Reynolds stress model for hypersonic flows [Elektronische Ressource] / Arianna Bosco

Informations

• Publié par: rheinisch-westfalischen_technischen_hochschule_-rwth-_aachen
• Publié le: 01 janvier 2011
• Nombre de lectures: 32
• Langue: English
• Poids de l'ouvrage: 6 Mo

Extrait

Reynolds Stress Model
for Hypersonic Flows
Von der Fakultät für Maschinenwesen der
Rheinisch-Westfälischen Technischen Hochschule Aachen
zur Erlangung des akademischen Grades
einer Doktorin der Ingenieurwissenschaften
vorgelegt von
Arianna Bosco
Berichter: Univ.-Prof. M. Behr, Ph.D.
apl. Prof. Dr. rer. nat. S. Müller
Tag der mündlichen Prüfung: 27. Mai 2011
“Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek online
verfügbar.”Acknowledgement
I would like to express my gratitude to Prof. Marek Behr who agreed to be my supervisor. A
particular thanks goes to Birgit Reinartz, for her guidance through the three years of my PhD,
for her encouragements, her inexhaustible patience and for being a source of inspiration as a
scientist and as a woman. A big thank you to Siegfried Müller for his time, his help and his
corrections. To my colleagues Martin Krause, Gero Schieffer and Frank Bramkamp for their
invaluable help and support and for sharing my frustration, a big thank you.
I would like to thank Prof. Russel Boyce for inviting me to Brisbane; Fabrice Schloegel
and Melrose Brown for their help in the preparation of the experimental campaign. A special
thanks to four fantastic persons without whom I would have never been able to successfully
conduct the experiment and survive to the T4 stress: Keith, Grant, James and Tom, you have
helped, encouraged and praised me well beyond your duty as co-workers and friends and
made me have a great time despite the hard work.
I would like to thank mum, dad and Giulia for being an inexhaustible source of inspiration
and encouragement and for coming to visit me around the world. A special thanks to my
friends at AICES Francesca and Markus, for the lunches and coffee breaks together and for
listening to my complaints and to my friends at home who have no idea of what I am doing
but are strongly convinced that I am doing it well.
The Financial support from the Deutsche Forschungsgemeinschaft (German Research As-
sociation) through grant GSC 111, the Forschungszentrum Jülich and the Rechenzentrum of
RWTH Aachen are gratefully acknowledged.
iiiContents
1. Introduction 1
2. Hypersonic flows: a Brief Review 5
2.1. Main Characteristics of Hypersonic Flows . . . . . . . . . . . . . . . . . . . 5
2.1.1. Thin Shock Layer and Shock-Shock Interaction . . . . . . . . . . . . 5
2.1.2. Entropy Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.3. High Temperature Flows . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.4. Viscous Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2. Shock Wave/Boundary Layer Interaction (SWBLI) . . . . . . . . . . . . . . 9
2.2.1. SWBLI on a Compression Corner Configuration . . . . . . . . . . . 10
2.2.2. Impinging-Reflecting Shock Wave . . . . . . . . . . . . . . . . . . . 15
2.3. Turbulence Modeling in Hypersonic Flows . . . . . . . . . . . . . . . . . . . 15
2.3.1. Experimental Databases . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.2. LES and DNS of SWBLI . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.3. Main RANS Results for Hypersonic 2D SWBLI . . . . . . . . . . . 17
3. Physical Modeling of Turbulent Compressible Flows 21
3.1. The Navier-Stokes Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2. Material Laws and Thermodynamic Relations . . . . . . . . . . . . . . . . . 21
3.3. Turbulent Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.4. Reynolds Averaged Navier-Stokes Equations . . . . . . . . . . . . . . . . . 25
3.4.1. RANS Equations for Compressible Flows . . . . . . . . . . . . . . . 26
3.4.2. Closure for RANS Equations . . . . . . . . . . . . . . . . . . . . . . 27
3.4.3. Reynolds Stress Models . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4.4. Eddy Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5. SSG/LRR-! Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.5.1. Additional Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5.2. Boundary Conditions at Solid Walls . . . . . . . . . . . . . . . . . . 37
3.6. Reynolds Stress Models versus Eddy Viscosity Models . . . . . . . . . . . . 38
4. QUADFLOW code 39
4.1. General Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.1.1. Turbulence and Transition Models . . . . . . . . . . . . . . . . . . . 40
