Nicholas J. Georgiadis, Manan A. Vyas, and Dennis A. Yoder

Glenn Research Center, Cleveland, Ohio

Wind-US Code Contributions to the First

AIAA Shock Boundary Layer Interaction

Prediction Workshop

NASA/TM—2013-217837

February 2013
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Nicholas J. Georgiadis, Manan A. Vyas, and Dennis A. Yoder

Glenn Research Center, Cleveland, Ohio

Wind-US Code Contributions to the First

AIAA Shock Boundary Layer Interaction

Prediction Workshop

NASA/TM—2013-217837

February 2013

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

This work was jointly sponsored by the Department of Defense (DoD) Test Resource Management Centers (TRMC) Test and 

Evaluation/Science and Technology (T&E/S&T) Program through the High Speed Systems Test (HSST) area (formerly APTT) 

and the NASA Fundamental Aeronautics Hypersonics Project.

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Available electronically at http://www.sti.nasa.gov

This work was sponsored by the Fundamental Aeronautics Program 

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management. 
This report discusses the computations of a set of shock wave / turbulent boundary

layer interaction (SWTBLI) test cases using the Wind-US code, as part of the 2010 American Institute of Aeronautics and Astronautics (AIAA) shock / boundary layer interaction

workshop. The experiments involve supersonic flows in wind tunnels with a shock generator

that directs an oblique shock wave toward the boundary layer along one of the walls of the

wind tunnel. The Wind-US calculations utilized structured grid computations performed

in Reynolds-averaged Navier-Stokes mode. Four turbulence models were investigated: the

Spalart-Allmaras one-equation model, the Menter Baseline and Shear Stress Transport k-ω

two-equation models, and an explicit algebraic stress k-ω formulation. Effects of grid resolution and upwinding scheme were also considered. The results from the CFD calculations

are compared to particle image velocimetry (PIV) data from the experiments. As expected,

turbulence model effects dominated the accuracy of the solutions with upwinding scheme

selection indicating minimal effects.

Nomenclature

k turbulent kinetic energy

M∞ freestream Mach number

u axial velocity

v normal velocity

x, y, z Cartesian coordinates

y

+ wall normal coordinate

δ boundary layer thickness

 turbulent dissipation rate

μ dynamic molecular viscosity

μt dynamic eddy viscosity

ω specific turbulent dissipation rate = /k

θ shock generator angle

Introduction

In supersonic flows, the shock wave / turbulent boundary layer interaction (SWTBLI) is a very common

phenomena that has significant effects on the operability of specific components such as aircraft inlets and

also on overall performance of aerospace vehicles. The problem has been studied extensively over the past

few decades in laboratory experiments and in computational fluid dynamics (CFD) efforts. While gains

in understanding of the underlying fluid dynamics of SWTBLI have been made, research continues into

understanding the complex interaction of a shock wave with a turbulent boundary layer. In a typical

SWTBLI, the adverse pressure gradient induced by the shock system causes a flow separation that frequently

Wind-US Code Contributions to the First AIAA Shock

Boundary Layer Interaction Prediction Workshop

Nicholas J. Georgiadis, Manan A. Vyas, and Dennis A. Yoder

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

NASA/TM—2013-217837 1
is unsteady and three-dimensional. Without question, control of SWTBLI has yet to be mastered. While

there have been numerous CFD studies, there is not a single approach that has been identified as optimal

for calculation of SWTBLI.

Until recently, Reynolds-averaged Navier-Stokes (RANS) methods were used almost exclusively, and for

practical aerodynamic analyses that contain one or more SWTBLIs, RANS is still the only feasible approach.

More recently, large eddy simulation (LES) and hybrid RANS-LES techniques have been investigated for

application to the SWTBLI problem, but typically have been restricted to small subset problems, as applying

an LES-based technique to a more complex system (i.e. aircraft inlet) involving SWTBLIs is still largely

prohibitive due to the large range of scales that are important. Knight and Degrez1 and Knight et al2 provide

comprehensive overviews of a broad range in CFD methods as applied to SWTBLIs, in particular those

investigated under AGARD and RTO working groups. Consideration of both RANS and LES methods is

made. Reference 3 focuses on an assessment of RANS-based methods while a survey of LES-based approaches

as applied to SWTBLIs is presented in Edwards.4 The overall conclusions of these survey papers is that

RANS methods are inherently unable to calculate some of the crucial features of SWTBLI, in particular the

unsteadiness of the shock system and separated flow. In addition, the three dimensional features are also

troublesome for RANS-based techniques. LES-based techniques may be promising, but neither sufficient

maturity of these techniques nor understanding of their ability to properly handle the underlying fluid

dynamics has been realized.

