Review and assessment of turbulence models for hypersonic flows: 2D/Axisymmetric cases

Collection of Technical Papers - 44th AIAA Aerospace Sciences Meeting

Volumn 12, Issue , 2006, Pages 8562-8660

  Roy, Christopher J ^a   Blottner, Frederick G ^b  

^a AUBURN UNIVERSITY   (United States)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

AERODYNAMICS; BOUNDARY LAYER FLOW; COMPUTATIONAL METHODS; DATABASE SYSTEMS; HYPERSONIC FLOW;

AXISYMMETRIC HYPERSONIC FLOWS; COMPUTATIONAL PREDICTION; HYPERSONIC SHOCK; MODELING EFFORTS;

TURBULENCE MODELS;

EID: 34250895585     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (241)

1. G. S. Settles and L. J. Dodson, "Hypersonic Shock/Boundary-Layer Interaction Database," NASA CR 177577, April 1991.
2. G. S. Settles and L. J. Dodson, "Hypersonic Turbulent Boundary-Layer and Free-Shear Layer Database," NASA CR177610, April 1993.
3. G. S. Settles and L. J. Dodson, "Hypersonic Shock/Boundary-Layer Interaction Database: New and Corrected Data," NASA CR 177638, April 1994.
4. Gary S. Settles and Lori J. Dodson, "Supersonic and Hypersonic Shock/Boundary-Layer Interaction Database," AIAA Journal, Vol. 32, pp. 1377-1383, July 1994.
5. Wilcox, D. C., Turbulence Modeling for CFD, 2nd Ed., DCW Industries, Inc. 5354 Palm Drive, La Canada, CA 91011, 1998.
6. Menter, F. R., "Eddy Viscosity Transport Equations and Their Relation to the k-ε Model," Journal of Fluids Engineering, Vol. 119, No. 4, 1997, pp. 876-884.
7. Spalart, P. R., and Allmaras, S. R., "A One-Equation Turbulence Model for Aerodynamic Flows," AIAA Paper 92-0439, 1992.
8. Spalart, P. R., and Allmaras, S. R., "A One-Equation Turbulence Model for Aerodynamic Flows," La Recherche Aerospatiale, No. 1, 1994, pp. 5-21.
9. Roy, C. J., and Blottner, F. G., "Further Assessment of One- and Two-Equation Turbulence Models for Hypersonic Transitional Flows," AIAA Paper 2001-0210, January 2001.
10. Jones, W. L., and Launder, B. E., "The Prediction of Laminarization with a Two-Equation Model of Turbulence," International Journal of Heat and Mass Transfer, Vol. 15, 1972, pp. 301-314.
11. Launder, B. E., and Sharma, B. I., "Application of the Energy Dissipation Model of Turbulence to the Calculation of Flow Near a Spinning Disk," Letters in Heat and Mass Transfer, Vol. 1., No. 2, 1974, pp. 131-138.
12. Roy, C. J., and Blottner, F. G., "Methodology for Turbulence Model Validation: Application to Hypersonic Flows," Journal of Spacecraft and Rockets, Vol. 40, No. 3, May-June 2003, pp. 313-325.
13. Menter, F. R., "Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications," AIAA Journal, Vol. 32, No. 8, Aug. 1994, pp. 1598-1605.
14. Robinson, D. F., Harris, J. E., and Hassan, H. A., "Unified Turbulence Closure Model for Axisymmetric and Planar Free Shear Flows," AIAA Journal, Vol. 33, No. 12, December 1995, pp. 2324-2331.
15. Robinson, D. F., and Hassan, H. A., "Further Development of the k-ζ (Enstrophy) Turbulence Closure Model," AIAA Journal, Vol. 36, No. 10, October 1998, pp. 1825-1833.
16. McDaniel RD, and Hassan HA. Study of transition in a high disturbance environment. Journal of Aircraft, Vol. 38, No. 6, pp. 1051-1055.
17. Craft, T. J., Launder, B. E., and Suga, K., "Prediction of Turbulent Transitional Phenomena with a Nonlinear Eddy-Viscosity Model," International Journal of Heat and Fluid Flow, Vol. 18, No. 1, 1997, pp. 15-28.
