F P J ( I ) Z P Z s = I T H C N S Z G
S I O N C = N C A l
S Z O N E X T
I
S SO
SAO
SSO
S60
S 70
SSO
590
R E M * * * . . * C A L C U L A I ION OF M A C H NO. ( M ) , S T A G N A T I O N T E M P . ( T N )
H E M . .. .. . V E L O C I T Y ( U ) , D E N S I T Y ( 0 ) , V I S C O S I T Y ( V S ) ,
........ * R E Y N O L D S NO. ( R Z ) U . R . T . P R O S E D I A M E T E R ( D M ) ,
R t M . . . . . . F R O M P J Z P Z A N D S U P P L Y T E M P . (TS)
FS-O
F O R I=I TO N
P( I ) =P 3( I ) ZP Z
D O O
IF
P d X I
T H E N
S Z O
300)
85
610 P<1X1.8929 THEN ?Z0
6Z0 H(I)»(.5*P<I))**(1/1.6)
630 S(I)«<<7.«<I>«.Z-1)/6)*(<7.Z«*1<I)**Z)/<?*M(I)**Z-1>)**3.S
6t0 *'(Pd)-S(I))/Pd)
650 If ABS(R)0.001 THEN 680
660 H(I)«M(l)>R
670 GOTO 630
680 If I>6 THEN 770
6
TN
I«
)T
»T
S«(
70
00
0T
((I)
Nd
>(
/.(0
I5♦«
.Y71*M((II)
>ZoTiK)E))*.95)
710 GOTO 780
770 f1d>»S0R((Pd)«•(I/$.$>-1)•$)
730 If DE GOTO 770
7(0 TN(I)»TS«((.05*r1(I)/Yl(E)>*.95)
750 T(I)«TN(I)/(1».7'Md)*«7)
760 GOTO 780
773 T(I>»TS/(I♦.?•*(!>**7)
750 U(I)SN(I).(I.(SWIG-T(I))AA.S
790 0(I)sP7«7.77(Z(I716*T(I)>
800 VS(I)-((Z.?7A(T(I))AAl.5)/(T(I)t198.6))Al0AA(-8)
810 RE(I)s(0(I)AU(l>A(OM/30.(8>)/VS(l)
870 NEXT I
8(
30
0 RIEfM f3*IGO TO 910
8
THlRB EVALUATION Of BELTA (TKE))
850 TOR l«1 TO N
860 If U(l)>*.99AU(E) A N B U(I><*1.01 U ( £ ) GO TO 880
870 NEXT I
880 EsI
890 f3*1
900 GO TO 580
97
10
0 If OO THE
N II70C U R V E f I T O f V E L O C I T Y (U) VS.
9
L I N E A R
930 ....
D I S P L A C E M E N T
( T l )
T O fI N O “ S H I f T " I N
9(0 R E " VELOCITY PROflLE OUE TO "PROBE EffECT1KONLT fOR SMOOTH MODEL)
950 CHsO
960 (71*0
970 C3l*0
980 C(l*0
990 C5l«0
1000 C6L»0
1010 fOR I»1 TO 15
1070 If PdXI THEN 1090
1030 C1L*C1L*1
10(3 C?L*C7LATI(I)
1050 C3l»C?L
1060 C(l*Cd«YI(I)•«7
1070 C5l*C5L*U(l>
1080 C6L*C6LAT1(I)au(I)
1090 NEXT I
I130 ALs((C5LAC?L)-<C6L*ClL))/((C3L*C7L)“(C(L*ClL>)
1110 UL*((C5L'C(L)-(C6l«C3L))/((C1LAC(L)-(C7L«C3L))
1173 TS*-(UL/AL)
II30 fOR I-I TON
I1(0 Tl(DsYld)-YS
1150 NEXT I
I160 R E M . . . . . . SUBSCRIPT "E" CORRESPONDS TO fREE STREAM PROPERTIES
1170 fOR I«1 TON
I180 If PdXI THEN I730
1190 UE(I)*U(I)ZU(E)
I700 TE(I)*r(I)ZT(E)
1710 T7(I)*TI(I>/Tl(E)
I770 BE(I)SB(I)ZO(E)
If
A . . . S A A A
a
REMAAAAA
86
IZSO NEXT I
1240 Ol-O
1250 02-0
1260 FOR I-XCO TO E
1270 IfPdXI THENI320
1280 Ifl»NC*1 THEND2-02MUE(I>/TEd )>*<1-UE<I>X(YZd)/?>
I290 IfI>NC♦I THENOZ-DZdUE<I>/TE(I>Xd-UE( I>>•(Y2(IXYZd-I>>
I500 IfI-NCd THENOI=DTdT-UE(D/TECI>X<YZ(I>/Z>
I310 IfDNC-T THEN01*01dl-UE<I>/TE<I>)dYZ<I>-T2dd)>
1320 NEXT I
I330 fOR I-I TO N
I340 YCAP(I)-O
I350 NEXT I
1360 fOR J-NC-I TO N
I370 If P(JX) THEN 1430
1380 fOR I-NC-1 TO J
I
30
90
If
ZO
I4
0I
F PdXI
I-NC-T T
TH
HE
EN
N1
Y4
CA
P(J)=YCAP(J)-DE(I)-(YT(I)ZZ)
1410 If DNC-T THEN TCAP(J>»YCAP(J)-DE(I>-(Y1(1)-YT(I-D)
1420 NEXT I
1430 NEXT J
1440 REM-------- THETA IS THE MOMENTUM THICKNESS
1450 THETA=DZ-YT(E)
1460 MSP«SOR(((PO/PZ)--(1/3.5)-1)/.Z)
1470 ..... - TSUR IS THE SURfACE TEMPERATURE
1480 TSUR-.95-TS
T490 REM - ----- VSU IS THE SURfACE VISCOSITY
1500 V S H - ((Z.Z7-(TSUR)--1.5)/(TSUR-T98.6))-10»‘(-8)
I510 If OO THEN GOSUB 1850
1520 VELGRADIENT-Al-30.48
1
DP
E)-(
15
53
40
0R
EM.
-S
..O
-(
••
CU
A(
LE
C)
ULAZ
T)
ION Of fRICTION COEfS. (CfT) AND (Cf2)
1550 CfT-(VSH-VELGRADIENT)ZOP
I560 CFZ«(VS(E)-VELGRAOIENT)/OP
1570 If C-O THEN PRINT"----------* SMOOTH MODEL •»•«••«
15*0 If C-T THEN PRINT"••••••••••• 60 GRIT MODEL -----I590 If C-Z THEN PRINT"---.... - SCREW MODEL ... .
I600 PRINT
I610 print"group no.:“;g
I620 PRINT"DISTANCE FROM TRAILING EDGE Of MODEL (CM.):"/X
1630 PRINT"SURFACE ROUGHNESS COOE IC
I640 PRINT*'SURFACE ROUGHNESS HEIGHT (CM.):",*KK
165: print**supply pressure-do* (mm.hg.abs>:”;po
1660 P
RINT"SUPPLY TEMPERATURf-'T$' (OEG RANKINE)("/TS
1670 PRINfEDCE REYNOLDS NO. (CM-T)SmJRE(E)ZDM
I680 PRiNfEXTERNAL MACH NO.SmJM(E)
I690 PRINT"SURFACE PRESSURE (MM.HG.A8S)S"JPZ
1700 PRINT"SXIN FRICTION COEf. fROM HALL VISCOSITY-'CfI'ShJCFT
I710 PRINT-SXIN fRICTION COEf. FROM STREAM VISCOSITY-'CfZ's"JCf2
I7Z0 PRINT'"THETA'-(CM.):"JTHETA
1730 PRINT"SHIfT IN Y-AXIS DUE TO 'PROBE EFFECT' (CM.)s"JYS
1740 PRINfBOUNOARY LAYER THICXNESS-'OELTA' (CM.>S"JYI(E)
I750 PRINT"'DELTA STAR' (CM.)s"JDl-Yl(E)
I763 P R I N T "'DELTAZDELTA STAR'S"JT/OT
1770 PRiHT"'Oeltaztheta1SmJ1/02
I780 PRINT"'RETHETA's"J(RE(E)ZDM)-(DZ-YKE))
I790 PRINT"EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.SmJM(E)
I800 PRINT-EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRES.SmJMSP
1810 GO TO 2930
TtZO REM......- SUBROUTINE TO fIND A POLYNOMIAL fIT
1830 REM------- Of the FIRST 30 PIS. FROM THE SURFACE TO
I843 REM---.... COMPUTE fRICTION COEfS. FOR THE "SCREWm MODEL
87
1850 R E N POLEIT
I860 M"60
1870 NO
1880 0IN *05),0(15),SS(IS),GG(IS),UU(15)
I890 DIM 0(100),PP(100),X(100),TY(IOO),CC(IOO)
1900 LET 1*0
1910 LET 0*1
1920 LET K*12
1930 L E T N«N*1
1940 IE N> 12 THEN 2930
1950 IE M<N THEN 2930
1960 IF M>100 THEN 2930
1970 LET T7«Z
1980 LET T8*Z
I990 LET U7*Z
2000 FOR 1*1 TO M
2010 X(I)-YI(NCM)
2020 YY(I)-U(NCM)
2030 If KS THEN X(t)»YY(I)»0
20*0 If I>30 THEN X(I)«YY(I>*0
2050 LET U7*U7*X(I)
2060 L
ET T7*T7+YY(I)
2070 L E T T8«T8»YY(I)**2
2080 NEXT I
2090 CLOSE (I)
2100 L ET T9*(MM8-T7««2)/(M»»2-M)
2110 FOR 1*1 TO N
2120 LET PP(I) * I
2130 LET O(I) * O
21*0 NEXT I
2150 FOR I» I TO 11
2160 L ET A(I) « Z
2170 L E T 8(1) « Z
2180 LET SS(I) •
2190 NEXT I
2200 LET EI*Z
2210 LET E1*Z
2220 LET UI*M
2230 LET N*•K
22*0 LET 1*1
2250 LET XI»2
2260 IF N»0 THEN 2280
2270 LET X1»N*
2280 LET W»Z
2290 FOR L=I TO M
2300 LET W=JYYY(L)=O(L)
2310 NEXT L
2320 LET SS(I)=WZWl
2330 IF 1-N*>»0 THEN 2530
23*0 IF l-M>*0 THEN 2530
2350 LET EI=Z
2360 FOR L=I TO M