A recent workshop considering CFD calculations for a set of SWTBLI cases was held in conjunction

with the 48th American Institute of Aeronautics and Astronautics (AIAA) Aerospace Sciences Meeting. An

overview of the workshop objectives is presented in Benek5 with a summary of overall findings presented

in Benek and Babinsky.6 The focus of this workshop was SWTBLI as occurs in supersonic inlets. Several

investigators contributed solutions to this workshop. Contributions included RANS and LES-based computations. DeBonis et al7 provides a comprehensive assessment of the CFD calculations, including uncertainty

analysis of the submitted CFD results and experimental data obtained for the same configurations. Hirsch8

examined some of the CFD trends, in particular effects of turbulence modeling, RANS versus LES, and

numerical schemes submitted by several investigators and includes the results from our efforts described

herein.

In this paper, we discuss the solutions obtained with the Wind-US code for the two sets of cases that

were the focus of the SWTBLI workshop. A brief description of the test cases is provided first. The CFD

approach is presented next including construction of the computational grids, turbulence models used, and

other code settings. Comparisons of CFD calculations to experimental data for the test cases are presented,

followed by conclusions.

Experimental Configurations

The experimental data set for the first SWTBLI test case was obtained at the Institut Universitaire des

Systemes Thermiques Industriels (IUSTI) in Marseille, France.9 The experimental data was utilized in the

European Union SWTBLI research project referred to as UFAST.10 The UFAST experiments utilized an 8

degree shock generator which spanned the entire width of the tunnel with an approaching Mach 2.25 flow.

The supply stagnation pressure was 50.5 kPa and the stagnation temperature was 293 K.

The second SWTBLI test case was investigated at the University of Michigan (UM)11 as part of the

Collaborative Center for the Aeronautical Sciences (CCAS) sponsored by the United States Air Force. The

UM experiments utilized three shock generator angles with an approaching Mach 2.75 flow. The shock angles

were 7.75, 10.0 and 12.0. The supply stagnation pressure was 101.0 kPa and the stagnation temperature

was 293 K. Unlike the UFAST experiments, the UM shock generators did not span the entire width of the

wind tunnel and were supported by a strut from the top of the wind tunnel.

A schematic of the experimental configuration generally representing that used in both sets of experiments

is shown in Fig. 1 as taken from DeBonis et al.7 Cross sectional views of these two cases are provided in

Fig. 2. Particle Image Velocimetry (PIV) was used in all cases to characterize the interaction regions, with

both mean flow velocities and turbulent statistics obtained. Specifics of the experimental measurements are

discussed in Ref. 10 for the UFAST case and in Ref. 11 for the UM case.

NASA/TM—2013-217837 2
CFD Approach

The CFD calculations described in this report used the Wind-US code, which is the production RANS

solver of the NPARC Alliance, a formal partnership of NASA Glenn Research Center (GRC) and the U.S.

Air Force Arnold Engineering Development Center (AEDC), with significant participation by the Boeing

Company. An overview of the current capabilities in the Wind-US flow solver may be found in Nelson12

and Georgiadis et al.13 This section describes the computational grids generated for these SWTBLI cases,

numerical schemes examined, and turbulence models utilized as part of this study.

Computational Grids

The Wind-US calculations described in this report utilized structured grid computations performed in RANS

mode. Rumsey presented results obtained with the CFL3D CFD code in Ref. 14, obtained using the same

computational grids that were constructed for simulations described in this report. The UFAST grid is shown

in Fig. 3. The overall grid had approximately 7.4 million points spread across 10 structured grid zones.

Point-to-point connectivity was used at zonal interfaces through most of the overall grid, with mismatched

zones just upstream and downstream of the interaction region, shown in Fig. 3(b), in order to allow greater

resolution in the SWTBLI focused region. Walls were packed such that the first point was placed at a

position corresponding to a nominal y+ of approximately 1.0, using the fully expanded tunnel conditions

corresponding to Mach 2.25 flow and an assumed reference skin friction coefficient of 0.0025. One half of the

geometry was modeled with a symmetry plane placed at the middle of the spanwise direction.

