David J. Friedlander

Glenn Research Center, Cleveland, Ohio

Understanding the Flow Physics of

Shock Boundary-Layer Interactions

Using CFD and Numerical Analyses

NASA/TM—2013-218081

October 2013
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David J. Friedlander

Glenn Research Center, Cleveland, Ohio

Understanding the Flow Physics of

Shock Boundary-Layer Interactions

Using CFD and Numerical Analyses

NASA/TM—2013-218081

October 2013

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

The author would like to acknowledge the support from the Air Force Research Laboratory, Air Vehicle Directorate, AFRL/RB 

and the interaction with the U.S. Air Force Collaborative Center for Aeronautical Sciences as well as the NASA Fundamental 

Aeronautics Program for supporting this research. The author would also like to thank NASA’s High End Computing Program 

(HECC) for providing super-computing resources that were vital in this endeavor. Also appreciated is the base grid (of which all 

grids used in this thesis were derived from) and grid modifi cation codes that were developed by Marshall Galbraith and guidance 

from Daniel Galbraith. A special thanks goes to Dr. Mark Turner, Dr. Paul Orkwis, and Dr. Nicholas Georgiadis for all their 

guidance and support with this thesis work.

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

Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by technical management. 
Abstract

Mixed compression inlets are common among supersonic propulsion systems. However they are

susceptible to total pressure losses due to shock/boundary-layer interactions (SBLI's). Because of their

importance, a workshop was held at the 48th American Institute of Aeronautics and Astronautics (AIAA)

Aerospace Sciences Meeting in 2010 to gauge current computational uid dynamics (CFD) tools abilities

to predict SBLI's. One conclusion from the workshop was that the CFD consistently failed to agree with

the experimental data. This thesis presents additional CFD and numerical analyses that were performed

on one of the congurations presented at the workshop.

The additional analyses focused on the University of Michigan's Mach 2.75 Glass Tunnel with a semispanning 7.75 degree wedge while exploring key physics pertinent to modeling SBLI's. These include

thermodynamic and viscous boundary conditions as well as turbulence modeling. Most of the analyses

were 3D CFD simulations using the OVERFLOW ow solver. However, a quasi-1D MATLAB code

was developed to interface with the National Institute of Standards and Technology (NIST) Reference

Fluid Thermodynamic and Transport Properties Database (REFPROP) code to explore perfect verses

non-ideal air as this feature is not supported within OVERFLOW. Further, a grid resolution study was

performed on the 3D 56 million grid point grid which was shown to be nearly grid independent. Because

the experimental data was obtained via particle image velocimetry (PIV), a fundamental study pertaining

to the eects of PIV on post-processing data was also explored.

Results from the CFD simulations showed an improvement in agreement with experimental data with

certain settings. This is especially true of the v velocity eld within the streamwise data plane. Key

contributions to the improvement include utilizing a laminar zone upstream of the wedge (the boundarylayer was considered transitional downstream of the nozzle throat) and the necessity of mimicking PIV

particle lag for comparisons. It was also shown that the corner ow separations are highly sensitive to

the turbulence model. However, the center ow region, where the experimental data was taken, was not

as sensitive to the turbulence model. Results from the quasi-1D simulation showed that there was little

dierence between perfect and non-ideal air for the conguration presented.

Understanding the Flow Physics of Shock Boundary-Layer 

Interactions Using CFD and Numerical Analyses 

David J. Friedlander 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

NASA/TM—2013-218081 iii

Table of Contents

Abstract ii

List of Figures viii

List of Tables xiii

Nomenclature xiv

1 Background 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Experimental Research Literature Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Computational Research Literature Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Geometry and Numerical Modeling 10

2.1 Geometry and Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 Case Overviews 15

3.1 CFD Cases with OVERFLOW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 PIV Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

4 Flat Plate 20

4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5 Quasi-1D Code 24

5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

5.2 Calorically Perfect Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

5.3 Non-Ideal Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

5.4 Quasi-1D Exploration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

6 Grid Resolution Study 33

NASA/TM—2013-218081 v

i
7 Results 37

7.1 Standard Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

7.2 Particle Lag Eects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

7.3 Isothermal Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

7.4 Trip Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

7.5 Turbulence Modeling Eects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

7.6 Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

7.7 Blockage Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

8 Conclusions/Future Work 56

References 58

A Velocity Contours 64

B Velocity Proles 68

B.1 Standard Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

B.2 Combined Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

B.3 Modied Geometry, Isothermal, and Trip Cases . . . . . . . . . . . . . . . . . . . . . . . . . . 74

B.4 TKE and MUT Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

B.5 Standard Case with Various Turbulence Models . . . . . . . . . . . . . . . . . . . . . . . . . . 80

C Combined Case with Various Turbulence Models 83

D Shock Angle Calculation 88

E Simulation Checklists 91

E.1 Initial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

E.2 Standard Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

E.3 Isothermal Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

E.4 Modied Geometry Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

E.5 All-Laminar Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

E.6 Trip Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

E.7 Combined Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

E.8 TKE Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

E.9 MUT Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

NASA/TM—2013-218081 vi
E.10 Standard Case with SST-GY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

E.11 Standard Case with BSL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

E.12 Flat Plate with SST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

E.13 Flat Plate with K-Omega . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

E.14 Flat Plate with SST-GY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

E.15 Flat Plate with BSL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

NASA/TM—2013-218081 vii
List of Figures

1 A supersonic mixed compression inlet (used with permission from Pitt Ford and Babinsky [1]). 1

2 Sketch of the oblique shock / boundary-layer interaction (used with permission from Touber

and Sandham [2]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

3 Iso-surfaces of density gradients in the downstream direction around the wedge, colored by

the derivative of the density gradients in the downstream direction (from Galbraith [3]). . . . 2

4 Datum groove, 8mm wide groove and variations (from Holden and Babinsky [4]). . . . . . . . 3

5 Three-dimensional bumps (from Holden and Babinsky [4]). . . . . . . . . . . . . . . . . . . . 4

6 Velocity proles 94 mm downstream of micro-ramp controlled SBLI, h = 3 mm (used with

permission from Pitt Ford and Babinsky [1]). . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

7 Mach number contours of the converged mesoap array simulations, (used with permission

from Ghosh et al. [5]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

8 Contours of the skin friction coecient of a at plate SBLI with time averaged (top) and

instantaneous (bottom) snapshots (from Morgan et al. [6]). . . . . . . . . . . . . . . . . . . . 6

9 Comparison of RANS and LES results on a square duct (from Medic et al. [7]). . . . . . . . . 6

10 Congurations run with DNS, LES, and RANS (used with permission from Knight et al. [8]). 7

11 Flow pattern sketches for the experiment (left) and DNS (right) for a 24 degree compression

corner (from Wu et al. [9]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

12 Comparison of the size of the separation bubble with (new) and without (old) a dissipation

limiter (from Wu and Martin [10]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

13 Skin friction distribution (RANS models) for a 28 degree compression corner at Mach 5 (used

with permission from Edwards et al. [11]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

14 Cut-away view of the University of Michigan Glass Tunnel (from Lapsa [12]). . . . . . . . . . 10

15 Schematic of the University of Michigan Glass Tunnel with upstream ow straightener and

seeder (from Lapsa [12]). Note units are in inches. . . . . . . . . . . . . . . . . . . . . . . . . 11

16 7.75 degree wedge geometry. Dimensions courtesy of Lapsa [12]. . . . . . . . . . . . . . . . . . 11

17 Grid throat region packing with original (left) and nal (right). . . . . . . . . . . . . . . . . . 12

18 Side view of the grid representing the tunnel and 7.75 degree wedge with center-span wedge

and throat inserts shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

19 Sample modied nozzle contour. Note the dierence between the old and new throat heights

is exaggerated compared to what was actually used. . . . . . . . . . . . . . . . . . . . . . . . 16

20 Momentum thickness Reynolds number at the bottom wall (half-span) for the laminar case. . 17

NASA/TM—2013-218081 viii
21 Momentum thickness Reynolds number at the bottom wall, center-span. . . . . . . . . . . . . 17

22 Measured particle response through an oblique shock (from Lapsa [12]). The velocity component normal to the shock, un, is normalized by the pre-shock (un1) and post-shock (un2)

velocities and shown as a function of the shock-normal direction, n. An exponential t to the

data reveals the particle relaxation time, τ p = 5.5 μs. . . . . . . . . . . . . . . . . . . . . . . . 19

23 Flat plate 2D grid and boundary conditions [13]. . . . . . . . . . . . . . . . . . . . . . . . . . 20

24 Skin friction coecient proles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

25 u

+ verses y+ for the various turbulence models at Rex = 4.2E6. . . . . . . . . . . . . . . . . 22

26 Normalized turbulent parameters for various turbulence models at Rex = 4.2E6 . . . . . . . 23

27 Normalized turbulent parameters at various freestream turbulent viscosities at Rex = 4.2E6 . 23

28 Sample enthalpy verses entropy diagram for calculating across an oblique shock for a non-ideal

gas. 1: total conditions at Station 1, 1S: static conditions at Station 1, 2S: static conditions

at Station 2, 2: total conditions at Station 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

29 Oblique shock notation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

30 Percentage dierences between non-ideal and perfect air for various parameters. . . . . . . . . 32

31 Percentage dierences of the shock angle between non-ideal and perfect air for varying wedge

angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

32 Streamwise cross-sections at center-span for the various grid levels. . . . . . . . . . . . . . . . 33

33 L2 residuals for the Standard case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

34 u velocity proles within the streamwise plane. . . . . . . . . . . . . . . . . . . . . . . . . . . 35

35 Data plane location in reference to the grid. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

36 u velocity (left) and v velocity (right) streamwise contours for the experiment (top) and

Standard case (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

37 Bottom wall separation underneath the wedge for the Standard case. . . . . . . . . . . . . . . 38

38 v velocity streamwise contours for the experiment (top), short lag (middle-top), medium lag

(middle-bottom), and long lag (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

39 Select velocity proles at the most-upstream axial location (x = 18.191 mm) for the Standard

case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

40 Select velocity proles at the rst intersecting spanwise plane (x = 20.76 mm) for the Standard

case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

41 Select velocity proles at the most-upstream axial location (x = 18.191 mm) for the Combined

case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

NASA/TM—2013-218081 ix
42 Select velocity proles at the rst intersecting spanwise plane (x = 20.76 mm) for the Combined case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

43 Freestream thermal boundary-layer at x = −63.9 mm. Temperature cut o is at 99%

freestream (121.2 K). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

44 Temperature proles at the most-upstream axial location (x = 18.191 mm). . . . . . . . . . . 43

45 Total temperature centerspan prole at the bottom wall with the following stations marked:

1. Throat, 2. Trip location, 3. Start of the tunnel straight section, 4. Wedge leading edge, 5.

Wedge trailing edge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

46 Select velocity proles at the most-upstream axial location (x = 18.191 mm). . . . . . . . . . 44

47 u velocity dierence contours. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

48 v velocity dierence contours. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

49 Static temperature dierence contours. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

50 Select velocity proles at the most-upstream axial location (x = 18.191 mm). . . . . . . . . . 45

51 Select velocity proles at the rst intersecting spanwise plane (x = 20.76 mm). . . . . . . . . 46

52 Turbulent kinetic energy proles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

53 Select velocity proles at the most-upstream axial location (x = 18.191 mm). . . . . . . . . . 47

54 Select velocity proles at the rst intersecting spanwise plane (x = 20.76 mm). . . . . . . . . 48

55 Turbulent kinetic energy proles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

56 Velocity proles at the most-upstream axial location (x = 18.191 mm) for various turbulence

models, Standard Case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

57 Velocity proles at the rst intersecting spanwise plane (x = 20.76 mm) for various turbulence

models, Standard Case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

58 Bottom wall separation underneath the wedge for the Standard case with various turbulence

models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

59 Point locations within the centerspan plane. Mach number contour of the Standard case CFD

solution is shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

60 Shock angle verses Mach number. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

61 Bottom wall separation underneath the wedge for the Isothermal and Modied Geometry cases. 54

62 Bottom wall separation underneath the wedge for the Trip and Combined cases. . . . . . . . 55

A.1 u velocity contours for the Standard (left) and Combined (right) cases with lag. . . . . . . . . 64

A.2 u (left) and v (right) velocity contours for Isothermal and Modied Geometry cases. . . . . . 65

A.3 u (left) and v (right) velocity contours for Trip and Combined cases. . . . . . . . . . . . . . . 65

A.4 u (left) and v (right) velocity contours for TKE and MUT cases. . . . . . . . . . . . . . . . . 66

NASA/TM—2013-218081 x
A.5 u (left) and v (right) velocity contours for the Standard case with SST-GY and BSL. . . . . . 66

A.6 u (left) and v (right) velocity contours for the Combined case with SST-GY and BSL. . . . . 67

B.1 Velocity proles at x = 26.76 mm, Standard case. . . . . . . . . . . . . . . . . . . . . . . . . . 68

B.2 Velocity proles at x = 30.76 mm, Standard case. . . . . . . . . . . . . . . . . . . . . . . . . . 68

B.3 Velocity proles at x = 34.76 mm, Standard case. . . . . . . . . . . . . . . . . . . . . . . . . . 69

B.4 Velocity proles at x = 38.76 mm, Standard case. . . . . . . . . . . . . . . . . . . . . . . . . . 69

B.5 Velocity proles at x = 41.76 mm, Standard case. . . . . . . . . . . . . . . . . . . . . . . . . . 70

B.6 Velocity proles at x = 53.76 mm, Standard case. . . . . . . . . . . . . . . . . . . . . . . . . . 70

B.7 Velocity proles at x = 26.76 mm, Combined case. . . . . . . . . . . . . . . . . . . . . . . . . 71

