Investigation of Three-Dimensional Shock-Wave/Turbulent Boundary Layer Interactions.

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ABSTRACT

FUNDERBURK, MORGAN LEE. Investigation of Three-Dimensional Shock-Wave/Turbulent Boundary Layer Interactions. (Under the direction of Venkateswaran Narayanaswamy.)

Ramjet and scramjet type engines represent the future of high-speed air-breathing propul-sion, providing superior efficiency compared to conventional turbojet and rocket engines. This improved efficiency is the result of using a shock-wave train to produce the compression of the intake air necessary for combustion. However, the inlet/isolators of these systems are partic-ularly susceptible to the effects of turbulent shock-wave/boundary layer interactions (SBLIs) for flight Mach numbers less than 5. As the boundary layer along the inlet wall is compressed by the shock wave, it thickens and in some situations may separate. In a time-averaged sense, separated SBLIs cause numerous undesireable effects, including increased flowpath distortion and reduced total pressure recovery. The shock-induced separation is also intensely unsteady, and can produce low-frequency transient wall pressure loads that couple with the underlying aerostructure leading to fatigue. In rare circumstances, the separated boundary layer can cause a blockage of the inviscid core flow and induce the ejection of the oblique shock train in an event known as unstart.

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begun to elucidate the transient nature of the confined 3-D SBLIs, these simulations are incred-ibly resource intensive due to the presence of small-scale turbulent flow structures that must be resolved to accurately replicate the interaction dynamics. While physical experiments are not subject to the same computational resource and time restrictions, experimental data regarding the unsteady physics of 3-D, confined SBLIs is scarce. Further, while rectangular inlet confine-ment effects are an active research topic, little information exists regarding the confineconfine-ment effects on SBLIs occuring in axisymmetric inlet/isolator geometries despite the commonality of these configurations.

Due to these experimental deficits, the aim of this work is to study the mean and unsteady characteristics of 3-D SBLIs confined by rectangular and axisymmetric bounding geometries. Experiments were conducted in the North Carolina State University supersonic wind tunnel at a nominal test section Mach number of 2.5 and unit Reynolds number of 5.1×107 m−1. Com-pression ramp interactions were used as surrogates for the impinging/reflected SBLIs present in isolator shock trains. In isolators, combustion-induced heat release typically results in a rise in the duct back pressure ratio, which strengthens SBLIs and increases the unsteady loading magnitude at the wall. Eventually, enough back pressure will precipitate the formation and strengthening of a globally connected SBLI that sweeps upstream resulting in the aforemen-tioned unstart phenomenon. Hence, an emphasis was placed on determining the effect of the shock strength/compression ramp angle on the unsteady wall load and the observed coupling between the various SBLI regions. Conventional experimental techniques such as surface streak-line visualizations, mean pressure sensitive paint (PSP) imaging, high-frequency transducer wall static pressurements, and off-body planar laser scattering techniques allowed insights into the confined 3-D SBLI structure and dynamics that are sorely needed.

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to be exacerbated by stronger shock waves. The effects of the enlarged separations and three-dimensionality on the unsteady features of the interactions are explored. Contributions are also made to the field of SBLI control using axisymmetric microramp vortex generators. The devices are found to decrease separation length and the unsteadiness of the SBLIs in controlled areas but actually worsen bulk confinement effects, increasing separation length in uncontrolled portions of the flow and amplifying the unsteady loading there.

Over the course of these experiments, a significant need for better unsteady wall pressure diagnostic tools was identified. The heavy three-dimensionality of the observed shock-induced separations resulted in unsteady wall pressures that varied in two dimensions. To gain a complete understanding of the 3-D interaction dynamics using conventional point sensors, large arrays would need to be used leading to wetted surface access/data acquisition infrastructure require-ments that were impractical. Therefore, it became desirable to develop/adapt non-intrusive optical techniques capable of resolving the entire unsteady wall pressure field simultaneously. To this end, significant efforts were made toward implementing and validating innovative fast-response PSP methods for use in the 3-D SBLIs. Particular importance was placed on quan-tifying the effect of the imaging system noise on the spectral signal quality of the obtained results. Comparisons of high-frequency transducer and fast PSP data revealed the unsteady wall pressure of the interactions could be accurately resolved for pulsation frequencies up to several kHz in regions of peak SBLI unsteadiness.

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©Copyright 2019 by Morgan Lee Funderburk

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Investigation of Three-Dimensional Shock-Wave/Turbulent Boundary Layer Interactions

by

Morgan Lee Funderburk

A dissertation submitted to the Graduate Faculty of North Carolina State University

in partial fulfillment of the requirements for the Degree of

Doctor of Philosophy

Aerospace Engineering

Raleigh, North Carolina

2019

APPROVED BY:

Jack Edwards Pramod Subbareddy

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DEDICATION

This work is dedicated to my friends and family. This journey wouldn’t have been possible without you, and I love you all dearly.

To my mother Ginger, thank you for always supporting and loving me unconditionally. Your grace and patience have not gone unappreciated. To my father Al, you are my biggest role model and fan, and one of my best friends. You have both endowed me with the work ethic and the morality necessary for navigating life’s challenges, and I am forever grateful.

To Shelby and Tyler, Nana, and all the Funderburks and Coxes past and present, thank you for being the best family I could possibly ask for. You have all helped me grow as a man and the fond memories I share with you keep me going.

To my stepfather Danny, you have set a shining example for me in more ways than I can list and I couldn’t have made it here without you. To my entire stepfamily - you are all great people. Know that in my heart I am as much a Mullis as I am anything else.

Caroline, you are my rock and made it possible for me to persevere throughout the last five years. Let’s make the end of this chapter in my life the beginning of a new, exciting one in ours. To all the LaFaves and Dutnells who have welcomed me with open arms, I greatly enjoy the time we spend together and am looking forward to more of your company.

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BIOGRAPHY

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ACKNOWLEDGEMENTS

First and foremost I wish to thank my faculty advisor, Dr. Venkat Narayanaswamy, for his constant guidance and for the countless opportunities he has afforded me over the course of this graduate research. Dr. Venkat has provided me with a wealth of knowledge, particularly in the areas of wind tunnel testing methodology and shock-wave/boundary layer interaction physics. The countless discussions that we’ve had on technical matters have made me a much better engineer.

I would also like to acknowledge the NDSEG Fellowship program, which was instrumental to my success. My NDSEG Fellowship has allowed me to conduct the research in the present work completely unimpeded, and to elevate it to a level that would have been otherwise impossible. My sincere thanks go out to each of my committee members, who could always be counted on for constructive advice and assistance regarding the subject matter on display here. To Dr. Pramod Subbareddy and Balachandra Reddy Mettu, thank you for lending me your computa-tional expertise. Similarly, to the MAE department laboratory managers and research fabrica-tion supervisors (particularly Dr. James Kribs, Gary Lofton and Steve Cameron), none of the present work would have been possible without your continued support.

To all of the great industry engineers who have mentored me over the course of my education - in particular Bill Shepard and Tom Hatfield - thank you for instilling me with a passion for this discipline that has propelled me to this point.

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to you. To Dean, Vaibhav and Jonathan, keep pounding and don’t panic, you’ll make it. To all of the undergraduate research assistants I worked with, thanks for your dedication; hopefully I taught you something useful. We all learned plenty of valuable lessons together and shared at least as many laughs along the way. I wish all of you the best in your future endeavors, and am blessed to count you among my friends.

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TABLE OF CONTENTS

LIST OF TABLES . . . xi

LIST OF FIGURES . . . .xiii

NOMENCLATURE . . . xx

Chapter 1 Introduction . . . 1

1.1 Historical Context and Background . . . 1

1.2 Previous Work in SBLIs . . . 6

1.2.1 2-D SBLIs . . . 6

1.2.2 3-D SBLIs . . . 15

1.2.3 Effects of Internal Confinement on SBLIs . . . 21

1.3 Motivation . . . 25

Chapter 2 Experimental Setup . . . 27

2.1 Experimental Facility . . . 27

2.1.1 Supersonic Wind Tunnel . . . 27

2.1.2 Test Conditions . . . 27

2.2 Experimental Models . . . 29

2.2.1 W-B Compression Ramp Model . . . 29

2.2.2 H-I Compression Ramp Model . . . 31

2.2.3 2-D Compression Ramp Model . . . 32

2.3 Experimental Methods . . . 34

2.3.1 SSVs . . . 34

2.3.2 High-Frequency WSP Measurements . . . 37

2.3.3 Pitot Boundary Layer Measurements . . . 40

2.3.4 PLS Measurements . . . 42

2.3.5 PSP Measurements . . . 44

2.4 Dissertation Structure . . . 46

Chapter 3 Fundamental Investigations of Wall-Bounded Compression Ramp Shock-Wave/Boundary Layer Interactions . . . 49

3.1 Motivation . . . 49

3.2 General Experimental Description . . . 50

3.3 Inflow Characterization . . . 51

3.4 Mild Back Pressure Ratio Results . . . 54

3.4.1 Mean Results . . . 54

3.4.2 Unsteady Results . . . 59

3.4.3 Intermediate Conclusions for Mild Back Pressure Ratios . . . 69

3.5 Large Back Pressure Ratio Results . . . 70

3.5.1 Mean Results . . . 70

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3.6 Summary . . . 80

Chapter 4 Fundamental Investigations of Half-Isolator Compession Ramp Shock-Wave/Boundary Layer Interactions . . . 83