The computational grid for the UM case (7.75 degree shock generator) is shown in Fig. 4. The grids

for the 10 degree and 12 degree shock generator were built in exactly the same manner as was the 7.75

degree case. Each grid had approximately 8.4 million points spread across 16 structured grid zones. The

same grid strategy was utilized as for the UFAST case, i.e. walls were packed to a nominal y+ =1.0 and

point-to-point connectivity was used everywhere except just upstream and downstream of the interaction

regions. As discussed in the experimental configurations section, the UM shock generator did not span the

entire width of the tunnel, and was mounted via a support strut originating in the tunnel ceiling. All of these

details were modeled in the computational grids constructed here. One half of the geometry was modeled

with the symmetry plane placed at the middle of the spanwise direction and cutting through the center of

the support strut.

Numerical Schemes

Three spatial flux methods available in Wind-US were investigated for the UM test case. The first is the

Roe scheme,15 which is the default setting in Wind-US. The second is the well known method due to Van

Leer,16 and the third is that of Harten et al17 as modified by Toro18 and commonly referred to as the HLLC

scheme. Second order schemes were used in all cases with TVD limiters applied. For the UFAST case, only

the default 2nd order Roe scheme was utilized.

Turbulence Modeling

As discussed in the introduction, turbulence modeling has been found to be the most important factor

affecting the calculation of SWTBLI, and was the focus of efforts described in this report. In Wind-US and

many production CFD solvers, the Shear-Stress Transport (SST) two-equation turbulence model of Menter19

is widely used because it is robust and accurate for a broad range of flows, including wall boundary layers

and free shear layer regions. The SST model is a two-layer model which employs the k−ω model of Wilcox20

in the inner region of boundary layers and switches to a k −  model in the outer region of boundary layers

and in mixing regions. The outer k −  model is transformed to provide a second set of k − ω equations

with a blending function used to transition between the two sets of equations. A modification to the eddy

viscosity limits the shear stress, per the Bradshaw assumption that the shear stress in a boundary layer is

proportional to the turbulent kinetic energy. The SST model has been found to provide reasonably accurate

calculations of wall bounded flows, provided there are not large flow separations. The second turbulence

model used here was the Menter baseline (BSL) k − ω model, which is the very close relative of the Menter

SST formulation. It is also a two layer model, with primary difference being the absence of the shear stress

limiter that is employed with SST.

NASA/TM—2013-217837 3
The third turbulence model investigated in this study is the one-equation model due to Spalart and

Allmaras.21, 22 We will refer to this model in this report as the “SA” model.

The fourth turbulence model investigated in these SWTBLI cases is a k − ω based non-linear explicit

algebraic stress model (ASM) formulation based on the work of Rumsey.23 Unlike linear two-equation

models, ASM formulations are sensitive to turbulent stress anisotropies and have a direct relation to the

full Reynolds stress model. As a result, ASMs have the capability to include more relevant flow physics

than the linear models. However, they are also solved using a two-equation approach and as a result are

not significantly more computationally expensive than linear two-equation models. In Ref. 13, Wind-US

was applied to a Mach 5 SWTBLI problem using the SST and k-ω models. These models provided similar

predictions of skin friction coefficient for this test case. A linear k- model and k- based ASM were also

applied to this problem and significantly overpredicted the skin friction coefficient downstream of the key

interaction region. Because of this result and similar findings by other investigators employing k- models

for SWTBLI problems, we did not examine k- models in this work.

UFAST Test Case

The Mach number approaching the SWTBLI region for the UFAST case is lower than that for the UM

case and as a result, the oblique shock wave angle is higher than for the UM test case. In turn, the resultant

adverse pressure gradient effects are actually relatively stronger through the SWTBLI region. Axial velocity

contours for the UFAST test case obtained with the SST turbulence model are shown in Fig. 5. The

oblique wave originating from the sharp leading edge of the shock generator may be observed, along with

the SWTBLI region centered about x = 320mm. The complex interaction on the top of the tunnel results

in a flow separation that is much larger than that in the SWTBLI focus region and resulted in unsteadiness

that was sustained even after the focus SWTBLI region on the bottom stopped changing and was considered

to be converged. Eddy viscosity contours corresponding to the flowfield solution shown in Fig. 5 are shown

in Fig. 6. The eddy viscosity values shown are normalized by the local molecular viscosity. For plotting

purposes, the normalized eddy viscosity values shown are capped at μt/μ = 500 for clarity in the focus region

although the maximum values in the region near the top of the domain reached nearly 1500.

