Measurements have been made of the mean flow properties and turbulent fluctuations in adiabatic turbulent boundary layer flows subjected to distributed adverse pressure gradients. In the freestream region upstream of the adverse pressure gradient the Mach number was 3.86, the unit Reynolds number 5.3 million per foot. The boundary layer developed on the wall of an axisymmetric nozzle and straight test section. In order to avoid the effects of streamwise surface curvature the adverse pressure gradients at the test section wall were induced by contoured centerbodies mounted on the wind tunnel centerline. The flow under study simulated that which might be found in an axially symmetric engine inlet of a supersonic aircraft

Childs, M. E.

Gootzait, E.

English

NASA Technical Reports Server

ABSTRACT
MEAN AND FLUCTUATING FLOW MEASUREMENTS IN AXISYMIMETRIC
SUPERSONIC BOUNDARY LAYER FLOW SUBJECTED TO DISTRIBUTED
ADVERSE PRESSURE GRADIENTS
by
Edward Gootzait N 3
ol eand
SOU Morris E. Childs
E University of Washington, Seattle, Washington
4 0 -, Measurements have been made of the mean flow properties and
turbulent fluctuations in adiabatic turbulent boundary layer flows
1 subjected to distributed adverse pressure gradients. In the freestream
region upstream of the adverse pressure gradient the Mach Number was 3.86,
S the unit Reynolds Number 5.3 x 106 per foot. The boundary layer developed
r4 mE-40
m=' M , on the wall of an axisymmetric nozzle and straight test section. In order
;n UrH
o Z = a to avoid the effects of streamwise surface curvature the adverse pressure
m gradients at the test section wall were induced by contoured centerbodies
L 4 (m H.- mounted on the wind tunnel centerline. The flow under study simulated
that which might be found in an axially symmetric engine inlet of a
supersonic aircraft.
Mean flow measurements made with a pitot probe and a normal hot-wire
probe used as a resistance thermometer will be described and compared with
Predoctoral Research Associate, Department of Mechanical Engineering,
University of Washington, Seattle, Washington. Member AIAA.
Professor and Chairman, Department of Mechanical Engineering,
University of Washington, Seattle, Washington. Member AIAA.
This work was supported by NASA Grant NGR-48-002 -047 under administra-
tion of the Aerodynamics Branch, Ames Research Center.
https://ntrs.nasa.gov/search.jsp?R=19740021537 2020-03-23T06:10:05+00:00Z
2existing supersonic boundary layer data. Normal hot-wire.turbulence
results taken at several locations in each of two adverse pressure gradients
will be reported and compared with existing data. The turbulence results
include total temperature, mass-flow and longitudinal velocity fluctua-
tions and the longitudinal Reynolds stress (p u'2 + 2u p'u'). A
constant temperature anemometer system was used during these experiments.
There have been numerous investigations of the mean flow properties
of undisturbed supersonic boundary layers and supersonic boundary layers
in adverse pressure gradients. Only recently, however, have investigators
1-5
concentrated on obtaining turbulence measurements in high speed flow-5
Although there have been some studies detailing the turbulence properties
of undisturbed boundary layers, very few measurements have been made in
flows subjected to adverse pressure gradients. Furthermore, very few
investigations have been conducted for axisymmetric flows. To the authors'
knowledge no other turbulence data have been reported for axisymmetric
distributed adverse pressure gradient boundary layer flows of the type
examined in this study. Some of the difficulties and probable errors
associated with performing turbulence measurements in high speed flows
will be discussed in the paper, as will the data handling procedure and
the effect of various mean flow and fluctuating flow quantities on the
computed turbulence properties.
In the remainder of this abstract, results typical of those obtained
in the investigation will be described. Figure (1) shows the wall static
pressure distributions for the two adverse pressure gradients considered
in this study, along with a pressure distribution for a shock wave-
1boundary layer int actiont th  wallof a similar st sec ion