B.8 Velocity proles at x = 30.76 mm, Combined case. . . . . . . . . . . . . . . . . . . . . . . . . 71

B.9 Velocity proles at x = 34.76 mm, Combined case. . . . . . . . . . . . . . . . . . . . . . . . . 72

B.10 Velocity proles at x = 38.76 mm, Combined case. . . . . . . . . . . . . . . . . . . . . . . . . 72

B.11 Velocity proles at x = 41.76 mm, Combined case. . . . . . . . . . . . . . . . . . . . . . . . . 73

B.12 Velocity proles at x = 53.76 mm, Combined case. . . . . . . . . . . . . . . . . . . . . . . . . 73

B.13 Velocity proles at x = 26.76 mm, various cases. . . . . . . . . . . . . . . . . . . . . . . . . . 74

B.14 Velocity proles at x = 30.76 mm, various cases. . . . . . . . . . . . . . . . . . . . . . . . . . 74

B.15 Velocity proles at x = 34.76 mm, various cases. . . . . . . . . . . . . . . . . . . . . . . . . . 75

B.16 Velocity proles at x = 38.76 mm, various cases. . . . . . . . . . . . . . . . . . . . . . . . . . 75

B.17 Velocity proles at x = 41.76 mm, various cases. . . . . . . . . . . . . . . . . . . . . . . . . . 76

B.18 Velocity proles at x = 53.76 mm, various cases. . . . . . . . . . . . . . . . . . . . . . . . . . 76

B.19 Velocity proles at x = 26.76 mm, TKE and MUT cases. . . . . . . . . . . . . . . . . . . . . . 77

B.20 Velocity proles at x = 30.76 mm, TKE and MUT cases. . . . . . . . . . . . . . . . . . . . . . 77

B.21 Velocity proles at x = 34.76 mm, TKE and MUT cases. . . . . . . . . . . . . . . . . . . . . . 78

B.22 Velocity proles at x = 38.76 mm, TKE and MUT cases. . . . . . . . . . . . . . . . . . . . . . 78

B.23 Velocity proles at x = 41.76 mm, TKE and MUT cases. . . . . . . . . . . . . . . . . . . . . . 79

B.24 Velocity proles at x = 53.76 mm, TKE and MUT cases. . . . . . . . . . . . . . . . . . . . . . 79

B.25 Velocity proles at x = 26.76 mm, Standard case with various turbulence models. . . . . . . . 80

B.26 Velocity proles at x = 30.76 mm, Standard case with various turbulence models. . . . . . . . 80

B.27 Velocity proles at x = 34.76 mm, Standard case with various turbulence models. . . . . . . . 81

B.28 Velocity proles at x = 38.76 mm, Standard case with various turbulence models. . . . . . . . 81

B.29 Velocity proles at x = 41.76 mm, Standard case with various turbulence models. . . . . . . . 82

B.30 Velocity proles at x = 53.76 mm, Standard case with various turbulence models. . . . . . . . 82

C.1 Velocity proles at x = 18.191 mm, Combined case with various turbulence models. . . . . . 83

NASA/TM—2013-218081 xi
C.2 Velocity proles at x = 20.76 mm, Combined case with various turbulence models. . . . . . . 84

C.3 Velocity proles at x = 26.76 mm, Combined case with various turbulence models. . . . . . . 84

C.4 Velocity proles at x = 30.76 mm, Combined case with various turbulence models. . . . . . . 85

C.5 Velocity proles at x = 34.76 mm, Combined case with various turbulence models. . . . . . . 85

C.6 Velocity proles at x = 38.76 mm, Combined case with various turbulence models. . . . . . . 86

C.7 Velocity proles at x = 41.76 mm, Combined case with various turbulence models. . . . . . . 86

C.8 Velocity proles at x = 53.76 mm, Combined case with various turbulence models. . . . . . . 87

C.9 Bottom wall separation underneath the wedge for the Combined case with various turbulence

models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

D.1 Shock angle diagram/nomenclature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

D.2 Velocity proles for determining shock line end location (Standard case shown). . . . . . . . . 89

D.3 Arc length prole for determining shock line end location (Standard case shown). . . . . . . . 89

D.4 Derivative proles for determining shock line end location (Standard case shown). . . . . . . 90

NASA/TM—2013-218081 xii
List of Tables

1 Summary of CFD Cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2 Various ow parameters used to determine grid convergence. . . . . . . . . . . . . . . . . . . 35

3 Mass ow rates (kg/s) used to determine grid convergence. . . . . . . . . . . . . . . . . . . . 35

4 Coordinates for grid resolution study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5 Workshop error metric comparisons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6 u velocity and velocity dierences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

7 Shock angle comparisons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

NASA/TM—2013-218081 xiii
Nomenclature

Acronyms

AGS Abu-Ghannam and Shaw

AIAA American Institute of Aeronautics and Astronautics

CFD Computational Fluid Dynamics

DNS Direct Numerical Simulation

LES Large-Eddy Simulation

NIST National Institute of Standards and Technology

PIV Particle Image Velocimetry

RANS Reynolds-Averaged Navier-Stokes

SBLI Shock Boundary Layer Interaction

SST Shear Stress Transport

UM University of Michigan

VG Vortex Generator

a speed of sound

A/A∗ geometric throat area ratio

b∗ throat blockage parameter

C constant

cf skin friction coecient

cp specic heat at constant pressure

E (f) error metric of f

e (f)nlocal error of f

f function/lookup

h enthalpy

NASA/TM—2013-218081 xiv
i, n index

k turbulent kinetic energy

L length scale

l arc length

M Mach number

m power coecient

m ̇ ∗ geometric throat mass ow rate

p pressure

R specic gas constant

rc thermal recovery factor

Re Reynolds number

s entropy

T temperature

u, v streamwise and transverse velocity components

V velocity

x, y, z cartesian coordinates

x ̃, y ̃ adjusted cartesion coordinates

y

+, u+ wall coordinates

Greek Symbols

β shock angle

γ ratio of specic heats

θ turning/wedge angle

κ Von Karmin constant

μ dynamic viscocity

NASA/TM—2013-218081 xv
ρ density

τ time constant

Subscripts

1 upstream

2 downstream

∞, Inf freestream condition

n normal

ref reference condition

∗ sonic condition

T turbulent

t total condition

NASA/TM—2013-218081 xvi
1 Background

1.1 Introduction

Mixed compression inlets are often found in supersonic aircraft propulsion systems with a typical mixed

compression inlet shown in Fig. 1. These inlets are susceptible to shock boundary-layer interactions (SBLI)

with a typical SBLI shown in Fig. 2. As one can see, SBLI's are not trivial in nature and beyond the

situation shown in Fig. 2, are very three dimensional ows, shown in Fig. 3. SBLI's are a concern for

supersonic aircraft propulsion system designs as the separation induced by the shock interacting with the

turbulent boundary-layer results in a total pressure loss that is not accounted for in inviscid theory. As mixed

compression inlets become more at the forefront of aviation technology, it becomes crucial to understand

SBLI's and how they aect propulsion system performance. This can be achieved in several ways, including

fundamental and ow control experiments as well as computational work, all of which will be discussed

further in the next sections.

Figure 1: A supersonic mixed compression inlet (used with permission from Pitt Ford and Babinsky [1]).

Figure 2: Sketch of the oblique shock / boundary-layer interaction (used with permission from Touber and

Sandham [2]).

NASA/TM—2013-218081 1
Figure 3: Iso-surfaces of density gradients in the downstream direction around the wedge, colored by the

derivative of the density gradients in the downstream direction (from Galbraith [3]).

In order to determine how eectively computational uid dynamics (CFD) tools can currently predict SBLI's, a workshop was held at the 48th American Institute of Aeronautics and Astronautics (AIAA)

Aerospace Sciences Meeting featuring an array of CFD analyzes [14, 15, 16] with experimental data sets

provided by the Institut Universitaire des Systemes Thermiques Industriels [17] and the University of Michigan (UM) [18]. The CFD results from the workshop are summarized in DeBonis et al. [19] with workshop

conclusive remarks documented in works by Benek et al. [20, 21] as well as Hirsch [22]. One key conclusion

of the workshop was that the CFD analyses failed to match experimental data. Because of the complex

nature of SBLI's, it is of great interest within the aero-propulsion and CFD communities to see if there are

ways to improve CFD methods or more eectively use existing methods. This will enable better prediction

of SBLI's as well as aid in future inlet design.

Thus further CFD analyses were performed at the University of Cincinnati's Gas Turbine Simulation

Laboratory as a compliment to work done by Galbraith [3, 23] in hopes to better understand the computational factors involved in calculating SBLI's as well as to explore alternatives to the error metric used

in the workshop. One of the data sets provided to the workshop by UM was their Glass Tunnel with a

semi-spanning 7.75 degree wedge at a freestream Mach number of 2.75. The UM experimental data was

obtained using stereo particle image velocimetry (PIV) techniques [18]. The CFD analyses presented here

focus on that particular UM case while exploring various key physics associated with SBLI's, including,

but not limited to, heat transfer boundary conditions, geometry sensitivities, laminar verses turbulent ow

assumptions, and turbulence modeling. Special attention was paid to the u and v velocity components,

NASA/TM—2013-218081 2
particularly around the oblique shock o the leading edge of the wedge. This is because it was felt that the

CFD and post-processing calculations from the workshop missed the peak u velocity as well as the location

of the shock as dened by the v velocity prole. If the upstream proles are not in agreement, it is fair to

say that the solutions downstream should not agree. Aside from the CFD cases, a preliminary exploration

into the eects on PIV obtained data is also presented.

1.2 Experimental Research Literature Survey

The workshop was not the rst and certainly not the last time SBLI's have been examined both experimentally and numerically. Experiments by Holden and Babinsky [4] attempted SBLI ow control via a series of

streamwise grooves and bumps, shown in Figs. 4 and 5, with hopes of smearing the shock footprint. They

showed that the ow elds inherent with SBLI's are highly sensitive to geometry deviations, such as the slot

and bump geometries, or for that matter any foreign debris or geometry imperfections. Another experiment

by Holden and Babinsky [24] explored the use of vortex generators (VG's) for SBLI ow control. Two types

were tested: wedge-shaped, more commonly known as micro-ramps, and counter rotating vanes. It was

found that the use of the VG's greatly reduced the separation region of the SBLI interaction region, with

the vane type VG's going as far as to eliminate the separation region completely. Experiments by Pitt Ford

and Babinsky [1] as well as by Lapsa [12] also explored the eects of micro-ramps on SBLI ow elds. Pitt

Ford and Babinsky showed that micro-ramps located upstream of the interaction region can break up the

separation bubble but not completely eliminate it while increasing downstream velocities, shown in Fig. 6.

Lapsa showed that the use of inverse micro-ramps can decrease the displacement thickness and thus allow

for less separation around the interaction region.

Figure 4: Datum groove, 8mm wide groove and variations (from Holden and Babinsky [4]).

NASA/TM—2013-218081 3
Figure 5: Three-dimensional bumps (from Holden and Babinsky [4]).

Figure 6: Velocity proles 94 mm downstream of micro-ramp controlled SBLI, h = 3 mm (used with permission from Pitt Ford and Babinsky [1]).

While the above mentioned experiments focused mostly on ow control, more fundamental experiments

have been performed in order to understand the nature of SBLI's. An experiment performed by Babinsky

et al. [25] explored the importance of corner ows in relation to SBLI's. They showed that the corner ow

separations have a coupled eect with the separation bubble of the interaction region of SBLI's. Thus by

decreasing the corner ow separation it was shown that the interaction region separation would be reduced

and approach a 2D nature. This coupling nature was also shown in a prior experiment by Titchener et al.

[26].

1.3 Computational Research Literature Search

Over the years there have been plenty of numerical simulations exploring all facets of SBLI's: from ow

control to numerical modeling eorts. For ow control, Ghosh et al. [5] investigated the use of aeroelastic

mesoaps via two and three dimensional simulations, shown in Fig. 7. The simulations utilized both

NASA/TM—2013-218081 4
Reynolds-Averaged Navier-Stokes (RANS) and Large-Eddy/Reynolds-Averaged Navier-Stokes (LES/RANS)

means for solving the ow equations. The simulations showed that the use of mesoaps for ow control

resulted in a slightly larger interaction region compared to the non-controlled case.

Figure 7: Mach number contours of the converged mesoap array simulations, (used with permission from

Ghosh et al. [5]).

Morgan et al. [6] performed LES simulations with a at plate geometry to explore SBLI's. An instantaneous as well as time-averaged snapshot of the skin friction coecient within the interaction region is shown

in Fig. 8. It can be seen that the time-averaged snapshot greatly smooths out the chaotic nature of the

SBLI, including the separation region. In fact, the instantaneous snapshot shows that the separation region

consists of many separation bubbles and not just a single separation zone as shown in the time-averaged snap

shot. This is important as steady RANS simulations only have the capability to reproduce time-averaged

behavior unlike LES instantaneous solutions. The comparison between LES and RANS solutions were further explored by Medic et al. [7] using a simple square duct with results shown in Fig. 9. It can be seen that

the RANS solution over predicts the boundary layer growth at the duct corners relative to the LES solution.

This over prediction can have a tremendous eect in SBLI simulations, especially when using a tunnel-like

geometry, due to the coupling eects between the corner ows and interaction region separation discussed

earlier. Other LES solution eorts have been conducted by Hunt and Nixon [27], based on experimental

data obtained by Dolling and Murphy [28], as well as by Jamalamadaka et al. [29].

NASA/TM—2013-218081 5
Figure 8: Contours of the skin friction coecient of a at plate SBLI with time averaged (top) and instantaneous (bottom) snapshots (from Morgan et al. [6]).