The experimental data was collected within a select region around the bottom wall interaction. Axial

velocity contours for the UFAST test case using the four turbulence modeling approaches are compared

to the experimental PIV measurements in Fig. 7. As will be the case for the UM experiments discussed

in the next section, the CFD solution slices represent the same physical domain, with the same contour

levels as the experimental data. Further, the CFD solutions were interpolated to the same physical locations

where the PIV data were taken, as was required by the organizers of the AIAA workshop, for purposes of

computing differences between solutions and experimental data.7 Examining these contours, the extent of

the adverse pressure gradient effects indicated by the Menter SST solution are larger than the other solutions

and experimental data.

Further comparisons of the CFD solutions and experimental data are made for the axial velocity profiles

at four axial locations in Fig. 8. One may observe that the CFD solutions plotted do not go all the way to the

wall, and again this is due to interpolation of the CFD results to the PIV measurement locations. While most

CFD-to-experimental comparisons are made with the CFD solutions actually plotted at the computational

grid points, the manner of comparison used here and in the workshop does allow one to determine what the

CFD would predict with a “probe” placed at a specific location, in analogy to the experiments. For this case

and the UM cases, however, with a rather fine experimental PIV grid, there are no observable differences

between plotted lines using the CFD solutions mapped to the experimental physical locations and the CFD

solutions at the actual computational grid points.

The comparisons in Fig. 8 show the same trends as indicated by the contour plots of Fig. 7. In particular,

the size of the flow separation indicated by the SST solution is greater than that indicated by the experimental

data and the other turbulence models. One may note an especially large difference between the Menter SST

and BSL results, which is due to the eddy viscosity limiter in the SST formulation. Normal velocity profiles

are compared in Fig. 9. While the most commonly used quantity for comparing boundary layer profiles

is axial velocity, these normal velocity comparisons show how substantial the effect of turbulence model is

on the boundary layer details, and in particular how none of the models are able to capture the behavior

indicated by the experimental data.

NASA/TM—2013-217837 4
University of Michigan (UM) Test Case

As described previously, three shock generator configurations were examined as part of the UM experiments. For the first case with shock generator angle set to 7.75 degrees, experimental data was made

available to CFD analysts prior to the workshop, and is the focus of the discussion in this section. Data for

the other two test cases was held back to enable “blind” comparisons of experimental data and submitted

CFD solutions. From our calculations with Wind-US using the SST turbulence model, axial velocity contours for all three UM test cases, where the shock generator angle was varied, are shown in Fig. 10. Eddy

viscosity contours for the UM test case are shown in Fig. 11. As expected, the strength and size of the

interaction increases with larger shock generator angle. The focus of the comparisons between solutions at

the workshop was made for the smallest shock generator angle, 7.75 degrees, and we will concentrate on this

case for the remainder of this discussion. For simplicity, we will refer to this as the “UM test case.”

Axial velocity contours for the UM test case in the SWTBLI focus region using the four turbulence

modeling approaches are compared to experimental measurements in Fig. 12. As discussed for the UFAST

test case, the CFD solution slices represent the same physical domain, with the same contour levels as the

experimental data, and with the CFD solutions interpolated to the experimental measurement locations.

Normal velocity contours are compared in Fig. 13 and contours of the velocity shear component are shown

in Fig. 14.

Further comparisons of the CFD solutions and experimental data are made for the axial velocity profiles

at four axial locations in Fig. 15. In this and subsequent figures, two sets of experimental data are also

presented. The first was obtained with stereoscopic PIV measured along spanwise (or “yz cut”) planes at

seven axial locations, and the second along a streamwise plane, referred to in the figures as “xy cut.” In the

UFAST experiments, the lower approaching Mach number (2.25 in UFAST versus 2.75 in UM) produces a

steeper shock wave (approximately 33 degrees versus 27 degrees) for a very similar wedge angle (8.0 degrees

versus 7.75 degree). This results in a relatively stronger interaction region, and flow separation, while such

a flow separation is not obvious for this lowest wedge angle case in the UM experiments.