boundary layer interaction at the wall of a similar test section . The
3interaction was produced by a 90 half-angle cone placed on the axis of
the test section and was strong enough to essentially separate the
boundary layer. The gradients for the present study are seen to be quite
strong. Indeed, pressure gradient 1 is seen to cause a somewhat steeper
overall rise than was observed for the shock-boundary layer interaction.
However, the distributed adverse pressure gradients show gradual initial
rises, and only near the end of the rises do the gradients approach or
exceed the steepest gradient for the shock interaction. Figures (2a) and
(2b) show pitot profiles obtained in the two pressure gradient regions.
In Figures (3a) and (3b) the pitot pressures and total temperatures for
one station in the undisturbed flow and one in the gradient 1 flow (at a
location where P /P =1.95) are shown. The boundary layer edge based on
the total temperature profile is indicated on the figures. For the upstream
station the total temperature boundary layer thickness is seen to agree
closely with the boundary layer thickness based on the pitot pressure
profile.
One of the difficulties associated with analyzing mean flow or turbu-
lence data in adverse pressure gradients is the determination of the
normal static pressure distribution in the boundary layer. The effect of
normal pressure gradients on the turbulence measurements has been examined.
In Figure (4) the longitudinal Reynolds shear stress is shown for an axial
station in adverse pressure gradient 1 where P /P = 1.95. The figurew m
shows the turbulence data computed for two normal distributions of the
static pressure. In one instance the pressure has been taken as constant
across the boundary layer and equal to the wall value. In the other the
static pressure as calculated by the method of characteristics (NASA TN-6083)
has been used. The difference between the two distributions is seen to
be quite small and apparently is associated with differences in mean flow
properties which appear in the stress term. The basic normal hot-wire
sensing variables, T T'2
, 
( u) '2 and TT ' (pu)', were found to be virtually
identical for the two cases.
Some of the turbulence data for the undisturbed flow are shown in
Figures (5a) and (5b). The total temperature fluctuations (see Fig. (5a))
are similar to those reported by Kistler6 for a Mach 3.56 flow on a wind
tunnel wall. The observed longitudinal velocity fluctuations are shown in
Fig. (5b). In the inner half of the boundary layer the results from this
study agree rather well with data reported by Rose and Johnson2 for boundary
layer flow along the wall of a two-dimensional wind tunnel. In the outer
half of the layer the fluctuation level is somewhat higher than has been
reported in previous studies. The fluctuations increase at a fairly con-
stant rate as the wall is approached. This trend confirms recent results
of other investigators (see Reference 7 for a review of turbulence measure-
ments in compressible flow) which indicate that the velocity fluctuations
do not begin to decrease as far from the surface as has been reported
previously1'6
In Figures (6a) and (6b) the longitudinal velocity fluctuation and the
longitudinal Reynolds stress in the undisturbed flow are compared with
those observed for pressure gradient 1 at a station where PP, = 1.95.
Also shown in Figure (6b) are the longitudinal shear stress distributions
for an undisturbed flow and for a station where P /P = 2.05 in a shock
induced adverse pressure gradient region as reported in Reference 1. The
results from Reference 1 were obtained in a straight walled test section
5almost identical to the one used in the present study but the anemometer
systems used in the two investigations were different. The freestream
Mach Numbers and Unit Reynolds Numbers in the two studies were almost the
same. As is shown the distributions for both the velocity fluctuations
and the Reynolds stress terms are altered considerably by the pressure
gradient, especially in the lower two thirds of the boundary layer. As
Figure (6b) shows, the distributions of longitudinal shear stress in the
present study and in that of Reference 1 are quite similar at cross
sections with approximately equal value of P /Pm.