2370 LET EI=EI=X(L)=O(L)=O(L)
2380 NEXT L
2390 LET ET=EIZWI
2*00 LET A(I=I)=EI
2*10 LET W=Z
2*20 FOR L=I TO N
2430 LET VMX(L)-EI)=0(L)-FI=PP(L)
2 * * 0 L ET P P ( L ) * a ( L >
2*50 LET O(L)=V
2*60 LET W=W=V=V
I
88
2473 NEXT L
2480 LET M» W/Wl
2490 LET aa*2)»M
2500 LET Ulsw
2510 LET IsI»1
2520 GOTO 2280
2550 FOR L • I TO 13
2540 LET GG(L)'2
2553 NEXT L
2560 LET GG(I)SQ
2570 FOR J*1 TO N
2580 LET SI »Z
2593 FOR L=I TO N
2600 IF L■I THEN 2630
2610 IF L-2»0 THEN GG(L>»GG(L)-A(L)SGG(L-I)
2620 IF l-2>0 THEN GG(L)=GG(L)-A(L)'GG(L-I)-8(L)*GG(L-Z)
2633 LET SI•SI♦SStL)•GG(L>
2640 NEXT L
2650 LET UU(J)=SI
2660 LET LSN
2670 FOR 12*2 TO N
2683 LET GG(L)=GG(L-I)
2690 LET L«1-1
2700 NEXT 12
2710 LET GG(T)=Z
2720 NEXT J
2750 AL=UU(Z)
2 740 PRINT
2750 LET T=Z
2760 FOR L=I TO N
2770 LET CC(L)=Z
2780 LET J=N
2790 FOR 12=1 TO N
2800 LET CC(L)=CC(L)'X(L)'UU(J)
2810 LET J=J-I
2820 NEXT 12
2830 LET T3=YV(L)-CC(L)
2840 LET T=T'T3"2
2850 NEXT L
2860 IF MON THEN 2890
2870 LET TS=O
2880 GOTO 2900
2893 LET TS=TZ(M-N)
2900 LET 07 = 1-TZ(T9'(M-1)>
2910 PRINT
2920 RETURN
2930 END
APPENDIX II
DATA REDUCTION PROGRAM TO BUILD DATAFILES FOR PLOT ROUTINES
10 REN OATA REDUCTION PROGRAM FOR PROFILES
REM****
THE OUTPUT OF THIS PROGRAM IS CONVERTED TO A DATAFILE
JO REM*****
FOR THE PROGRAMS WHICH PLOT THE PROFILES
40 D I M P3<300),P<3OO),P4CJ00>.V(JOO),M(JOO),TE(300),VZ(300),T(300),TEC300)
SO DIM VK300),UE(JOO),D(JOO),RE(JOO),U(JOO)
60 DIM VS(300), T N ( 300),S(JOO),YCAP(300),OE(JOO)
70 REM****** READ DATAFILE
80 INPUT FIS
90 OPEN FIS TO I,INPUT
100 INPUTR I, G,X,PO,C,K,DM,TS,A1,AZ,A3
110 INPUT# I,A4,E,N,PZ
IZO AZ'OM/Z
130 FOR 1=1 TO N
I40 INPUT* I,V(I),P4<I)
ISO NEXT I
I
I6
70
0C
RL
EO
MS
*E
*(
*I
*)
** CONVERT DISPLACEMENT (V) AND PRESSURE (P4> COUNTS
1
8
0
F
O
R
1
=
1
N >-Y(I))*AZ
I90 YI<I)=AIT
•O
(Yd
ZOC Tl(E)=AI*(V(1)-V(E))*AZ
ZIO VZ(I)=(VKI)ZVl(E))
ZZO PJ(I)«(AJ*P4(I))*A4
Z30 NEXT I
Z40 IF C>0 GO TO 490
ZSO R
EM* SECOND EVALUATION OF DELTA (Vl(E)KONLV FOR SMOOTH MODEL)
Z60 PEA=O
Z70 FOR I=E TO N
Z80 PEA=PEA*P3<I)
Z90 NEXT I
JOO PT=PEA/(N-E*1>
3
310ZOFOIRF1
P=J6(3I)T
>O=.N999*PT AND P3(I)<»1.001*PT GO TO 340
330 NEXT I
3S
4O
0E
J
R=
EI
M****** CALCULATION OF STATIC PRESSURE (PZ) JSING
360 REM****** PARABOLIC EXTRAPOLATION OF THE PITOT PRESSURE (P3)
J70 REM****** AND THE SOUARE OF THE DISTANCE (VT) FROM THE SURFACE
580 RE".. (ONLY FOR SMOOTH MODEL)
390 Cl=CZ*C3*C4»C5«C6«0
400 FOR 1*1 TO 10
410 CI=CKI
4Z0 CZ*CZ*V1(I)»*Z
430 CJ=CZ
440 C4*C4*Y1(I>*»4
4S0 CS=C5*PJ(!>
460 C6=C6*CY1(I)»*Z)*PJ(I)
48070PZ
N=
E(
XT
4
(C5I*C4)-(C6«C3))/((C1*C4)-(CZ*C3>)
4
FJ
59
00
0R
E=MO****** CALCULATION OF MACM NO.(M), STAGNATION TEMP (TN)
S10 RE"*... VELOCITY (U). DENSITY (O), VISCOSITY (VS),
SZO ..... REYNOLDS NO. W.R.T. PROBE DIAMETER (DM), FROM PJZPZ
SJO RF ...*** AND SUPPLY TEMP. (TS)
540 FOR 1=1 TO N
550 P(I)=P3(I)ZPZ
560 IF PdXI THEN 780
570 IF P(I><1.89Z9 THEN 680
SRO M(I)=(.5*P(I))••(IZ1.6)
590 S(I)=((Z*M(I)**Z-1)Z6)*((7.Z*M(I)**Z)Z(7*M(I)**2-1))**3.5
600 R=(P(I)-S(I))ZP(I)
20
90
62
10
0M
I<
FIA
<».001 THEN 6*0
6
)B
.S
N(dR)
HR
630 GOTO 593
6*0 IF I>E THEN 730
66
50
0T
TN
I»
>T
»N
T(S«
(/
((
.105
E)>».95)
6
((
I)
I)
♦«
.r
Zl-(Mld))/r•l
•(
Z)
670 GOTO 7*3
69
80
0N
<I)
0R((P(
6
IF
Is
>S
E
GI
O)
T»
O«(713/
03.5)-1)»5)
700 TN(I)»TS*((.05*Y1<I)/T1(E>)*.95>
710 T(I)*TN(I)/(1».Z*N(I)«»Z)
7ZO GOTO 7*0
730 T(I)*TS/<I♦.Z»M(I).«Z)
7*3 U(I>*M(I).(1.*.1716«T(I))»».5
750 0(I)»PZ«Z.77*/(I716*T(I))
7
6
0
V
S
<
I
)
»
<
(
Z
.
2
7
»
<
T
<
I
)
)
»
»
1
.
S
>
/
<
r
<
I
)<
*I
1)
98.6>>»10*»<-8>
7
7
0
R
E
(
I
)
»
(
0
(
I
)
«
U
<
I
)
«
<
0
M
/
3
O
.
*
8
)
)
/
V
S
7SO N E X T I
790 IF F3*1 GO TO 870
SOO REM««»* THIRD EVALUATION OF DELTA (TKE))
810 FOR 1*1 TO N
8ZO IF U(I)>».99«U(£) AND U(I><*1.01*U(E> G3 TO 8*0
830 NEXT I
8*0 E*I
850 F3*I
860 GO TO 5*0
870 IF C>0 THEN IIZO
880 ....
LINEAR CURVE FIT OF VELOCITY (U) VS.
890 REM....» DISPLACEMENT (Tl) TO FIND "SHIFThIN VELOCITY
903 R E M . . . . . PROFILE DUE TO "PROBE EFFECT"(ONLY FOR SMOOTH MODEL)
910 CIL*0
920 CZL-O
930 C3L*0
9*0 C*L»0
950 C5L*0
960 C6L*0
970 FOR 1*1 TO 15
980 IF P d X I T H E N 1050
990 C1L*C1L*1
1003 CZL«CZL»Y1(I)
1010 CSL-CZL
ICZO C4L*C*L*Y1(I)*.Z
ICJO C
SL-CSL-U(I)
10*0 C6L-C6L-Yl(I)-U(I)
1050 NEXT I
1060 AL*((C5L*CZL>-(C6L-CU))/((CJL-CZD-(C*L.CID)
1
10
07
80
0U
YL
S»
-(
((UCLSZLA.LC)*L)-(C6L.C3L))/C(C1L.C*L)-(CZL»CJL>)
1090 FOR 1*1 TO N
IIOO YI(I)-YI(I)-YS
1110 NEXT I
1120 NC-O
1I30 FOR I*1 TO N
II35 IF PdXI THEN NC*NC-1
11*3 IF U(I)XU(E) GO TO 1160
II50 NEXT I
1160 N-I-IO
II70 NN-N-NC
I180 PRINT NN
I190 FOR 1*1 TO N
IZOO IF Pd)<1 THEN IZZO
IZiO PRINi yid ); " , " ; u ( i ) ; " , " ; o d > ; " , " ; v s ( i > ; " , " ; r (I)
91
1220 NEXT I
I230 FOR 1*1 TO N
1240 If P(1X1 THEN 1260
1250 print »<i>;",";ii<i>;"*h;pa<i>;"*-;p3<i>
1260 NEXT I
I270 REM"««* THE SUBCRIPT ”£“ CORRESPONDS TO FREc STREAM PROPERTIES
1280 FOR 1*1 TO N
1260 IF PdXI THEN IJSO
IJOO UE(I)*U(I)ZU(E)
IJIO TE(I)«T(I)ZT(E)
IJ20 0E(IXO(I)ZO(E)
IJJO T2(I)«YI(I)ZYI(E)
iJ40 print Y2(i
M(i
TE(i o E(I)
IJSO NEXT I
IJ60 01*0
I370 02*0
I380 FOR I*NC♦I TO E '
I390 If P(I)<1 THEN 1*40
1*00 IF I*NC♦! THEN 02*02*(UE(I)/TE(I)>*<1-UE(I))*(Y2(1)Z2)
1*10 IF I>NC*1 THEN D2*02*(UE(I)ZTE(I))•(I-UE(I))•(Y2(I>-Y2(I-I))
1*20 If I*NC♦I THEN 01*01♦(I-UE(I)ZTE(I>)•(Y2(I)/2)
1*30 If I>NC•I THEN 01*01*(1-UE(I)ZTE(I))•(Y2(I)-Y2(I-I))
1**0 NEXT I
1ASO FOR 1*1 TO N
1*60 YCAP(I)-O
1*20 NEXT I
1*80 FOR XNCd TO N
1*90 If P(J)<1 THEN ISSO
ISOO FOR 1*1 TO J
IS10 IF PdXI THEN I5*0
1520 IF I*NC♦I THEN YCAP(J)*YCAP(J)*0£(I)•(Yl(I)/2)
ISJO IF ISNC*I THEN YCAPd>*YCAr»U)*0E(l)*(Y1d)-YI(I-I)J
15*0 NEXT I
ISSO NEXT J
1560 THETA*D2*Y1(E)
I570 REM***** OUTPUT SUMMARY (SAME AS BEFORE)