All of the turbulence modeling approaches show a smaller effect of the shock interaction on the boundary

layer thickening than indicated by the experiment with the SST solution being closest to the data. Recall

that back in the UFAST results with flow separation, the SA and ASM results indicated smaller effects of

shock interaction on boundary layer thickening, with SST indicating too large of a response relative to the

experimental data. These results are very similar to those reported for SA and SST by Bhagwandin and

DeSpirito24 and also to other participants in the workshop as shown in Ref. 8. Normal velocity profiles

are compared in Fig. 16 and show considerable scatter among the turbulence models and magnify the

discrepancies with experimental data in the SWTBLI region.

Using the grid sequencing capability within Wind-US, a grid sensitivity study was made for SST turbulence model solutions using the complete grid and the sequenced grid where every other point in each

computational direction, termed “medium” was used. Recalling that the full (fine) grid had 8.4 million

points, the medium grid had approximately 1 million total points. A comparison of axial and normal velocities using the two grid levels is provided in Fig. 17. This does not suffice as a thorough grid sensitivity

study as a grid independent solution was not achieved. While the qualitative behavior is similar between

the fine and medium grids, especially in the axial velocity profiles, it appears that the near wall behavior is

less affected by removing every other grid point as is the behavior near the top of the boundary layer. This

is not surprising, as with the wall spacing set to a nominal y+ of 1, removing every other grid point still has

the first point well within the laminar sublayer. It does emphasize the need to consider grid resolution away

from the wall, however, for cases that are not straightforward equilibrium boundary layers.

An investigation of the effects of upwinding scheme, also using the Menter SST model, is provided in

Fig. 18. In all cases, second order versions of the Roe, Van Leer, and HLLC schemes were used and there

appears to be minimal effect of the upwinding scheme on prediction of the SWTBLI region. Interestingly,

Rumsey found more significant effects of upwinding scheme when using the SA turbulence model on the same

computational grids as we have employed here. Our finding, from consideration of the differences observed

among turbulence models and upwinding schemes, is that turbulence model effects dominate the accuracy

of SWTBLI calculations.

NASA/TM—2013-217837 5
Conclusions

Two sets of SWTBLI flows were investigated using the Wind-US CFD code, in efforts towards participating in the 2010 AIAA Shock Boundary Layer Interaction Prediction Workshop. The results obtained

here were qualitatively similar to most of the results obtained by investigators of other similar RANS flow

solvers, indicating that the capabilities of most mature production flow CFD solvers are comparable, especially when using similar turbulence modeling and numerical schemes. Further, it appears that turbulence

modeling remains the pacing technology affecting the accuracy of SWTBLI simulations.

Calculations used the SA one-equation turbulence model and SST two-equation turbulence model, which

were not only used by other participants in this workshop for their simulations of the same SWTBLI cases,

but are two of the most widely used RANS models in the aerospace community for calculating boundary

layer dominated flow problems in RANS mode. While the qualitative agreement with experimental data

may be considered acceptable, the boundary layer details were not accurate. We also obtained calculations

using the Menter BSL two-equation model and an explicit algebraic stress model which did not provide

better results than the linear turbulence models. Comparison of the BSL and SST results illustrated effects

of the shear stress limiter. For SWTBLI flows without separation, the SST performs well as shown by

the UM results. Once separation occurs, however, the SST model tends to over-react relative to BSL,

as was shown by the UFAST results. At the workshop, some attempts at using LES based techniques

were presented, but production usage of LES for complex SWTBLI dominated flows is far from a mature

science. A few key limitations are difficulties in prescribing sufficient inflow turbulent boundary conditions,

simulating experiments at the actual Reynolds numbers investigated, and when employing hybrid RANSLES approaches, the manner in which the switch from a RANS region to an LES region is handled. As

computer resources, including processor speed, available memory, and storage capacity improve, LES-based

methods will become more practical.

In the near term, there still is a need for RANS model improvements, and RANS will still likely be the

technique of choice for some time in concept screening and evaluation. There has been little effort in the past

decade to improve pure RANS models. Most interest and support in the area of turbulent flow computations

has been in the area of LES and hybrids. Some investment in RANS-based methods still seems warranted.

References

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of Current CFD Prediction Capability,” AGARD AR-319 , Vol. 2, 1998.

2Knight, D., Yan, H., Panaras, A. G., and Zheltovodov, A., “Advances in CFD Prediction of Shock Wave Turbulent

Boundary Layer Interactions,” Progress in Aerospace Sciences, Vol. 39, No. 2, February 2003, pp. 121–184.