4.1 Motivation . . . 83

4.2 General Experimental Description . . . 84

4.3 Computational Setup . . . 85

4.3.1 RANS Computations . . . 85

4.3.2 Grid Resolution Study . . . 86

4.4 Inflow Characterization . . . 86

4.5 Mean Results . . . 88

4.5.1 Unsteady SSV Results . . . 88

4.5.2 Mean Pressure Profiles . . . 91

4.5.3 Comparison of Near-Wall H-I and 2-D Interaction Flowfields . . . 92

4.5.4 H-I SBLI Flowfield Structure . . . 96

4.5.5 Effect of Confinement on H-I SBLI . . . 102

4.5.6 Potential Mechanisms Inflating H-I SBLI Separation . . . 107

4.6 Unsteady Results . . . 112

4.6.1 RMS Pressure Profiles . . . 112

4.6.2 Pressure Power Spectra . . . 114

4.6.3 Two-Point Coherence Analysis . . . 114

4.6.4 Cross-Correlation Analysis . . . 116

4.7 Summary . . . 119

Chapter 5 Microramp Vortex Generator Control of Half-Isolator Compres-sion Ramp Shock-Wave/Boundary Layer Interactions . . . .121

5.1 Introduction to Microramp VGs . . . 121

5.2 Motivation . . . 123

5.3 General Experimental Description . . . 124

5.4 VG Geometry and Placement . . . 125

5.5 Microramp VG Flowfield . . . 126

5.5.1 Unsteady SSV Results . . . 127

5.5.2 Mean Wall Pressure Field . . . 128

5.5.3 Downstream Boundary Layer Characterization . . . 129

5.5.4 PLS Intensity Fields . . . 132

5.5.5 Pressure Power Spectra . . . 134

5.6 Application of Microramp VGs to the H-I SBLI . . . 135

5.6.1 Unsteady SSV Results . . . 135

5.6.2 Mean Wall Pressure Fields . . . 140

5.6.3 PLS Intensity Fields . . . 144

5.6.4 Physical Model of H-I SBLI Pressure Increase with Microramp VGs . . . 147

5.6.5 RMS Pressure Profiles . . . 150

5.6.6 Pressure Power Spectra . . . 152

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5.7 Summary . . . 156

Chapter 6 Fast Fluoro-Isopropyl-Butyl Polymer Pressure-Sensitive Paint Measurements . . . .159

6.1 Introduction to Fast PSPs . . . 159

6.2 Motivation . . . 163

6.3 General Experimental Description . . . 163

6.4 Fast FIB PSP Measurements . . . 164

6.4.1 Paint Characteristics and Application . . . 164

6.4.2 Imaging Methodology and Data Reduction Process . . . 165

6.4.3 Paint Thickness and Roughness Measurements . . . 168

6.5 Results and Discussion . . . 169

6.5.1 Mean Results . . . 169

6.5.2 Uncorrected Unsteady Results . . . 171

6.5.3 Paint Response Time and Amplitude Ratio . . . 173

6.5.4 Spectral Signal-to-Noise Ratio . . . 178

6.5.5 Corrected RMS Wall Pressure Field . . . 184

6.5.6 Paint Thickness Variations . . . 185

6.6 Summary . . . 187

Chapter 7 Polymer-Ceramic Pressure-Sensitive Paint Measurements . . . .189

7.1 Motivation . . . 189

7.2 General Experimental Description . . . 191

7.3 PC-PSP Measurements . . . 192

7.3.1 Paint Composition, Mixture and Application . . . 192

7.3.2 Imaging Methodology and Data Reduction Process . . . 194

7.3.3 Minimum Resolvable Pressure Amplitude . . . 198

7.4 Results and Discussion . . . 199

7.4.1 Mean Results . . . 199

7.4.2 Uncorrected Unsteady Results . . . 201

7.4.3 Simultaneous Unsteady Intermittent Region Measurement Results . . . . 204

7.4.4 Spectral Signal-to-Noise Ratios . . . 207

7.4.5 Unsteady Signal Quality and Corrected RMS Wall Pressure Field . . . 212

7.4.6 Two-Point Unsteady Measurement Results . . . 214

7.5 Summary . . . 219

Chapter 8 Advanced Investigations of Wall-Bounded Compression Ramp Shock-Wave/Boundary Layer Interactions . . . .221

8.1 Motivation . . . 221

8.2 General Experimental Description . . . 222

8.3 Mean Results . . . 224

8.3.1 Unsteady SSV Results . . . 224

8.3.2 Mean Wall Pressure Fields . . . 231

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8.4.1 Corrected RMS Wall Pressure Fields . . . 236

8.4.2 Pressure Power Spectra . . . 242

8.4.3 Two-Point Unsteady Measurement Results . . . 245

8.5 Flow Structure . . . 256

8.5.1 PLS Intensity Fields . . . 256

8.5.2 Potential Mechanisms Inflating W-B SBLI Separation . . . 262

8.5.3 Proposed Open Separation Model . . . 265

8.6 Summary . . . 268

Chapter 9 Concluding Remarks and Recommendations for Future Work . . .272

9.1 Concluding Remarks . . . 272

9.2 Recommendations for Future Work . . . 274

9.2.1 General . . . 274

9.2.2 W-B SBLI . . . 274

9.2.3 H-I SBLI . . . 275

9.2.4 2-D SBLI . . . 276

9.2.5 Fast PSP Implementation in SBLIs . . . 276

References. . . .278

Appendices . . . .292

Appendix A Supplemental Experimental Information . . . 293

A.1 Computation of Freestream Test Conditions . . . 293

A.2 Pitot Probe Description . . . 294

A.3 Computation of Boundary Layer Parameters . . . 295

A.4 Tunnel Boundary Layer Measurements . . . 297

A.5 Spherical Bow Shock Calibration . . . 298

A.6 A Note Regarding the Minimum Streamwise Spacing of WSP Transducers for Two-Point Measurements . . . 300

A.7 Repeatability of PC-PSP Application/Calibration . . . 301

Appendix B Investigations of Two-Dimensional Compression Ramp Shock-Wave/Boundary Layer Interactions . . . 304

B.1 Motivation . . . 304

B.2 General Experimental Description . . . 304

B.3 Inflow Characterization . . . 305

B.4 Mean Results . . . 306

B.4.1 Unsteady SSV Results . . . 306

B.4.2 Mean Wall Pressure Fields . . . 307

Appendix C Supplemental Wall-Bounded Compression Ramp Investigations . . . 311

C.1 W-B Inflow Unsteady SSV Results . . . 311

C.2 Comparison of Tunnel Ceiling and Sidewall-Mounted W-B SBLIs . . . 315

C.3 Bias in Previous W-B Boundary Layer Measurements . . . 317

C.4 A Note Regarding the Definition of the Inverse Viscous Aspect Ratio . . . . 319

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LIST OF TABLES

Table 2.1 Freestream test conditions . . . 28 Table 2.2 W-B compression ramp configurations and planar inviscid pressure ratios . . . 30 Table 2.3 H-I compression ramp configurations and planar inviscid pressure ratios . . . 32 Table 2.4 2-D compression ramp configurations and planar inviscid pressure ratios . . . 34 Table 2.5 Pitot probe tip location for baseline boundary layer measurements of

com-pression ramp models . . . 42

Table 3.1 W-B compression ramp configurations examined in Chapter 3 . . . 50 Table 3.2 Incoming boundary layer characteristics for the W-B and 2-D models . . . 53 Table 3.3 Values of Lsep and Lv discerned from the RMS pressure profiles for the W-B

interactions . . . 77

Table 4.1 H-I compression ramp configurations examined in Chapter 4 . . . 84 Table 4.2 Incoming boundary layer characteristics for the H-I and 2-D models and

RANS simulations . . . 88 Table 4.3 Circumferential average values of Lsep discerned from the SSVs for the H-I

interactions . . . 90 Table 4.4 Centerline values ofLsep discerned from the RMS pressure profiles for the H-I

compression ramp interaction . . . 113

Table 5.1 H-I compression ramp configuration selected for the microramp VG study . . 125 Table 5.2 Boundary layer characteristics downstream of microramp VGs . . . 130 Table 5.3 Circumferential average values ofLsep and Lu for baseline and VG-controlled

interactions . . . 137 Table 5.4 PLS-determined outer shock angle, density rise, and pressure rise for baseline

and VG-controlled interactions . . . 146

Table 6.1 H-I compression ramp configuration selected for fast FIB PSP study . . . 164 Table 6.2 Representative camera noise cutoff frequencies for fast FIB PSP measurements

in different regions along the centerline of the H-I interaction . . . 183 Table 6.3 Fast FIB PSP thickness and roughness sample values . . . 186 Table 6.4 Uncertainty in σp,c/pw due to local paint thickness/time constant variation

for different regions of the H-I interaction . . . 187

Table 7.1 W-B compression ramp configuration selected for the PC-PSP study . . . 192 Table 7.2 Representative camera noise cutoff frequencies for PC-PSP measurements in

different regions along the centerline of the W-B compression ramp interaction 209 Table 7.3 Representative camera noise cutoff frequencies for PC-PSP measurements in

different regions along the corner junction of the W-B compression ramp in-teraction . . . 210