Figure 9: Comparison of RANS and LES results on a square duct (from Medic et al. [7]).

Further, a series of simulations were performed by Knight et al. [8] exploring SBLI's. Five congurations

were run, shown in Fig. 10, and utilized Direct Numerical Simulations (DNS), LES, and RANS. There were

a multitude of lessons learned from these simulations, especially regarding the RANS simulations. With

RANS, the case of the 3D single n correctly predicted the secondary separation region with use of the

Wilcox-Durbin model. However, the RANS simulation of the 3D double n failed to accurately predict

the surface heat transfer using the linear and weakly non-linear Wilcox-based models. This is common for

RANS simulations of SBLI ows, as also shown by simulations conducted by Knight and Degrez [30]. Other

overviews of SBLI simulations involving DNS, LES, and LES/RANS methods can be found in works by

NASA/TM—2013-218081 6
Zheltovodov [31] and Edwards [32], the latter of which touches briey on experiments exploring the eects

of heat transfer on SBLI's by Zheltovodov et al. [33, 34].

Figure 10: Congurations run with DNS, LES, and RANS (used with permission from Knight et al. [8]).

Wu et al. [9, 35, 36, 37, 10, 38, 39] have performed a series of DNS simulations on a 24 degree compression

ramp with experimental data provided by Bookey et al. [40]. Originally they showed that the DNS simulations under predicted the separation region within the SBLI interaction, as shown in Fig. 11. Numerical

code bugs as well as the incoming conditions to the corner were eliminated as factors of the discrepancy

due to the agreement between the DNS simulation and the experimental data upstream of the compression

corner. In turn, they determined that numerical modeling of SBLI's is sensitive to the numerical dissipation

and suggested the use of a limiter on the dissipation schemes. Rerunning the DNS simulations with the

limiter showed great improvements in predicting the size of the separation region, shown in Fig. 12.

Continuing with the compression corner theme, Edwards et al. [11] used LES/RANS to explore a 28

degree compression corner ow interaction. Menter's Shear Stress Transport (SST) [41] turbulence model

was used for the RANS portion. Although the simulations captured the shock behavior well, it was noted

that there was a great dependence on the shear stress transport limiter within the SST turbulence model,

shown in Fig. 13. Further analyses of the SST and other k-omega based turbulence models as related to

SBLI's have been performed by Georgiadis and Yoder [42] as well as Tan and Jin [43]. One draw back

to LES/RANS method used was the need to calibrate the blending function constant per case. This was

NASA/TM—2013-218081 7
eliminated by Giesking et al. [44, 45] by using an estimate of the outer-layer length scale based on the resolved

turbulent kinetic energy, ensemble-averaged modeled turbulence kinetic energy, and ensemble-averaged and

time-resolved turbulence frequencies. This estimated length scale, in conjunction with the inner-layer length

scale, was then used to determine to blending function model constant.

Figure 11: Flow pattern sketches for the experiment (left) and DNS (right) for a 24 degree compression

corner (from Wu et al. [9]).

Figure 12: Comparison of the size of the separation bubble with (new) and without (old) a dissipation limiter

(from Wu and Martin [10]).

NASA/TM—2013-218081 8
Figure 13: Skin friction distribution (RANS models) for a 28 degree compression corner at Mach 5 (used

with permission from Edwards et al. [11]).

NASA/TM—2013-218081 9
2 Geometry and Numerical Modeling

2.1 Geometry and Mesh

The UM Glass Tunnel [12] is a suck down tunnel shown in Figs. 14 and 15 with the oblique shock generating

wedge shown in Fig. 16. Although the upstream converging-diverging nozzle is interchangeable, only runs

with the Mach 2.75 nozzle are explored in this thesis. The wedge is centered about the center-span of the

tunnel and the tunnel sits in a room controlled to a temperature of 295.7 K ±1 K [46]. At the freestream

velocity of the tunnel, the static temperature is about 118 K. The top and bottom walls are made of aluminum

while the side walls and bottom window are composed of glass. The test section was designed to be 2.25 x

2.75 with a throat cross-section of 2.25 x 0.742. However, the current as installed dimensions deviated

from this with a test section and throat cross-section of 2.25 x 2.72 and 2.25 x 0.725, respectively [46].

These measurements were taken well after the experimental data had been collected for the workshop and

the tunnel has been taken apart and reassembled since then. As such, it only oers an approximation of

what the dimensions might have been for those runs.

Figure 14: Cut-away view of the University of Michigan Glass Tunnel (from Lapsa [12]).

NASA/TM—2013-218081 10
Figure 15: Schematic of the University of Michigan Glass Tunnel with upstream ow straightener and seeder

(from Lapsa [12]). Note units are in inches.

Figure 16: 7.75 degree wedge geometry. Dimensions courtesy of Lapsa [12].

The tunnel, along with the wedge, was modeled by a modied version of a 3D over-set grid by Marshall

Galbraith. The original grid, containing 53 million grid points divided into 15 zones, paid particular attention

to the packing along the walls and around the oblique shock location. However, it was felt that the throat

region could benet from a more dense axial clustering. Thus an additional 50 axial points were inserted to

dene the throat contour, shown in Fig. 17. The nal grid of 56 million grid points is shown in Fig. 18. Like

the original grid, the nal grid was packed very tightly to the wall such that y

+ = 0.25 at the rst point o

the wall, based on fully expanded tunnel conditions at Mach 2.75.

The grid coordinate system uses a left-handed coordinate system non-dimensionalized by the tunnel

height of 2.75 in. However, the coordinate system used for data comparison is consistent with the one used

in the workshop, which was dimensionalized in mm with the origin at the strut leading edge, bottom wall,

NASA/TM—2013-218081 11
and center-span. To convert from the grid coordinate system to the data comparison coordinate system:

x = 25.4 (2.75xgrid − 38.265) (1)

y = (25.4 × 2.75) zgrid (2)

z = 25.4 (2.75ygrid − 1.125) (3)

Note that the grid coordinate system has the z-coordinate and y-coordinate ipped relative to the data

coordinate system. It should also be noted that the data coordinate system is slightly dierent than the

one used by Lapsa [12], in which the axial origin was at the inviscid shock impingement location. Both are

dierent than the coordinate system used by Eagle et al. [46] for the planned second SBLI Workshop, which

is a left-handed coordinate system with the origin located at the wedge leading edge, bottom wall, right wall

(looking downstream).

Figure 17: Grid throat region packing with original (left) and nal (right).

Figure 18: Side view of the grid representing the tunnel and 7.75 degree wedge with center-span wedge and

throat inserts shown.

NASA/TM—2013-218081 12
2.2 Solver

OVERFLOW [47, 48], a RANS ow solver for structured over-set grids, was chosen as the CFD solver for

the SBLI analyses. Version 2.2e was used on a cluster of 20 Quad-Core Xeon X5570 processors (NASA

Pleiades-Nehalem). Runtime for each analysis took approximately three days on the 80 processors. For

solving the Navier-Stokes equations, spatial integration used the HLLC scheme [49] with the Koren limiter

[50] to third-order accuracy while temporal integration used SSOR [51] to rst-order accuracy. All analyses

utilized the SST turbulence model with all zones considered turbulent, unless otherwise specied.

OVERFLOW requires a set of reference conditions to non-dimensionalize the input parameters and set

the freestream conditions. Because OVERFLOW uses the freestream conditions to initialize the ow eld

when not given an initial solution, Mach 2.75 conditions were chosen for the reference state with total

quantities equaling the room statics due to the vacuum driven nature of the tunnel. Using 1D perfect gas

equations yields the following reference values:

Tt = 295.7 K (4)

pt = 98 kPa (5)

Mref = 2.75 (6)

Lref = 0.06985 m (2.75 in) (7)

γ = 1.4 (8)

R = 287 J/ (kg  K) (9)

T∞ = Tt



1 +

γ − 1

2

M2

ref−1

= 117.69 K (10)

p∞ = pt



1 +

γ − 1

2

M2

ref−

γ

γ−1

= 3.898 kPa (11)

NASA/TM—2013-218081 13
a∞ =

p

γRT∞ = 217.46 m/s (12)

V∞ = Mref a∞ = 598.01 m/s (13)

ρ∞ =

p∞

RT∞

= 0.1154 kg/m3(14)

μ∞ = 1.716x10−5



T∞

491.6

1.5 

491.6 + 198.6

T∞ + 198.6



= 8.163 × 10−6kg/(m  s) (15)

ReL =

ρ∞V∞Lref

μ∞

= 592, 876 (16)

Note the test section height was chosen as the reference length due to the grid being non-dimensionalized

by this parameter and μ∞ was calculated using Sutherland's Law. Specics on the direct OVERFLOW

input variables and redimensionlizing scheme are outlined in reference [3].

NASA/TM—2013-218081 14
3 Case Overviews

3.1 CFD Cases with OVERFLOW

To explore the key physics mentioned earlier, seven cases were run as outlined in Table 1. A baseline case

(denoted as Standard) was rst run with various parameters set to reect prior CFD analyzes. To explore

heat transfer boundary conditions, a case was run such that the top and bottom walls (along with the wedge)

were isothermal while all other surfaces (including the bottom window) remained adiabatic. The window was

approximated from 45 mm to 140 mm axially and -16.575 mm to 14.425 mm spanwise [46]. The isothermal

surfaces were set to the room temperature of 295.7 K. Although the actual temperature of the aluminum

varies due to heat transfer, assuming it is isothermal at the room temperature is likely to be better than

considering it to be adiabatic.

To explore geometry sensitivities, a case was run with the grid modied to reect the as-installed geometry

with greatest measured tolerances accounted for. The grid was modied by raising the bottom wall to achieve

the desired test-section height and redening the nozzle curve to obtain the desired throat height. The

nozzle curve modication was achieved by dividing the contour into two sections and scaling accordingly.

The upstream section was dened from the trailing edge of the inlet straight section to the geometric throat

while the downstream section was dened from the geometric throat to the leading edge of the tunnel straight

section. The new upstream contour section was then dened as:

ynew = (ythroat,new − ythroat,old)



x1 − x

x1 − xthroat m

+ yold (17)

where

m = 0.5 + 1.5



xthroat − x

xthroat − x1



(18)

Note the subscript 1 denotes the inlet trailing edge match point. Likewise, the downstream contour section

was dened as:

ynew = (ythroat,new − ythroat,old)



x2 − x

x2 − xthroat m

+ yold (19)

where

m = 1 + 2 

xthroat − x

xthroat − x2



(20)

Note the subscript 2 denotes the tunnel straight section leading edge match point. A sample modied nozzle

NASA/TM—2013-218081 15
contour with an exaggerated throat area based on this scheme is shown in Fig. 19.

Figure 19: Sample modied nozzle contour. Note the dierence between the old and new throat heights is

exaggerated compared to what was actually used.

To explore laminar verses turbulent ow, two cases were run. A base case was run with laminar ow from

the nozzle plenum inlet to the leading edge of the wedge in order to establish a trip location for the second

case. In OVERFLOW, the eect of a boundary-layer trip was simulated by forcing upstream zones to be

laminar. OVERFLOW handles laminar zones by zeroing out the production terms of the turbulence model in

use [47]. At the desired trip location, or transition point, the production terms within the turbulence model

are activated for all zones downstream of this point. As a result, eddy viscosity is calculated, and added to

the laminar viscosity in the transport equations. Figure 20 shows the momentum thickness Reynolds number

contour for the bottom wall (half-span) while Fig. 21 shows the corresponding values at the bottom wall

center-span. The trip location was dened where the momentum thickness Reynolds number approximately

equaled 400. This value is suggested by Abu-Ghannam and Shaw (AGS) [52] as the start of transition for

turbulence intensities of 1.5%; however several values of momentum thickness Reynolds number could have

been chosen to dene the trip location. Using a momentum thickness Reynolds number of 400 yields a trip

location at an axial location of -470 mm. Thus the second case (denoted as Trip) had laminar ow dened

from the nozzle inlet up to that trip point. OVERFLOW uses a grid line to set transition, so the gridline

located at the trip point on the bottom wall was used as the trip location for all four walls. From Fig. 21, it

can be seen that the momentum thickness Reynolds number is approximately 260 at the nozzle throat. The

turbulence intensity must be greater than 2.3 for this ow transition to occur upstream of the throat based

on the at zero pressure gradient AGS [52]. Considering this and the favorable pressure gradient situation

NASA/TM—2013-218081 16
of the accelerating nozzle ow, which in turn tends to delay transition, it is likely that the ow transitions

downstream of the throat.

Figure 20: Momentum thickness Reynolds number at the bottom wall (half-span) for the laminar case.

Figure 21: Momentum thickness Reynolds number at the bottom wall, center-span.

A case was also run that combined the attributes of the isothermal, as-installed geometry, and trip cases

to demonstrate the combined eects each parameter has on the ow eld. In addition, a sweep of cases was

run to explore sensitivities to turbulence quantities and turbulence modeling. Two of these cases explored

sensitivities to the freestream turbulent kinetic energy and freestream turbulent viscosity by running the

NASA/TM—2013-218081 17
Standard case with higher values of each. The Standard and Combined cases were also run with an array of

varying turbulence models, of which a turbulence model case study was performed prior to running the SBLI

conguration and discussed later in this thesis. It should be noted that one sensitivity already accounted for

in the above cases is the sensitivity to total temperature. The total temperature used for the workshop CFD

cases was 293 K, a value that was not experimentally measured at the time. Using 1D perfect gas equations

yields a velocity increase of 2.8 m/s (or 0.47% of a 600 m/s freestream velocity) for the 2.7 K increase in total

temperature. Further, the ±1 K in the total temperature measurement would yield an additional uctuation

of ±1 m/s (or 0.17% of a 600 m/s freestream velocity). These are all relatively small numbers, however,

additively they may have an important combined eect.