18. Cebici, T., and Bradshaw, P., "Ch. 6: Uncoupled Turbulent Boundary Layers," Physical and Computational Aspects of Convective Heat Transfer, Springer-Verlag, New York, 1984, p. 173.
19. Marvin, J. G., "Perspective on Computational Fluid Dynamics Validation," AIAA Journal, Vol. 33, No. 10, 1995, pp. 1778-1787.
20. Marvin, J. G., and Huang, G. P., "Turbulence Modeling - Progress and Future Outlook," in Computational Fluid Dynamics Review 1998, Vol. II, edited by M. Hafez and K. Oshima, World Scientific, 1998, pp. 891-906.
21. Moore, J. G., and Moore, J., "Realizeability in Two-Equation Turbulence Models," AIAA Paper 99-3779, June 1999.
22. Roache, P. J., "Ch. 3: A Methodology for Accuracy Verification of Codes: the Method of Manufactured Solutions," Verification and Validation in Computational Science and Engineering, Hermosa Publishers, New Mexico, 1998.
23. P. Knupp, K. Salari, in: K.H. Rosen (Ed.), Verification of Computer Codes in Computational Science and Engineering, Chapman and Hall/CRC, Boca Raton, FL, 2003.
24. Roache, P. J., "Perspective: A Method for Uniform Reporting of Grid Refinement Studies," ASME Journal of Fluids Engineering, Vol. 116, No. 3, 1994, pp. 405-413.
25. Carpenter, M. H., and Casper, J. H., "Accuracy of Shock Capturing in Two Spatial Dimensions," AIAA Journal, Vol. 37, No. 9, 1999, pp. 1072-1079.
26. Roy, C. J., "Grid Convergence Error Analysis for Mixed-Order Numerical Schemes," AIAA Journal, Vol. 41, No. 4, 2003, pp. 595-604.
27. C. J. Roy, C. C. Nelson, T. M. Smith, and C. C. Ober, "Verification of Euler / Navier-Stokes Codes using the Method of Manufactured Solutions," International Journal for Numerical Methods in Fluids, Vol. 44, No. 6, 2004, pp. 599-620.
28. Craft, T. J., Launder, B. E., and Suga, K., "Prediction of Turbulent Transitional Phenomena with a Nonlinear Eddy-Viscosity Model," International Journal of Heat and Fluid Flow, Vol. 18, No. 1, 1997, pp. 15-28.
29. Cebici, T., and Bradshaw, P., "Ch. 6: Uncoupled Turbulent Boundary Layers," Physical and Computational Aspects of Convective Heat Transfer, Springer-Verlag, New York, 1984, p. 173.
30. H. H. Femholz and P. J. Finley, "A Critical Compilation of Compressible Turbulent Boundary Layer Data," AGARDograph No. 223, 1977.
31. H. H. Femholz and P. J. Finley, "A Critical Commentary on Mean Flow Data for Two-Dimensional Compressible Turbulent Boundary Layers," AGARDograph No. 253, May 1980.
32. H. H. Femholz and P. J. Finley, "A Further Compilation of Compressible Boundary Layer Data with a Survey of Turbulence Data," AGARDograph No. 263, November 1981.
33. G. T. Coleman and J. L. Stollery, "Heat Transfer from Hypersonic Turbulent Flow at a Wedge Compression Corner," Journal of Fluid Mechanics, Vol. 56, pp. 741-752, 1972.
34. M. I. Kussoy and C. C. Horstman, "Documentation of a Two- and Three Dimensional Hypersonic Shock Wave/Turbulent Boundary Layer Interaction Flows," NASA TM 101075, January 1989.
35. M. S. Holden, A. G. Havener, and C. H. Lee, "Shock Wave/Turbulent Boundary Layer Interaction in High-Reynolds Number Hypersonic Flows," Calspan-University of Buffalo Research Center, CUBRC-86681, Buffalo, NY, 1986.
36. M. S. Holden, "Experimental Studies of Quasi-Two-Dimensional and Three-Dimensional Viscous Interaction Regions Induced by Skewed-Shock and Swept-Shock Boundary Layer Interactions," AIAA Paper 1984-1677, 1984.
37. M. I. Kussoy and C. C. Horstman, "An Experimental Documentation of a Hypersonic Shock-Wave Turbulent Boundary Layer Interaction Flow - With and Without Separation," NASA TM X-62412, Feb. 1975.