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Table 8.3 Values ofLsepandLvdiscerned from the noise-corrected RMS pressure profiles

from PC-PSP for the W-B compression ramp interaction . . . 243

Table A.1 Stern-Volmer coefficients forin-situ PC-PSP calibrations . . . 301

Table B.1 2-D compression ramp configurations examined in Appendix B . . . 305

Table B.2 Incoming boundary layer characteristics for the 2-D model . . . 306

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LIST OF FIGURES

Figure 1.1 Schematic of a propulsion-airframe integrated scramjet, showing oblique

in-let/isolator shock train and SBLIs . . . 2

Figure 1.2 An SR-71 ignites its afterburners . . . 5

Figure 1.3 Separated, 2-D impinging/reflected SBLI structure . . . 6

Figure 1.4 Separated, 2-D compression ramp SBLI structure . . . 7

Figure 1.5 Shock-induced separation length as a function of Reynolds number . . . 9

Figure 1.6 Wall pressure profiles beneath a 2-D compression ramp SBLI . . . 11

Figure 1.7 Power spectra of unsteady pressure loading beneath a compression ramp SBLI 12 Figure 1.8 Wall pressure time-series beneath intermittent region of separation shock motion . . . 13

Figure 1.9 Wall pressure contours beneath a compression ramp SBLI with varying angle 14 Figure 1.10 Flow features of a glancing fin SBLI . . . 16

Figure 1.11 Mean and RMS wall pressure profiles beneath a glancing fin SBLI . . . 17

Figure 1.12 Unsteady pressure power spectra at maximum RMS location near separation in glancing fin SBLIs . . . 18

Figure 1.13 Corner vortex pair transverse/vertical flow vectors . . . 18

Figure 1.14 Physical model for corner SBLI induced bifurcation . . . 19

Figure 1.15 Wall-bounded compression ramp interaction . . . 20

Figure 1.16 Impinging/reflected SBLI centerline separation length as a function of inverse viscous aspect ratio . . . 22

Figure 1.17 Results of RANS simulations of impinging/reflected SBLIs in rectangular channels for different inverse viscous aspect ratios . . . 23

Figure 2.1 North Carolina State University (NCSU) supersonic wind tunnel facility . . . 28

Figure 2.2 Isometric view of W-B compression ramp model and example flow features of interest . . . 29

Figure 2.3 Isometric view of H-I compression ramp model and example flow features of interest . . . 32

Figure 2.4 Isometric view of 2-D compression ramp model and example flow features of interest . . . 33

Figure 2.5 Side-view of W-B compression ramp model mounted from the ceiling of the NCSU supersonic wind tunnel . . . 35

Figure 2.6 Top-view of W-B compression ramp model mounted from the sidewall of the NCSU supersonic wind tunnel . . . 36

Figure 2.7 WSP transducer instrumentation for the W-B compression ramp model . . . 38

Figure 2.8 WSP transducer instrumentation for the H-I compression ramp model . . . . 39

Figure 2.9 Side-view and inset isometric view of 2-D compression ramp model and pitot measurement setup in the NCSU supersonic wind tunnel . . . 41

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Figure 2.11 Top-view of H-I compression ramp model and conventional PSP setup in the

NCSU supersonic wind tunnel . . . 44

Figure 2.12 Conventional PSP calibration . . . 45

Figure 3.1 Incoming boundary layer profiles for the W-B and 2-D models . . . 52

Figure 3.2 Time-averaged SSVs along the floor of the W-B interaction,α = 12° . . . 54

Figure 3.3 Mean of unsteady SSV along the floor of the W-B interaction, α= 12° . . . . 57

Figure 3.4 Mean pressure profiles for the W-B interaction, α= 12° . . . 58

Figure 3.5 RMS pressure profiles for the W-B interaction,α= 12° . . . 59

Figure 3.6 Intermittent region WSP time-series comparison for the W-B interaction, α= 12° . . . 61

Figure 3.7 Pressure power spectra comparison for intermittent regions of W-B interac-tion,α= 12° . . . 62

Figure 3.8 Comparison of nondimensional corner unsteadiness frequencies with LES . . 65

Figure 3.9 Two-point coherences of WSP fluctuations of primary and corner SBLI in-termittent regions with various flowfield locations for the W-B interaction, α= 12° . . . 68

Figure 3.10 Time-averaged SSV along the floor of the W-B interaction, α= 24° . . . 70

Figure 3.11 Mean of unsteady SSV along the floor of the W-B interaction, α= 24° . . . . 71

Figure 3.12 Mean of unsteady SSV in the corner junction of the W-B interaction, α= 24° 72 Figure 3.13 Oblique view of unsteady SSV mean along the W-B interaction floor plate/sidewall, α= 24° . . . 73

Figure 3.14 Mean WSP profiles for the W-B interaction,α= 24° . . . 75

Figure 3.15 RMS pressure profiles for the W-B interaction,α= 24° . . . 77

Figure 3.16 Pressure power spectra comparison for intermittent regions of W-B interac-tion,α= 24° . . . 78

Figure 3.17 Comparison of Strouhal number spectra based on Lsep and Lv values from Table 3.3 . . . 79

Figure 4.1 RANS simulation grid slices for H-I configuration,α= 20°,h/R= 0.246 . . . 86

Figure 4.2 Incoming boundary layer profiles for the H-I and 2-D models and RANS simulations . . . 87

Figure 4.3 Means of unsteady SSVs for H-I interactions at various compression ramp angles . . . 89

Figure 4.4 Comparison of spanwise average separation length scale between H-I and 2-D interactions for varous compression ramp angles . . . 91

Figure 4.5 Mean pressure profiles at the centerline of the H-I interaction (φ = 0°) for various compression ramp angles . . . 92

Figure 4.6 Top-view of unsteady SSV mean and averaged PSP pressure field for H-I interaction, α= 20°,h/R= 0.246, and 2-D interaction, α= 20° . . . 93

Figure 4.7 Comparison of smoothed PSP wall pressure profiles alongside transducer data at the centerline of the H-I and 2-D interactions . . . 95

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Figure 4.9 Transverse/vertical PLS density and RANS slices for the H-I interaction,

α= 20°,h/R= 0.246 . . . 97

Figure 4.10 Centerline RANS simulation contours . . . 99

Figure 4.11 Iso-surface of density displaying outer H-I SBLI shock structure . . . 101

Figure 4.12 Illustration showing effect of confinement ratio h/Ron outer shock strength . 103 Figure 4.13 Experimental results for H-I interaction, α= 20°,h/R= 0.194 . . . 104

Figure 4.14 Comparison of smoothed PSP wall pressure profiles atφ= 5°for theα= 20° H-I SBLI cases . . . 105

Figure 4.15 Comparison of smoothed PSP wall pressure profiles for H-I and 2-D interac-tions with similar reattachment pressure magnitudes . . . 108

Figure 4.16 Illustration of virtual throat formation at outflow of 2-D SBLI . . . 110

Figure 4.17 RANS results illustrating virtual throat formation at outflow of H-I and 2-D SBLIs . . . 111

Figure 4.18 RMS pressure profiles at the centerline of the H-I interaction (φ = 0°) for various compression ramp angles . . . 113

Figure 4.19 Pressure power spectra at intermittent region of the H-I interaction for var-ious compression ramp angles . . . 115

Figure 4.20 Two-point coherences between intermittent region shock motion of H-I in-teraction and upstream/downstream pressure signals for various compression ramp angles . . . 116

Figure 4.21 Two-point cross-correlation coefficients between separation shock motion and pressure fluctuations at various streamwise stations for the H-I interaction, α= 20°,h/R= 0.246 . . . 118

Figure 4.22 Maximum broad mode values of cross-correlation between separation shock motion and pressure fluctuctuations at various streamwise stations for various compression ramp angles . . . 119

Figure 5.1 Axisymmetric microramp VG geometry . . . 125

Figure 5.2 Microramp VG flowfield . . . 128

Figure 5.3 Boundary layer profiles downstream of microramp VGs . . . 130

Figure 5.4 Instaneous and mean transverse/vertical PLS intensity fields downstream of microramp VG . . . 131

Figure 5.5 Boundary layer pressure power spectra downstream of microramp VG . . . . 134

Figure 5.6 Means of unsteady SSVs for various VG configurations . . . 136

Figure 5.7 Mean PSP pressure fields for baseline and VG-controlled interactions . . . . 140

Figure 5.8 Smoothed PSP wall pressure profiles alongside transducer data for baseline and VG-controlled interactions . . . 142

Figure 5.9 Instantaneous and mean transverse/vertical PLS intensity fields in down-stream portion of baseline and VG-controlled interactions . . . 145

Figure 5.10 Schematic illustration of outer shock formation for uncontrolled and VG-controlled interactions . . . 148

Figure 5.11 Instaneous and mean transverse/vertical PLS intensity fields in upstream portion of baseline and VG-controlled interactions . . . 149

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Figure 5.13 Pressure power spectra at intermittent region for baseline and VG-controlled

interactions . . . 152

Figure 5.14 Two-point coherences between intermittent region shock motion and up-stream/downstream pressure signals for various VG configurations . . . 154