Table 1: Summary of CFD Cases.

Case A/A* Turbulence Model Heat Transfer Boundary

Conditions

Freestream

Turbulent

Kinetic Energy



m2/s

2



Normalized

Freestream

Turbulent

Viscosity

Standard 3.7062 SST All surfaces adiabatic 3.576x10−1 0.3

Isothermal 3.7062 SST Top/bottom walls and

wedge isothermal at

T=295.7 K. All other

surfaces (including

bottom window)

adiabatic.

3.576x10−1 0.3

Modied

Geometry

3.7847 SST All surfaces adiabatic 3.576x10−1 0.3

Trip 3.7062 Laminar from nozzle

inlet up till trip,

SST downstream of

trip. Trip location

at x=-470 mm

All surfaces adiabatic 3.576x10−1 0.3

Combined 3.7847 Laminar from nozzle

inlet up till trip,

SST downstream of

trip. Trip location

at x=-470 mm

Top/bottom walls and

wedge isothermal at

T=295.7 K. All other

surfaces (including

bottom window)

adiabatic.

3.576x10−1 0.3

TKE 3.7062 SST All surfaces adiabatic 3.576x103 0.3

MUT 3.7062 SST All surfaces adiabatic 3.576x103 3.0

3.2 PIV Exploration

To better compare the CFD with the experimental data, the CFD solutions from the Standard and Combined

cases were re-post-processed to explore particle lag that is associated with the PIV techniques used to acquire

the experimental data. To account for the particle lag, a crude model adjusted the coordinates of each CFD

data point using the following equations:

NASA/TM—2013-218081 18
x ̃ = x + uxτ (21)

y ̃ = y + vyτ (22)

Three time constants, τ , were chosen to represent a 50%, 75%, and 100% total velocity reduction shown in

Fig. 22. This yields time constants of 1.8 (short), 3.7 (medium), and 5.5 (long) μs, respectively. Because

the model was only applied to the center-span and the spanwise velocity is nearly zero, only the axial and

transverse directions were accounted for in the particle lag calculation. Note that this model only attempts

to mimic the eect of particle lag and that it is not based on the actual physics under consideration. To

complement the particle lag model, a window averaging scheme was initially explored using a similar method

used by Garman, Visbal, and Orkwis [53, 54] to average out the values within the center spanwise plane.

However, the PIV grids proved to be nearly as ne as the CFD grids for the method to be eective with

the prescribed window of 0.24 x 0.24 mm [46]. Window averaging was also attempted by averaging three

spanwise planes, which included the centerspan and ±0.75 mm to cover the 1.5 mm spanwise dierance [12].

This was shown to have little eect; the results of which are not shown in this thesis.

Figure 22: Measured particle response through an oblique shock (from Lapsa [12]). The velocity component

normal to the shock, un, is normalized by the pre-shock (un1) and post-shock (un2) velocities and shown as

a function of the shock-normal direction, n. An exponential t to the data reveals the particle relaxation

time, τ p = 5.5 μs.

NASA/TM—2013-218081 19
4 Flat Plate

4.1 Overview

Before exploring turbulence model sensitivities with the complex SBLI cases, a fundamental study was

performed to gauge the eectiveness of various turbulence models available. The 2D Zero Pressure Gradient

Flat Plate Verication Case provided by the Turbulence Model Benchmarking Working Group [13] was

chosen for this study. Boundary conditions along with the nest grid are shown in Fig. 23. The ow across

the plate is at Mach 0.2 with a Reynolds number of 5 million per foot and a reference temperature of 540

°R. The plate itself is modeled as an adiabatic solid wall. Because OVERFLOW can only handle 3D grids,

the 210,000 point 2D grid was converted into a 3D grid by duplicating the grid in three depthwise planes,

for a total of 630,000 grid points. The 2D boundary condition was then applied within OVERFLOW to

handle the extra dimension. Four turbulence models were explored: SST, Menter's baseline model (BSL)

[41], Wilcox's 1988 k-omega model [55], and a modied version of the SST model by Georgiadis and Yoder

(SST-GY) [42]. All of these models are variations of the k-omega model with one of the biggest dierences

being the limitation on the turbulent shear stress. The limit is dened as a percentage of the turbulent

kinetic energy, with 31% for SST, 35.5% for SST-GY, and no limit for BSL and k-omega. For this study,

BSL and SST-GY models were coded manually by modifying the existing SST model within OVERFLOW.

Figure 23: Flat plate 2D grid and boundary conditions [13].

NASA/TM—2013-218081 20
4.2 Results

A benchmark test with the SST turbulence model was rst performed and compared to outputs from CFL3D

and FUN3D, courtesy of reference [13]. The skin friction coecient prole for the SST turbulence model for

all three ow solvers is shown in Fig. 24. It can be seen that the OVERFLOW solution agrees well with the

other codes. With this condence, the other turbulence models were run and compared to the SST solution,

shown in Fig. 24. Experimental data was from Wieghardt and Tillman [56]. It can be seen that the BSL

and SST-GY models predict a slightly higher skin friction coecient compared to SST (within 2%) while

the k-omega model predicts a larger skin friction coecient compared to SST (within 6%). All models, with

the exception of k-omega, agree well with the experimental data.

(a) SST turbulence model. (b) OVERFLOW results.

Figure 24: Skin friction coecient proles.

To further examine the dierences, Fig. 25 shows u

+ verses y+ at a Reynolds number of 4.2 million

(x = 0.84 ft). It can be seen that all the models agree well with the experimental data and Spalding's

formula [57], although the k-omega model under-predicts u

+ in the outer boundary layer. This is consistent

with the over-prediction of the skin ction coecient because the upper bound on u

+ is inversely proportional

to the square root of the skin friction coecient. Note, the following form of Spalding's formula was used

[58]:

y

+ = u+ + e−5.033κ



e

κu+

− 1 − κu+ −

1

2



κu+

2

−

1

6



κu+

3



(23)

NASA/TM—2013-218081 21
Figure 25: u

+ verses y+ for the various turbulence models at Rex = 4.2E6.

The stark prediction dierences between the k-omega model compared to SST, SST-GY, and BSL are

more clearly shown in Fig. 26, which includes proles of the normalized turbulent shear stress and turbulent

viscosity at the same Reynolds number of 4.2 million. Experimental data in this case was from Klebano [59].

With the exception of the k-omega model, the CFD solutions agree reasonably well with the experimental

data. Because of the non-conformity of the k-omega model to the other models tested, an additional study

varying the freestream turbulent viscosity was performed. The freestream turbulent viscosity was singled

out because it has been widely known that the 1988 version of the k-omega model is extremely dependent

on it for a given turbulent kinetic energy state [60]. In fact, one of the motivations behind Mentor's BSL

and SST models was to eliminate the freestream turbulent viscosity dependence [41]. The normalized shear

stress and turbulent viscosity proles are shown in Fig. 27 from this additional study. Note that the value of

(μT /μ)

Inf used for all prior analyses was 0.3. It can be seen that the k-omega solutions approach the SST

solution with decreasing freestream turbulent viscosity. However, it most likely would take an unrealisticly

low freestream turbulent viscosity value for the k-omega model to be within the ballpark of the SST solution

at a more realistic value. Thus it is not recommended that the 1988 k-omega model be used for the SBLI

analyses.

NASA/TM—2013-218081 22
(a) Normalized turbulent shear stress. (b) Normalized turbulent viscosity.

Figure 26: Normalized turbulent parameters for various turbulence models at Rex = 4.2E6

(a) Normalized turbulent shear stress. (b) Normalized turbulent viscosity.

Figure 27: Normalized turbulent parameters at various freestream turbulent viscosities at Rex = 4.2E6

NASA/TM—2013-218081 23
5 Quasi-1D Code

5.1 Overview

For the cases presented, the static temperature of the air in the test section is quite cold at nearly 118 K due

in part to the high Mach number. Such cold temperatures put the perfect gas assumption in question. In

particular, the assumption that the specic heat at constant pressure is constant and that the ideal gas law

holds true. This sensitivity could not be explored by using the production version of OVERFLOW as the

code cannot handle varying specic heats. Thus, a quasi-1D MATLAB [61] code was developed to compute

various thermodynamic and ow parameters for calorically perfect and non-ideal air. The latter half required

the use of the National Institute of Standards and Technology (NIST) Reference Fluid Thermodynamic and

Transport Properties Database (REFPROP) code [62]. The MATLAB code has the capability to calculate

the properties at a single station and over an oblique shock for either a given u velocity or A/A∗ ratio. Total

conditions must also be provided for the code to run. Station nomenclature in the code uses 1 for upstream

of the oblique shock and 2 for downstream of the oblique shock. The code is currently set up for air and

utilizes a predened mixture [63, 64] containing, by mass fraction, 75.57% nitrogen, 23.16% oxygen, and

1.2691% argon when interfacing with REFPROP. The code, however, can be modied for a variety of gases,

such as carbon dioxide. Regardless if the gas is perfect or non-ideal, the code assumes the total enthalpy is

conserved and that the normal v velocity is constant across the oblique shock, as shown in Figs. 28 and 29.

The code also assumes single phase states.

Figure 28: Sample enthalpy verses entropy diagram for calculating across an oblique shock for a non-ideal

gas. 1: total conditions at Station 1, 1S: static conditions at Station 1, 2S: static conditions at Station 2, 2:

total conditions at Station 2.

NASA/TM—2013-218081 24
Figure 29: Oblique shock notation.

5.2 Calorically Perfect Code

The calorically perfect side of the code (runType options 0 and 10) utilizes the perfect gas equations along

with the ideal gas law [65]. Station 1 conditions are calculated as follows:

γ = 1.4 (24)

cp,1 =

γR

γ − 1

(25)

ht,1 = cp,1Tt,1 (26)

h1 = ht,1 −

u

2

1

2

(27)

T1 =

h1

cp,1

(28)

M1 =

u1

√

γRT1

(29)

p1 = pt,1



1 +

γ − 1

2

M2

1

−

γ

γ−1

(30)

NASA/TM—2013-218081 25
ρ1 =

p1

RT1

(31)

To calculate the shock angle and respective Mach number and velocity components ahead of the oblique

shock [66]:

0 = tan3 β + C1 tan β + C2 tan β + C3 (32)

where

C1 = C3



1 − M2

1



(33)

C2 =

γ+1

γ−1M2

1 +

2

γ−1

M2

1 +

2

γ−1

(34)

C3 =

2

γ−1

tan θ



M2

1 +

2

γ−1

 (35)

and

un,1 = u1 sin β (36)

Mn,1 = M1 sin β (37)

To calculate Station 2 conditions, mass, momentum, and energy equations were balanced across the oblique

shock.

ρ1un,1 = ρ2un,2 (38)

p1 + ρ1u

2

n,1 = p2 + ρ2u

2

n,2

(39)

1

2

u

2

n,1 + h1 =

1

2

u

2

n,2 + h2 (40)

NASA/TM—2013-218081 26
p2 = ρ2RT2 (41)

cp,2 = cp,1 (42)

h2 = cp,2T2 (43)

Equations (38) through (43) were solved numerically using a bisection scheme. Once converged, the remaining

Station 2 conditions could be calculated.

u2 =

un,2

sin (β − θ)

(44)

M2 =

u2

√

γRT2

(45)

Mn,2 =

un,2

√

γRT2

(46)

Tt,2 = Tt,1 (47)

ht,2 = ht,1 (48)

pt,2 = p2



1 +

γ − 1

2

M2

2

 γ

γ−1

(49)

Once station conditions were found, sonic properties could be calculated for either station.

A

A∗

=



2

γ + 1 γ+1

2(γ−1)

M−1



1 +

γ − 1

2

M2

 γ+1

2(γ−1)

(50)

T∗ = Tt



1 +

γ − 1

2

−1

(51)

h∗ = cpT∗ (52)

NASA/TM—2013-218081 27
p∗ = pt



1 +

γ − 1

2

−

γ

γ−1

(53)

u∗ =

p

γRT∗ (54)

M∗ =

u

u∗

(55)

5.3 Non-Ideal Code

The non-ideal side of the code (runType options 2 and 12) utilizes REFPROP for most of the calculations

and does not take into consideration the ideal gas law. Station 1 conditions are found as follows:

ht,1 = f (Tt,1, pt,1) (56)

st,1 = f (Tt,1, pt,1) (57)

h1 = ht −

u

2

1

2

(58)

T1 = f (h1, st,1) (59)

p1 = f (h1, st,1) (60)

ρ1 = f (h1, st,1) (61)

a1 = f (h1, st,1) (62)

M1 =

u1

a1

(63)

NASA/TM—2013-218081 28
γ1 = f (h1, st,1) (64)

cp,1 = f (h1, st,1) (65)

To calculate the shock angle and respective Mach number and velocity components ahead of the oblique

shock:

tan (β − θ)

tan β

=

un,2

un,1

(66)

un,1 = u1 sin β (67)

Mn,1 = M1 sin β (68)

Equations (66) through (68) were solved numerically using a bisection scheme as an outer-loop to Equations

(69) through (72), which numerically balance the mass, momentum, and energy equations across the oblique

shock.