38. M. I. Kussoy and C. C. Horstman, "Intersecting Shock-Wave/Turbulent Boundary-Layer Interactions at Mach 8.3," NASA TM 103909, Feb. 1992.
39. C. H. Law, "3D Shock Wave-Turbulent Boundary Layer Interactions At Mach 6," Aeronautical Research Laboratory, ARL TR 75-0191, 1975.
40. M. I. Kussoy and C. C. Horstman, "Documentation of a Two- and Three Dimensional Shock Wave/Turbulent Boundary Layer Interaction Flows at Mach 8.2," NASA TM 103838, May 1991.
41. M. I. Kussoy and C. C. Horstman, "Three-Dimensional Shock-Wave/Turbulent Boundary-Layer Interaction," AIAA Journal, Vol. 31, pp. 8-9, 1993.
42. M. S. Holden and J. R. Moselle, "A Database of Aerothermal Measurements in Hypersonic Flow for CFD Validation," AIAA Paper 1992-4023, July 1992.
43. M. S. Holden, "Experimental Studies of the Effects of Asymmetric Transition on the Aerothermal Characteristics of Hypersonic Blunted Slender Cones," AIAA Paper 1985-0325, January 1985.
44. M. S. Holden, "Studies of the Mean and Unsteady Structure of Turbulent Boundary Layer Separation in Hypersonic Flow," AIAA Paper 1991-1778, June 1991.
45. Holden et al? An experimental investigation of turbulent boundary layers at high mach number a reynolds numbers. Calspan Report No. AB-5072-A-1, also NASA CR-112147, 1972.
46. M. S. Holden, "A Database of Aerothermal Measurements in Hypersonic Flows in "Building Block" Experiments for CFD Validation," AIAA paper 2003-1137, January 2003.
47. Holden MS. Shock wave-turbulent boundary layer interaction in hypersonic flow. AIAA Paper 1972-0074, 1972.
48. Holden MS. Shock wave-turbulent boundary layer interaction in hypersonic flow. AIAA Paper 1977-0045, 1977.
49. H. G. Hornung, "28th Lanchester Memorial Lecture- Experimental Real-Gas Hypersonics," The Aeronautical Journal, pp. 379-389, December 1988.
50. Hans Groenig and Herbert Olivier, "Experimental Hypersonic Flow Research in Europe," JSME International Journal, Series B, Vol. 41, No. 2, pp. 397-407, 1998.
51. F. Grasso, G. Leone, and J. M. Delery, "Validation Procedure for the Analysis of Shock-Wave/Boundary-Layer Interaction Problems," AIAA Journal, Vol. 32, pp. 1820-1827, 1994.
52. J.-A. Desideri, R. Glowinski, and J. Periaux (Editors), Hypersonic Flows for Reentry Problems, Volumes I and II, Springer-Verlag, 1991.
53. D. Kumar and J. L. Stollery, "Hypersonic Control Flap Effectiveness," The Aeronautical Journal, pp. 197-208, June/July 1996.
54. G. T. Coleman and J. L. Stollery, "Incipient Separation of Axially Symmetric Hypersonic Turbulent Boundary Layers," AIAA Journal, Vol. 12, pp. 119-120, 1974.
55. K. Kontis and J. L. Stollery, "Incipient Separation on Flared Bodies at Hypersonic Speeds," The Aeronautical Journal, pp 405-414, September 1999.
56. Babinsky H, Edwards JA. On the incipient separation of a turbulent hypersonic boundary layer. Aeronautical Journal 1996; 100(996):209-214.
57. Babinsky H, A study of roughness in turbulent hypersonic boundary-layers, Ph.D. Thesis, Cranfield University, College of Aeronautics, December 1993.
58. M. S. Holden, "Viscous Interactions at Hypersonic Speeds," AFOSR TR 86-2072, Oct. 1986.
59. M. I. Kussoy and K. C. Horstman, "Intersecting Shock-Wave/Turbulent- Boundary-Layer Interactions," AIAA Journal, Vol. 31, pp. 2197-2203, 1993.
60. M. I. Kussoy, K. C. Horstman, and C. C. Horstman, "Hypersonic Crossing Shock-Wave/ Turbulent-Boundary-Layer Interactions," AIAA Journal, Vol. 31, pp. 8-9, 1993 (see also AIAA Paper 1993-0781).