3Zheltovodov, A. A., “Some Advances in Research of Shock Wave Turbulent Boundary Layer Interactions,” AIAA Paper

2006-0496, January 2006.

4Edwards, J. R., “Numerical Simulations of Shock/Boundary Layer Interactions Using Time-Dependent Modeling Techniques: A Survey of Recent Results,” Progress in Aerospace Sciences, Vol. 44, No. 6, Aug. 2008, pp. 447–465.

5Benek, J., “Overview of the 2010 AIAA Shock Boundary Layer Interaction Workshop,” AIAA Paper 2010-4821, January

2010.

6Benek, J. and Babinsky, H., “Lessons Learned from the 2010 AIAA Shock Boundary Layer Interaction Workshop,” AIAA

Paper 2010-4825, January 2010.

7DeBonis, J. R., Oberkampf, W. L., Wolf, R. T., Orkwis, P. D., Turner, M. G., Babinsky, H., and Benek, J. A., “Assessment

of Computational Fluid Dynamics and Experimental Data for Shock Boundary-Layer Interactions,” AIAA Journal, Vol. 50,

No. 4, Apr. 2012, pp. 891–903.

8Hirsch, C., “SBLI Lessons Learned - CFD Simulations of Two Test Cases ,” AIAA Paper 2010-4824, January 2010.

9Dupont, P., Piponniau, S., Sidorenko, A., and Debieve, J., “Investigation by Particle Image Velocimetry Measurements

of Oblique Shock Reflection with Separation,” AIAA Journal, Vol. 46, No. 6, 2008, pp. 1365–1370.

10Unsteady Effects in Shock Wave Induced Separation, edited by P. Doerffer, C. Hirsch, J.-P. Dussauge, H. Babinsky, and

G. Barakos, Springer, 2010.

11Lapsa, A. P. and Dahm, W. J. A., “Stereo Particle Image Velocimetry of Nonequilibrium Turbulence Relaxation in a

Supersonic Boundary Layer,” Experiments in Fluids, Vol. 50, No. 1, 2011, pp. 89–108.

12Nelson, C., “An Overview of the NPARC Alliance’s Wind-US Flow Solver,” AIAA Paper 2010-27, January 2010.

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Nelson, C. C., “Wind-US Physical Modeling Improvements to Complement Hypersonic Testing and Evaluation,” AIAA Paper

2009-193, January 2009.

NASA/TM—2013-217837 6
14Rumsey, C. L., “CFL3D Contribution to the AIAA Supersonic Shock Boundary Layer Interaction Workshop,” NASA

TM 2010-216858, October 2010.

15Roe, P. L., “Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes,” J. Comp. Phys., Vol. 43, 1981,

pp. 357–372.

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laws,” SIAM Rev., Vol. 25, 1982, pp. 35–61.

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Vol. 4, 1994, pp. 25–34.

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1994, pp. 1598–1605.

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Vol. 26, No. 11, February 1988, pp. 1299–1310.

21Spalart, P. R. and Allmaras, S. R., “A One-Equation Turbulence Model for Aerodynamic Flows,” AIAA Paper 92-0439,

1992.

22Spalart, P. R. and Allmaras, S. R., “A One-Equation Turbulence Model for Aerodynamic Flows,” La Recherche Aerospatiale, No. 1, 1994, pp. 5–21.

23Rumsey, C. L., Gatski, T. B., and Morrison, J. H., “Turbulence Model Predictions of Strongly Curved Flow in a U-Duct,”

AIAA Journal, Vol. 38, No. 8, August 2000, pp. 1394–1402.

24Bhagwandin, V. A. and DeSpirito, J., “Numerical Prediction of Supersonic Shock Boundary-Layer Interaction,” AIAA

Paper 2011-859, January 2011.

θ 

M∞ 

PIV Plane 

y 

x 

Figure 1. Schematic of SWTBLI experimental configuration (courtesy of DeBonis et al7).

NASA/TM—2013-217837 7
170 mm

120 mm

! " 10 mm

57 mm

7

! " 10 mm

32 mm

(a) UFAST (b) UM

Figure 2. Cross sectional views of SWTBLI test configurations (courtesy of DeBonis et al7).

(a) entire domain

(b) detail near shock generator

Figure 3. Computational grid for UFAST test case.

NASA/TM—2013-217837 8
(a) entire domain

(b) streamwise detail near shock generator

(c) spanwise detail near shock generator

Figure 4. Computational grid for UM test case.