ρ1un,1 = ρ2un,2 (69)

p1 + ρ1u

2

n,1 = p2 + ρ2u

2

n,2

(70)

1

2

u

2

n,1 + h1 =

1

2

u

2

n,2 + h2 (71)

ρ2 = f (h2, p2) (72)

Once Equations (66) through (72) were converged, the remaining Station 2 conditions could be calculated.

s2 = f (h2, p2) (73)

T2 = f (p2, s2) (74)

NASA/TM—2013-218081 29
a2 = f (p2, s2) (75)

γ2 = f (p2, s2) (76)

cp,2 = f (p2, s2) (77)

u2 =

un,2

sin (β − θ)

(78)

M2 =

u2

a2

(79)

Mn,2 =

un,2

a2

(80)

ht,2 = ht,1 (81)

Tt,2 = f (ht,2, s2) (82)

pt,2 = f (ht,2, s2) (83)

Once station conditions were found, sonic properties could be calculated for either station. Sonic conditions

were found by rst numerically solving for the sonic enthalpy and velocity.

h∗ = ht −

u∗

2

2

(84)

u∗ = f (h∗, s) (85)

Once converged, rest of the sonic properties could be calculated.

p∗ = f (h∗, s) (86)

NASA/TM—2013-218081 30
T∗ = f (h∗, s) (87)

M∗ =

u

u∗

(88)

γ∗ = f (h∗, s) (89)

A

A∗

=

p∗

p

T

T∗

1

M∗

(90)

5.4 Quasi-1D Exploration

Several parameters of interest were calculated for a range of Mach numbers, spanning Mach 1.4 to 3.5. The

percentage dierence between these parameters for the calorically perfect and non-ideal air are shown in Fig.

30. The percentage dierence is dened as:

%Diff = 100x

NonIdeal − P erfect

P erfect (91)

Also, the perfect dynamic viscosity values were obtained using the following form of Sutherland's law [67]:

μ = 1.458x10−6 T

1.5

T + 110.4

(92)

It can be seen that there is not a drastic dierence between the solutions, with at most a 0.4% dierence

between non-ideal and perfect air at Mach 2.75. The only exception to this would be the Prandtl number,

which is upwards of 9% dierence. For this study the perfect air Prandtl number was assumed to be a

constant value of 0.702, which is associated with air at standard atmospheric conditions. It is known that

the Prandtl number varies with temperature and therefore most of the dierence between the non-ideal and

perfect Prandtl numbers is due to temperature variance and not from assuming perfect or non-ideal air.

Also explored was the eect of the shock angle for varying wedge angles, shown in Fig. 31. It can be seen

that there is not much of a dierence between the non-ideal and perfect shock angles with a dierence of

about 0.2% at Mach 2.75, regardless of the wedge angle. The noise within Fig. 31 is most likely due to

the convergence tolerance when solving Equations (66) through (72). Based on these 1D studies it can be

concluded that although there is some eect from assuming the air is perfect, it is a good enough assumption,

especially given the extra computational power needed to compute non-ideal air in 3D simulations.

NASA/TM—2013-218081 31
(a) Full range. (b) Zoomed in to ± 0.5%.

Figure 30: Percentage dierences between non-ideal and perfect air for various parameters.

Figure 31: Percentage dierences of the shock angle between non-ideal and perfect air for varying wedge

angles.

NASA/TM—2013-218081 32
6 Grid Resolution Study

A grid resolution study was performed on the standard SBLI grid with the Standard Case conditions. The

study looked at solutions obtained on the coarse, medium, and ne grid levels in a similar manor as Galbraith

[3], with streamwise cross-sections of the grids shown in Fig. 32. Due to OVERFLOW interpolating nal

solutions onto the nest mesh, regardless of grid level, solutions were read into Tecplot [67, 68] by reading

every fourth point for the coarsest grid level and every other point for the medium grid level. Convergence

of the solutions was based on the L2 residual, shown in Fig. 33. In addition, the ne grid level solution was

run out an additional 1000 iterations and showed that the u and v velocity proles of interest changed by

no more than 0.1 m/s. Thus, all solutions presented are considered iteratively converged.

(a) Coarse grid.

(b) Medium grid.

(c) Fine grid.

Figure 32: Streamwise cross-sections at center-span for the various grid levels.

NASA/TM—2013-218081 33
(a) Coarse grid level. (b) Medium grid level.

(c) Fine grid level.

Figure 33: L2 residuals for the Standard case.

Several parameters were looked at to determine grid convergence. First, total pressure, total temperature,

and Mach number were computed at three dierent locations, shown in Table 2. Location coordinates can

be found in Table 4. It can be seen that the totals ahead of the oblique shock are converging to the input

totals of 98,000 Pa and 295.7 K and that the Mach numbers at the throat and upstream of the oblique shock

are converging to their 1D expected values of 1.00 and 2.75, respectively. Also, it can be seen that the total

pressure and Mach number downstream of the oblique shock are correctly converging to lower values than

their upstream counterparts while the total temperature is mostly conserved.

Second, mass ow rates at the inlet, exit, and throat regions were computed and shown in Table 3.

Mass ow rates were computed using the mass ow integration routine within Tecplot [67]. Like the total

quantities and Mach number, the mass ow rates are converged well with less than 0.5% loss throughout

the tunnel (with 86% of this total mass loss upstream of the throat) on the nest grid level. The mass loss

is primarily due to round-o error within the discretization process. Finally, u velocity proles of interest

within the streamwise plane located underneath the wedge were examined, as shown in Fig. 34. It can be

seen that while the u velocity proles are very close for the medium and ne grid levels, they themselves are

NASA/TM—2013-218081 34
not fully grid converged. Because the proles are crucial for the results presented in this thesis, it is fair to

say that this parameter is the dominating one out of the parameters presented. Thus while the results are

shown to be still converging, the ne grid level is considered most suitable for the studies presented here.

(a) At x = 18.191 mm. (b) At x = 20.76 mm.

Figure 34: u velocity proles within the streamwise plane.

Table 2: Various ow parameters used to determine grid convergence.

Coarse Medium Fine

Throat

pt (P a)

Tt (K)

M ach

98761.8

296.530

0.952165

98199.4

295.909

0.947367

98009.4

295.701

0.947031

Upstream

pt (P a)

Tt (K)

M ach

98134.4

296.504

2.73365

98103.0

295.960

2.73637

97996.9

295.704

2.74482

Downstream

pt (P a)

Tt (K)

M ach

96083.7

296.173

2.49111

96459.3

296.073

2.48308

96247.1

295.742

2.47317

Table 3: Mass ow rates (kg/s) used to determine grid convergence.

Coarse Medium Fine

Inlet 0.250120 0.247012 0.245282

Throat 0.246334 0.245170 0.244326

Exit 0.247058 0.245823 0.244169

NASA/TM—2013-218081 35
Table 4: Coordinates for grid resolution study.

X (mm) Y (mm) Z (mm)

Throat -538.6808 8.7612 -2.1299

Upstream -188.1651 36.4712 -2.1299

Downstream 34.7961 21.8123 -0.6699

Inlet -971.9310 All All

Throat -538.6808 All All

Exit 403.6530 All All

NASA/TM—2013-218081 36
7 Results

7.1 Standard Case

The streamwise data plane from the SBLI experiment was used as the primary plane to compare experimental

and CFD data as it is considered to be the most accurate of all the experimental data planes [19]. The location

of the plane is shown in Fig. 35, which is located at center-span. Velocity contours for the Standard case

along with the experimental data are shown in Fig. 36. For consistency with the prior workshop, velocities

were normalized by UInf = 603 m/s. Although the contours appear similar, the CFD solution under predicts

the velocities (particularly u). In addition, the reected oblique shock in the CFD solution is upstream of

the experimental data. To further inspect the ow eld, Fig. 37 shows contours of negative u velocities just

above the bottom wall underneath the wedge. These contours provide a convenient way to approximate the

bottom wall separation region underneath the wedge. The resulting blockage, derived from the corner ows,

is typical of prior CFD analysis and has been shown by Galbraith et. al. [23] to play a major role in the ow

eld for this tunnel due to the tunnel's small size. The blockage at the throat is also important and can be

quantied by introducing a throat blockage parameter, b∗, which is dened by the following equations [23]:

m ̇ ∗ = (1 − b∗)  ̇m∗ideal (93)

where

m ̇ ∗ideal = A ∗

pt √

Tt

s

γ

R



2

γ + 1 γ+1

γ−1

(94)

The blockage parameter calculation assumes adiabatic, ideal perfect gas, and choked ow and is shown to

be 1.53% for the Standard Case.

Figure 35: Data plane location in reference to the grid.

NASA/TM—2013-218081 37
Figure 36: u velocity (left) and v velocity (right) streamwise contours for the experiment (top) and Standard

case (bottom).

Figure 37: Bottom wall separation underneath the wedge for the Standard case.

7.2 Particle Lag Eects

Velocity contours with the particle lag incorporated are shown in Fig. 38, with the remaining velocity

contour plots located in appendix A. Note only the Standard and Combined cases are shown as they are

representative of the spectrum of presented cases. Figures 39 through 42 show u and v velocity proles with

and without particle lag at the most upstream axial location along with the rst intersecting spanwise data

plane. See appendix B for remaining axial stations within the streamwise plane. The lag is shown to bring

both the Standard and Combined cases closer to the experimental data with increasing lag time constant.

Because the lag has such an eect, it is not advisable to use the workshop metric for comparing CFD to

this PIV obtained experimental data without accounting for the lag. Recall that it is a fraction of the entire

experimentally derived time constant that is used for the lag model. Although it is a very short time, it

creates an error in the velocity eld that is higher than the desired match between the CFD and experiment.

NASA/TM—2013-218081 38
Figure 38: v velocity streamwise contours for the experiment (top), short lag (middle-top), medium lag

(middle-bottom), and long lag (bottom).

NASA/TM—2013-218081 39
(a) u velocity proles. (b) v velocity proles.

Figure 39: Select velocity proles at the most-upstream axial location (x = 18.191 mm) for the Standard

case.

(a) u velocity proles (b) v velocity proles

Figure 40: Select velocity proles at the rst intersecting spanwise plane (x = 20.76 mm) for the Standard

case.

NASA/TM—2013-218081 40
(a) u velocity proles. (b) v velocity proles.

Figure 41: Select velocity proles at the most-upstream axial location (x = 18.191 mm) for the Combined

case.

(a) u velocity proles. (b) v velocity proles.

Figure 42: Select velocity proles at the rst intersecting spanwise plane (x = 20.76 mm) for the Combined

case.

7.3 Isothermal Case

The eects of the Isothermal case can be seen in Figs. 43 and 44. Figure 43 and the static temperature

prole in Fig. 44 show little dierence in the thermal boundary layer between the Standard and Isothermal

cases. However, assuming the aluminum is isothermal is more realistic as there is likely heat transfer between

the aluminum and the tunnel's surroundings. The temperature dierence is evident in the total temperature

NASA/TM—2013-218081 41
center-span prole at the bottom wall, shown in Fig. 45. For reference, several notable stations have

been marked to orient the prole. Figure 45 also conrms that the isothermal boundary conditions were

implemented correctly and that the deviation from the constant total temperature for the Isothermal and

Combined cases is due to the presence of the adiabatically modeled bottom window. Further, the isothermal

boundary conditions were shown to have an eect on the total temperature prole, as shown in Fig. 44. The

thermal recovery factor, rc, is determined to be 92.3% from the following equation:

Taw

T∞

= 1 +

rc

2

(γ − 1) M2

∞ (95)

where Taw is the adiabatic wall temperature, or the total temperature evaluated from an adiabatic calculation.

This value of rc is reasonable for turbulent ows as the recovery factor is approximately equal to the cube

root of the Prandtl number.

(a) Standard case CFD.

(b) Isothermal case CFD.

Figure 43: Freestream thermal boundary-layer at x = −63.9 mm. Temperature cut o is at 99% freestream

(121.2 K).

NASA/TM—2013-218081 42
(a) Static temperature proles. (b) Total temperature proles.

Figure 44: Temperature proles at the most-upstream axial location (x = 18.191 mm).

Figure 45: Total temperature centerspan prole at the bottom wall with the following stations marked: 1.

Throat, 2. Trip location, 3. Start of the tunnel straight section, 4. Wedge leading edge, 5. Wedge trailing

edge.

The dierences in temperature do correspond to dierences in velocity, as shown in Fig. 46. The

Isothermal case is shown to be slightly worse than the Standard case as compared to the experimental data.

The dierences in the velocities can be seen more clearly in the dierence contour plots shown in Figs. 47

and 48. The dierence is dened as the Isothermal case minus the Standard case. It is shown that the

NASA/TM—2013-218081 43
interaction region for the Isothermal case is further upstream compared to the Standard case, and therefore

further away compared to the experimental data. The movement of the interaction region is also veried in

the static temperature dierence contour, shown in Fig. 49.

(a) u velocity proles. (b) v velocity proles.

Figure 46: Select velocity proles at the most-upstream axial location (x = 18.191 mm).

(a) Positive dierence (m/s). (b) Negative dierence (m/s).

Figure 47: u velocity dierence contours.

(a) Positive dierence (m/s). (b) Negative dierence (m/s).

Figure 48: v velocity dierence contours.

NASA/TM—2013-218081 44
(a) Positive dierence (K). (b) Negative dierence (K).

Figure 49: Static temperature dierence contours.

7.4 Trip Case

The eects of the Trip case are shown in Figs. 50 through 52. Figures 50 and 51 show that Trip and Combined

cases agree well with the experimental data for the u velocity which suggests that assuming the ow is laminar

at some portion upstream of the wedge is likely more correct than assuming it to be turbulent throughout.

This further supports likely transition downstream of the throat based on the momentum thickness Reynolds

number of the rst laminar case. The closeness of the u velocity proles in Figs. 50 and 51 for the Trip

and Combined case indicates that the trip is a dominating factor that sets the Combined case apart from

the Standard case. This is also evident in the turbulent kinetic energy proles shown in Fig. 52. Having a

laminar region upstream of the wedge allows for thinner boundary layers, and thus less blockage, upstream

of the wedge. This is further quantied by the throat blockage parameter, with the Trip case having a throat

blockage of 1.11%, which is less than the 1.53% that it was for the Standard case.