Figure 6.1 Schematic of various fast PSP structures . . . 160

Figure 6.2 Fast PSP unsteady signal attenuation and phase shift curves as a function of nondimensional frequency . . . 163

Figure 6.3 Fast FIB PSP setup in the NCSU supersonic wind tunnel . . . 166

Figure 6.4 Fast FIB PSP calibration . . . 167

Figure 6.5 Top-view of mean fast FIB PSP pressure field and unsteady SSV mean for H-I interaction,α= 20°,h/R= 0.246 . . . 169

Figure 6.6 Comparison of mean wall pressure profiles from fast FIB PSP and transducers near the centerline of the H-I interaction . . . 171

Figure 6.7 Uncorrected unsteady fast FIB PSP pressure data for the H-I interaction, α= 20°,h/R= 0.246 . . . 172

Figure 6.8 Comparison of intermittent region power spectra from fast FIB PSP and transducers near the centerline of the H-I interaction,α= 20°,h/R= 0.246 . 174 Figure 6.9 Comparison of model amplitude response curve and measured fast FIB PSP amplitude response in the intermittent region of the H-I interaction . . . 176

Figure 6.10 Minimum resolvable unsteady pressure amplitude vs. mean wall pressure for fast FIB PSP . . . 179

Figure 6.11 Comparison of intermittent region fast FIB PSP and camera noise power spectra . . . 180

Figure 6.12 Power spectra and spectral signal-to-noise ratios from response time cor-rected fast FIB PSP and transducers near the centerline of the H-I interaction182 Figure 6.13 Corrected unsteady fast FIB PSP pressure data for H-I interaction . . . 185

Figure 7.1 PC-PSP setup in the NCSU supersonic wind tunnel . . . 194

Figure 7.2 PC-PSP calibration . . . 196

Figure 7.3 PC-PSP coat on W-B model . . . 197

Figure 7.4 Minimum resolvable unsteady pressure amplitude vs. mean wall pressure for PC-PSP . . . 199

Figure 7.5 Top-view of mean PC-PSP pressure field and unsteady SSV mean for W-B interaction, α= 24° . . . 200

Figure 7.6 Comparison of mean wall pressure profiles from PC-PSP and transducers for the W-B interaction,α= 24° . . . 201

Figure 7.7 Top-view of uncorrected PC-PSP RMS pressure field for the W-B interaction, α= 24° . . . 202

Figure 7.8 Comparison of uncorrected RMS pressure profiles from PC-PSP and trans-ducers for the W-B interaction,α = 24° . . . 203

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Figure 7.10 Spectral comparison of PC-PSP and transducer pressure signals beneath the centerline intermittent region of the W-B interaction . . . 205 Figure 7.11 Power spectra and spectral signal-to-noise ratios from PC-PSP and

trans-ducers near the centerline of the W-B interaction, α= 24° . . . 208 Figure 7.12 Comparison of dimensional model amplitude response curve and measured

amplitude response between fast FIB and PC-PSP . . . 209 Figure 7.13 Power spectra and spectral signal-to-noise ratios from PC-PSP and

trans-ducers near the corner junction of the W-B interaction, α= 24°. . . 211 Figure 7.14 Top-view of PC-PSP-based signal quality field and noise-corrected RMS

pres-sure field for the W-B interaction, α= 24° . . . 213 Figure 7.15 Comparison of noise-corrected RMS wall pressure profiles from PC-PSP and

transducers for the W-B interaction, α= 24° . . . 214 Figure 7.16 Top-view of PC-PSP-based integrated coherence fields for the W-B

interac-tion,α= 24° . . . 215 Figure 7.17 Comparison of two-point coherence spectra between upstream and

down-stream RMS peaks for PC-PSP and transducers . . . 216 Figure 7.18 Top-view of PC-PSP-based fields of cross-correlation at zero time-lag for the

W-B interaction,α= 24° . . . 217 Figure 7.19 Comparison of cross-correlation coefficients between upstream and

down-stream RMS peaks for PC-PSP and transducers . . . 219

Figure 8.1 Means of unsteady SSVs along the floor of the W-B interaction at various compression ramp angles . . . 225 Figure 8.2 Means of unsteady SSVs along the sidewall of the W-B interaction at various

compression ramp angles . . . 230 Figure 8.3 Mean PC-PSP pressure fields along the floor of the W-B interaction at various

compression ramp angles . . . 232 Figure 8.4 Comparisons of mean wall pressure profiles from PC-PSP for the W-B

inter-action . . . 234 Figure 8.5 Noise-corrected RMS pressure fields from PC-PSP along the floor of the W-B

interaction at various compression ramp angles . . . 238 Figure 8.6 PC-PSP signal quality fields along the floor of the W-B interaction at various

compression ramp angles . . . 239 Figure 8.7 Comparison of noise-corrected RMS wall pressure profiles from PC-PSP for

the W-B interaction at various compression ramp angles . . . 242 Figure 8.8 Power spectra and spectral signal-to-noise ratios from PC-PSP for the W-B

interaction at different compression ramp angles . . . 244 Figure 8.9 Comparison of Strouhal number spectra based on Lsep and Lv values from

Table 8.3 . . . 245 Figure 8.10 Top-view of PC-PSP-based integrated coherence fields for the W-B

interac-tion,α= 12° . . . 247 Figure 8.11 Top-view of PC-PSP-based fields of cross-correlation at zero time-lag for the

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Figure 8.12 Top-view of PC-PSP-based integrated coherence fields for the W-B interac-tion,α= 16° . . . 249 Figure 8.13 Top-view of PC-PSP-based fields of cross-correlation at zero time-lag for the

W-B interaction,α= 16° . . . 250 Figure 8.14 Top-view of PC-PSP-based integrated coherence fields for the W-B

interac-tion,α= 20° . . . 251 Figure 8.15 Top-view of PC-PSP-based fields of cross-correlation at zero time-lag for the

W-B interaction,α= 20° . . . 252 Figure 8.16 Top-view of PC-PSP-based integrated coherence fields for the W-B

interac-tion,α= 24° . . . 253 Figure 8.17 Top-view of PC-PSP-based fields of cross-correlation at zero time-lag for the

W-B interaction,α= 24° . . . 254 Figure 8.18 Mean and instantaneous transverse/vertical PLS intensity fields thoughout

the W-B interaction,α= 24° . . . 257 Figure 8.19 Proposed shock structure for W-B interaction,α= 24° . . . 260 Figure 8.20 Qualitative comparison of separation-induced fluid blockage effects for W-B

and H-I interactions . . . 263 Figure 8.21 Effective reduction in inviscid core flow Mach number vs. separation-induced

displacement thickness for the W-B and H-I models . . . 264 Figure 8.22 Physical model of separated glancing fin SBLI showing secondary vortex

along fin/sidewall junction . . . 265 Figure 8.23 Owl face of the second kind . . . 267 Figure 8.24 Open separation horseshoe vortex . . . 267 Figure 8.25 Proposed open ejection pathways for W-B interaction, α= 24° . . . 268

Figure A.1 Custom-manufactured pitot probe utilized for boundary layer profile mea-surements . . . 295 Figure A.2 Boundary layer profiles at the center of the NCSU supersonic wind tunnel

test section ceiling and sidewall . . . 298 Figure A.3 Time-average of freestream-normalized sphere PLS sequence . . . 299 Figure A.4 Sphere PLS intensity-density calibration . . . 299 Figure A.5 Profiles of pressure signal probability density function skewness and kurtosis

for theα= 20° H-I interaction,h/R= 0.246 . . . 300 Figure A.6 In-situPC-PSP calibrations for W-B interaction at various compression ramp

angles . . . 303

Figure B.1 Incoming boundary layer profile for the 2-D model . . . 305 Figure B.2 Means of unsteady SSVs for the 2-D interaction at various compression ramp

angles . . . 308 Figure B.3 Top-view of unsteady SSV means and mean PSP pressure fields for the 2-D

interaction at various compression ramp angles . . . 309

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Figure C.3 Comparison of spanwise average primary separation location between ceiling and sidewall-mounted W-B interactions at various compression ramp angles . 316 Figure C.4 Comparison of mean pressure profiles at the centerline of the of the

W-B interaction with the model mounted from the wind tunnel ceiling and sidewall,α= 24° . . . 317 Figure C.5 Comparison of centerline boundary layer profile for the W-B compression

ramp model and previous separation-biased centerline boundary layer profile 318

Figure D.1 Post-refinement Euler simulation grid for α = 20° H-I configuration,h/R = 0.246 . . . 322 Figure D.2 Euler simulation contours ofp/p∞ for the H-I flowfield, α= 20°,h/R= 0.246 323

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NOMENCLATURE ABBREVIATIONS

2-D Two-dimensional 3-D Three-dimensional AA Anodized aluminum

CFD Computational fluid dynamics FIB Fluoro-isopropyl-butyl

FOV Field-of-view

FWHM Full-width-at-half-maximum H-I Half-isolator

HVLP High-volume, low-pressure

KL Korkegi limit for incipient separation LES Large-eddy simulations

PC Polymer-ceramic PLS Planar laser scattering PSP Pressure sensitive paint

RANS Reynolds-averaged Navier-Stokes RMS Root-mean-squared

SBLI Shock-wave/boundary layer interaction SSV Surface streakline visualization

VG Vortex generator

W-B Wall-bounded

WSP Wall static pressure

ANNOTATIONS

BL Boundary layer

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CIR Corner intermittent region