NASA/TM—2013-217837 9
Figure 5. Velocity contours for UFAST test case using SST.

Figure 6. Normalized eddy viscosity contours for UFAST test case using SST (contour levels trimmed at μt/μ

= 500).

NASA/TM—2013-217837 10
(a) Experiment

(b) Menter SST

(c) Menter BSL

(d) Spalart-Allmaras

(e) k − ωASM

Figure 7. Axial velocity contours for UFAST test case in vicinity of SWTBLI.

NASA/TM—2013-217837 11
u (m/s)

y (mm)

0 200 400 600 0

5

10

15

Expt

SST

BSL

SA

k-t ASM

(a) x = 280 mm

u (m/s)

y (mm)

0 200 400 600 0

5

10

15

Expt

SST

BSL

SA

k-t ASM

(b) x = 300 mm

u (m/s)

y (mm)

0 200 400 600 0

5

10

15

Expt

SST

BSL

SA

k-t ASM

(c) x = 320 mm

u (m/s)

y (mm)

0 200 400 600 0

5

10

15

Expt

SST

BSL

SA

k-t ASM

(d) x = 340 mm

Figure 8. Axial velocity profiles for UFAST test case in vicinity of SWTBLI.

NASA/TM—2013-217837 12
v (m/s)

y (mm)

-40 0 40 0

5

10

15

Expt

SST

BSL

SA

k-t ASM

(a) x = 280 mm

v (m/s)

y (mm)

0 40 80 0

5

10

15

Expt

SST

BSL

SA

k-t ASM

(b) x = 300 mm

v (m/s)

y (mm)

0 40 80 0

5

10

15

Expt

SST

BSL

SA

k-t ASM

(c) x = 320 mm

v (m/s)

y (mm)

-80 -40 0 0

5

10

15

Expt

SST

BSL

SA

k-t ASM

(d) x = 340 mm

Figure 9. Normal velocity profiles for UFAST test case in vicinity of SWTBLI.

NASA/TM—2013-217837 13
(a) 7.75 degree shock generator

(b) 10 degree shock generator

(c) 12 degree degree shock generator

Figure 10. Axial velocity contours for UM test cases using the SST model.

NASA/TM—2013-217837 14
(a) 7.75 degree shock generator

(b) 10 degree shock generator

(c) 12 degree degree shock generator

Figure 11. Eddy viscosity contours for UM test cases using the SST model.

NASA/TM—2013-217837 15
(a) Experiment

(b) Menter SST

(c) Menter BSL

(d) Spalart-Allmaras

(e) k − ωASM

Figure 12. Axial velocity contours for UM test case in vicinity of SWTBLI.

NASA/TM—2013-217837 16
(a) Experiment

(b) Menter SST

(c) Menter BSL

(d) Spalart-Allmaras

(e) k − ωASM

Figure 13. Normal velocity contours for UM test case in vicinity of SWTBLI.

NASA/TM—2013-217837 17
(a) Experiment

(b) Menter SST

(c) Menter BSL

(d) Spalart-Allmaras

(e) k − ωASM

Figure 14. dv/dx contours for UM test case in vicinity of SWTBLI.

NASA/TM—2013-217837 18
u (m/s)

y (mm)

200 400 600 0

5

10

15

20

Expt (yz cut)

Expt (xy cut)

SST

BSL

SA

ASM

(a) x = 20.76 mm

u (m/s)

y (mm)

0 200 400 600 0

5

10

15

20

Expt (yz cut)

Expt (xy cut)

SST

BSL

SA

ASM

(b) x = 30.76 mm

u (m/s)

y (mm)

0 200 400 600 0

5

10

15

20

Expt (yz cut)

Expt (xy cut)

SST

BSL

SA

ASM

(c) x = 38.76 mm

u (m/s)

y (mm)

0 200 400 600 0

5

10

15

20

Expt (yz cut)

Expt (xy cut)

SST

BSL

SA

ASM

(d) x = 53.76 mm

Figure 15. Turbulence model effects on axial velocity profiles for UM test case in vicinity of SWTBLI.

