Three dimensional viscous flow analysis is performed for a configuration where two crossing and glancing shocks interact with a turbulent boundary layer. A time marching 3-D full Navier-Stokes code, called PARC3D, is used to compute the flow field, and the solution is compared to the experimental data obtained at the NASA Lewis Research Center's 1 x 1 ft supersonic wind tunnel facility. The study is carried out as part of the continuing code assessment program in support of the generic hypersonic research at NASA Lewis. Detailed comparisons of static pressure fields and oil flow patterns are made with the corresponding solution on the wall containing the shock/boundary layer interaction in an effort to validate the code for hypersonic inlet applications

Reddy, D. R.

English

NASA Technical Reports Server

NASA Technical Memorandum 104469
AIAA-91-1758
3-D Navier-Stokes Analysis of Crossing,
Glancing Shocks/Turbulent Boundary
Layer Interactions
D.R. Reddy
= =Lewis Research Center
Cleveland, Ohio
: :z: :
(NASA-TM-IO44&g) THE 3-0 NAVIER-STnKES
ANALYSIS qF CROSSING, GLANCING
SHOCKS/TURBULENT BOUNDARY LAYrR INTERACTIONS
(NASA) 14 p C_CE OIA
G3/02
Ngi-24130 ....
unclas
0019777 _
Prepared for the ..............
22nd Fluid Dynamics, Plasma Dynamics and Lasers Conference
sponsored by the American Institute of Aeronautics and Astronautics
Honolulu, Hawaii, June 24-26, 1991
NASA ..........
https://ntrs.nasa.gov/search.jsp?R=19910014817 2020-03-19T17:41:53+00:00Z

3-D NAVIER-STOKES ANALYSIS OF CROSSING, GLANCING
SHOCKS/TURBULENT BOUNDARY LAYER INTERACTIONS
D. R. Reddy*
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135
Abstract
Three-dimensional viscous flow
analysis is performed for a configuration
where two crossing and glancing shocks
interact with a turbulent boundary layer.
A time marching 3-D full Navier-Stokes
code, called PARC3D, is used to compute
the flow field and the solution is
compared to the experimental data
obtained at the NASA Lewis Research
Center I ft. X I ft. supersonic wind
tunnel facility. The study is carried out
as part of the continuing code assessment
program in support of the Generic
Hypersonic research at NASA Lewis.
Detailed comparisons of static pressure
fields and oil flow patterns is made
with the corresponding solution on the
wall containing the shock/boundary layer
interaction in an effort to validate the
code for hypersonic inlet applications.
Introduction
The
interaction
occurrence
shock wave/boundary-layer
phenomenon is a common
in many of the important
propulsion components such as supersonic
inlets, nozzles and supersonic
combustors. The strong pressure
gradients, secondary flows and possible
flow separations associated with these
interactions can have significant effect
on the flow through the individual
components and consequently affect the
overall performance of the engine.
Therefore, a thorough understanding of
these phenomena is essential for an
efficient design of the propulsion
components in the supersonic flow regime.
To simulate these complex flows with a
reasonable accuracy, a full 3-D Navier-
Stokes code with a fairly reliable
turbulence model is required. Therefore,
it is important that the code selected
for computation of these flows be
thoroughly assessed using experimental
data to verify the code's capability to
correctly simulate the flow features
mentioned above. The object of this
study is to assess the numerical code,
used to compute such flows, using
experimental data obtained for a
*Chief, Computational Fluid Dynamics Branch. Member AIAA.
configuration where two crossing and
glancing shocks interact with a turbulent
boundary layer. The experiment was
carried out at the NASALewis Research
Center I ft X I ft supersonic wind
tunnel facil.ity.
The numerical code is a time
marching full Navier-Stokes code, called
PARC3DI, which solves the full three
dimensional Reynolds averaged Naviero
Stokes equations in strong conservation
form using Beamand Warming approximate
factorization. The code was originally
developed as AIR3D by Pulliam and
Steger2, and Pulliam3 later added the
Jameson4 artificial dissipation and
called the code ARC3D. CooperI adapted
the code for internal flow in propulsion
application and namedthe code PARC3D.