CV Corner vortex

DS Downstream separation

E Expansion fan

IR Intermittent region

PIR Primary intermittent region PS Primary separation

R Reattachment location Ref. Reference signal location S Separation location

T Triple-point

U Upstream influence location η High-pressure core region

GREEK

α Compression ramp angle, degrees β Wave angle, degrees

δ0 99% Boundary layer thickness

δ∗ Compressible boundary layer displacement thickness, mm φ Azimuthal coordinate, degrees

ρ Density, kg/m3

ρ(x, y) Cross-correlation coefficient between signals xand y σ Standard deviation

τ Cross-correlation time-lag, ms

τdif f Diffusion-limited PSP response time, ms

τL PSP luminophore luminescence liftetime, µs

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SUBSCRIPTS

b Back, corresponding to the interaction maximum ef f Effective

p Pressure

ref Reference, corresponding to atmospheric pressure T E Microramp vortex generator trailing edge

sep Separation

u Upstream influence

v Vortex

w Wall

∞ Freestream

SYMBOLS

A Stern-Volmer intercept B Stern-Volmer slope

Coh(x, y) Spectral coherence between signals x and y D Half-isolator inner diameter, mm

Dm PSP mass diffusivity, µm2/s

f Frequency, Hz

G Power spectral density, kPa2

h Compression ramp height, mm

Microramp vortex generator height, mm PSP layer thickness, µm

H Boundary layer shape factor, δ∗/θ I Intensity, counts

ICoh(x, y) Integrated full-width-at-half-maximum coherence between signals x and y

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M Mach number p Static pressure, kPa

R Half-isolator inner radius, mm Re Reynolds number, ρ∞u∞L/µ∞

St Strouhal number, f L/u∞

t time, ms

T Temperature, K

u Velocity, m/s

W Channel width, mm

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Chapter 1

Introduction

1.1

Historical Context and Background

Ramjet and scramjet type engines represent the future of air-breathing propulsion, enabling flight at extreme altitudes and velocities with greatly improved specific impulses when compared to the conventional rocket engine [1]. This improvement is a result of bypassing the weight penalties associated with the payload of oxidizer necessary onboard a rocket powered vehicle. Ram/scramjets instead achieve the necessary mass flow rate of oxidizer to the combustion chamber in a manner similar to that of conventional turbojet engines, namely the intake and compression of the low-density freestream air. The specific impulse of any type of air-breathing jet engine differs from that of a rocket engine in that it decreases with the flight Mach number, which acts to continually increase the stagnation temperature of the intake air. Because of this mounting stagnation temperature rise, the use of conventional turbomachinery eventually becomes impractical.

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normal shock in the ramjet isolator begins to introduce losses more significant than those asso-ciated with the inefficiencies of supersonic combustion [1]. Consequently, the scramjet provides superior efficiencies to flight Mach numbers that are as of yet unknown (although it is sus-pected that the ever-increasing stagnation temperature of the intake air will eventually reduce scramjet efficiency to rocket-like levels). Subsequently, there is a desire to use ram/scramjet type engines onboard vehicles capable of hypersonic flight in the upper atmosphere. There are however, several important implications associated with the use of such engines. One such im-plication is the inability of the ram/scramjet engine to produce static thrust, as they require the incoming air to be near sonic to generate compression. Therefore, a vehicle that is powered by a ram/scramjet will need to utilize a multi-mode engine to produce thrust from takeoff, employing a conventional turbojet at subsonic and low supersonic flight Mach numbers, before transitioning to ramjet and finally scramjet operation with increasing airspeed. This concept has become known as the turbine-based combined cycle (TBCC) propulsion system.

When considering the complexity of multi-mode TBCC flowpaths, it becomes evident that the elimination of the intermediate ramjet phase is desirable. This elimination both cuts down on the total complexity of the propulsion system (eliminating potential points of failure) and reduces weight, providing two key engineering benefits. Hence, the scramjet mode must be

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ble of starting at reduced flight Mach numbers. Again, there is a serious implication associated with such a reduction in starting speed. For scramjet operations at flight Mach numbers less than 7, the compression caused by the impinging shock waves can thicken and even separate the low-momentum flow in the boundary layer at the inlet wall. Separated shock-wave/boundary layer interactions (SBLIs) tend to precipitate deterimental effects. They enhance the viscous dissipation of momentum and enhance the production of tubulence, increasing flowpath distor-tion decreasing total pressure recovery. Transient mechanical and thermal loads also accompany SBLIs [2, 3], which can lead to enhanced structural fatigue. Further, separated regions impose an area blockage on the inviscid core flow and cause a subsequent deceleration [4]. In extreme situations, the core flow area may approach the sonic condition with additional compression re-sulting in mechanical choking prior to the combustor entrance. This results in a process known as unstart, wherein the oblique shock train is disgorged and thrust is severely reduced [5–15]. Unstart is also associated with the onset of a high-amplitude transient mechanical loading that can couple with the resonant frequencies of the nearby aerostructure to result in premature panel failure and even the complete loss of the vehicle.

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of highly experimental scramjet testbed vehicles like the Boeing X-51 Waverider [18]. The dif-ficulty and persistence of the unstart issue necessitate a brief review of the unstart process and its driving mechanisms.

The potential initiating mechanisms of unstart events are numerous, and include changes in inflow conditions as well as combustion-induced instabilities which are propagated from within the engine itself [1]. Choby [5] investigated the sensitivity of two axisymmetric mixed-compression inlets to inflow variation experimentally by changing the angle of attack. The maximum supercritical angle of attack was limited by a leeward overcompression on the cen-terbody upstream of the throat, which resulted in unstart. A near doubling of the boundary layer thickness in the region of overcompression was also noted. A reduction in the flight Mach number at zero angle of attack resulted in a similar overcompression around the entire in-let circumference that coincided with unstart. Later Reynolds-averaged Navier-Stokes (RANS) simulations by Zha et al. [7] showed that for the angle of attack case, circumferential fluid migration from the upstream windward portion of the centerbody to the leeward side resulted in severe thickening of the boundary layer, which reduced the Mach number inbound to the terminal shock wave and caused propagation upstream of the throat. Once the terminal shock crossed the centerbody shoulder, heavy localized flow separation occured and quickly spread circumferentially, unstarting the entire inlet.

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Figure 1.2: An SR-71 ignites its afterburners.

of oblique waves [12–14]. Once established, the unstart shock system strengthens due to an increasing duct back pressure ratio before finally propagating upstream, disgorging the isolator shock train [6]. After propagation, the downstream flow is heavily separated and oscillatory.

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1.2

Previous Work in SBLIs

1.2.1 2-D SBLIs

Due to the importance of SBLIs a great deal of work has accrued in this area over the last five decades, particularly in the area of two-dimensional (2-D) SBLIs. In the interest of brevity, only a few of these results will be discussed here. For the interested reader, a number of books and reviews capture the progress made in SBLIs as a whole [2, 3, 19–22].

Here the phrase “2-D SBLIs” refers to the interactions between a shock-wave and a canonical 2-D compressible turbulent boundary layer. In the rectangular inlet/isolator of a scramjet, this definition applies loosely to the regions of the flow where the spanwise velocity is negligible. Due to the structure of the corner boundary layers that form at the junctions of the isolator floor/ceiling and sidewalls (to be discussed in the following section), only the boundary layers well away from the corner junctions can be considered 2-D. Furthermore, the swept SBLIs along the sidewall share many characteristics with swept compression ramp and sharp fin SBLIs, which are classified as three-dimensional (3-D) interactions [23]. Therefore, the use of the term 2-D SBLI here is relegated to the impinging oblique shock train interactions along the isolator floor

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and ceiling.

In the impinging/reflected SBLI, the impinging wave angle dictates the strength of the adverse pressure gradient along the floor that the incoming boundary layer must traverse [21]. If this adverse pressure gradient is large enough, a pocket of separated flow forms beneath the impinging shock (see Fig. 1.3 for a schematic of the impinging SBLI flow features). This separation bubble is closed, in that the fluid within it recirculates [25]. The separating boundary layer turns away from the wall, forming a separation shock wave upstream of the inviscid reflection point. The separation shock wave penetrates the incoming boundary layer to the sonic line; this point of maximum penetration is known as the separation shock foot. The separated boundary layer in the free shear layer atop the separation bubble eventually regains enough momentum through turbulent mixing to reattach to the wall, forming reattachment waves that coalesce with the separation shock and form the reflected shock [21]. The boundary layer relaxes downstream of reattachment, albeit with some alteration to its unsteady frequency content (to be discussed below). While the mean structure of the 2-D compression ramp interaction (shown in Fig. 1.4) differs slightly, the boundary layer separation and reattachment processes are extremely similar, as is the coalescence of the separation/reattachment shock waves. For the same incoming flow conditions and total flow turn angleα, the two cases can effectively be

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substituted for one another [21, 26].