I580 FOR 1*1 TO N
1
50
90
0 pIrint
F PdXI
T/
HE
N 1610
16
Yid)
theTa;",";YCAPd);".~;ycap(i)/theta;",";uEd>
1
6
1
0
N
E
X
T
I
1 6 2 0
;', * ; ; " , ,,; ; ,,. " ; ; “ » “ ;
" , ~ ;
; ” * " ;
( ) /
; " , ~ ; < ) ; " . " ;
1 6 j o
p r i n t
p r i n t
g
y i
h
( e )
x
c
k
p o j
t s
r e
e
o m
m
e
p
o i * y i ( e > ; ” * ” ; i / o i ; “ . " ; i / 0 2 ; " , " ; ( r e ( e ) / o m > * ( d 2 * y i ( £ ) )
16*0 MSP»SOR(((PO/P2)**(1/J.5)-1>/.2)
1650 PRINT M(E)J",";MSP
I660 END
2
APPENDIX III
TABULAR FORM OF RESULTS FOR SMOOTH MODEL
***********
s
M
O
O T
H
M
O
D
E
L
***********
GROUP NO.: 1600
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 2.54
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.): O
SUPPLY P R E S S U R E - ' PO' (MM.H G .A B S ) : 600
SUPPLY T E M P E R A T U R E - ' TS' (DEG RANKING): 559.67
E D G E R E Y N O L D S N O . ( C M t I); 4 7 6 4 4 . 3
E X T E R N A L MACII N O . : 2 . 6 9 1 1 8
SURFACE PRESSURE (MM.HG.ABS): 18.9084
SKIN FRICTION COEF. FROM WALL VISCOSITY-'CFI': 1.1
SKIN FRICTION COEF. FROM STREAM VISCOSITY-'CF2': 5
'THE TA'-(CM.): I. 34662E-2
S H I F T IN Y - A X I S DUE TO ' P R O B E E F F E C T ” (C M . ) : - 7 . 3 2 4
B O U N D A R Y L A Y E R TH I C K N E S S - ' D E L T A ' ( C M . ) : . 2 0 3 2 6 8
'DELTA STAR' (CM.): 6.69732E-2
'DELTA/DELTA S T A R ” : 3.03506
'DELTA/THETA': 15.0947
' R E T H E T A ': 6 4 1 . 5 8 6
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.:
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRES.:
***********
$
M
O
O
T
H
M
O
D
E
L
9532E-3
. 7 6 0 1 9 E-4
4 0 E- 3
2.69118
2.90288
***********
GROUP N O . : 2600
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 5.08
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.): O
SUPPLY P R E S S U R E - 'PO! (MM.HG.ABS): 600
SUPPLY T E M P E R A T U R E - 'T S ' (DEG RANKING): 559.67
EDGE REYNOLDS NO. ( C M - I ) : 51229.8
EXTERNAL MACH NO.: 2.76263
SURFACE PRESSURE (MM.HG.ABS): 18.9147
SKIN FRICTION COEF. FROM WALL VISCOSITY-'CFl': 1.0
S K I N F R I C T I O N C O E F . FR OM S T R E A M V I S C O S I T Y - ”C F 2': 4
' T H E T A ' - ( C M . ): 1 . 5 2 0 4 3 E - 2
SH IF T IN Y- AX I S DUE TO 'PROBE E F FE C T ' (C M .):-5 . 3 2 0
B O U N D A R Y LAYER TH I C K N E S S - 'DELTA' (CM,): . 2 0 92 7 8
■'DELTA STAR' (CM.): 8.28781 E-2
'DELTA/DELTA STAR': 2.52513
'DELTA/THETA': 13.7644
'R E T H E T A ' : 778.91 2
EDGE MACH NO. FROM SURFACE PRES. AND PITOT P R E S . I
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRES.:
1981E-3
.76746E-4
4 5 E - 3
2,76263
2.90266
93
***********
$
M
O
O
T
H
M
O
D
E
L 1*****,******
GROUP N O . : 3600
DISTANCE FROM T R AI L I N G EDGE OF MODEL (CM.): 7
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.): O
SUPPLY P R E S S U R E - * PO 8 (MM.HG.ABS): 600
SUPPLY T E M P E R A T U R E - 8TS 8 (DEG RANKING) : 559.67
E D G E R E Y N O L D S N O . ( C M - I ): 51 5 8 8 . 6
EXTERNAL MACH N O . : 2.60415
SURFACE PRESSURE ( M M. H G . A B S ) : 22.3772
SKIN FRICTION C O E F . FROM WALL VISCOSITY-* C F V
S K I N F R I C T I O N C O E F . F R O M S T R E A M VI S C O S I T Y - 8C F
8 T H E T A 8- ( C M 0 ): 1 . 4 0 3 1 I E - 2
S H IF T IN Y-AXIS DUE TO 8PROBE E F F E C T 8 (CM.):
B O U N D A R Y L A Y E R TH I C K N E S S - 8D E L T A * ( C M . ) : .1 8 7 3
8DELTA S T A R 8 (CM.): 7.9741 0E-2
* DELTA/DELTA STAR 8 : 2.34947
6De l t a z t h e t a 8: 13.35 24
6 R E T H E T A 6 : 723.845
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PR
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE P
***********
$
M
O
O
T
H
M
O
D
E
L
.62
; 7.9481 4E-4
2 8 : 3.97390E-4
'
7.71827E-4
49
ES.: 2.60415
RES.: 2.7921
***********
GROUP N O , : 4600
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 10.16
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.): O
SUPPLY P R E S S U R E - 6P O 8 (MM.HG.ABS): 600
SUPPLY T E M P E R A T U R E - 8T S 8 (DEG RANKING): 559.67
EDGE R E Y N O L D S NO. ( C M - I ) : 5 4 8 2 6 . 8
EXTERNAL MACH N O . : 2.7284
SURFACE PRESSURE (MM.HG.ABS): 20.9537
S K I N F R I C T I O N C O E F . F ROM W A L L V I SC OS I T Y - * C F I 8 : 9 . 5281
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I S C O S I T Y - 8C F 2 8 : 4 . 5 1
6 T H E T A ( C M . ); 1 . 0 6 7 4 1 E-2
S H I F T IN Y - A X I S DUE TO 8P R O B E E F F E C T 8 (C M „ ) : - 1 . 584 7 0 E
B O U N D A R Y L A Y E R T H I C K N E S S - ‘ D E L T A ' 8' ( C M . ) : . 1 5 6 6 9 6
6DELTA S T A R 8 (CM.)
6,278296-2
•DELTA/DELTA STAR 6 : 2.49584
6DELTA /THETA 8: 14.68
8RETHETA 8: 5 85.229
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.: 2.7
EDGE MACH NO. FROM SUPPLY PRES. AND S U RFACE P R E S . : 2.
3E-4
956E-4
- 3
284
83521
94
***********
S M O O T H
M O D E L
***********
GROUP M O . : 5600
DISTANCE FROM TRAI L I N G EDGE OF MODEL (CM.); 12.7
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.); O
S U P P L Y P R E S S U R E - ieP O e ( M M . H G . A B S ) : 5 0 0 . .
SUPPLY T E M P E R A T U R E - " T S e (DEG RANKI NE): 559.67
EDGE R E YN O L D S NO. ( C M - I ) : 51649.2
EXTERNAL MACH NO.: 2.70771
SURFACE PRESSURE (M M . H G . A B S ) : 20.1569
SKIN FRICTION COEF. FROM WALL V I S C O S ITY-'CFI*: 1.081
SKIN F R I C T I O N COEF. FROM S T R E A M V I S COS I T Y C F 2': 5.1
1 T H E T A 1- ( C M e ): 9 . 8 8 6 4 7 E -3
S H I F T IN Y - A X I S D U E TO " P R O B E E F F E C T " (C M . ) ; - 2 . 0 6 6 7 5
BOUNDARY LAYER T H I C K N E S S - eD E L T A 6 (CM.): .144013
"DELTA STAR' (CM.): 5.69036E-2
"DELTA/DELTA STAR": 2.53082
eDELTA/THETA 1: 14.5666
"RETHETA " : 510.629
E D G E M A C H NO". F R O M S U R F A C E P R E S . A N D P I T O T P R E S . : 2 .