The PARC3Dcode uses central differencing
on a generalized curvilinear coordinate
system with implicit and explicit second
and fourth order artificial dissipation.
To simplify the solution of the block
pentadiagonal system of discretized
equations, the block implicit operators
are diagonalized by decomposingthe flux
Jacobians, resulting in a scalar
pentadiagonal system. The loss of time
accuracy from the diagonalization does
not affect the spatial accuracy of the
steady state solution. 3 The turbulence
model used in the code for this study is
the Baldwin-Lomaxmodels
The PARC3Dcode has been verified
previously with experimental data for 3-D
supersonic and 2-D hypersonic flow
configurations having flow features
similar to those of the present
study6'7'a. These studies demonstrated
the capability of PARC3Dto simulate with
reasonable accuracy the shock/boundary-
layer interaction phenomenontypically
present in the supersonic inlet
configurations. This study is a
continuation of the code validation
process being carried out at NASALewis
ResearchCenter for computations of flows
through supersonic/hypersonic propulsion
components in support of the Generic
Hypersonic research program.
Experimental Configuration
The crossing shock/boundary-layer
experiment was configured by using two
shock generator plates that span the
tunnel test section. The 20.3 cm long
shock generators arranged symmetrically
produce oblique shocks which cross each
other on the centerline. The interaction
of these shocks with the naturally
occurring incoming flow boundary layer on
the tunnel wall defines the experiment.
This interaction is shown schematically
in Fig. I. The incoming boundary layer
was observed to be uniform and fully
turbulent. The thickness of the boundary
layer varied between 3.0 to 3.5 cm
depending on the inflow Mach number.
The experiment was run at different
shock generator angles of 4, 6, 10 and 12
degrees for a Mach number varying from
2.5 to 4.0. However, all the angles were
not run at each Mach number because the
model would unstart and produce a normal
shock ahead of the shock generator for
some combinations of Mach number and
angles; for example for Mach 2.5, a shock
generator angle of 9 deg. is the limiting
value. The experimental data include
surface static pressure measurements and
oil flow visualization on the tunnel
2
walI. Complete detai I s of the
experimental configuration and
instrumentation used in the experiment
can be found in reference 9.
Computations
The computations are performed on
the Numerical Aerodynamic Simulation's
Cray-2 computer, located at NASAAmes
ResearchCenter, using a grid size of ]51
X 71 X 71. The computational grid
showing one each of the streamwise and
cross planes is shown in Fig. 2. To
resolve the viscous layers, the grid
lines are clustered in regions close to
the walls using hyperbolic tangent
functions such that the first grid line
away from the wall is located at a y+ of
approximately 2.0. Since the
configuration is symmetric in both
directions in the cross plane, only a
quarter of the full flow field is
computed with symmetry imposed in the
vertical as well as the transverse
direction along the planes passing
through the centerline of the wind
tunnel. The flow field at the inflow
boundary, which is a plane just ahead of
the shock generators, is held fixed.
This flow field consists of an incoming
2-D turbulent boundary layer, on the
tunnel wall, which is matched with that
of the experiment. Since most of the
flow in this plane including a large part
of the boundary layer is supersonic, the
fixed boundary condition at this plane
does not violate any physics of the flow.
At the outflow boundary, once again since
the flow is mostly supersonic, the flow
variables are extrapolated from inside.
The outflow boundary is located several
planes beyond the shock generator
trailing edges. The distance between the
trailing edge and the boundary is about
25%of the length of the shock generator.