The length scale Lsep shown in Fig. 1.3 & 1.4 is the distance between the point at which the boundary layer initially separates to cross the pocket of recirculating flow, and the point at which it reattaches downstream. Following the work of Babinsky & Harvey [21], for canonical closed SBLIs the magnitude ofLsephas been characterized as a competition between boundary layer momentum/shear forces and the adverse pressure gradient across the shock (back pressure ratio). The main parameters affectingLsep in 2-D situations are [21]:

ˆ Incoming Mach numberM∞

ˆ Incoming boundary layer thickness δ0

ˆ Reynolds number based on incoming boundary layer velocity thicknessReδ0 or momentum

thicknessReθ

ˆ Back pressure ratio/shock strength, expressed through the flow turn angleα

ˆ Incoming boundary layer incompressible shape factorH, which is approximately in

pro-portion to the height of the incoming sonic line

If Lsep is assumed to scale in direct proportion to the incoming boundary layer thickness, then for a fixed value ofReδ0,Lsep/δ0 scales as follows:

ˆ Lsep/δ0 increases with α for a fixed incoming Mach number M∞ [27, 28], so long as an

attached inviscid shock solution exists (i.e. for α < αmax) [19, 29]

ˆ Lsep/δ0 decreases with increasing values ofM∞ for a fixed total turn angleα

The separation lengths of 2-D compression ramp interactions, when normalized by incoming boundary layer thickness, δ0, are on the order of unity (i.e. Lsep/δ0 ≈ 1−9) [27, 28, 30–33]).

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Lsep/h≈4.2−5.0. To the author’s knowledge, this range effectively represents the upper limit of separation size for a turbulent SBLI in situations where reattachment eventually occurs.

The direct effect of Reynolds number on separation length is not obvious. In general, it is agreed thatLsep/δ0 should first increase and then decrease with increasingReδ0, with the trend

reversal occuring somewhere around Reδ0 ≈ 10

5 [21, 34]. The work of Zheltovodov et al. [34]

compiled separation length data for 2-D compression ramp SBLIs at different Reδ0 values.

Empirically, they defined a characteristic separation length scale Lc by which Lsep could be normalized to evaluate Reδ0 dependencies (see Ref. 34 regarding the definition of Lc). Figure

1.5 plots the normalized separation length against Reδ0, the aforementioned increasing and

decreasing separation length tendencies centered around Reδ0 ≈ 10

5 are observable in their

data. In terms of Reθ, Ringuette et al. [31] showed that the same separation length trends indicated by Zheltovodovet al.[34] occur. They noted larger separation lengths for Reθ /103, and a reduction in separation size for Reθ≈104−105.

With respect to shape factor, a larger subsonic channel in the incoming boundary layer inherently leads to a larger upstream influence, henceLsep/δ0scales in proportion toH. Changes

in shape factor with Reynolds number are suspected to be the dominant mechanism behind the

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behavior observed in Fig. 1.5 [21].

A salient feature of the separated 2-D SBLI is that it is highly unsteady, and induces fluctuating mechanical and thermal loads with frequencies considerably lower than those of the turbulent fluctuations in the incoming boundary layer, which are of orderf ≈u∞/δ0(whereδ0is

the incoming boundary layer velocity thickness) [2]. Typically,u∞/δ0 is in excess of several tens

of kHz, whereas the characteristic unsteady motion of the SBLI is broadband and ranges from a few hundred Hz to several kHz. The oscillatory pressure loading is attributed to the unsteady motion of the separation shock foot, which traverses upstream and downstream across what is known as the intermittent region which is characterized by a length scale Li as depicted in Fig. 1.3. Interestingly, across various interaction types with closed separation bubbles including impinging shock, compression ramp, and blunt fin SBLIs, when the peak unsteady frequencies of the shock foot oscillation are nondimensionalized usingLi (StLi=f Li/u∞), they collapse into

a range betweenStLi= 0.01−0.03 [3]. This is significant, as it suggests that the physics behind the separation shock motions of closed SBLIs are similar regardless of the downstream geometry. Therefore, a 2-D compression ramp SBLI is also an effective analog for a 2-D impinging shock type interaction from an unsteady perpsective.

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The mean and root-mean-square (RMS) wall pressure distributions from Dolling [2] are displayed in Fig. 1.6(a, b), respectively. Note that in Fig. 1.6 the abscissa is the streamwise coordinatex normalized by the incoming boundary layer thicknessδ0. The ramp corner lies at

x/δ0 = 0, with the freestream flow in the positive x-direction. In Fig. 1.6(a), the ordinate is

the time-averaged wall pressure at each station pw normalized by the incoming boundary layer pressure p∞. The flow is gradually compressed as it passes the point of upstream influence,

which corresponds to the maximum upstream location of the separation shock foot. There is an inflection point in the mean pressure contour at the separation point S, followed by a substantially decreased pressure gradient across the separation bubble, which can be attributed to the overhead free shear layer. This is followed by a significant increase in compression strength just before the reattachment location R, which continues until the inviscid pressure limit is

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reached on the ramp face some distance downstream.

In Fig. 1.6(b), the ordinate is the RMS deviation of the pressure signal at each station σp normalized by pw at the same station over the time of interest. σp/pw effectively describes the magnitude of unsteady loading at each location. As the flow traverses the interaction, there is a sharp increase in σp/pw from the level caused by the passage of turbulent structures in the incoming boundary layer to a distinct maximum occurring very near S, which is due to the frequent passage of the separation shock foot. There is a momentary lapse in unsteady loading across the separation bubble followed by a second maximum near R. Both of the local maxima

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inσp/pw observed here are a result of the unsteady expansion and contraction of the separation bubble [2].

The power spectra of the unsteady wall pressure loading beneath the 2-D compression ramp SBLI of Erengil & Dolling [37] evolve from station to station as shown in Fig. 1.7. The ordinate is the pressure signal frequencyf, whereas the abscissa represents the premultiplied power spectra of the unsteady pressure at each station G(f)×(f) (note that at some stations G(f)×(f) is scaled byσ2

p for ease of comparison). The frequency content of the incoming boundary layer at station 1 is distributed across a range from f ≈10−50 kHz, with peak frequencies off ≈ 40 kHz. This frequency range is again associated with the jitter of the passing turbulent boundary layer. The power spectra of stations 2 and 3 correspond to the motion of the separation shock foot across Li, and are bimodal with dominant frequencies of f < 1 kHz. An example time-series of wall pressure below the intermittent region is shown in Fig. 1.8, where two distinct pressure levels can be observed. The lower level signal from t ≈ 12 ms is similar to that of the incoming turbulent boundary layer, whereas the occasional transitions to the higher level

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at t ≈ 2 ms and back down at t ≈ 3 ms are indicative of the intermittent passage of the separation shock foot. Downstream of the intermittent region, the flow at stations 4 and 5 loses the low-frequency contribution from the separation shock unsteadiness and begins to resemble the incoming boundary layer. Near the downstream reattachment point on the ramp face (not shown here), the flow regains some low-frequency content from the flapping of the separation bubble that corresponds to the peak inσp/pw at R in Fig. 1.6(b).

In the context of propulsion flowpaths, it is also important to understand how the mean and

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unsteady features of 2-D SBLIs vary with the shock-induced separation lengthLsep. Dolling & Or [28] performed wall pressure measurements at the centerline of a 2-D SBLI generated by a compression ramp of variable angle in a Mach 3 flow. The mean and unsteady pressure distri-butions over the range of compression angles tested are displayed in Fig. 1.9(a, b), respectively. In general, the qualitative trends observed in Fig. 1.9 are in agreement with those shown by Dolling [2] for all ramp angles, although it should be noted that no measurements could be taken on the ramp face by Dolling & Or [28]. In general, an increase in ramp angle corresponds to an increase in the separated flow length scale Lsep due to the increased magnitude of the inviscid pressure ratio, in agreeement with the previous discussion. Similarly, the low-frequency oscillation of the separation shock foot was seen to grow in power with increasing ramp angle, alongside a lengthening of the intermittent region.

As discussed previously, the results here are somewhat limited in their relevance to rectan-gular inlets. However, they provide several key insights into the mean and unsteady nature of a portion of the SBLIs present in rectangular channels. They also introduce several key concepts, an understanding of which will prove useful in analyzing the similarities and differences between the SBLI along the isolator floor and the highly complex interactions that takes place along the inlet sidewalls and corner junctions.

1.2.2 3-D SBLIs

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Figure 1.10: Flow features of a glancing fin SBLI. Figure adapted from Alvi & Settles [38].

induced by a wide range of fin half angles at various incoming Mach numbers. They observed a similar interaction structure across all the cases tested, an example of which is shown in Fig. 1.10 in spherical coordinates. The near wall bifurcation of the glancing shock into aλ-structure is evident, with a streamwise separation vortex forming below the rear shock that entrains fluid and carries it downstream, hence the classification as an open SBLI mentioned previously [38]. A supersonic jet issues from behind the rear shock leg, which turns toward the wall and eventually impinges on it.

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Figure 1.11: Mean and RMS wall pressure profiles beneath a glancing fin SBLI, from Garg & Settles [40]. Figure adapted from Dolling [2].

beneath the separation shock foot of sharp fin SBLIs at angles of attack. The spectral shape is shown in Fig. 1.12. Schmisseur [41] showed that the frequencies of the separation shock foot motions are considerably higher for fin SBLIs than for 2-D interactions. This type of glancing interaction is of considerable importance in the rectangular isolator flowfield, particularly along the sidewalls [23].