E D G E M A C H NO. F R O M S U P P L Y P R E S . AND. S U R F A C E P R E S . : 2
***********
s
M
O
O
T
H
M
O
D
E L
43E-3
7492E-4
E -3
70771
.74125
***********
GROUP N O . : 6600
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 15.24
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.): O
SUPPLY P R E S S U R E - " P O " (MM.HG.ABS): 600
SUPPLY TEMP E R A TU R E - "T S ' (DEG RANKING): 559.67
E D G E R E Y N O L D S N O . ( C M - 1 ): 5 0 4 0 7 . 9
E X T E R N A L MACH NO.:. 2 . 77 1 5
SURFACE PRESSURE (MM.HG.ABS): 18.4461
SKIN FRICTION COEF. FROM WALL V I S C O S I T Y - " C F I 6 : 1.1
SKIN FRICTION COEF. FROM STREAM VISCOSITY- "CF2 " : 5
6T H E T A " - (C M . ) : 1.04533E-2
S H I F T IN Y - A X I S D U E TO " P R O B E E F F E C T " (C M . > : - 5 . 6 8 1
B O U N D A R Y L A Y E R TH I C K N E S S - " D E L T A " ( C M . ) : . 1 55451
"DELTA STAR" ( C M . ) : 5.82562E-2
* DELTA/DELTA STAR": 2.6684
"D E L T A / T H E T A ": 14.871
!RETHETA": 526.929
EDGE MACH NO. FROM SURFACE P R E S i AND PITOT P R E S 0 :
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRES.:
7062E-3
.451 87E-4
8 2 E - 3
2.7715
2.91924
95
***********
S M
O
O
T
H
M
O
D
E
L
***********
GROUP NO.: 7600
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 17.78
SURFACE ROUGHNESS C O D E : O
SURFACE ROUGHNESS HEIGHT (CM.): O
S U P P L Y P R E S S U R E - 1lP O t ( M M . H G . A B S ) : 6 0 0
SUPPLY T E M P E R A T U R E - ' TS ' (DEG RANKING): 559.67
E D G E R E Y N O L D S N O . ( C M - I ) : 48585.8
EXTERNAL MACH N O . : 2.75718
SURFACE PRESSURE (MM.HG.ABS): 18.0371
S K I N F R I C T I O N C O E F . F R O M W A L L V ISC OS I T Y - 6 CF I 9 : 1 . 1 2 3 0 9 E
SKIN FRICTION C O E F . FROM STREAM V ISCOS IT Y - ' C F 2 ': 5.2624
e T H E T A t - ( C M a ): 1 . 2 0 6 7 O E - 2
S H I F T IN Y - A X I S D U E TO 9P R O B E E F F E C T * ( C M . ) : - 4 . 8 3 4 9 2 E - 3
BOUNDARY LAYER T H I C K N E S S - eD E L T A t (CM.): .164144
eDELTA STAR' (CM.): 6.83064E-2
* D E L T A / D E L T A S T A R * : 2.40306
'DELTA/THETA': 13.6027
* R E T H E T A t : 586.287
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.: 2.757
EDGE M A CH NO. FROM SUPPLY PRES. AND S U R F A C E PRES.: 2 . 9 3
***********
s
M
O
O
T
H
M
O
D
E
L
-3
5E-4
18
409
***********
GROUP N O . : I 500
DISTANCE FROM TRAI L I N G EDGE OF MODEL (CM.): 2.54
SURFACE ROUGHNESS CODE : O
SURFACE ROUGHNESS HEIGHT (CM.): O
SUPPLY P R E S S U R E - 6P O t (MM.HG.ABS): 500
SUPPLY TEMPE R A T U R E - 'T S 6 (DEG RANKING): 559.67
E D G E R E Y N O L D S N O . ( C M - 1 ): 39163.9
EXTERNAL MAC H NO.: 2.70385
SURFACE PRESSURE (MM.HG.ABS): 15.3443
SKIN FRICTION C O E F . FROM WALL V l S C O S I T Y - eC F l e: 1 . 3
SKIN F R I C T I O N C O E F . FROM S T R E A M V I S C O S I T Y - eC F 2 e : 6
0 T H E T A t- ( C M a ): 1 . 2 1 0 8 6 E -2
S H I F T IN Y - AX I S DUE TO 'PROBE E F F E C T 6 (C M . ) : - 2 . 3 7 6
B O U N D A R Y L A Y E R TH I C K N E S S - tD E L T A ' (CM.): . 1 8 2 2 9 3
0 D E L T A S T A R ' ( C M . ) : 6.53309E-2
'DELTA/DELTA STAR': 2.7903
' D E L T A / T H E T A ': 1 5 . 0 5 4 8
0 R E T H E T A ' : 474.22
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.:
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRES.:
9 8 4 1 E - 3
.70274 E-4
9 5 E-3
2.70385
2.92043
96
***********
5
M
O
O
T
H
M
O
D
E
L
***********
GROUP NO. : 2 500
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 5.08
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.): O
SUPPLY P R E S S U R E - * PO' ( M M . H G . A B S ) : 500
S U P P L Y T E M P E R A T U R E - 'TS ' (DEG RANKI NE ) : 5 5 9. 6 7
EDGE REYN O L D S NO. ( C M - I ) g 40619.5
EXTERNAL MACH N O . : 2.64988
SURFACE PRESSURE ( M M . H G . A B S ) : 16.813
SKIN FRICTION COEF . FROM WALL VISCOSITY-'CFI': I
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I S C O S I T Y - ' C F 2' :
' T H E T A '-(CM.): 1.45465E-2
S H I F T IN Y - A X I S D U E TO ‘P R O B E E F F E C T 8 (CM . ):- 2.1
BOUNDARY LAYER THICKNESS-'DELTA' (CM.): .200739
"DELTA STAR' (CM.): 7.85732E-2
"DELTA/DELTA STAR': 2.55481
'DELTA/THETA': 13.7999
" RETHETA': 590.87
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE P R E S
***********
§
M
O
O
T
H
M
O
O
E
L
.1 5 3 9 2 E - 3
5.65887E-4
2 4 60 E- 3
: 2.64988
. : 2.86009
***********
GROUP N O . : 3500
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 7.62
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.): O
SUPPLY P R E S S U R E - ' P O 8 (MM.HG.ABS): 500
SUPPLY T E M P E R A T U R E - ' T S ' (DEG RANKINE): 559.67
EDGE R E YN O L D S NO. ( C M - I ) : 41839.5
EXTE R N A L MAC H NO. : 2.57132
SURFACE PRESSURE (MM.HG.ABS): 18.7724
SKIN FRICTION COEF. FROM WALL V I S C O S I T Y - 8CFI': 1.
SKIN FRICTION COEF . FROM STREAM V ISCOSITY- 'CF2' :
8 T H E T A '-(CM.)" I . 3 6 0 4 1 E-2
S H I F T IN Y - A X I S DU E TO 'P RO B E EFFECT.' (CM. ) :- 1 . 8 8
B O U N D A R Y L A Y E R TH I C K N E S S - ' D E L T A 8 ( C M . ) : .1 8 7 3 3 6
'DELTA STAR' (CM.): 7.33038E-2
'DELTA/DELTA STAR 8 : 2.55562
8 D E L T A / T H E T A ': 1 3 . 7 7 0 5
'RETHETA': 569.19
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.:
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE P R E S .
03587E-3
5.251 40E-4
697E-3
2.57132
: 2.78774
97
***********
$
M
O
O
T
H
M
O
D
E
L
***********
GROUP N O . : 4500
DISTANCE FROM TRAI L I N G EDGE OF MODEL (CM.): 10.16
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.): O
SUPPLY P R E S S U R E - ' PO* (MM.HG.A8S): 500
SUPPLY T E M P E R A T U R E - ' T S e (DEG RANKINE): 559.67
EDGE REYNOLDS NO. ( C M- I ) : 45389.8
EXTERNAL MACH N O , : 2.76607
SURFACE PRESSURE (MM.HG.ABS): 16.7007
S K I N F R I C T I O N C O E F . F R OM W A L L V I S C O S I T Y - ' CF I 8 ; I .0 8
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I S C O S I T Y - 8C F Z ' : 5 .
' T H E T A '-(CM.): 1.10245E-2
S H I F T IN Y - A X I S D U E TO ' P R O B E E F F E C T ' ( C M . ) ; - 1 . 4 7 5 8
B O U N D A R Y L A Y E R TH I C K N E S S - ' D E L T A 8 ( C M . ) : „1 64 0 2 9
'DELTA S T A R 8 (CM.): 6 . 6 8 4 7 4 E - 2
'DELTA/DELTA S T A R 8 ; 2.45378
'DELTA/THETA': 14.8786
'RETHETA 8 : 500.4
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.: 2
EDGE MACH N O . FROM SUPPLY PRES. AND SURFACE P R E S . :
***********
5
M
O
O
T
H
M
O
D
E
L
4 9 3 E - 3
06447E-4
8E-3
.76607
2.86451
***********
GROUP N O . : 5500
DISTANCE FROM TRAILING EDGE OF MODEL. (CM.): 12.7 .
SURFACE ROUGHNESS C O D E : O
SURFACE ROUGHNESS HEIGHT (CM.): O
SUPPLY P R E S S U R E - ' PO 8 (MM.HG.ABS): 500
SUPPLY T E M P E R A T U R E - 'TS ' (DEG R A N K I N E ) : 559,67
EDGE REYNOLDS NO. ( C M - I ) : 42298.1
EXTERNAL MACH NO.: 2.69731
SURFACE PRESSURE (MM.HG.ABS): 16.6826
SKIN FRICTION COEF. FROM WALL V I S C O S ITY-"CFI 8: 1.225 1 2 E-3
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I S C OS IT Y - 8C F Z ' : 5 „ 8 8 8 4 6 E - 4
' T H E T A ' - ( C M . ); 1 . 0 7 0 9 8 E - 2
S H I F T IN Y - A X I S D U E T O 8P R O B E E F F E C T ' ( C M „ ) : - 1 . 2 2 8 7 6 E - 3
BOUNDARY LAYER TH I C K N E S S - 'D E L T A 8 (CM.): . 1 5634
8DELTA S T A R 8 (CM.): 6 . 20356E-2
'DELTA/DELTA STAR 8 : 2.5201 7
'DELTA/THETA 8: 14 .5978
8RETHETA 8 : 4 53.005
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.: 2.69731
E D G E M A C H N O . F R O M S U P P L Y P R E S . A N D S U R F A C E P R E S . : 2«, 8 6 5 2 2
?
98
***********
$
M
O
O
T
H
M
O
D
E
L
***********
GROUP N O , : 6500
DISTANCE FROM TRAI L I N G EDGE OF MODEL (CM.): 15.24
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.): O
S U P P L Y P R E S S U R E - ePO 6 ( M M. H G . AB S ) : 500
S U P P L Y T E M P E R A T U R E - 'T S 0 (DEG RANKI NE) : 5 5 9. 6 7
EDGE REYNOLDS NO. ( C M - I ) : 42066.6
,
EXTERNAL MACH NO.: 2.83831
SURFACE PRESSURE (MM.HG.ABS): 14.3983
S K I N F R I C T I O N C O E F . F R O M W A L L V I S C O S I T Y - 11 C F V : I . 4
SKIN F R ICTION COEF . FROM STREAM V IS C OS I T Y- C F 2 * : 6
* T H E T A e - ( C M . ).: 1 . 1 1 6 4 8 E - 2
S H I F T IN Y - A X I S D U E T O 4P R O B E E F F E C T " (CM. ) :-5. 2 5 2
BOUNDARY LAYER T H I C K N E S S - eD E L T A 6 (CM.): ,165325
“DELTA STAR" (CM.): 6.40789E-2
“DELTA/DELTA S T A R 6 : 2.58002
*D E L T A / T H E T A 6 : 14. 80 77
*R E T H E T A " : 469.666
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES. :
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRES.:
***********
S
M
O
O
T
H ‘ ■ M. O
D
E
L
0249E-3
.34842E-4
57E-3
2. 8 3 8 3 1
2.96262
***********
G R O U P NO. : 7.500
D I S T A N C E F R OM T R A I L I N G EDGE OF M O D E L (CM..): 1 7 . 7 8
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.): O
SUPPLY P R E S S U R E - 4P O 6 (MM.HG.ABS): 500
SUPPLY T E M P E R A T U R E - 6T S e (DEG RANKING): 559.67
EDGE REYNOLDS NO. ( C M - I ) : 41096.3
E X T E R N A L MACH NO.: 2.,86006
SURFACE PRESSURE (MM.HG.ABS) : I3.7651
S K I N F R I C T I O N COE F . F R O M .WALL V I S C O S I T Y - 6 C F V :
1.271
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I S C O S I T Y ^ 6C F 2 “ : 5 . 7
4 T H E T A e- ( C M 0 ): 1 . 2 8 0 7 8 E - 2
S H I F T IN Y - A X I S D U E T O " P R O B E E F F E C T " - ( C M . ) : - 4 . 11 4 11
BOUNDARY LAYER T H I C K N E S S - " D E L T A 4 (CM.): .17678
"DELTA STAR" (CM.): 7.76389E-2
"DELTA/DELTA STAR": 2.27694
"DELTA/THETA": 13.8025
4 R E T H E T A e : 526.353
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.: 2.
EtiGE M A C H N O . F R O M S U P P L Y P R E S . A N D S U R F A C E P R E S . : 2
j
j
I
08E-3
0047E-4
E -3
86006
.99254
99
***********
S
M
O
O
T
H
M
O
D
E
L
***********
GROUP NO. : 1400
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 2.5
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.): O
S U P P L Y P R E S S U R E - e P O 11 ( M M . H G . A 8 S ) : 4 0 0
SUPPLY T E M P E R A T U R E - ' T S ' (DEG RANKING): 559.67
EDGE REYNOLDS N O . ( C M - I ) : 35244.4
EXTERNAL MACH NO.: 2.84832
SURFACE PRESSURE (MM.HG.ABS): 11.9436
S K I N F R I C T I O N C O E F . F R O M W A L L V I S C O S I TY-,'C Fl':
S KIN F R I C T I O N COEF. FROM S T R E A M V I SC O S I T Y C F 2'
' T H E T A ' - ( C M . ) : 1 .2 31 5 8 E-2
S H I F T IN Y - A X I S D U E TO 8P R O B E E F F E C T ' (C M . ) ; - 3 .