The results obtained in this investigation provide new information on
the behavior of an axisymmetric adiabatic turbulent boundary layer in a
supersonic adverse pressure gradient flow. Both mean flow properties and
turbulent fluctuations have been measured. The turbulence measurements,
which were obtained with a constant temperature anemometer system, are in
qualitative agreement with results which have been reported for studies
in two-dimensional configurations, and for one earlier known study of
axisymmetric adverse pressure gradient flow.
6REFERENCES
1. Rose, W.C., "The Behavior of a Compressible Turbulent Boundary
Layer in a Shock-Wave-Induced Adverse Pressure Gradient," NASA TN-
D-7092, 1973.
2. Rose, W.C. and Johnson, D.C., "A Study of Shock-Wave Turbulent
Boundary Layer Interaction Using Laser Velocimeter and Hot-Wire
Anemometer Techniques," AIAA Paper 74-95, January 1974.
3. Owen, F.K. and Horstman, C.C., "Turbulent Measurements in an Equilib-
rium Hypersonic Boundary Layer," AIAA Paper 74-93, January 1974.
4. Laderman, A.J. and Demetriades, A., "Measurements of the Mean and
Turbulent Flow in a Cooled-Wall Boundary Layer at Mach 9.37," AIAA
Paper 72-73, 1972.
5. Waltrup, P.J. and Schetz, J.A., "Supersonic Turbulent Boundary Layer
Subjected to Adverse Pressure Gradients," AIAA Journal, vol 11, no 1,
1973.
6. Kistler, A.L., "Fluctuation Measurements in a Supersonic Turbulent
Boundary Layer," Phys. of Fluids, vol 2, p 290, 1959.
7. Sandborn, V.A., "A Review of Turbulence Measurements in Compressible
Flow," NASA TM X 62,337,1974.
4.0 0 Gradient 1
SGradient 2 O
O 90 Cone, Ref. 1
O
3.0
2.0 0
• 0 @
8O
1.0 O O
2.8 3.2 3.6 4.0 4.4 4.8
X,(IN) - Distance from Tip of Compression Generator
Figure (1): Surface Static Pressure Distributions
O Undisturbed
rl X=3.6" F/Pc = 1.11
O =3 . 8 " = 1.38
.20 K =4.0" = 1.95 O n O >
A =4.2" = 2.79 O O 0 O A 
=4.4" = 3.69 O L O > A
o D O K A.
.15 - 0 O O a o
0 0 O A
z0 EO KA E
S .10 - 0 O K> A
o o > A
0 0 A AL
.05 0 o K O A 
oa0 Oa L
o I , iO L i I
0 .05 .10 .15 
.20 .25 
.30 .35
PTp/P'
Figure (2a) Pitot Pressures
Gradient 1
O Undisturbed
X x=3.6" P /P = 1.04
w,
0 =3.8" = 1.18
.20 A =4.0" = 1.43 O Fl0 o O x
L =4.2" = 1.75 O 0L KA x
O =4.4" = 2.11 O O F] O x
o o 0 XX =4.6" = 2.62
.15 -o LI> A L x
o [ > A O x
o 0O, A 0 >X
.o. 0 A o 0 x
0o O 0 x
O3 0 0 x
.o .O O x
0oE3 A L 0
0oLO O LO
o oc>A L 0 >
0ii DO Lx L
0 .05 .10 .15 .20 .25 .30
Tp/PT,
Figure (2b): Pitot Profiles
Gradient 2
(0
.25 O Pitot Pressure
O Total Temperature
.20 _ O
o ETTO D
O O]
.15 0 ]
0O
0
0 [
0 ]
0.0lO
.05 - 0
O E
O C
0
0 O I F I I
0 .05 .10 .15 .20 .25
PT,/PT
L I _ __I I
.92 .96 1.00 1.04
TT/TT
Figure (3a): Pitot Pressures and Total Temperatures
Undisturbed Flow
.25 O Pitot Pressure
L Total Temperature
.20 )
O
.15 [ O O
H0 
--
0 6TT
L 0
SO 0
.10. C-]
0 L
O
O
0 L
.05 -0 O
0 Li0 L
0 L
0
0 'L I.
0 .05 .10 .15 .20 .25
PTp/PT
I i IJ
.92 .96 1.00 1.04
TT/TTC
Figure (3b): Pitot Pressures and Total Temperatures
Gradient 1 P /P = 1.95
Distance from Tip of Compression Generator = 4.0 IN.
.20 -Txx p u' 2 + 2 u p'u' 0 Calculated Pressure
] Constant Pressure
.16
.12 C ..
0I I _J
0 4. 8. 12. 16. 20. 24.
Txx, (LB )2Ft )
Figure 4: Influence of Boundary Layer Static Pressures
on Longitudinal Reynolds Stress
Gradient 1
Distance from Tip of Compression Generator = 4.0 IN.
.08 - O Present Investigation
O -Kistler, Ref. 6
.06 -
.04 -
[3D E [
0 0
.02 0
* [30
[3 002 1-
0 I 1 I I i .
0 .2 .4 .6 .8 1.0 1.2
y/ 6
Figure (5a) Total Temperature Fluctuations
Undisturbed Flow
2.4 - Present Investigation
0 Rose, Ref. 1
K> K> Rose & Johnson, Ref. 2
2.0
O
1.6
O
1.2 .00
.8
0 .2 .4 .6 .8 1.0 1.2
y/6
Figure (5b): Longitudinal Velocity Fluctuations
Undisturbed Flow
2.4- O Undisturbed Flow
L Gradient 1, P /P = 1.95OW
2.0
0
O
1.6-
0 0
: 1.2
O
a.8
.4 O
0
0 .2 .4 .6 .8 1.0 1.2
y/6
Figure (6a): Longitudinal Velocity Fluctuations
1.2 Txx p u' 2 + 2up'u' O Undisturbed Flow
44 Gradient 1, P /P = 1.95
w
A Ref. 1, Undisturbed Flow
O Ref. 1i, P /P = 2.05
1.0 0 <
O
.8 A
.2 -
0
0 4. 8. 12. 16. 20. 2
Txx, (LBF/FT2)
Figure (6b): Longitudinal Reynolds Stress


Mean and fluctuating flow measurements in axisymmetric supersonic boundary layer flow subjected to distributed adverse pressure gradients

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