A nonreflective boundary condition,
using a simple Machwave extrapolation,
is applied on that portion of the
computational boundary extending from the
trailing edge of the shock generator to
the outflow boundary plane. This
boundary condition allows the expansion
wavesfrom the trailing edge of the shock
generator to pass through the free
boundary. Ano-slip condition is applied
on the solid walls. In the present
computations the turbulence model is
modified such that when a reversed flow
region is encontered, the outer layer
model chooses the maximumof the two eddy
viscosity values computed by Baldwin-
Lomax formulation and P. D. ThomasI°
model. In addition, based on the study of
Deiwert 11, the inner layer is replaced
with the outer model which extends all
the way upto the wall in this region. In
the absence of reversed flow regular
Baldwin-Lomax two-layer formulation is
used.
Results and Discussion
Solutions are obtained for the cases
corresponding to the experimental runs of
Mach numbers 3.5 and 4.0. Only two shock
generator angles, 6 and 10 deg., are
considered for computation because the
experimental flow visualization data are
available for only these two angles for
a Mach number of 3.5. For the Mach 3.5
case both 6 and 10 deg. configurations
are computed, whereas for the Mach 4.0
case only 6 deg. geometry is analyzed.
3
Figure 3a and 3b show the static
pressure contours on the tunnel wall for
the case of 6 deg. shock generator angle
and Mach numbers of 3.5 and 4.0 compared
with the experimental data. The
comparison shows a good agreement between
the experimental data and the solution.
The corresponding static pressure
contours for the 10 deg. shock generator
angle and Mach 3.5 case are shown in Fig.
3c in comparison with the experimental
data. The comparison shows that the
prediction in general agrees fairly well
with the experimental data.
Static pressure distributions along
the centerline of the tunnel wall for 6
deg. shock generator angle and Mach
numbers of 3.5 and 4.0 are presented in
Fig. 4a and 4b along with the
corresponding experimental data. The
comparison shows a very good agreement
between the solution and the experimental
data. The centerline pressure
distribution for the 10 deg. case and
Mach 3.5 is compared with the
experimental data in Fig. 4c. Except for
a slight diagreement upstream of the
plateau region of the curve, the solution
agrees fairly well with the experimental
data. This slight disgreement is due to
the discrepency in the location and
extent of the predicted reversed flow
region compared to that of the
experiment. The difference between the
predicted and the experimental reversed
flow region and its effect on the
pressure distribution are discussed later
in this section.
Figures 5a and 5b show the particle
traces close to the tunnel wall from the
prediction and the oil flow pattern from
the experimental data respectively for
the 6 deg. and Mach 3.5 configuration.
The particle traces are restricted to the
XY-plane to approximately duplicate the
oil flow pattern on the wall. Since these
pictures are supposed to show the flow
features qualitatively, the agreement
between the solution and the data is
good.
The particle traces and oil flow
pattern corresponding to the 10 deg. case
are shown in Fig. 6a and 6b. Both the
solution and experimental data show a
reversed flow region in the middle of the
tunnel wall. However, in the prediction,
the region is located slightly upstream
and extends over a larger area compared
to that in the experimental data. In the
experimental study 9 it was pointed out
that the presence of oil in the flow
could change the character of the flow
and so the extent and the location of the
reversed flow region could be different
from that of the flow without the oil.
Due to the difference in the location and
extent of the reversed flow region, the
predicted pressure distribution shows the
plateau, a characteristic of the reversed
flow, slightly upstream and larger in
extent compared to the experimental value
(see Fig. 4c). The discrepency between
the prediction and the experimental data
in the reversed flow region could also be
partly attributed to the approximations
in the turbulence model, used in the
code, which is an algebraic eddy
viscosity model. To improve the accuracy
of predictions in the reversed flow
regions it might be necessary to use
higher order turbulence models which are
currently being investigated at NASA
Lewis Research center under the code
4
validation efforts in the
Hypersonic reasearch program.
Generic
Summary
3-D viscous flow solutions have been
obtained for a configuration where two
crossing and glancing shocks interact
with a turbulent boundary layer in order
to assess the PARC3Dcode for hypersonic
inlet applications. The solutions for 4
different shock generator angles and Mach
numbers have been compared to the
experimental data which include static
pressure flelds and oil flow patterns on
the wall which contained the interaction.