BOUNDARY LAYER T H I C K N E S S - 'DELTA* (CM.): „186674
9DELTA STAR' (CM.): 7.19306E-2
9DELTA/DELTA STAR?: 2.5951 9
'DELTA/THETA': 15.1572
0 R E T H E T A e : 434.064
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRE
***********
S
M O
O
T
H
M
O
D
£
L
4
1 .565 96E-3
: 7.05816E-4
9 6 3 6 3 E -3
.: 2.84832
S.: 2.93858
***********
GROUP NO.: 2400
DISTANCE FROM T R AI L I N G EDGE OF MODEL (CM.): 5.08
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.): O
SUPPLY P R E S S U R E - ' PO' (MM.HG.ABS): 400
SUPPLY TEMPER A T U R E - 'TS ' (DEG RANKING) : 559.67
EDGE REYNOLDS NO. (CM-1): 36980.2
E X T E R N A L M A C H N O . : 2.83836
SURFACE PRESSURE (MM.HG.ABS): 12.6567
S K I N F R I C T I O N C O E F . F R O M W A L L V I S C Q S I T Y - 6 CF I = ; 1 .2
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I SC OS I T Y - 6C F 2 ' : 5
' T H E T A '-(CM.): I „ 4 4 9 4 4 E-2
S H IF T IN Y - AX I S DUE TO ' P ROBE E F F E C T ” (C M „ ) : - 2 . 5 4 8
B O U N D A R Y L A Y E R TH I C K N E S S - ' DEL TA' ( C M. ) : . 2 0 8 0 8 8
'DELTA S T A R ” ( C M . ) : 8.85559E-2
'DELTA/DELTA S T A R ” : 2.34979
'D E L T A / T H E T A ': 14.3564
' R E T H E T A 536.008
EDGE MACH NO. FROM SURFACE PRES. AND PITOT P R E S . :
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRES.:
3885E-3
.63 761 E-4
05 E-3
2.83836
2.9002
TOO
***********
s
M
O
O
T
H
M
O
D
E
L
***********
GROUP N O . : 3400
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 7.62
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.): O
SUPPLY P R E S S U R E - ePO 0 (MM.HG.ABS): 400
SUPPLY T E M P E R A T U R E - 6T S g (DEG R A N K I N E ) : 559.67
EDGE REYNOLDS NO. ( C M - I ) : 3 7 49 8 . 9
EXTERNAL MAC H NO.: 2.76049
SURFACE PRESSURE (MM.HG.ABS): I 3.875
SKIN FRICTION COE F . FROM WALL VISCOSITY-'CFI': I„1
SKIN FRICTION C O E F . FROM STREAM V ISCOS IT Y C F 2 8 : 5
e THE TA'-(CM.): I .42639E-2
S H I F T IN Y - A X I S DUE TO eP R O B E E F F E C T 8 (C M . ) : - 2 . 2 4 8
B O U N D A R Y L A Y E R T H I C K N E S S - ' D E L T A 8 ( C M . ) : .1 9 4 8 2 8
8 DELTA S T A R 6 (CM.): 8.7251 6E-2
8 DELTA/DELTA STAR': 2.23295
/ D E L T A / T H E T A ' : 13.6588
8 R E T H E T A ': 5 3 4 . 8 8 3
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES. :
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE P R E S . :
***********
$
M
O
O
T
H
M
O
D
E
L
4109E-3
. 33930E-4
11E - 3
2.76049
2.83965
***********
GROUP N O . : 4400
DISTANCE FROM TRAI L I N G EDGE OF MODEL ( C M . ) : 10.16
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.): O
SUPPLY P R E S S U R E - 8P O ' (MM.HG.ABS): 400
SUPPLY T E M P E R A T U R E - 8 T S ' (DEG RANKINE): 559.67
E D G E R E Y N O L D S 'NO. ( C M - I ) : 3 8 0 3 4 . 3
EXTERNAL MACH N O . : 2.73384
SURFACE PRESSURE (MM.HG.ABS): 14.4563
S K I N F R I C T I O N C O E F . F R O M W A L L V I S C O S I T Y - ' CFI *: I .1
SKIN FRICTION COEF . FROM STREAM V ISCOS IT Y - ' C F 2 8 : 5
8 T H E T A '-(CM.): 1.30023E-2
S H I F T IN Y - A X I S D U E TO 8P R O B E E F F E C T ' ( C M . ) :-2. 785
BOUNDARY LAYER TH I C K N E S S - ' DELTA' (CM.): . 1 74277
8 DELTA STAR' (CM.): 8 .04869E-2
'DELTA/DELTA S T A R 8 : 2.16528
'DELTA/THETA': 13.4035
8R E T H E T A ': 494.534
EDGE M A CH NO. FROM S U R F A C E P R ES . AND P I T O T PRES..:
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE P R E S . :
14 5 9 E - 3 '
.274 72E-4
28E-3
2.73384
2.81271
101
***********
S
M
0
O
T
H
M
O
O
E
(_ * * * * * * * * * * *
GROUP N O . : 5A OO
DISTANCE FROM T R AI L I N G EDGE OF MODEL (CM.): 12.7
SURFACE ROUGHNESS C O D E : O
SURFACE ROUGHNESS HEIGHT (CM.): O
S U P P L Y P R E S S U R E - ' P O * ( M M . H G . A B S ): 4 0 0
SUPPLY TEMPER A T U R E - 6TS* (DEG RANKING): 559.67
EDGE REYNOLDS NO. ( C M - I ) ; 36457.3
EXTERNAL MACH NO. : 2.75501
S U R F A C E P R E S S U R E ( M M . H G . A B S ): 1 3 . 5 6 4 2
SKIN FRICTION C O E F . FROM WALL VISCOSITY-'CFl*: 1
SKIN FRICTION COEF . FROM STREAM V ISCOS ITY - ' C F 2':
* THE T A '-( CM. ) : I . 2-36.39E - 2
S H I F T IN Y - A X I S D U E TO 8P R O B E E F F E C T 8 (C M . ) : - 1 . 6
B O U N D A R Y L A Y E R TH I C K N E S S - 8 D E L T A ' ( C M . ) : .1 7 0 2 5 8
*DELTA S T A R 8 (CM.): 7 . 63896E-2
* D E L T A / D E L T A S T A R ' : 2.22881 .
* D E L T A / T H E T A ' : 13.7706
e RETHETA': 450.754
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE P R E S
***********
$
M
O
O
T
H
M
O-D
E
L
.24724E-3
5.84962E-4
6 8 3 4 E-3
:
j
: 2. 7 5 5 0 1
. : 2.85455
***********
GROUP N O . : 6400
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 15.24
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.): O
SUPPLY PRESS U R E - e PO 8 (MM.HG.A8S): 400
SUPPLY T E M P E R A T U R E - 'T S ' (DEG RANKING): 559.67
EDGE R E Y N O L D S NO. ( C M - I ) : 3 5 39 7 . 2
EXTERNAL MACH NO.: 2.83384
S U R F A C E P R E S S U R E ( M M . HG.. ABS') : 1 2 . 1 6 9 6
S K I N F R I C T I O N C O E F . F R O M W A L L V I S C O S I T Y - 8 CFl 8 : 1 .4 2 2
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I S C O S I T Y - 8C F 2 8 : 6 . 4
e T H E T A '-(CM.): 1 . 2 0 2 3 5 E-2
S H I F T IN Y - A X I S D U E TO 8P R O B E E F F E C T 6 ( C M . ) : - 2 . 3 8 1 0 1
B O U N D A R Y L A Y E R TH I C K N E S S - 8D E L T A e ( C M . ) : .1 7 4 0 6 6
e DELTA S T A R 6 (CM.): 7.4801 3E-2
'DELTA/DELTA S T A R 8 : 2.32705
eDELTAZTHETA': 14.4771
e RETHETA': 425.599
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.: 2.
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE P R E S . : 2
'
96E-3
5 336E-4
E-3
83384
.92616
102
*********** S M O O T H
M O D E L
***********
GROUP MO. : 7400
D I S T A N C E F R OM T R A I L I N G EDGE OF M O D E L (CM..): 1 7 . 7 8
SURFACE ROUGHNESS CODE: O
SURFACE ROUGHNESS HEIGHT (CM.): O
S U P P L Y P R E S S U R E - ' P O ' ( M M . H G . A B S ): 4 0 0
SUPPLY T E M P E R A T U R E - ' T S ' (DEG RANKING): 559.67
EDGE REYNOLDS NO. (CM-1): 34801.2
EXTERNAL MAC H NO.I 2.84841
SURFACE PRESSURE (MM.HG.ABS): 11.7923
SKIN FRICTION COEF . FROM WALL VISCOSITY-'CFl': 1.3461 8E-3
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I S C O S I T Y - ' C F 2' : 6 . 0 6 7 3 4 E - 4
3 T H E T A ' - ( C M . ): 1 . 2 5 4 7 7 E - 2
S H I F T IN Y - A X I S D U E TO ' P R O B E E F F E C T ' ( C M . ) : - 2 . 3 9 6 0 9 E -3
B O U N D A R Y L A Y E R TH I CK N E S S - 'D E L T A ' (CM.): . 1 7 6 4 0 3
* DELTA STAR' (CM.): 8.03459E-2
'DEL T A /DELTA STAR': 2.19554
0 DELTA/THETA «: 14.0585
' RETHETA': 436.676
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.: 2.84841
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRES.: 2.94703
A P P ENDIX IV
TABULAR FORM OF RESULTS FOR SCREW MODEL
***********
s
c
R
E
W
M
o
D
E
^
***********
GROUP NO.: I 600
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 2.54
SURFACE ROUGHNESS CODE: 2
SURFACE ROUGHNESS HEIGHT (CM.); 3 . 55600F-2
SUPPLY P R E S S U R E - ' P O e ( M M. H G . AB S ) I 600
S U P P L Y T E M P E R A T U R E - e T S ' ( D E G R A N K I N E >: 5 5 9 . 6 7
EDGE R E Y N O L D S NO. ( C M - I ) : 5 6 89 1 . 3
EXTERNAL MACH N O . : 3.01113
SURFACE PRESSURE (MM.HG.ABS): 16.424
S K I N F R I C T I O N C O E F . F R O M W A L L V I S C O S I T Y - ' CFl ': 3 .