NASA/TM—2013-217837 19
v (m/s)

y (mm)

-60 -40 -20 0 20 40 60 0

5

10

15

20

Expt (yz cut)

Expt (xy cut)

SST

BSL

SA

ASM

(a) x = 20.76 mm

v (m/s)

y (mm)

-60 -40 -20 0 20 40 60 0

5

10

15

20

Expt (yz cut)

Expt (xy cut)

SST

BSL

SA

ASM

(b) x = 30.76 mm

v (m/s)

y (mm)

-60 -40 -20 0 20 40 60 0

5

10

15

20

Expt (yz cut)

Expt (xy cut)

SST

BSL

SA

ASM

(c) x = 38.76 mm

v (m/s)

y (mm)

-60 -40 -20 0 20 40 60 0

5

10

15

20

Expt (yz cut)

Expt (xy cut)

SST

BSL

SA

ASM

(d) x = 53.76 mm

Figure 16. Turbulence model effects on normal velocity profiles for UM test case in vicinity of SWTBLI.

NASA/TM—2013-217837 20
u (m/s)

y (mm)

200 400 600 0

5

10

15

20

Expt (yz cut)

Expt (xy cut)

SST (medium)

SST (fine)

(a) u-velocity at x = 20.76 mm

u (m/s)

y (mm)

200 400 600 0

5

10

15

20

Expt (yz cut)

Expt (xy cut)

SST (medium)

SST (fine)

(b) u-velocity at x = 53.76 mm

v (m/s)

y (mm)

-60 -40 -20 0 20 40 60 0

5

10

15

20

Expt (yz cut)

Expt (xy cut)

SST (medium)

SST (fine)

(c) v-velocity at x = 20.76 mm

v (m/s)

y (mm)

-60 -40 -20 0 20 40 60 0

5

10

15

20

Expt (yz cut)

Expt (xy cut)

SST (medium)

SST (fine)

(d) v-velocity at x = 53.76 mm

Figure 17. Effects of grid resolution on velocity profiles for UM test case in vicinity of SWTBLI.

NASA/TM—2013-217837 21
u (m/s)

y (mm)

200 400 600 0

5

10

15

20

Expt (yz cut)

Expt (xy cut)

Roe

Van Leer

HLLC

(a) u-velocity at x = 20.76 mm

u (m/s)

y (mm)

0 200 400 600 0

5

10

15

20

Expt (yz cut)

Expt (xy cut)

Roe

Van Leer

HLLC

(b) u-velocity at x = 53.76 mm

v (m/s)

y (mm)

-60 -40 -20 0 20 40 60 0

5

10

15

20

Expt (yz cut)

Expt (xy cut)

Roe

Van Leer

HLLC

(c) v-velocity at x = 20.76 mm

v (m/s)

y (mm)

-60 -40 -20 0 20 40 60 0

5

10

15

20

Expt (yz cut)

Expt (xy cut)

Roe

Van Leer

HLLC

(d) v-velocity at x = 53.76 mm

Figure 18. Effects of upwinding scheme on velocity profiles for UM test case in vicinity of SWTBLI.

NASA/TM—2013-217837 22

REPORT DOCUMENTATION PAGE Form Approved 

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1. REPORT DATE (DD-MM-YYYY)

01-02-2013 

2. REPORT TYPE

Technical Memorandum 

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Wind-US Code Contributions to the First AIAA Shock Boundary Layer Interaction 

Prediction Workshop 

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Georgiadis, Nicholas, J.; Vyas, Manan, A.; Yoder, Dennis, A. 

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5f. WORK UNIT NUMBER

WBS 599489.02.07.03.03.13.01 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

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E-18611 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

This report discusses the computations of a set of shock wave/turbulent boundary layer interaction (SWTBLI) test cases using the Wind-US 

code, as part of the 2010 American Institute of Aeronautics and Astronautics (AIAA) shock/ boundary layer interaction workshop. The 

experiments involve supersonic flows in wind tunnels with a shock generator that directs an oblique shock wave toward the boundary layer 

along one of the walls of the wind tunnel. The Wind-US calculations utilized structured grid computations performed in Reynolds-averaged 

Navier-Stokes mode. Four turbulence models were investigated: the Spalart-Allmaras one-equation model, the Menter Baseline and Shear 

Stress Transport k-ω two-equation models, and an explicit algebraic stress k-ω formulation. Effects of grid resolution and upwinding 

scheme were also considered. The results from the CFD calculations are compared to particle image velocimetry (PIV) data from the 

experiments. As expected, turbulence model effects dominated the accuracy of the solutions with upwinding scheme selection indicating 

minimal effects. 

15. SUBJECT TERMS

Turbulence; Boundary-layer; Shock-wave; Computational fluid dynamics 

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