The comparison showsthat the PARC3Dcode s
is capable of predicting the complex flow
features, typically present in supersonic
and hypersonic inlets, with a reasonably
good accuracy. To further improve the 6
accuracy in computing the reversed flow
regions, application of higher order
turbulence models needs to be examined in
the future code validation studies.
Acknowledgement
Part of this research was carried
out under contract NAS3-25366 supported
by NASA Lewis Research Center when the
author was employed at the Lewis Research
Center Group of SverdrupTechnology, Inc.
References
Cooper, G. K., Jordan, J. L., and
Phares, W. J., "Analysis Tool for
Application to Ground Testing of
Highly Underexpanded Nozzles", AIAA
87-2015, 1987.
Pulliam, T. H., and Steger, J. L.,
"Implicit Finite-Difference
Simulations of Three Dimensional
Compressible Flow", AIAA Journal,
Vol. 18, February 1980, pp. 159-
167.
Pulliam, T. H., "Euler and Thin
Layer Navier-Stokes Code: ARC2D,
ARC3D", Notes for Computational
Fluid Dynamics User's Workshop, The
University of Tennessee Space
Institute, Tullahoma, Tennessee,
March 12-16, 1984.
Jameson, A., Schmidt, W., and
Turkel, E., "Numerical Solutions of
the Euler Equations by Finite
Volume Method Using Runge-Kutta
Time Stepping Schemes", AIAA 81-
1259, 1981.
Baldwin, B., and Lomax, H., "Thin
Layer Approximtion and Algebraic
Model for Separated Flows,"AIAA
Paper 78-257, Jan. 1978.
Reddy, D. R., and Harloff, G. J.,
"Three Dimensional Viscous Flow
Computations and High Area Ratio
Nozzles for Hypersonic Propulsion",
Journal of Propulsion and Power,
Vol. 7, No. I, January-February
1991, pp. 84-89.
Reddy, D. R., Smith, G. E., Liou,
M.-F., and Benson, T. J., "Three
Dimensional Viscous Analysis of a
Hypersonic Inlet", AIAA paper 89-
0004, January 1989.
Reddy, D. R., Benson, T. J., and
Weir, L. S., "Comparison of 3-D
Viscous Flow Computations of Mach 5
Inlet with Experimental Data", AIAA
paper 90-0600, January 1990.
Hingst, W. R. and Williams, K. E.,
"Interaction of Two Glancing,
Crossing Shock Waves with a
Turbulent Boundary Layer at Various
Mach Numbers," NASA TM 103740,
1991.
5
io Thomas, P. D., "Numerical Method for
Predicting Flow Characteristics and
Performance of Nonaxisymmetric
Nozzles - Theory," Langley Research
Center, NASACR3147, September1979.
11
Deiwert, G. S., "Computation of
Separated Transonic Turbulent Flows,"
AIAA Journal, Vol. 14, No. 6, June
1976, pp. 735-740.
Invisid
Shocks
Tunnel
Centerline
Tunnel
Boundary
Layer
Shock
Generators
Fig. 1 Experimental Configuration
6
symmetry
symmetry
Z
Fig. 2 Computational Grid
7
c"
CJ
IC
>-
E
.m
O.
09
¢-
10 15 2O
X (inches)
Fig. 3a Pressure Contours for 6 deg. Mach 3.5
2
c-
u 0
r
-2
>-
' I ' ' ' ' I '
Fig. 3b
I
10 15
X (inches)
Pressure Contours for 6 deg. Mach 4.0
20
8
"%"
¢-
U
E
>-
2
0
-2
%
10 15 20
X (inches)
Fig. 3c Pressure Contours for 10 deg. Mach 3.5
4.0
5.5 -
c 3.O-
a_ 2.5-
d 2.0-
(1)
n
1.5-
o
o 1 0 -
O3
0.5-
Fig. 4a
A Experiment
Analysis
I I I I I I I 1
0.4 0.8 1.2 1.6
Distance Along the Center line (in ft.)