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I S C O S I T Y - eC F 2 1 :
«THE T A ' - ( C M . ) : 2.041 28E-2
S H I F T IN Y - A X I S DUE TO ' P R O B E E F F E C T ' ( C M . ) : - 2 . 3 9
B O U N D A R Y L A Y E R TH I C K N E S S - ' D E L T A ' ( C M. ) : . 3 9 41 0 1
5 DELTA STAR' (CM.): 8.66365E-2
6 DELTA/DELTA STAR' : 4.5489
'DELTA/THETA': 19.3066
* R E T H E T A ' : 1161.31
E D G E . M A C H NO. FROM. S U R F A C E P R E S . A N D P I T O T P R E S . :
EDGE MACH NO. FROM SUPPLY PRES. AND S U RF A C E P R E S .
***********
$
C
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W
M
O
D
E'L
66908E-3
1.54259E-3
6 0 9 E- 3
:
3.01113
2.99635
***********
GROUP N O . : 2600
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 5.08
SURFACE ROUGHNESS CODE: 2 .
SURFACE ROUGHNESS HEIGHT (CM.); 3 . 55600E-2
SUPPLY P R E S S U R E - 1 PO' ( M M. H G . AB S ) : 600
SUPPLY T E M P E R A T U R E - 'T S ' (DEG RANKING) : 559.67
EDGE REYNOLDS NO. (CM-1): 59631.9
EXTERNAL MAC H NO.: 2.94562
■SURFACE PRESSURE (MM.HG.ABS): 18.37
S K I N F R I C T I O N C O E F . F R O M W A L L VI S C O S I T Y-8 C F I ': 3 . 5 5 0 2 0 E - 3
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I S C O S I T Y - ' C F 2' ; 1 . 5 3 5 0 3 E - 3
1 T H E T A '- ( CM. ) : I . 7 5 5 2 6 E - 2
S H I F T IN Y - A X I S D U E TO ' P R O B E E F F E C T ' ( C M . ) : - 2 . 3 9 6 0 9 E - 3
B O U N D A R Y L A Y E R TH I C K N E S S - ' D E L T A ' ( C M . ) : „ 3672,85 '
'DELTA STAR' (CM.): 7.05244E-2
'DELTA/DELTA STAR': 5.20792
1 DELTAXTHETA':; 20.9248.
'RETHETA': 1047.58
EDGE MACH NO, FROM SURFACE PRES. AND PITOT PRES.: 2.94562
EDGE MACH NO. FROM SUPPLY PRES. AND S U RF A C E P R E S . : 2 . 92198
104
***********
5 C
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M
O
D
E
L
***********
GROUP NO,: 3600
DISTANCE FROM TRAILING EDGE OF MODEL (CM,): 7,62
SURFACE ROUGHNESS CODE: 2
SURFACE ROUGHNESS HEIGHT (CM*): 3 , 55600E-2
SUPPLY P R E S S U R E - * PO* (MM,HG,ABS): 600
SUPPLY T E M P E R A T U R E - 'TS ' (DEG RANKINE): 559.67
EDGE R E Y N O L D S NO. (CM-1): 5 8 34 2 . 3
EXTERNAL MACH NO.: 2.85142
SURFACE PRESSURE (MM.HG.ABS): 19.71
S K I N F R I C T I O N C O E F . F R O M W A L L V I S C O S I T Y - * C Fl * : 2 ^ . 9 6 9 81 E - 3
S K I N F R I C T I O N C O E F e F R O M S T R E A M V I S C O S I T Y - #C F 2 “ : 1 „ 3 3 6 8 0 E - 3
6 T H E T A t - ( C M e ): I . 1 7 6 4 0 E - 2
S H I F T IN Yr-AXIS DUE TO 'PROBE E F F E C T " (CM. ) :-2. 3 9 6 0 9 E - 3
B O U N D A R Y LA YE R TH I C K N E S S - 'DELTA* (CM.): . 1 8 1 8 2 7
* DELTA S T A R ’ (CM.): 5.47687E-2
* DELTA/DELTA S T A R 6 : 3.3199
6D E L T A Z T H E T A 6 : 15.4562
6RETHETA 6: 686.339
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.: 2.85142
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE P R E S . : 2.87547
***********
S
C
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M
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***********
GROUP NO.: 4600
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 10.16
.
SURFACE ROUGHNESS CODE: 2
SURFACE ROUGHNESS HEIGHT (CM.): 3 . 55600E-2
S U P P L Y P R F S S U R E - 6P O 6 ( M M . H G . A B S ) : 6 0 0
SUPPLY T E M P E R A T U R E - 6TS ' (DEG RANKING) : 559.67
EDGE REYNOLDS NO. (CM-1): 58196.1
EXTERNAL MACH N O . : 2.83123
SURFACE PRESSURE (MM.HG.ABS): 20.06
S K I N F R I C T I O N C O E F . F R O M W A L L V I SC OS I T Y - ' CF I *: 1 . 5 1 I
S K I N F R I C T I O N C OEF . F R O M S T R E A M V I S C O S I TY - 0C F 2 6 : 6 . 8
0 T H E T A 6- ( C M e ): 9 . 4 5 9 2 3 E - 3
S H I F T IN Y - A X I S D U E TO 6P R O B E E F F E C T 6 (C M . ) : - 2 . 3 9 6 0 9
B O U N D A R Y LA YE R TH I C K N E S S - 6D E L T A 6 (CM.); . 1 44 1 3 5
1 DELTA S T A R 6 (CM.): 5.49775E-2
* DELTA/DELTA S T A R 6 : 2.62171
6D E L T A Z T H E T A 6 : 15.2375
6RETHETA 6: 550.491
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES, : 2.
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRES.: 2
0 4 E - 3 .
6047E-4
E-3
8312 3
.86388
105
***********
$
Q
p
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0 . D
E
L
***********
GROUP N O . : 5600
D I S T A N C E F R O M T R A I L I N G E D G E O 1F M O D E L ( C M . ) : 1 2 . 7
SURFACE ROUGHNESS CODE: 2
SWRFAC E ROUGHNESS HEIGHT (CM.): 3 . 55600E-2
SUPPLY P R E S S U R E - * P O 0 ( M M . H G . A 8 S ) : 600
SUPPLY T E M P E R A T U R E - 1TS 1 (DEG RANKING): 559.67
EDGE REYNOLDS NO. (CM-1): 56450
EXTERNAL MAC H NO, ; 2.90362
SURFACE PRESSURE (MM^HG.ABS): 18.02
SKIN FRICTION C O E F . FROM WALL V l S C O S I T Y - eC F l 9: 3.33468ES K I N F R I C T I O N COEF . F R OM S T R E A M V I S C O S I T Y - eCF 2 9 : 1 . 3 3 3 04
' T H E T A '-(CM.); 7 . 32660E-3
S H I F T IN Y - A X I S DUE TO "P RO B E E F F E C T " (CM. > § - 2 . 39609E-3.
BOUNDARY LAYER THICKNESS-"DELTA* (CM.): .12449
* DELTA STAR"
(CM.): 3.73003E-2
8 DELTA/DELTA S T A R ' : 3.29336
*DEL T A/TH ETA 8: 1 6 . 9 9 1 5
* R E T H E T A ' :
4 13.587 .
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES. : 2.9086
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRES.: 2.934
***********
$
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M
O
D
E
L
3
E-3
.
2
72
***********
GROUP N O . : 6600
DISTANCE FROM TRAILING EDGE OF MODEL (CM.); 15.24
SURFACE ROUGHNESS CODE: 2
SURFACE ROUGHNESS HEIGHT (CM.): 3 . 55600E-2
SUPPLY P R E S S U R E - 9PO"
( M M . H G . A B S ) I 600
SUPPLY T E M P E R A T U R E - 9TS 9 (DEG RANKING): 559.67
EDGE R E Y N O L D S NO. ( C M - I ) : 5 4 7 7 1 . 6
EXTERNAL MAC H N O . : 2.93832
SURFACE PRESSURE (MM.HG.ABS): 16.98
SKIN F R I C T I O N COEF. FROM WALL V I S C O S I T Y - 9 CFl 9 : 3 . 6 3 9 8 2 E - 3
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I S C O S I T Y - *CF 2 9 : 1 . 5 7 8 7 0 E - 3
* T H E T A ' - ( C M . ): 8. 1 8 3 9 4 E - 3
■
S H I F T IN Y - A X I S D U E T O 9P R O B E E F F E C T 9 ( C M . ) ; - 2 . 3 9 6 0 9 E - 3
B O U N D A R Y L A Y E R TH I C K N E S S - 9D EL T A 9 ( C M . ) : . 1 3745.5
* D E L T A S T AR * (CM.).: 4 . 0 1 6 4 5 E - 2
' D E L T A / D E L T A S T A R " : 3.42229
* DEL T A / T H E TA V
16.795 7
8 RETHETA*: 448.248
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.: 2.93832.
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE P R E S . : 2.974 18
106
***********
s
C
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M
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L
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GROUP N O - : 7600
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 17.78
SURFACE ROUGHNESS CODE: 2
S U R F A C E R O U G H N E S S .HE L G H T ( C M . ): 3. 5 5 6 0 0 E - 2
SUPPLY P R E S S U R E - * PO' (MM.H G . ASS): 600
SUPPLY T E M P E R A T U R E - 8T S 1 (DEG RANKING) : 559.67
E D G E R E Y N O L D S N O . C C M - I ): 5 2 7 2 1 . 7
EXTERNAL MACH NO.: 2.9951 1
S U R F A C E P R E S S U R E (MM. HG.'ABS) : 1 5 .4 6
SKIN FRICTION C O E F . FROM WALL V I S C O S I T Y - ' CFI*: 3.1
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I SC OS I I Y - 'C F 2 8 : 1
" T H E T A 8 T-C C M . ) : 9 . 6 7 5 0 6 E - 3
S H I F T IN Y - A X I S D U E TO 8P R O B E E F F E C T ' ( C M . ) : - 2 . 3 9 6
B O U N D A R Y L A Y E R TH I C K N E S S - ' D E L T A 8 ( C M . ) : . 1 3 4 8 2 4
"DELTA STAR' (CM.): 5 .46118E-2
«DELTA/DELTA STAR 8 : 2.46878
* DELTA/THETA 8: 13.93 52
'RETHETA 6: 510.086
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES. :
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRES.:
***********
s
c
R
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M
O
D
E L
0 1 60E-3
.31 2 9 8E - 3
0 9 E - 3
2. 9 9 5 1 1
3.03674
***********
GROUP N O . : 1500
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 2.54
SURFACE ROUGHNESS CODE: 2
SURFACE ROUGHNESS HEIGHT (CM.): 3 . 55600E-2
SUPPLY PRESSURE - *P O ' . (MM.HG.ABS): 500
S UPPLY T E M P E R A T U R E - ' TS 8 (DEG R A NKING): 559.67
E D G E R E Y N O L D S NO. ( CM - 1): 4 4 2 0 5 . 6
EXTERNAL MACH NO.: 2.93961
SURFACE PRESSURE (MM.HG.ABS): 13.687
SKIN FRICTION COEF . FROM WALL VISCOS IT Y - 8C F V : 4.71
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I S C O S I T Y - 8C F 2 8 : 2 .