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Figure 1.12: Unsteady pressure power spectra at maximum RMS location near separation in glancing fin SBLIs, from Schmisseur [41]. Figure adapted from Dolling [2].

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flow through a square duct at Mach 3.91, noted the formation of a streamwise vortex pair about the corner bisector, as depicted in Fig. 1.13. These streamwise vortices grow with downstream distance as they entrain the inviscid core flow, resulting in an area blockage effect.

Where the corner boundary layer meets the impinging/reflected shock in the isolator, a corner SBLI is formed. The time-mean nature of the corner SBLI has only been investigated relatively recently, with the bulk of the work taking place over the last decade. Burtonet al. [43] and Bruceet al. [44] performed Schlieren imaging and surface streakline visualization (SSV) in a normal shock SBLI in a rectangular duct at Mach 1.4 and Mach 1.5. The corner flow was modified via suction or blowing through slots in the floor upstream of the interaction. Blowing drastically increased the size of the corner separation observed, and resulted in a decrease in the extent of mid-span (primary) separation observed. When suction was introduced, a reduced corner separation was seen but the primary separation increased considerably. The size of the λ-foot seen in the Schlieren images also increased with the size of the corner separation, leading to the development of the physical model depicted in Fig. 1.14. The presence of two dominant, 3-D corner vortices cause heavy, quasi-conical bifurcation of the normal shock wave

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in the corners, and increases the bifurcation at the centerline to a lesser extent. Static pressure measurements below the interactions at the centerline and corner confirmed this, with the initial rise inpw/p∞occurring farther upstream in the corner SBLI and with a lesser adverse pressure

gradient when compared to the centerline. The cases with larger corner separations exaggerated the primary bifurcation effect, leading to a milder adverse pressure gradient along the centerline and the reduced separation mentioned previously. This shows that the corner SBLI can act to significantly modify the characteristics of the primary SBLI.

Similarly, Babinsky et al. [46] investigated the effects of corner separation in a Mach 2.5 impinging/reflected oblique SBLI in a rectangular channel. In this case the initial pressure rise along the corner again occurred upstream of the primary interaction due to the formation of corner shock waves. It was found that, depending on the relative positions of the corner and centerline separations, the corner shocks could intersect within the separation along the floor, increasing its size. Thus, the corner SBLI is of importance in the shock trains of rectangular inlet/isolators, where it could act to modify the primary interaction and precipitate the

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tion/strengthening of the unstart shock system. It is, therefore, desirable to gain a quantitative understanding of the mean and unsteady features of the corner SBLI itself and its driving mechanisms, about which relatively little is known.

The large-eddy simulations (LES) of Bisek [45] directly investigated the nature of the corner SBLI induced by a 24°compression ramp in a Mach 2.25 flow through a rectangular channel. A

corner vortex similar to those seen in the aforementioned works was observed along the floor, although interestingly it was seen to coincide with the separation vortex of the glancing SBLI along the sidewall. The outflow plane of Fig. 1.15(a) shows the wave structure of the swept interaction. The corner separation vortex was seen to entrain and eject fluid from the incoming corner boundary layer and from the separation beneath the primary shock front, as shown in Fig. 1.15(b). Notably, the corner SBLI exhibited low-frequency content similar to the unsteady characteristic motions of the previously discussed 2-D SBLI.

1.2.3 Effects of Internal Confinement on SBLIs

As was noted previously, Babinsky et al. [46] investigated the effects of oblique imping-ing/reflected SBLIs in the presence of sidewall and corner boundary layers at Mach 2.5. They observed that the interplay between the corner and floor flows could have the effect of either reducing or enlarging the primary SBLI, reducing the effects to a function of a “inverse viscous aspect ratio,” defined as the boundary layer thickness inbound to the interaction normalized by the wind tunnel width (i.e. the width between the sidewalls), orδ0/W. Figure 1.16 depicts the

regimes of interplay between the primary and corner SBLIs based on δ0/W. In the model of

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Figure 1.16: Impinging/reflected SBLI centerline separation length as a function of inverse viscous aspect ratio, from Babinsky et al. [46].

extent of the primary separation.

From Fig. 1.16 it can be observed that for very small values ofδ0/W, this point of intersection

occurs well downstream of the primary SBLI and therefore does not influence its separation extent. For middling values of δ0/W, the corner waves intersect in the downstream portion of

the primary interaction, actually increasing its separation length. For very large values ofδ0/W

(i.e. small aspect ratio tunnels with thick boundary layers), the corner intersection takes place forward of the primary interaction, potentially decreasing the adverse pressure gradient there and reducing separation length much like what was observed on the periphery of the primary SBLI for lower inverse viscous aspect ratio cases.

Benek et al. [47] conducted a companion Reynolds-averaged Navier-Stokes (RANS) study to Ref. 46, investigating the effects of wind tunnel aspect ratio W/H and the inverse viscous aspect ratio δ0/W on the mean separation characteristics of an incident shock SBLI at Mach

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Babinskyet al.[46]. In general, the magnitude of the three-dimensionality observed throughout the interaction increased with decreasing tunnel width. An initial increase and then a decrease in separation length with increasing δ0/W was also observed, with a peak separation length

occurring atδ0/W ≈0.06 as shown in Fig. 1.17(a). Larger boundary layer thicknesses resulted

in an effective reduction in the wind tunnel width, with thicker boundary layers inducing more three-dimensionality for the same tunnel aspect ratio. While these trends are consistent with what is suggested by Fig. 1.16, it is not clear from Ref. 47 whether the interplay mechanism between the primary and corner SBLIs is actually the intersection of the corner waves at the floor centerline. The corner separation shock in the work of Beneket al.[47] appears to terminate at the primary separation shock surface (as is shown in Fig. 1.17(b)), rather than propagating through it and intersecting the companion wave originating from the opposite junction. This is consistent with what was observed in the compression ramp LES of Bisek [45]. In Ref. 47, it was further stated that the spanwise flow in the primary separation zone may be another important communication mechanism coupling the primary, corner and sidewall SBLIs.

Wang et al. [23] carried out wall-resolved LES of impinging/reflected SBLIs in

rectangu-(a) (b)

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lar channels with different aspect ratios at Mach 2.7. They noted that much of the three-dimensionality observed along the inlet floor at lower aspect ratios was induced by the incident shock wave being modified by its own sidewall separation prior to impinging upon the floor. Depending on the effective aspect ratio of the channel, the sidewall shocks (which propagate toward the mid-span symmetry plane) were observed to modify the impinging shock to differing extents. For very large aspect ratios, a 2-D portion of the impinging shock is preserved. As the aspect ratio decreases, the sidewall shocks affect the incident shock along more of its span, and the resulting floor interaction becomes more 3-D. Eventually, weak compression waves from either sidewall intersect near the center of the domain and the entire incident shock is weak-ened, which was observed to cause a reduction in the separation length along the floor. These trends are consistent with the those suggested by Babinsky et al. [46] with increasing δ0/W,

but the causal mechanism is slightly different. Babinskyet al.[46] do not clarify whether some pre-impingement modification of the incident shock may have taken place, but this does appear to occur to some degree in the RANS simulations of Beneket al. [47], as the incident shock in their work can be seen to be fairly curved before impinging in Fig. 1.17(b).

For wall-bounded compression ramp configurations, far less data exists to determine whether separation length obeys the trends indicated by Fig. 1.16. The aforementioned simulations of Bisek [45] had an inverse viscous aspect ratio ofδ0/W = 0.06, resulting in a centerline separation

length of Lsep/δ0 = 7.2. Poggie & Porter [48] recently conducted LES simulations on a setup

almost identical to that of Bisek [45], except for a thicker effective incoming boundary layer resulting in a higher inverse viscous aspect ratio (δ0/W = 0.12). They noted a smaller centerline

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1.3

Motivation

While the body of research into confined SBLIs is rapidly expanding, there are still several areas in which the existing literature is lacking. First, there is a conspicuous absence of un-steady experimental data regarding confined SBLI physics (note that each of the experimental confinement studies mentioned to this point are time-averaged in nature). While transient com-putational studies are emerging [45, 48] these simulations are expensive from a comcom-putational resource/time standpoint, often requiring thousands of computing cores for a single configu-ration. This is primarily due to the incredibly fine grids and time steps that must be used to resolve high-speed, small scale turbulent structures which can significantly impact the SBLI dy-namics. For the same reasons, these computations are usually limited to relatively low Reynolds numbers, which can be an order of magnitude less than those observed in a mixed-compression inlet/isolator during flight.

Second, while many studies have focused on the effect of varying confinement parameters [23, 46–48] little information (computational or otherwise) presently exists pertaining to the evolution of confined SBLI dynamics with varying back pressure ratio. The back pressure ratio is an important parameter for isolator flows, particularly during unstart events [12] where a large increase is observed prior to unstart shock system propagation. It is suspected that this increase may be responsible for the coupling of SBLI units around the inlet observed during the bulk motion phase.