(a) u velocity proles. (b) v velocity proles.

Figure 50: Select velocity proles at the most-upstream axial location (x = 18.191 mm).

NASA/TM—2013-218081 45
(a) u velocity proles. (b) v velocity proles.

Figure 51: Select velocity proles at the rst intersecting spanwise plane (x = 20.76 mm).

(a) At x = 18.191 mm. (b) At x = 20.76 mm.

Figure 52: Turbulent kinetic energy proles.

Examining the v velocity proles in Fig. 51 shows that the experimental data from the spanwise and

streamwise planes do not agree with each other. In fact, the CFD solutions are shown to match the experimental data from the spanwise plane better than compared to the streamwise plane. This is a key point when

developing an error metric as the error metric used in the prior workshop focused solely on the experimental

data in the streamwise plane and not the spanwise plane.

NASA/TM—2013-218081 46
7.5 Turbulence Modeling Eects

Figures 53 and 54 show velocity proles while Fig. 55 shows the turbulent kinetic energy prole for the TKE

and MUT case. It can be seen that the velocity proles for the TKE case compare better to the experimental

data than the Standard case does, however, the TKE case still predicts lower freestream velocities. It can

also be shown that the dominating factor is the increase in freestream turbulent kinetic energy and not

the increase in freestream turbulent viscosity. However this domination is in part due to that the inlet

freestream turbulent viscosity was increased by only 10x while the inlet freestream turbulent kinetic energy

was increased by 10,000x. The same conclusions can also be made with the turbulent kinetic energy proles

of Fig. 55.

(a) u velocity proles. (b) v velocity proles.

Figure 53: Select velocity proles at the most-upstream axial location (x = 18.191 mm).

NASA/TM—2013-218081 47
(a) u velocity proles. (b) v velocity proles.

Figure 54: Select velocity proles at the rst intersecting spanwise plane (x = 20.76 mm).

(a) At x = 18.191 mm. (b) At x = 20.76 mm.

Figure 55: Turbulent kinetic energy proles.

Figures 56 and 57 show the velocity proles for the various turbulence models tested for the Standard

case conditions. Additional velocity proles can be found in appendix B. It can be seen that both BSL and

SST-GY predict higher u velocities in the boundary layer and thus tend to agree better with the experimental

values compared to the SST case. This is also true for the v velocities within the boundary layer region.

However, all three turbulence models are the same for the freestream velocities. The greatest impact of the

turbulence models can be seen in the blockage eects. Figure 58 shows the bottom wall separation underneath

the wedge. It can clearly be seen that the corner ow separation greatly decreases with turbulence models that

NASA/TM—2013-218081 48
allow for greater shear stress transport. However, the center separation bubble is shown to increase slightly

in the spanwise direction with decreasing corner ow separation. This is consistent with the experimentally

shown coupling mentioned earlier. It is also shown that the corresponding throat blockage also decreases,

from the 1.53% with SST to 1.51% with SST-GY to 1.49% with BSL. A similar turbulence model study was

also performed for the Combined case conditions, which can be found in appendix C.

(a) u velocity proles. (b) v velocity proles.

Figure 56: Velocity proles at the most-upstream axial location (x = 18.191 mm) for various turbulence

models, Standard Case.

(a) u velocity proles. (b) v velocity proles.

Figure 57: Velocity proles at the rst intersecting spanwise plane (x = 20.76 mm) for various turbulence

models, Standard Case.

NASA/TM—2013-218081 49
(a) SST-GY (positive span) and SST (negative span).

(b) BSL (positive span) and SST (negative span).

Figure 58: Bottom wall separation underneath the wedge for the Standard case with various turbulence

models.

7.6 Metrics

To compare the CFD data with the prior CFD data from the workshop, the following error metric was used

[19]:

e (f)n =



(fcfd)n − (fexp)n



 (96)

E (f) = 1

N

Xe (f)n

(97)

The error metric was summed over the entire streamwise data plane with metric results shown in Table 5.

Cases submitted to the workshop are designated by letters while the cases presented in this paper are in bold

face. It can be seen that the Standard case ranks best out of the cases presented and the addition of the lag

improves both the Standard and Combined cases. Although the metric is a useful quantity for comparison,

it must be used in combination with all the data. All improvements to matching the data must be for the

right reasons. Although the Standard case with the PIV lag corrections have a smaller v velocity error, the

physics of the Combined case is likely more correct.

NASA/TM—2013-218081 50
Table 5: Workshop error metric comparisons.

U Error V Error

0.02373 Q 0.008947 Experiment

0.02633 B 0.01158 Standard (Medium Lag)

0.02669 P 0.01185 Standard (Long Lag)

0.02676 Standard (Long Lag) 0.01224 Standard (Short Lag)

0.02747 Standard (Medium Lag) 0.01308 MUT

0.02759 G 0.01331 TKE

0.02840 F 0.01348 Combined (Medium Lag)

0.02853 Standard (Short Lag) 0.01360 Combined (Short Lag)

0.02899 M 0.01375 Combined (Long Lag)

0.02957 I 0.01377 Standard

0.02964 Standard 0.01403 Combined

0.02999 K 0.01414 Trip

0.03020 Standard (SST-GY) 0.01449 B

0.03025 Combined (Short Lag) 0.01514 Isothermal

0.03035 N 0.01621 Modied Geometry

0.03036 Combined (Medium Lag) 0.01682 P

0.03043 TKE 0.01716 G

0.03043 MUT 0.01729 F

0.03047 Combined 0.01771 M

0.03064 Combined (Long Lag) 0.01828 Q

0.03090 Isothermal 0.01867 K

0.03114 Modied Geometry 0.01917 N

0.03115 Standard (BSL) 0.01950 Standard (SST-GY)

0.03129 O 0.01961 O

0.03163 Trip 0.02227 Standard (BSL)

0.03473 Experiment 0.02344 J

0.03571 H 0.02348 Combined (SST-GY)

0.03739 Combined (SST-GY) 0.02576 Combined (BSL)

0.03856 Combined (BSL) 0.02721 H

0.03980 L 0.03883 L

0.03995 J 0.04002 I

One possible metric to be used in conjunction with the workshop metric is a comparison of the u velocities

at points of interest. For this study, two points were chosen: points A and B in Fig. 59. Point A was chosen

outside the data plane, upstream of the wedge and at center height and span to capture a freestream point.

Point B was chosen within the data plane at umax at the upstream most axial location. Velocity and

velocity dierences are shown in Table 6. The velocity dierence is dened as the current case minus the

Standard case. Interestingly, the Combined case dierence at Point A is reected as a buildup of the previous

dierences. This is not true at Point B, but as seen in Fig. 59, the ow at Point B is not truly at freestream

conditions with an apparent decrease in Mach number (and thus decreases in u velocity). This in part

explains why the workshop error metric predicts the Standard case as being better than the Combined case

as the data used in workshop error metric is derived from at/downstream of Point B. Also, the highest u

NASA/TM—2013-218081 51
velocity at Point B from all the simulations is still 11.6 m/s lower than the experimental value and should

be just upstream of the shock.

Figure 59: Point locations within the centerspan plane. Mach number contour of the Standard case CFD

solution is shown.

Table 6: u velocity and velocity dierences.

Point A Point B

U (m/s) 4U (m/s) U (m/s) 4U (m/s)

Standard 594.600 0.000 587.042 0.000

Isothermal 594.454 -0.146 586.377 -0.665

Modied Geometry 596.567 1.967 586.413 -0.629

Trip 595.186 0.586 587.737 0.695

Combined 596.980 2.380 587.038 -0.004

Experiment - - 599.330 12.288

Another proposed complementary metric would be the use of the oblique shock angle o the leading

edge of the wedge. The shock angle was calculated by nding the angle between the leading edge of the

wedge and a point downstream with the max second derivative of a scaled arc length. For details on how

the shock angle was calculated, see appendix D. The calculated shock angles for the various cases as well as

for the experimental data are shown in Table 7. It can be seen that the shock angle does not change much

between the cases, but the addition of the lag brings it to within the experimental value. A comparison to

quasi-1D theory is shown in Fig. 60. It can be seen that the shock angle cannot be calculated based on the

quasi-1D theory due to the 3D nature of the shocks present in the ow. The advantage of this metric is that

separate experimental evaluations of the shock angle are possible: from detailed PIV to optical methods

such as schlieren.

NASA/TM—2013-218081 52
Figure 60: Shock angle verses Mach number.

Table 7: Shock angle comparisons.

Shock Angle (deg)

Standard 29.888

Standard (BSL) 29.888

Standard (SST-GY) 29.888

Isothermal 29.888

Modied Geometry 29.543

Trip 29.888

Combined 30.231

Combined (BSL) 30.231

Combined (SST-GY) 30.231

TKE 29.888

MUT 29.888

Standard (Short Lag) 29.196

Standard (Medium Lag) 29.196

Standard (Long Lag) 28.494

Combined (Short Lag) 29.543

Combined (Medium Lag) 29.543

Combined (Long Lag) 28.846

Experiment 29.196

NASA/TM—2013-218081 53
7.7 Blockage Revisited

Figures 61 and 62 show the bottom wall separations underneath the wedge for several of the cases presented.

Separations are shown to be similar between cases, but there are noticeable dierences. In particular, the

Modied Geometry case was shown to have the most corner ow separation while the Trip case was shown

to have the least corner separation out of all the cases run with SST. This is further quantied by the throat

blockage parameter as the Modied Geometry case had 1.56% throat blockage compared to 1.11% of the

Trip case. The separation regions can also help explain why velocities at Point B (located underneath the

wedge) tended to decrease compared to the Standard Case while the velocities at Point A (upstream of the

wedge) increased. The respective increase or decrease is most noticeable for cases with more separation. The

extent of the separations was thought to be due mostly to details within the turbulence model, however,

these results show that there are many sources that impact the separations and respective blockages.

(a) Isothermal case (positive span) and Standard case (negative span).

(b) Modied Geometry case (positive span) and Standard case (negative span).

Figure 61: Bottom wall separation underneath the wedge for the Isothermal and Modied Geometry cases.

NASA/TM—2013-218081 54
(a) Trip case (positive span) and Standard case (negative span).

(b) Combined case (positive span) and Standard case (negative span).

Figure 62: Bottom wall separation underneath the wedge for the Trip and Combined cases.

NASA/TM—2013-218081 55
8 Conclusions/Future Work

CFD analyses were performed on the UM Mach 2.75 Glass Tunnel with a 7.75 degree semi-span wedge (a

test case used at a recent SBLI workshop) to explore key physics pertaining to SBLI's. It was shown that

the CFD generally under predicted the freestream velocities, however the solutions showed improvement,

particularly the v velocity component, with several sensitivity insights. These included the addition of a

laminar region upstream of the wedge with a specied trip point as well as geometry that reects the current

state of the tunnel. The ow was shown to be most likely transitional downstream of the throat. This

is based on the analysis of the momentum thickness Reynolds number for the laminar case as well as the

improved velocity proles in the boundary layer upstream of the shock for cases that accounted for the

transition. Other sensitivities explored included using an isothermal boundary condition, throat geometry

modications, and several turbulence models and turbulence model parameter sensitivities. Also, a fraction

of the measured PIV lag was used with a simple model to modify the CFD solutions and showed improvement

to the comparison to the PIV results. It showed that the velocity of the PIV particle is not the velocity of

the air behind the shock, and the dierence is larger than one would like for a validation test case. Future

comparisons should have the CFD results augmented in a post-processing step to calculate particle velocities.

A variety of metrics were used to capture the results presented in this thesis. One metric used was the

primary metric from the workshop: a root mean square error norm of the dierence between the measured

u and v velocities. Almost all cases presented in this thesis show improvement in that metric for v velocities

as compared to the cases run for the workshop. The u velocity errors were better than the experimental

uncertainty except for two cases. Two new error metrics have been proposed that are felt to be complimentary

and help establish condence that the physics is correct. These include a velocity upstream of the interaction

and the center-span shock angle.

Although several sensitivities were presented in this thesis, there are still several sensitivities that have

not been addressed. Additional geometric parameters of interest include the wedge leading edge location and

angle, wedge width and location within the tunnel, and noticeable wall indents from micro ramp accommodations. These parameters would shed more insight into the sensitivity of the geometry on the oblique shock.

Sensitivities to the turbulence model and freestream turbulent kinetic energy should be explored further to

address the impact of the corner ows, and therefore replicate the correct blockage on the freestream ow

eld. Further explorations of the heat transfer boundary conditions should be explored, such as conjugate

heat transfer and the sensitivity to changes in wall temperature which is known to change throughout experimental test runs on a given day. Also, future studies should explore boundary-layer transition/trip location

as the ow is most certainly transitional downstream of the throat. Aside from the geometric and ow sensiNASA/TM—2013-218081 56
tivities, the simplied PIV models should be improved on in order to further understand the eects of PIV as

related to post-processing CFD data for experimental data comparison. Improvements include calculating

the particle lag based on the forces exerted on the individual particles by the air (including particle size

distribution) and obtaining ow eld snapshots at two instances in time. These snapshots would then be

processed using the same PIV post-processing algorithm used with the experimental data.

NASA/TM—2013-218081 57
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Laboratory, 1953.

[66] Emanuel, G., Analytical Fluid Dynamics, CRC Press, 2nd ed., 2000.

[67] Tecplot, Inc., Bellevue, WA, Tecplot 360, 2010 User's Manual, 2010.

[68] Tecplot, Inc., Tecplot 360, 2010, Bellevue, WA.

NASA/TM—2013-218081 63
A Velocity Contours

This appendix contains the u and v velocity contours for the CFD cases presented.

Figure A.1: u velocity contours for the Standard (left) and Combined (right) cases with lag.