Centerline Pressure Distibution for 6 deg. Mach 3.5
4.0
f-
o--
(3_
13_
,4
0_
(o
,-
El
bO
5.5
5.0
25
2.0
1.5
1.0
0.51
0.0 ....
0.0
Fig. 4b
A Experiment
Analysis
I I I E I I t t
0.4 0.8 1.2 1.6
Distance Along the Center line (in ft.)
Centerline Pressure Distibution for 6 deg. Mach 4.0
6
5
r--
o_
o_
-_4
13_
d 5
(D
13_
.2 2
C}
U3
I
0
0.0
Fig. 4c
,_ Experiment
Analysis
t I I I I i I 1
0.4 0.8 !.2 1.6
Distance Along the Center line (in ft.)
Centerline Pressure Distibution for 10 deg. Mach 3.5
10
Fig. 5a Particle traces (analysis) close to tunnel wall for 6 deg. Mach 3.5
Fig. 5b Oil flow pattern (experimental) on tunnel wall for 6 deg. Mach 3.5
11 0_!,._"i_'.._ P,%3,£ IS
CF [-",_ff _.tJ, LiTY
Fig. 6a Particle traces (analysis) close to tunnel wall for 10 deg. Mach 3.5
Fig. 6b Oil flow pattern (experimental) on tunnel wall for 10 deg. Mach 3.5
12 O_IG)."';AL P&_E IS
OF POOR Q4JAUTY
N/ A
..' Report Documentation Page
Spaoe Admlnlstratlon
1. Report No. NASA TM- 104469 2. Government Accession No. 3. Recipient's Catalog No.
AIAA-91-1758
5. Report Date4. Title and Subtitle
3-D Navier-Stokes Analysis of Crossing, Glancing Shocksfrurbulent
Boundary Layer Interactions
7. Author(s)
D.R. Reddy
9. Performing Organization Name and Address
National Aeronautics and Space Administration
Lewis Research Center
Cleveland, Ohio 44135- 3191
12. Sponsoring Agency Name and Address
National Aeronautics and Space Administration
Washington, D.C. 20546-0001
6. Performing Organization Code
8. Performing Organization Report No.
E-6318
10. Work Unit No.
505 - 62 - 52
11. Contract or Grant No.
13. Type of Report and Period Covered
Technical Memorandum
14. Sponsoring Agency Code
15. Supplementary Notes
Prepared for the 22nd Fluid Dynamics, Plasma Dynamics and Lasers Conference sponsored by the American
Institute of Aeronautics and Astronautics, Honolulu, Hawaii, June 24-26, 1991. Responsible person, D.R. Reddy,
(216) 433-8133.
16. Abstract
Three-dimensional viscous flow analysis is performed for a configuration where two crossing and glancing shocks
interact with a turbulent boundary layer. A time marching 3-D full Navier-Stokes code, called PARC3D, is used to
compute the flow field and the solution is compared to the experimental data obtained at the NASA Lewis Research
Center 1 ft. x 1 ft. supersonic wind tunnel facility. The study is carried out as part of the continuing code assessment
program in support of the Generic Hypersonic research at NASA Lewis. Detailed comparisons of static pressure fields
and oil flow patterns is made-with the corresponding solution on the wall containing the shock/boundary layer
interaction in an effort to validate the code for hypersonic inlet applications.
17. Key Words (Suggested by Author(s))
Computational fluid dynamics
Three dimensional flow
Shock wave/boundary layer interaction
Hypersonic inlets
19. Security Classif. (of the report)
Unclassified
18. Distribution Statement
Unclassified - Unlimited
Subject Category 02
20. Security Classif. (of this page) 21. No. of pages 22. Price*
Unclassified 14 A03
NASA FORM 1626 OCT 86
*Forsale bvthe NationalTechnicalInformation Service,Springfield,Virginia 22161
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The 3-D Navier-Stokes analysis of crossing, glancing shocks/turbulent boundary layer interactions

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