Finally, confinement effects to this point have primarily been investigated in rectangular configurations. In the design of mixed-compresion inlet/isolators, axisymmetric configurations are often preferred due to their superior total pressure recovery characteristics and lack of corner effects. While studies of axisymmetric shock trains are being conducted [49–51], these works have not focused on the effects that confinement might have on the fundamental characteristics of the SBLIs present in these geometries.

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and axisymmetric bounding geometries. It is of particular interest to gain insights into areas affecting the healthy/normal operation of a ram/scramjet type jet engine. From the preceding dicussion these include:

ˆ How the three-dimensionality of confined SBLIs scales with interaction strength/back

pressure ratio

ˆ How the mean three-dimensionality of the confined SBLIs affects the unsteady physics of

the interactions

ˆ How the mean and unsteady interplay between SBLI units around the inlet evolves with

increasing back pressure ratio to result in bulk unstart propagation

ˆ Factors influencing the shock-induced boundary layer separation length scale, as larger

separations induce larger losses and shift the inlet toward a mechanical choking situation

ˆ Factors influencing the magnitude of the high-amplitude, low-frequency unsteady

me-chanical loading at the wall, as these types of oscillations can be harmful to the inlet aerostructure

ˆ How inlet confinement affects SBLIs in axisymmetric geometries

ˆ Whether conventional planar SBLI control methods can be extended to axisymmetric

situations

ˆ The development of optical methods for measuring unsteady wall pressure in 3-D SBLIs

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Chapter 2

Experimental Setup

2.1

Experimental Facility

2.1.1 Supersonic Wind Tunnel

Experiments were performed in the North Carolina State University (NCSU) supersonic wind tunnel, shown in Fig. 2.1. The NCSU tunnel is of the blowdown type with an oblique shock diffuser and a variable test section Mach number range from M∞ = 1.75−4.5. The tunnel

test section is of constant area, measuring 150 mm × 150 mm in cross section and 650 mm long. Experimental models can be top-mounted from the tunnel ceiling or affixed to the test section sidewall via a customizable plug. Optical access to the test section is provided through removable sidewalls that house quartz windows. A computer with a custom LabVIEW VI was used to control the length and settling chamber pressures of each run.

2.1.2 Test Conditions

For all the present studies the freestream Mach number, M∞, was fixed at 2.5, yielding the

Figure

Figure 1.6:Wall pressure profiles beneath a 2-D compression ramp SBLI. Figure adapted fromDolling [2] (a) mean pressures (b) RMS pressures.

Figure 1.6:Wall

pressure profiles beneath a 2-D compression ramp SBLI. Figure adapted fromDolling [2] (a) mean pressures (b) RMS pressures. p.38
Figure 1.7:Power spectra of unsteady pressure loading beneath a compression ramp SBLI,from Erengil & Dolling [37]

Figure 1.7:Power

spectra of unsteady pressure loading beneath a compression ramp SBLI,from Erengil & Dolling [37] p.39
Figure 1.8:Wall pressure time-series beneath intermittent region of separation shock motion.Figure adapted from Erengil & Dolling [37].

Figure 1.8:Wall

pressure time-series beneath intermittent region of separation shock motion.Figure adapted from Erengil & Dolling [37]. p.40
Figure 1.9: Wall pressure contours beneath a compression ramp SBLI with varying angle, fromDolling & Or [28] (a) mean pressures (b) RMS pressures.

Figure 1.9:

Wall pressure contours beneath a compression ramp SBLI with varying angle, fromDolling & Or [28] (a) mean pressures (b) RMS pressures. p.41
Figure 1.11:Mean and RMS wall pressure profiles beneath a glancing fin SBLI, from Garg &Settles [40]

Figure 1.11:Mean

and RMS wall pressure profiles beneath a glancing fin SBLI, from Garg &Settles [40] p.44
Figure 1.12:Unsteady pressure power spectra at maximum RMS location near separation inglancing fin SBLIs, from Schmisseur [41]

Figure 1.12:Unsteady

pressure power spectra at maximum RMS location near separation inglancing fin SBLIs, from Schmisseur [41] p.45
Figure 1.13:Corner vortex pair transverse/vertical flow vectors. Figure adapted from Davis etal

Figure 1.13:Corner

vortex pair transverse/vertical flow vectors. Figure adapted from Davis etal p.45
Figure 1.16:Impinging/reflected SBLI centerline separation length as a function of inverseviscous aspect ratio, from Babinsky et al

Figure 1.16:Impinging/reflected

SBLI centerline separation length as a function of inverseviscous aspect ratio, from Babinsky et al p.49
Figure 2.1:North Carolina State University (NCSU) supersonic wind tunnel facility.

Figure 2.1:North

Carolina State University (NCSU) supersonic wind tunnel facility. p.55
Figure 2.2:Isometric view of W-B compression ramp model and example flow features ofinterest

Figure 2.2:Isometric

view of W-B compression ramp model and example flow features ofinterest p.56
Table 2.3:H-I compression ramp configurations and planar inviscid pressure ratios.

Table 2.3:H-I

compression ramp configurations and planar inviscid pressure ratios. p.59
Figure 2.4:Isometric view of 2-D compression ramp model and example flow features of inter-est

Figure 2.4:Isometric

view of 2-D compression ramp model and example flow features of inter-est p.60
Figure 2.6:Top-view of W-B compression ramp model mounted from the sidewall of the NCSUsupersonic wind tunnel

Figure 2.6:Top-view

of W-B compression ramp model mounted from the sidewall of the NCSUsupersonic wind tunnel p.63
Figure 2.9:Side-view and inset isometric view of 2-D compression ramp model and pitotmeasurement setup in the NCSU supersonic wind tunnel

Figure 2.9:Side-view

and inset isometric view of 2-D compression ramp model and pitotmeasurement setup in the NCSU supersonic wind tunnel p.68
Figure 2.12:Conventional PSP calibration. Equation 2.3 also shown.

Figure 2.12:Conventional

PSP calibration. Equation 2.3 also shown. p.72
Figure 3.1:Incoming boundary layer profiles for the W-B and 2-D models.

Figure 3.1:Incoming

boundary layer profiles for the W-B and 2-D models. p.79
Figure 3.2:Time-averaged SSVs along the floor of the W-B interaction, α = 12° (a) full-spanview (b) semi-span view.

Figure 3.2:Time-averaged

SSVs along the floor of the W-B interaction, α = 12° (a) full-spanview (b) semi-span view. p.81
Figure 3.3:Mean of unsteady SSV along the floor of the W-B interaction, α = 12°.

Figure 3.3:Mean

of unsteady SSV along the floor of the W-B interaction, α = 12°. p.84
Figure 3.4:Mean pressure profiles for the W-B interaction, α = 12°.

Figure 3.4:Mean

pressure profiles for the W-B interaction, α = 12°. p.85
Figure 3.5:RMS pressure profiles for the W-B interaction, α = 12°.

Figure 3.5:RMS

pressure profiles for the W-B interaction, α = 12°. p.86
Figure 3.6:Intermittent region WSP time-series comparison for the W-B interaction, α = 12°.

Figure 3.6:Intermittent

region WSP time-series comparison for the W-B interaction, α = 12°. p.88
Figure 3.7:Pressure power spectra comparison for intermittent regions of W-B interaction,α = 12°.

Figure 3.7:Pressure

power spectra comparison for intermittent regions of W-B interaction,α = 12°. p.89
Figure 3.8:Comparison of nondimensional corner unsteadiness frequencies with large-eddysimulations of Bisek [45] (a) using separation length scale (b) using vortex length scale.

Figure 3.8:Comparison

of nondimensional corner unsteadiness frequencies with large-eddysimulations of Bisek [45] (a) using separation length scale (b) using vortex length scale. p.92
Figure 3.9:Two-point coherences of WSP fluctuations of primary and corner SBLI intermittentregions with various flowfield locations for the W-B compression ramp interaction, α = 12° (a)incoming boundary layer (b) downstream separated flow.

Figure 3.9:Two-point

coherences of WSP fluctuations of primary and corner SBLI intermittentregions with various flowfield locations for the W-B compression ramp interaction, α = 12° (a)incoming boundary layer (b) downstream separated flow. p.95
Figure 3.10:Time-averaged SSV along the floor of the W-B interaction, α = 24°.

Figure 3.10:Time-averaged

SSV along the floor of the W-B interaction, α = 24°. p.97
Figure 3.11:Mean of unsteady SSV along the floor of the W-B interaction, α = 24°.

Figure 3.11:Mean

of unsteady SSV along the floor of the W-B interaction, α = 24°. p.98
Figure 3.12:Mean of unsteady SSV in the corner junction of the W-B interaction, α = 24°.

Figure 3.12:Mean

of unsteady SSV in the corner junction of the W-B interaction, α = 24°. p.99
Figure 3.14:Mean WSP profiles for the W-B interaction, α = 24°.

Figure 3.14:Mean

WSP profiles for the W-B interaction, α = 24°. p.102
Figure 3.15:RMS pressure profiles for the W-B interaction, α = 24°.

Figure 3.15:RMS

pressure profiles for the W-B interaction, α = 24°. p.104
Figure 3.16:Pressure power spectra comparison for intermittent regions of W-B interaction,α = 24°.

Figure 3.16:Pressure

power spectra comparison for intermittent regions of W-B interaction,α = 24°. p.105

References

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