8 T H E T A 8- ( C M a ): I . 0 9 0 4 8 E - 2
S H I F T IN Y - A X I S D U E T O 8P R O B E E F F E C T ' ( C M . ) : - 2 . 3 9 6 0
BOUNDARY LAYER T H I C K N E S S - 8DELTA' (CM.): . 189362
'DEL TA S T A R 8 (CM.): 4 . 85398E-2
*DELTA/DELTA STAR': 3.90118
8DELTA/THETA 8 : 17.365
8RETHETA 8: 482.056
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.: 2
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRES.:
360E-3
04330E-3
9E-3
.93961
2.99633
107
***********
$
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*.* * * * * * * * * *
GROUP NO.: 2500
DISTANCE FROM T R AI L I N G EDGE OF MODEL (CM.): 5.08
SURFACE ROUGHNESS CODE : 2
S U R F A C E R O U G H N E S S HF IGHT ( C M . ) : 3. 5 5 6 0 0 E - 2
SUPPLY P R E S S U R E - 'PO' ( M M. H G . AB S ) : 500
SUPPLY T E M P E R A T U R E - 'TS " (DEG RANKING): 559.67
E D G E R E Y N O L D S N O . (C M - I >: 4 5 3 7 5 . 9
EXTERNAL MAC H NO.: 2.85284
SURFACE PRESSURE (MM.HG.ABS): 15.308
SKIN FRICTION COEF. FROM WALL VISCOSITY-'CFl': 3.7
SKIN FRICTION C O E F . FROM STREAM V ISCOSITY- 'CF2' : 1
' T H E T A '-(CM.): 1..19965E-2
S H I F T IN Y - A X I S DUE TO 'PROBE E F F E C T ’ ( C M . ) ; - 2 . 3 9 6
B O U N D A R Y L A Y E R TH I C K N E S S - ' D E L T A ? ( C M . ) : .1 8 8 4 1 7
'DELTA STAR' ( C M . ) : 5.64226E-2
, DELTA/DELTA STAR': 3.33939
' D E L T A / T H E T A ' : 15.7059
«RETHETA ' : 544.354
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.:
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRES.:
***********
s
C
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W
M
O
D
E
L
0085E-3
.66486E-3
09E-3
2.85284
2.92199
***********
GROUP N O . : 3500
#
^
D I S T A N C E F R O 1M T R A I L I N G E D G E O F M O D E L ( C M . ) : 7 . 6 2
SURFACE ROUGHNESS CODE : 2
SURFACE ROUGHNESS HEIGHT (CM.): 3.55600E-2
SUPPLY P R E S S U R E - ' PO* (MM.HG.ABS): 500
SUPPLY TEMPERATURE-.= TS ' (DEG RANKING): 559.67
E D G E R E Y N O L D S N O . ( C M - 1 ):. 4 6 9 2 0 . 4
EXTERNAL MAC H NO.: 2.81576
SURFACE PRESSURE (MM.HG.ABS): 16.425
SKIN FRIC T I O N C O E F . FROM WALL V ISCOS IT Y - * CF I ’ : 2 1
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I S C OS I T Y - ' C F 2' : 9
' T H E T A '-(CM.): I. I 3 9 I 8 E-2
S H I F T IN Y - A X I S DUE TO 'PROBE E F F E C T * ( C M . ) : - 2 . 3 9 6
B O U N D A R Y L A Y E R TH I C K N E S S - ' D E L T A * ( C M . ) : . 1 72 72
*DELTA STAR' (CM.): 6 . 22S70E-2
* DELTA/DELTA STAR': 2.77297
* DELTA/THETA': 15.1618
* R E T H E T A ': 5 3 4 . 5 0 8
A N D P I T O T P R E S . :■
EDGE MACH. NO. FROM SURFACE PRES.
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRES.:
5205E-3
. 8 3 5 4 7 E-4
0 9 E
2. 8 1 5 7 6
2.87547
108
***********
S
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M
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L
***********
GROUP N O . : 4 500
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 10.16
SURFACE ROUGHNESS CODE: 2
SURFACE ROUGHNESS HEIGHT (CM.): 3 . 55600E-2
SUPPLY P R E S S U R E - ' PO* ( M M. H G . A B S ) : 500
SUPPLY T E M P E R A T U R E - 1TS ' (DEG R A N K I N G ) : 559.67
EDGE R E YN O L D S NO. ( C M - I ) : 4 8 2 0 6 . 3
EXTE R N A L MAC H NO.: 2.8251 9
S U R F A C E P R E S S U R E (MM. HG. ABS) : 1 6 .7 1 7
SKIN FRICTION C O E F . FROM WALL VISCOSITY-* C F V : 1 .36563E-3
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I S C O S I T Y - 9C F 2 ' : 6 . 2 1 6 2 6 E - 4
* T H E T A '-(CM.): 9 . 92222E-3
S H I F T IN Y - AX I S DUE TO 9P R OB E E F F E C T 9 ( C M . ) : - 2 . 3 9 6 0 9 E-3
B O U N D A R Y L A YE R TH I C K N E S S - 9D E L T A 9 (CM.): . I 58 53 6
*DELTA S T A R 9 (CM.) : 5.78064E-2
* DELTA/DELTA S T A R 4 : 2.74253
1 D E L T A / T H E T A 9 : 15.9779
1 RETHETA 9: 478.31 4
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES. : 2.8251 9
E D G E M A C H N O . F R O M S U P P L Y P R E S . A N D S U R F A C E P R E S . : 2.86386
***********
s
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***********
GROUP N O . : 5500
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 12.7
SURFACE ROUGHNESS CODE: 2
SURFACE ROUGHNESS HEIGHT (CM.): 3 . 55600E-2
SUPPLY P R E S S U R E - 9P O 9 (MM.H G . ABS): 500
S U P P L Y T E M P E R A T U R E - 9 T S 9 ( D E G R A N K I N E ): 5 5 9 . 6 7
E D G E R E Y N O L D S N O . ( C M - 1 ): 4 6 0 0 1
E X T E R N A L MAC H NO.: 2. 88597
SURFACE PRESSURE ( M M . HG.ABS): 15.017
SKIN F R I C T I O N COEF . FROM WALL V I S C O S I T Y - 9CFl 9 : 2 .
SKIN F R I C T I O N COEF . FROM STREAM. V I S C O S I T Y - 9C F 2 9 :
U H E T A 9- ( C M e ): 8 . 4 0 8 5 5 E - 3
SHIFT IN Y - AX I S DUE TO 9PR OB E E F F E C T 9 (C M . ) I- 2 . 3 9
B O U N D A R Y L A Y E R TH I C K N E S S - 9D E L T A 9 ( C M . ) ; . 1 4 0 2 7 3
eDELTA S T A R 9 (CM.) : ,4. 72 1 4 4 E - 2
e DELTA/DELTA STAR 9 : 2.97098
9 D E L T A / T H E T A 9 : 16. 68 22
eRETHETA 9: 386.802
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.:
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE P R E S .
78320E-3
1..23446 E-3
6 0 9 E-3 '
2.88597
: 2.9347
109
***********
$
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E
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M
O
D
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L
***********
GROUP N O . : 6500
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 15.24
SURFACE ROUGHNESS C O D E : 2
SURFACE ROUGHNESS HEIGHT (CM.): 3 . 55600E-2
SUPPLY PRESSURE-'PO'
(MM.HG.ABS)i 500
SUPPLY T E M P E R A T U R E - 'TS 1 (DEG RANKINE) : 559.67
EDGE R E Y N O L D S NO. ( C M - 1 ) : 4 4 1 6 8 . 8
EXTERNAL MACH N O . : 2.90501
SURFACE PRESSURE ( M M . HG.ABS): 14.15
SKIN FRICTION COEf. FROM WALL V I S C O S I T Y - 1C F 1^ ; 3.8
SKIN FRICTION COEF . FROM STREAM V ISCOS ITY- ' C F 2': 1
0 T H E T A 1- I C M . ): 9 . 3 0 8 5 6 E - 3
S H I F T IN Y - A X I S DUE TO 1P R OB E E F F E C T 1 ( C M . ) ; - 2 . 3 9 6
B O U N D A R Y L A Y E R TH I C K N E S S - 1D E L T A 6 ( C M . ) ; . 1 36891
0 D E L T A S T A R 1 (CM,.): 4 . 7 9 6 6 3 E - 2
"DELTA/DELTA STAR 1 : 2.8539
0 DELTA/THETA 1 : 14 . 70 5 9
9RETHETA 1 : 411.148
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.:
EDGE MACH NO. FROM SUPPLY PRES. AND S U RFACE PRES.:
***********
5 C
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D
E
L
6399E-3
.69996E-3
09E-3
2.90501
2.97418
***********
GROUP N O , : 7500
DISTANCE FROM T R A I L I N G EDGE OF MODEL (CM,): 17.78
SURFACE ROUGHNESS CODE: 2
SURFACE ROUGHNESS HEIGHT (CM.): 3 . 55600E-2
SUPPLY P R E S S U R E - 0P O 1 (MM.H G . ABS): 500
SUPPLY T E M P E R A T U R E - 1T S 1 (DEG RANKING): 559.67
EDGE R E YN O L D S NO. ( C M - I ) : 4 2 63 9 . 8
EXTERNAL MACH NO.: 2.96454
SURFACE PRESSURE ( M M . HG . ABS): 12.883
S K I N F R I C T I O N C O E F . F R O M W A L L V l S C O S I T Y - 1C F I 0 : 2 .
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I S C O S I T Y - 1C F Z 1 :
flT H E T A 0 - ( C M o ) : I . 0 6 4 4 9 E - 2
S H I F T IN Y - A X I S D U E TO 1P R O B E E F F E C T 0 ( C M . ) : - 2 . 3 9
B O U N D A R Y LA YE R TH I C K N E S S - 1DELTA.1 (CM.): . 1 47977
6DELTA S T A R 1 (CM.): 6.3721 IE-2
0DELTA/DELTA STAR 1 : 2.32226
0D E L T A Z T H E T A 1: 13.9012
0RETHETA 0 : 4 5 3.396
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.:
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE P R E S .