NASA/TM—2013-218081 64
Figure A.2: u (left) and v (right) velocity contours for Isothermal and Modied Geometry cases.

Figure A.3: u (left) and v (right) velocity contours for Trip and Combined cases.

NASA/TM—2013-218081 65
Figure A.4: u (left) and v (right) velocity contours for TKE and MUT cases.

Figure A.5: u (left) and v (right) velocity contours for the Standard case with SST-GY and BSL.

NASA/TM—2013-218081 66
Figure A.6: u (left) and v (right) velocity contours for the Combined case with SST-GY and BSL.

NASA/TM—2013-218081 67
B Velocity Proles

This appendix contains velocity proles for all remaining spanwise intersecting planes within the streamwise

plane.

B.1 Standard Case

(a) u velocity proles. (b) v velocity proles.

Figure B.1: Velocity proles at x = 26.76 mm, Standard case.

(a) u velocity proles. (b) v velocity proles.

Figure B.2: Velocity proles at x = 30.76 mm, Standard case.

NASA/TM—2013-218081 68
(a) u velocity proles. (b) v velocity proles.

Figure B.3: Velocity proles at x = 34.76 mm, Standard case.

(a) u velocity proles. (b) v velocity proles.

Figure B.4: Velocity proles at x = 38.76 mm, Standard case.

NASA/TM—2013-218081 69
(a) u velocity proles. (b) v velocity proles.

Figure B.5: Velocity proles at x = 41.76 mm, Standard case.

(a) u velocity proles. (b) v velocity proles.

Figure B.6: Velocity proles at x = 53.76 mm, Standard case.

NASA/TM—2013-218081 70
B.2 Combined Case

(a) u velocity proles. (b) v velocity proles.

Figure B.7: Velocity proles at x = 26.76 mm, Combined case.

(a) u velocity proles. (b) v velocity proles.

Figure B.8: Velocity proles at x = 30.76 mm, Combined case.

NASA/TM—2013-218081 71
(a) u velocity proles. (b) v velocity proles.

Figure B.9: Velocity proles at x = 34.76 mm, Combined case.

(a) u velocity proles. (b) v velocity proles.

Figure B.10: Velocity proles at x = 38.76 mm, Combined case.

NASA/TM—2013-218081 72
(a) u velocity proles. (b) v velocity proles.

Figure B.11: Velocity proles at x = 41.76 mm, Combined case.

(a) u velocity proles. (b) v velocity proles.

Figure B.12: Velocity proles at x = 53.76 mm, Combined case.

NASA/TM—2013-218081 73
B.3 Modied Geometry, Isothermal, and Trip Cases

(a) u velocity proles. (b) v velocity proles.

Figure B.13: Velocity proles at x = 26.76 mm, various cases.

(a) u velocity proles. (b) v velocity proles.

Figure B.14: Velocity proles at x = 30.76 mm, various cases.

NASA/TM—2013-218081 74
(a) u velocity proles. (b) v velocity proles.

Figure B.15: Velocity proles at x = 34.76 mm, various cases.

(a) u velocity proles. (b) v velocity proles.

Figure B.16: Velocity proles at x = 38.76 mm, various cases.

NASA/TM—2013-218081 75
(a) u velocity proles. (b) v velocity proles.

Figure B.17: Velocity proles at x = 41.76 mm, various cases.

(a) u velocity proles. (b) v velocity proles.

Figure B.18: Velocity proles at x = 53.76 mm, various cases.

NASA/TM—2013-218081 76
B.4 TKE and MUT Cases

(a) u velocity proles. (b) v velocity proles.

Figure B.19: Velocity proles at x = 26.76 mm, TKE and MUT cases.

(a) u velocity proles. (b) v velocity proles.

Figure B.20: Velocity proles at x = 30.76 mm, TKE and MUT cases.

NASA/TM—2013-218081 77
(a) u velocity proles. (b) v velocity proles.

Figure B.21: Velocity proles at x = 34.76 mm, TKE and MUT cases.

(a) u velocity proles. (b) v velocity proles.

Figure B.22: Velocity proles at x = 38.76 mm, TKE and MUT cases.

NASA/TM—2013-218081 78
(a) u velocity proles. (b) v velocity proles.

Figure B.23: Velocity proles at x = 41.76 mm, TKE and MUT cases.

(a) u velocity proles. (b) v velocity proles.

Figure B.24: Velocity proles at x = 53.76 mm, TKE and MUT cases.

NASA/TM—2013-218081 79
B.5 Standard Case with Various Turbulence Models

See appendix C for Combined case equivilant.

(a) u velocity proles. (b) v velocity proles.

Figure B.25: Velocity proles at x = 26.76 mm, Standard case with various turbulence models.

(a) u velocity proles. (b) v velocity proles.

Figure B.26: Velocity proles at x = 30.76 mm, Standard case with various turbulence models.

NASA/TM—2013-218081 80
(a) u velocity proles. (b) v velocity proles.

Figure B.27: Velocity proles at x = 34.76 mm, Standard case with various turbulence models.

(a) u velocity proles. (b) v velocity proles.

Figure B.28: Velocity proles at x = 38.76 mm, Standard case with various turbulence models.

NASA/TM—2013-218081 81
(a) u velocity proles. (b) v velocity proles.

Figure B.29: Velocity proles at x = 41.76 mm, Standard case with various turbulence models.

(a) u velocity proles. (b) v velocity proles.

Figure B.30: Velocity proles at x = 53.76 mm, Standard case with various turbulence models.

NASA/TM—2013-218081 82
C Combined Case with Various Turbulence Models

This appendix contains velocity proles and bottom wall separation plots for the Combined case with the

SST-GY and BSL turbulence models. Similar trends were noticed compared to the turbulence model study

with the Standard case conditions. However unlike the Standard conditions, the throat blockage was inconsistent with the turbulent shear stress limiter, with blockage values of 0.930% with SST, 0.997% with SST-GY,

and 0.988% with BSL. This is most likely because unlike the Standard case conditions, the Combined case

conditions modeled the throat region laminar and thus should be independent of turbulence quantities. The

discrepancy between the turbulence models shown is therefore due to numerical error.

(a) u velocity proles. (b) v velocity proles.

Figure C.1: Velocity proles at x = 18.191 mm, Combined case with various turbulence models.

NASA/TM—2013-218081 83
(a) u velocity proles. (b) v veloicty proles.

Figure C.2: Velocity proles at x = 20.76 mm, Combined case with various turbulence models.

(a) u velocity proles. (b) v velocity proles.

Figure C.3: Velocity proles at x = 26.76 mm, Combined case with various turbulence models.

NASA/TM—2013-218081 84
(a) u velocity proles. (b) v velocity proles.

Figure C.4: Velocity proles at x = 30.76 mm, Combined case with various turbulence models.

(a) u velocity proles. (b) v velocity proles.

Figure C.5: Velocity proles at x = 34.76 mm, Combined case with various turbulence models.

NASA/TM—2013-218081 85
(a) u velocity proles. (b) v velocity proles.

Figure C.6: Velocity proles at x = 38.76 mm, Combined case with various turbulence models.

(a) u velocity proles. (b) v velocity proles.

Figure C.7: Velocity proles at x = 41.76 mm, Combined case with various turbulence models.

NASA/TM—2013-218081 86
(a) u velocity proles. (b) v velocity proles.

Figure C.8: Velocity proles at x = 53.76 mm, Combined case with various turbulence models.

(a) SST-GY (positive span) and SST (negative span).

(b) BSL (positive span) and SST (negative span).

Figure C.9: Bottom wall separation underneath the wedge for the Combined case with various turbulence

models.

NASA/TM—2013-218081 87
D Shock Angle Calculation

This appendix outlines how the shock angle was computed for the various cases. One would think computing

a shock angle would be a trivial exercise, but that is not the case. The method outlined below utilizes v

velocity proles since they vary dramatically after being turned through a wedge angle. The method adopted

is then consistent for the experimental as well as the CFD results. The shock angle was dened as the angle

of the line formed by two points, denoted as the shock line, and shown in Fig. D.1. The start point of the

shock line was chosen to be the wedge leading edge in the streamwise plane as this point is xed for all

cases examined. To nd the end point of the shock line, a v velocity prole was rst obtained at an axial

station of interest. In this case, the axial location was chosen to be the most upstream location within the

streamwise data plane (x = 18.191 mm). For consistency with the experimental data, the v velocity prole

was obtained by interpolating the CFD data onto the PIV grid. Second, the v velocity prole was scaled by

the prole aspect ratio to obtain the prole quantity, x ́:

x ́= v

ymax − ymin

vmax − vmin

(D.1)

Third, the arc length prole was computed, with the arc length dened as:

li =

q

(x ́i+1 − x ́i)

2 + (yi+1 − yi)2 + li−1 (D.2)

Forth, the rst and second derivatives of the arc length with respect to y were computed using a forward

dierentiating scheme.



dl

dy 

i

=

li+1 − li

yi+1 − yi

(D.3)



d

2

l

dy2



i

=



dl

dy

i+1

−



dl

dy

i

yi+1 − yi

(D.4)

The point with the maximum d

2

l

dy2 became the end point for the shock line. The shock angle was then

computed as:

β = tan−1



∆y

∆x



(D.5)

For a visual example, see Fig. D.2 through Fig. D.4, which show the above mentioned proles for the

Standard case.

NASA/TM—2013-218081 88
Figure D.1: Shock angle diagram/nomenclature.

(a) v velocity prole at x = 18.191 mm. (b) x ́prole at x = 18.191 mm.

Figure D.2: Velocity proles for determining shock line end location (Standard case shown).

Figure D.3: Arc length prole for determining shock line end location (Standard case shown).

NASA/TM—2013-218081 89
(a) dl

dy prole at x = 18.191 mm. (b) d

2l

dy2 prole at x = 18.191 mm.

Figure D.4: Derivative proles for determining shock line end location (Standard case shown).

NASA/TM—2013-218081 90
E Simulation Checklists

Checklists for the simulations were used to document each run in a consistent manner as outlined by Galbraith

[3].