4.1.2. Multiscale Analysis for Grid Adaptation . . . . . . . . . . . . . . . . 41
4.2. Computational Approach for the RSM . . . . . . . . . . . . . . . . . . . . . 42
iiiContents
4.2.1. Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.2. Initial and Boundary Conditions . . . . . . . . . . . . . . . . . . . . 43
4.2.3. Convergence Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3. RSM Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3.1. Non-Dimensional Form of the RSM Equations . . . . . . . . . . . . 46
4.3.2. Source Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3.3. Turbulence Contribution to the Mean Flow . . . . . . . . . . . . . . 48
4.3.4. Realizability Constraints . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3.5. Adaptive Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5. Model Validation 51
5.1. Definition of Non-Dimensional Variables . . . . . . . . . . . . . . . . . . . 51
5.2. Model Sensitivity Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.2.1. Freestream Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.2.2. Grid Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.2.3. !-wall Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2.4. Adaptive Simulations: Threshold Value and Refinement Levels . . . 60
5.3. Validation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3.1. Hypersonic Flow over a Flat Plate . . . . . . . . . . . . . . . . . . . 65
5.3.2. Supersonic Flow over a Flat Plate . . . . . . . . . . . . . . . . . . . 66
5.3.3. Subsonic Flow over a Flat Plate . . . . . . . . . . . . . . . . . . . . 68
5.3.4. Hypersonic Flow over a Double Wedge . . . . . . . . . . . . . . . . 70
5.3.5. Comparison Between Adaptive and Structured Grids . . . . . . . . . 75
6. Scramjet Results 77
6.1. Experimental Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.2. Numerical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.2.1. 2D Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.2.2. 3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
7. Three-dimensional hypersonic SWBLI 93
7.1. Experimental Investigation of a Compression Corner . . . . . . . . . . . . . 93
7.1.1. T4 Shock Tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
7.1.2. Operating and Freestream Conditions . . . . . . . . . . . . . . . . . 94
7.1.3. Freestream Non-Uniformities . . . . . . . . . . . . . . . . . . . . . 95
7.1.4. Experimental Model and Sensors . . . . . . . . . . . . . . . . . . . 97
7.1.5. Analysis and Postprocessing Tools . . . . . . . . . . . . . . . . . . . 102
7.2. Numerical Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.3. 40 degrees Compression Corner Results . . . . . . . . . . . . . . . . . . . . 104
7.3.1. 40 degrees 6 mm Condition with Boundary Layer Trip . . . . . . . . 108
7.3.2. 40 degrees 3 mm with Layer Trip . . . . . . . . 117
7.3.3. 40 degrees 6 mm Condition without Boundary Layer Trip . . . . . . 120
ivContents
7.3.4. 40 degrees 3 mm Condition without Boundary Layer Trip . . . . . . 122
7.4. 15 degrees Compression Corner Results . . . . . . . . . . . . . . . . . . . . 124
7.4.1. 15 degrees 6 mm Condition with Boundary Layer Trip . . . . . . . . 125
7.4.2. 15 degrees 3 mm with Layer Trip . . . . . . . . 129
7.4.3. 15 degrees 6 mm Condition without Boundary Layer Trip . . . . . . 131
7.4.4. 15 degrees 3 mm Boundary Layer Trip . . . . . . 134
7.5. Investigation Using an Adaptive Procedure . . . . . . . . . . . . . . . . . . . 137
8. Conclusions 141
A. Sensor Positions 143
B. Thermocouples Calibration 147
Bibliography 149
vviList of Symbols
Scalar Variables
: Boundary layer thickness
C : Cross-diffusion term for!D
c : Sound speed
c : Specific heat at constant pressure, pressure coefficientp
c : heat at volumev
CFL : Courant-Friedrichs-Levy number
!D : Destruction of!
d : distance from the wall
e : Specific internal energy
E : total energy
: Turbulence dissipation rate, Adaptive threshold
: Specific heat ratio
H : Total specific enthalpy
I : Turbulence intensity
k : Turbulent kinetic energy
II : Second invariant of the anisotropy tensor
L : Separation length, Refinement level
: Thermal conductivity
: Molecular viscosity
: Turbulentt
! : Specific turbulence dissipation rate
!P : Production of!
p : Pressure
Q : Heat flux
q : Component of heat flux vectori
(t)
q : Turbulent heat fluxk
R : Radius, Specific gas constant
: Density
t : Time
T : Temperature
T : Constant of Sutherland lawS
u : Shear stress velocity
u : Velocity componenti
viiContents
visc ratio : R