9384 8E-3
I .26029E-3
609E-3
:
2.96454
3.03675
no
***********
$
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O
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L
***********
GROUP NO-: 1400
DISTANCE FROM TRAI L I N G EDGE OF MODEL (CM.): 2.54
SURFACE ROUGHNESS CODE: 2
SURFACE ROUGHNESS HEIGHT (CM.): 3 . 55600E-2
S U P P L Y P R E S S U R E - * P O * ( M M . H G . A B S ): 4 0 0
SUPPLY T E M P E R A T U R E - 1T S 6 (DEG RANKING): 559.67
E D G E R E Y N O L D S N O . (CM-I); 3 5 6 1 5 . 2
E X TE R N A L MAC H NO. : 2.94676
SURFACE PRESSURE (MM.HG.ABS): I 0.95
SKIN FRICTION COEF . FROM WALL V I S C O S I T Y - * CFl': 4.0841 9E-3
SKIN FRICTION C O E F . FROM STREAM V ISCOS IT Y -'C F 2 'I I „ 7 6 5 0 5 E - 3
' T H E T A '-(CM.): 9 . 3 2 5 9 7 E-3
S H I F T IN Y - A X I S DUE TO 'PROBE E F FE C T ' (CM. ): - 2 . 3 9 6 0 9 E - 3
B O U N D A R Y L A Y E R TH I C K N E S S - * DE L T A ' ( C M . ) : .1 6 3 8 6 6
'DELTA STAR' (CM.): 4.94534E-2
'DELTA/DELTA STAR': 3.31354
'DELTA/THETA': 17 .5 7 0 9
* RETHETA': 332.1 46
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES. : 2.94676
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRES.: 2.99631
***********
5 C
R
E
W
M
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GROUP N O . : 2400
DIST A N C E FROM T R A I L I N G EDGE OF MODEL (CM.): 5.08
SURFACE ROUGHNESS CODE: 2
SURFACE ROUGHNESS HEIGHT (CM.): 3 . 55600E-2
SUPPLY P R E S S U R E - ' PO' (MM.HG.ABS): 400
SUPPLY T E M P E R A T U R E - 'T S 9 (DEG RANKING) : 559.67
EDGE R E YN O L D S NO. ( C M - I ) : 35 58 1 . 9
EXTERNAL MACH N O . ; 2.8327
SURFACE PRESSURE. (MM.HG.ABS): 12.247
S K I N F R I C T I O N C O E F . F R O M W A L L V I S C O 1S I T Y - ' C F l ' : 2
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I SC O S I T Y - ' C F 2 *:
' T H E T A '-(CM.): I. 0 9 1 60E-2
S H I F T IN Y - A X I S D U E TO ' P R O B E E F F E C T ' (C M . ) : - 2 . 3
B O U N D A R Y L A Y E R TH I C K N E S S - ' D E L T A ' ( C M . ) : . 1 7 7 1 3 6
'DELTA STAR' (CM.): 5.85970E-2
'DELTA/DELTA STAR': 3.02294
'DELTA/THETA': 16.2272
'RETHETA': 388.411
EDGE MACH NO. FROM SURFACE PRES. AND PITOT PRES.
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE P R E S
.96788E-3
I .34664E-3
9 6 0 9 E - 3
: 2.8327
. : 2.92196
Ill
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GROUP NO.: 3400
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 7.62
SURFACE ROUGHNESS CODE: 2
SURFACE ROUGHNESS HEIGHT (CM.): 3 . 55600E-2
SUPPLY P R E S S U R E - " PO' (MM.HG.A8S): 400
S U P P L Y T E M P E R A T U R E - 8 TS " (DEG RANKI NE) : 5 5 9 . 6 7
E D G E R E Y N O L D S N O . ( C M - I ): 3 6 3 9 3 . 1
E X T E R N A L M A C H NO.: 2.73486
SURFACE PRESSURE ( M M . HG.A B S ) : 13.14
S K I N F R I C T I O N C O E F . F R O M W A L L V I S C O S I TY-'" C F V : 2 . 0
S K I N F R I C T I O N C O E F . F R OM S T R E A M V I S C OS I TY - 8CF 2 8 : 9
" T H E T A '-(CM.): 1 . 1 7921E-2
SHIFT IN Y - AX I S DUE TO "PROBE EFFECT" ( C M . ) : - 2 . 3 9 6
B O U N D A R Y L A Y E R TH I C K N E S S - 8D E L T A ’ ( C M . ) : . 1 7 8 8 1 8
"DELTA S T A R 8 (CM.): 6.42486E-2
"DELTA/DELTA S T A R 8 : 2.73321
8D E L T A Z T H E T A 8 : 15.1642
8R E T H E T A 8: 429.151
EDGE MACH NO. FROM SURFACE PRES. AND PITOT P R E S . S
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE PRES.:
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4344E-3
.48598E-4
0 9 E - 3
2.78486
2.87547
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GROUP N O , : 4400
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 10.16
SURFACE ROUGHNESS CODE: 2
SURFACE ROUGHNESS HEIGHT (CM.): 3 . 55600E-2
SUPPLY P R E S S U R E - " P O 8 <MM.HG.ABS): 400
S U P P L Y T E M P E R A T U R E - 8 TS 8 (DEG RANKI NE) : 5 5 9. 6 7
E D G E R E Y N O L D S N O . ( C M - 1 ): 3 7 5 7 4 . 8
E X T E R N A L MAC H NO.: 2.79921
S U R F A C E P R E S S U R E C M M . H G . A B S ): 1 3 . 3 7 3
S K I N F R I C T I O N C O E F . FROM WALL V I S C O S I T Y - 8 CFI 8 : 1.5 3 2 2 0 E - 3
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I SC OS I T Y - 8C F 2 8 : 7 . 0 5 21 5 E - 4
" T H E T A 8- ( C M . ) : 1 , 0 9 1 1 4 E - 2
S H I F T IN Y - A X I S D U E TO 8P R O B E E F F E C T 8 ( C M . ) : - 2 . 3 9 6 0 9 E - 3
BOUNDARY LAYER THICKNESS-"DELTA" (CM.): .164427
"DELTA S T A R 8 (CM.): 6.29104E-2
"DELTA/DELTA S T A R 8 : 2.61366
" D E L T A / T H E T A 8: 15.0693
8RETHETA 8 : 409.994
E D G E M A C H N O . F R O M S U R F A C E P R E S . A N D P I T O T P R E S . : 2. 7 9 9 2 1
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE P R E S . : 2.86389
112
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GROUP NO.: 5400
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): 12.7
SURFACE ROUGHNESS CODE: 2
SURFACE ROUGHNESS HEIGHT (CM.): 3 . 55600E-2
SUPPLY P R E S S U R E - ' PO' (MM.HG.A8S): 400
S U PP L Y T E M P E R A T U R E - 6 TS 6 (DEG R A N K I N G ) : 5 5 9 . 6 7
EDGE REYNOLDS NO. ( C M - I ) : 3 6 948.5
EXTERNAL MACH N O . : 2.89006
S U R F A C E P R ES S U R E (M M . H G.AB S ) S 12.013
S K IN F R I C T I O N C O E F . FROM WALL V ISC OS I T Y - ' C F I ' : 2.805 2 5 E - 3
SKIN FRICTION C O E F . FROM STREAM V ISCOS ITY- *C F 2 ' : 1 . 2 4 2 0 7 E - 3
' T H E T A * - ( C M . ): 9 . 7 2 1 8 5 E - 3
S H I F T I N Y - A X I S D U E T O ' P R O B E E F F E C T ® ( C M . ) : - 2 «, 3 9 6 0 9 E - 3
BOUNDARY LAYER TH IC K N E S S - ' DELTA* (CM.): . I 56443
* DELTA S T A R ’ (CM.): 5.39504E-2
*DELTA/DELTA STAR': 2.89975
'DELTA/THETA': 16.0919
* R E T H E T A ': 3 5 9 . 2 0 7
E D G E M A C H N O . F R O M S U R F A C E P R E S . A N D P I T O T P R E S . : 2.89006
EDGE MACH NO. FROM SUPPLY PRES. AND SURFACE P R E S . : 2,93474
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GROUP N O . : 6400
DISTANCE FROM TRAILING EDGE OF MODEL (CM.): I 5.24
SURFACE ROUGHNESS CODE: 2
SURFACE ROUGHNESS HEIGHT (CM.): 3 . 55600E-2
S U P P L Y P R E S S U R E - ' PO' ( M M . H G . A B S ): 4 0 0
SUPPLY T E M P E R A T U R E - ' T S ' (DEG RANKING): 559.67
E D G E R E Y N O L D S N O . ( C M - 1 ): 3 6 3 8 0
EXTERNAL MAC H N O . : 2.93457
SURFACE PRESSURE (MM.HG.ABS): 11.32
SKIN F R I C T I O N COEF. FROM WALL V ISC OS I T Y - ® C F 1 9 : 3,9
S K I N F R I C T I O N C O E F . F R O M S T R E A M V I S C O S I T Y - 'Cf 2' : I
' T H E T A '-(CM.): I. 0 1 059E-2
S H I F T IN Y - A X I S DUE TO ' P R O B E E F F E C T * ( C M . ) : - 2 . 3 9 6
BOUNDARY LAYER THICKNESS-'DELTA' (CM.); . I 6238
' DE LT A STAR' (CM.): '5.47521 E-2
'DELTA/DELTA S T A R ' ; 2.96574
'DELTA/THETA*: 16.0679
'RETHETA': 367.652
EDGE MACH NO. FROM SURFACE PRES, AND PITOT PRES.:
EDGE M A C H NO. FROM S U P P L Y PRES. AND S U R F A C E PRES..*
18 77E-3
.70241 E-3
0 9 E-3
2.93457
2.974 18
113
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GROUP N O . : 7400
DISTANCE FROM TRAILING EDGE OF MODEL (CM.); 17.78
SURFACE ROUGHNESS CODE: 2
SURFACE ROUGHNESS HEIGHT (CM.); 3 . 55600E-2
SUPPLY PRESSURE-'* PO* (MM.HG.ABS): 400
SUPPLY T E M P E R A T U R E - #TS 1 (DEG RANKING): 559.67
EDGE R E YN O L D S NO. ( C M - I ) : 3 4 54 0 . 8
EXTERNAL MACH N O . ; 2.97725
SURFACE PRESSURE (MM.HG.ABS) : 10.307
S K I N F R I C T I O N C O E F . F R O M W A L L V I S C O S I T Y - " C F 1 *; 2 . 8 1
SKIN FRICTION COEF. FROM STREAM V I S C O S I T Y - * C F 2 < : I .
* T H E T A " - ( C M . ): 1 .1 7 7 6 7 E - 2
S H I F T IN Y - A X I S D U E T O eP R O B E E F F E C T " ( C M . ) : - 2 . 3 9 6 0
B O U N D A R Y L A Y E R TH I C K N E S S - " D E L T A e ( C M . ) ; .1 7 0 2 3 3
* DELTA STAR* (CM.); 7.05763E-2
* DELTA/DELTA STAR": 2.41204
"DELTA/THETA"; 14.4551
" R E T H E T A ": 4 0 6 . 7 7 7
EDGE MACH NO. FROM SURFACE PRES. AND PITOT P R E S . J 2
EDGE MACH NO. FROM SUPPLY PRES, AND SURFACE P R E S . :
687E-3
2 0 1 59E-3
9 E-3
.97725
3.03671
MONTANA STATE UNIVERSITY LIBRARIES
stksN378.D848@Theses
Characteristicsofa supersonic laminar
3 1762 00109137 8
N 378
D848
cop.2
D'sa, J. M.
Characteristics of a
supersonic laminar
boundary layer over a
rough wall