E.1 Initial

Pre-Processing

Orient meshes X

No negative volumes X

Check boundary

conditions for gaps X

Initial Solution None

Check reference

conditions X

RefMach 2.75

XKInf 1E-2

RetInf 0.3

RefL (m) 0.06985

Ttot (K) 292.778

Ptot (Pa) 101125

Check the initial

solution X

Remove orphan

nodes X

Use most resent

INTOUT le X

Input File

Spatial order (FSO) 1

Time order (TFOSO) 1

Time-step scaling

ag (ITIME) 4

CFL 0.5-2

Turbulence CFL

(CFLT) 1

Turbulence order

(FSOT) 1

Turbulence model SST

Turbulent Input

Quantities

K 1E-2

Epsilon 0.1

Reference

Quantities

Mach 2.75

Tref (R) 205.771

Re 636160

Post Processing

Iterations (Coarse,

Medium, Fine) 2000, 2000, 2000

Dimensionalize the

solution X

Comments Unconverged

NASA/TM—2013-218081 91
E.2 Standard Case

Pre-Processing

Orient meshes X

No negative volumes X

Check boundary

conditions for gaps X

Initial Solution Initial

Check reference

conditions X

RefMach 2.75

XKInf 1E-6

RetInf 0.3

RefL (m) 0.06985

Ttot (K) 295.7

Ptot (Pa) 98000

Check the initial

solution X

Remove orphan

nodes X

Use most resent

INTOUT le X

Input File

Spatial order (FSO) 3

Time order (TFOSO) 1

Time-step scaling

ag (ITIME) 1

CFL 5-20

Turbulence CFL

(CFLT) 1

Turbulence order

(FSOT) 1

Turbulence model SST

Turbulent Input

Quantities

K 1E-6

Epsilon 0.3

Reference

Quantities

Mach 2.75

Tref (R) 211.845

Re 592877

Post Processing

Iterations (Coarse,

Medium, Fine) 0, 0, 20000

Dimensionalize the

solution X

Comments Converged

NASA/TM—2013-218081 92
E.3 Isothermal Case

Pre-Processing

Orient meshes X

No negative volumes X

Check boundary

conditions for gaps X

Initial Solution Standard Case

Check reference

conditions X

RefMach 2.75

XKInf 1E-6

RetInf 0.3

RefL (m) 0.06985

Ttot (K) 295.7

Ptot (Pa) 98000

Check the initial

solution X

Remove orphan

nodes X

Use most resent

INTOUT le X

Input File

Spatial order (FSO) 3

Time order (TFOSO) 1

Time-step scaling

ag (ITIME) 1

CFL 5-20

Turbulence CFL

(CFLT) 1

Turbulence order

(FSOT) 1

Turbulence model SST

Turbulent Input

Quantities

K 1E-6

Epsilon 0.3

Reference

Quantities

Mach 2.75

Tref (R) 211.845

Re 592877

Post Processing

Iterations (Coarse,

Medium, Fine) 0, 0, 20000

Dimensionalize the

solution X

Comments Converged

NASA/TM—2013-218081 93
E.4 Modied Geometry Case

Pre-Processing

Orient meshes X

No negative volumes X

Check boundary

conditions for gaps X

Initial Solution Initial

Check reference

conditions X

RefMach 2.75

XKInf 1E-6

RetInf 0.3

RefL (m) 0.06985

Ttot (K) 295.7

Ptot (Pa) 98000

Check the initial

solution X

Remove orphan

nodes X

Use most resent

INTOUT le X

Input File

Spatial order (FSO) 3

Time order (TFOSO) 1

Time-step scaling

ag (ITIME) 1

CFL 5-20

Turbulence CFL

(CFLT) 1

Turbulence order

(FSOT) 1

Turbulence model SST

Turbulent Input

Quantities

K 1E-6

Epsilon 0.3

Reference

Quantities

Mach 2.75

Tref (R) 211.845

Re 592877

Post Processing

Iterations (Coarse,

Medium, Fine) 0, 0, 20000

Dimensionalize the

solution X

Comments Converged

NASA/TM—2013-218081 94
E.5 All-Laminar Case

Pre-Processing

Orient meshes X

No negative volumes X

Check boundary

conditions for gaps X

Initial Solution Initial

Check reference

conditions X

RefMach 2.75

XKInf 1E-6

RetInf 0.3

RefL (m) 0.06985

Ttot (K) 295.7

Ptot (Pa) 98000

Check the initial

solution X

Remove orphan

nodes X

Use most resent

INTOUT le X

Input File

Spatial order (FSO) 3

Time order (TFOSO) 1

Time-step scaling

ag (ITIME) 1

CFL 5-20

Turbulence CFL

(CFLT) 1

Turbulence order

(FSOT) 1

Turbulence model SST

Turbulent Input

Quantities

K 1E-6

Epsilon 0.3

Reference

Quantities

Mach 2.75

Tref (R) 211.845

Re 592877

Post Processing

Iterations (Coarse,

Medium, Fine) 0, 0, 20000

Dimensionalize the

solution X

Comments Converged

NASA/TM—2013-218081 95
E.6 Trip Case

Pre-Processing

Orient meshes X

No negative volumes X

Check boundary

conditions for gaps X

Initial Solution All-Laminar Case

Check reference

conditions X

RefMach 2.75

XKInf 1E-6

RetInf 0.3

RefL (m) 0.06985

Ttot (K) 295.7

Ptot (Pa) 98000

Check the initial

solution X

Remove orphan

nodes X

Use most resent

INTOUT le X

Input File

Spatial order (FSO) 3

Time order (TFOSO) 1

Time-step scaling

ag (ITIME) 1

CFL 5-20

Turbulence CFL

(CFLT) 1

Turbulence order

(FSOT) 1

Turbulence model SST

Turbulent Input

Quantities

K 1E-6

Epsilon 0.3

Reference

Quantities

Mach 2.75

Tref (R) 211.845

Re 592877

Post Processing

Iterations (Coarse,

Medium, Fine) 0, 0, 10000

Dimensionalize the

solution X

Comments Converged

NASA/TM—2013-218081 96
E.7 Combined Case

Pre-Processing

Orient meshes X

No negative volumes X

Check boundary

conditions for gaps X

Initial Solution Modied Geometry

Case

Check reference

conditions X

RefMach 2.75

XKInf 1E-6

RetInf 0.3

RefL (m) 0.06985

Ttot (K) 295.7

Ptot (Pa) 98000

Check the initial

solution X

Remove orphan

nodes X

Use most resent

INTOUT le X

Input File

Spatial order (FSO) 3

Time order (TFOSO) 1

Time-step scaling

ag (ITIME) 1

CFL 5-20

Turbulence CFL

(CFLT) 1

Turbulence order

(FSOT) 1

Turbulence model SST

Turbulent Input

Quantities

K 1E-6

Epsilon 0.3

Reference

Quantities

Mach 2.75

Tref (R) 211.845

Re 592877

Post Processing

Iterations (Coarse,

Medium, Fine) 0, 0, 20000

Dimensionalize the

solution X

Comments Converged

NASA/TM—2013-218081 97
E.8 TKE Case

Pre-Processing

Orient meshes X

No negative volumes X

Check boundary

conditions for gaps X

Initial Solution Initial

Check reference

conditions X

RefMach 2.75

XKInf 1E-2

RetInf 0.3

RefL (m) 0.06985

Ttot (K) 295.7

Ptot (Pa) 98000

Check the initial

solution X

Remove orphan

nodes X

Use most resent

INTOUT le X

Input File

Spatial order (FSO) 3

Time order (TFOSO) 1

Time-step scaling

ag (ITIME) 1

CFL 5-20

Turbulence CFL

(CFLT) 1

Turbulence order

(FSOT) 1

Turbulence model SST

Turbulent Input

Quantities

K 1E-2

Epsilon 0.3

Reference

Quantities

Mach 2.75

Tref (R) 211.845

Re 592877

Post Processing

Iterations (Coarse,

Medium, Fine) 0, 0, 20000

Dimensionalize the

solution X

Comments Converged

NASA/TM—2013-218081 98
E.9 MUT Case

Pre-Processing

Orient meshes X

No negative volumes X

Check boundary

conditions for gaps X

Initial Solution Initial

Check reference

conditions X

RefMach 2.75

XKInf 1E-2

RetInf 3.0

RefL (m) 0.06985

Ttot (K) 295.7

Ptot (Pa) 98000

Check the initial

solution X

Remove orphan

nodes X

Use most resent

INTOUT le X

Input File

Spatial order (FSO) 3

Time order (TFOSO) 1

Time-step scaling

ag (ITIME) 1

CFL 5-20

Turbulence CFL

(CFLT) 1

Turbulence order

(FSOT) 1

Turbulence model SST

Turbulent Input

Quantities

K 1E-2

Epsilon 3.0

Reference

Quantities

Mach 2.75

Tref (R) 211.845

Re 592877

Post Processing

Iterations (Coarse,

Medium, Fine) 0, 0, 20000

Dimensionalize the

solution X

Comments Converged

NASA/TM—2013-218081 99
E.10 Standard Case with SST-GY

Pre-Processing

Orient meshes X

No negative volumes X

Check boundary

conditions for gaps X

Initial Solution Standard Case

Check reference

conditions X

RefMach 2.75

XKInf 1E-6

RetInf 0.3

RefL (m) 0.06985

Ttot (K) 295.7

Ptot (Pa) 98000

Check the initial

solution X

Remove orphan

nodes X

Use most resent

INTOUT le X

Input File

Spatial order (FSO) 3

Time order (TFOSO) 1

Time-step scaling

ag (ITIME) 1

CFL 5-20

Turbulence CFL

(CFLT) 1

Turbulence order

(FSOT) 1

Turbulence model SST-GY

Turbulent Input

Quantities

K 1E-6

Epsilon 0.3

Reference

Quantities

Mach 2.75

Tref (R) 211.845

Re 592877

Post Processing

Iterations (Coarse,

Medium, Fine) 0, 0, 20000

Dimensionalize the

solution X

Comments Converged

NASA/TM—2013-218081 100
E.11 Standard Case with BSL

Pre-Processing

Orient meshes X

No negative volumes X

Check boundary

conditions for gaps X

Initial Solution Standard Case with

SST-GY

Check reference

conditions X

RefMach 2.75

XKInf 1E-6

RetInf 0.3

RefL (m) 0.06985

Ttot (K) 295.7

Ptot (Pa) 98000

Check the initial

solution X

Remove orphan

nodes X

Use most resent

INTOUT le X

Input File

Spatial order (FSO) 3

Time order (TFOSO) 1

Time-step scaling

ag (ITIME) 1

CFL 5-20

Turbulence CFL

(CFLT) 1

Turbulence order

(FSOT) 1

Turbulence model BSL

Turbulent Input

Quantities

K 1E-6

Epsilon 0.3

Reference

Quantities

Mach 2.75

Tref (R) 211.845

Re 592877

Post Processing

Iterations (Coarse,

Medium, Fine) 0, 0, 5000

Dimensionalize the

solution X

Comments Converged

NASA/TM—2013-218081 101
E.12 Flat Plate with SST

Pre-Processing

Orient meshes X

No negative volumes X

Check boundary

conditions for gaps X

Initial Solution None

Check reference

conditions X

RefMach 0.2

XKInf 1E-6

RetInf 0.3

RefL (ft) 1

Ttot (K) 302.39

Ptot (Pa) 386192

Check the initial

solution X

Remove orphan

nodes X

Use most resent

INTOUT le X

Input File

Spatial order (FSO) 3

Time order (TFOSO) 1

Time-step scaling

ag (ITIME) 1

CFL 5-40

Turbulence CFL

(CFLT) 1

Turbulence order

(FSOT) 1

Turbulence model SST

Turbulent Input

Quantities

K 1E-6

Epsilon 0.3

Reference

Quantities

Mach 0.2

Tref (R) 540

Re 5E6

Post Processing

Iterations (Coarse,

Medium, Fine) 5000, 5000, 220000

Dimensionalize the

solution X

Comments Converged

NASA/TM—2013-218081 102
E.13 Flat Plate with K-Omega

Pre-Processing

Orient meshes X

No negative volumes X

Check boundary

conditions for gaps X

Initial Solution Flat Plate with SST

Check reference

conditions X

RefMach 0.2

XKInf 1E-6

RetInf 0.3

RefL (ft) 1

Ttot (K) 302.39

Ptot (Pa) 386192

Check the initial

solution X

Remove orphan

nodes X

Use most resent

INTOUT le X

Input File

Spatial order (FSO) 3

Time order (TFOSO) 1

Time-step scaling

ag (ITIME) 1

CFL 5-40

Turbulence CFL

(CFLT) 1

Turbulence order

(FSOT) 1

Turbulence model K-Omega

Turbulent Input

Quantities

K 1E-6

Epsilon 0.3

Reference

Quantities

Mach 0.2

Tref (R) 540

Re 5E6

Post Processing

Iterations (Coarse,

Medium, Fine) 0, 0, 180000

Dimensionalize the

solution X

Comments Converged

NASA/TM—2013-218081 103
E.14 Flat Plate with SST-GY

Pre-Processing

Orient meshes X

No negative volumes X

Check boundary

conditions for gaps X

Initial Solution Flat Plate with SST

Check reference

conditions X

RefMach 0.2

XKInf 1E-6

RetInf 0.3

RefL (ft) 1

Ttot (K) 302.39

Ptot (Pa) 386192

Check the initial

solution X

Remove orphan

nodes X

Use most resent

INTOUT le X

Input File

Spatial order (FSO) 3

Time order (TFOSO) 1

Time-step scaling

ag (ITIME) 1

CFL 5-40

Turbulence CFL

(CFLT) 1

Turbulence order

(FSOT) 1

Turbulence model SST-GY

Turbulent Input

Quantities

K 1E-6

Epsilon 0.3

Reference

Quantities

Mach 0.2

Tref (R) 540

Re 5E6

Post Processing

Iterations (Coarse,

Medium, Fine) 0, 0, 180000

Dimensionalize the

solution X

Comments Converged

NASA/TM—2013-218081 104
E.15 Flat Plate with BSL

Pre-Processing

Orient meshes X

No negative volumes X

Check boundary

conditions for gaps X

Initial Solution Flat Plate with SST

Check reference

conditions X

RefMach 0.2

XKInf 1E-6

RetInf 0.3

RefL (ft) 1

Ttot (K) 302.39

Ptot (Pa) 386192

Check the initial

solution X

Remove orphan

nodes X

Use most resent

INTOUT le X

Input File

Spatial order (FSO) 3

Time order (TFOSO) 1

Time-step scaling

ag (ITIME) 1

CFL 5-40

Turbulence CFL

(CFLT) 1

Turbulence order

(FSOT) 1

Turbulence model BSL

Turbulent Input

Quantities

K 1E-6

Epsilon 0.3

Reference

Quantities

Mach 0.2

Tref (R) 540

Re 5E6

Post Processing

Iterations (Coarse,

Medium, Fine) 0, 0, 180000

Dimensionalize the

solution X

Comments Converged

NASA/TM—2013-218081 105
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PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 

1. REPORT DATE (DD-MM-YYYY)

01-10-2013 

2. REPORT TYPE

Technical Memorandum 

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Understanding the Flow Physics of Shock Boundary-Layer Interactions Using CFD and 

Numerical Analyses 

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Friedlander, David, J. 

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 984754.02.07.03.13.02 

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 

8. PERFORMING ORGANIZATION

 REPORT NUMBER

E-18767 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

10. SPONSORING/MONITOR'S

 ACRONYM(S)

NASA 

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/TM-2013-218081 

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Categories: 07 and 64 

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

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

This report was submitted as a dissertation in partial fulfillment of the requirements for the degree of Master of Science to the University of 

Cincinnati, Cincinnati, Ohio, April 2013. 

14. ABSTRACT

Computational fluid dynamic (CFD) analyses of the University of Michigan (UM) Shock/Boundary-Layer Interaction (SBLI) experiments 

were performed as an extension of the CFD SBLI Workshop held at the 48th AIAA Aerospace Sciences Meeting in 2010. In particular, the 

UM Mach 2.75 Glass Tunnel with a semi-spanning 7.75° wedge was analyzed in attempts to explore key physics pertinent to SBLI’s,

including thermodynamic and viscous boundary conditions as well as turbulence modeling. Most of the analyses were 3D CFD simulations 

using the OVERFLOW flow solver, with additional quasi-1D simulations performed with an in house MATLAB code interfacing with the 

NIST REFPROP code to explore perfect verses non-ideal air. A fundamental exploration pertaining to the effects of particle image 

velocimetry (PIV) on post-processing data is also shown. Results from the CFD simulations showed an improvement in agreement with 

experimental data with key contributions including adding a laminar zone upstream of the wedge and the necessity of mimicking PIV 

particle lag for comparisons. Results from the quasi-1D simulation showed that there was little difference between perfect and non-ideal air 

for the configuration presented. 

15. SUBJECT TERMS

Shock waves; Boundary layers; Computational fluid dynamics 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU 

18. NUMBER

 OF 

 PAGES

126 

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email:help@sti.nasa.gov) 

a. REPORT

U 

b. ABSTRACT

U 

c. THIS 

PAGE

U 

19b. TELEPHONE NUMBER (include area code)

443-757-5802 

Standard Form 298 (Rev. 8-98)

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