61. G. T. Coleman, G. M. Elfstrom, and S. L. Stollery, "Turbulent Boundary Layers at Supersonic and Hypersonic Speeds," AGARD-CP-93, January 1972.
62. E. J. Hopkins, E. R. Keener, T. E. Polek, and H. A. Dwyer, "Hypersonic Turbulent Skin-Friction and Boundary-Layer Profiles on Nonadiabatic Flat plates," AIAA Journal, Vol. 10, pp. 40-48, Jan. 1972.
63. E. R. Keener and E. J. Hopkins, "Turbulent Boundary Layer velocity Profiles on a Non-Adiabatic Flat Plate at Mach 6.5," NASA TN D-6907, 1972.
64. F. Grasso and D. Falconi, "High-Speed Turbulence Modeling of Shock-Wave/Boundary-Layer Interaction," AIAA Journal, Vol. 31, pp. 1199-1206, 1993.
65. D. J. Mee, "Boundary-Layer transition Measurements in Hypervelocity Flows in a Shock Tunnel," AIAA Journal, Vol. 40, pp. 1542-1548, August 2002.
66. John J. Bertin, Anthony Martellucci, and Richard D. Neumann, "Developing a Data Base for the Calibration and Validation of Hypersonic CFD Codes - Sharp Cones," AIAA Paper 93-3044, 1993.
67. L. B. Lin and J. K. Harvey, "Experimental Study of the Hypersonic Turbulent Boundary Layer on a Cold Slender Cone," Journal of Thermophysics, Vol. 3, pp. 105-111, April 1989.
68. R. Hillier, D. C. Kirk, M. Sell and S. Soltani, "Studies of Hypersonic Viscous Flows," in AGARD Conference Proceedings 514, Theoretical and Experimental Methods in Hypersonic Flows, May 4-8, 1992.
69. P. D. Germain and H. G. Homung, "Transition on a Slender Cone in Hypervelocity Flow," Experiments in Fluids, Vol. 22, pp. 1883-190, 1997.
70. Philippe H. Adam and Hans G. Homung, "Enthalpy Effects on Hypervelocity Boundary-Layer Transition: Ground Test and Flight Data," Journal Spacecraft and Rockets, Vol. 34, pp. 614-619, Sept.-Oct. 1997.
71. P. G. Huang, P. Bradshaw, and T. J. Coakley, "Skin Friction and Velocity Profile Family for Compressible Turbulent Boundary Layers," AIAA Journal, Vol. 31, pp. 1600-1604, September 1993.
72. Squire, L. C., "The Accuracy of Flat Plate, Turbulent Skin Friction at Supersonic Speeds," The Aeronautical Journal, Vol. 104, No. 1036, 2000, pp. 257-263.
73. Van Driest, E. R., "Turbulent Boundary Layer in Compressible Fluids," Journal of the Aeronautical Sciences, Vol. 18, 1951, pp. 145-160.
74. E. R. Van Driest, "Turbulent Boundary Layer on a Cone in a Supersonic Flow at Zero Angle of Attack," Journal of the Aeronautical Sciences, Vol. 19, pp. 55-57, 72, 1952.
75. Frank M. White, Viscous Fluid Flow, McGraw-Hill Book Company, New York, 1974.
76. E. V. Zoby and E. M. Sullivan, "Correlation of Free-Flight Turbulent Heat-Transfer Data from Axisymmetric Bodies with Compressible Flat-Plate Relations," NASA TN D-3802, 1967.
77. Ernest V. Zoby and Randolph A. Graves Jr., "Comparison of Turbulent Prediction Methods with Ground and Flight Test Heating Data," AIAA Journal, Vol. 15, pp. 901-902, July 1977.
78. Roy, C. J., and Blottner, F. G., "Further Assessment of One- and Two-Equation Turbulence Models for Hypersonic Transitional Flows," AIAA Paper 2001-0210, Jan. 2001.
79. S. K. Lele, "Compressible Effects on Turbulence," in Annual Review of Fluid Mechanics, Vol.26, 1994.
80. G. N. Coleman, J. Kim and R. D. Moser, "A Numerical Study of Turbulent Supersonic Isothermal-Wall Channel Flow," Journal of Fluid Mechanics, Vol. 305, pp. 159-183, 1995.
81. Nateri K. Madavan, "Direct Numerical Simulation of Transitional and Turbulent Flow over a Heated Flat Plate Using Finite-Difference Schemes," NASA-CR-197753, Jan. 1995.
82. Chien JY. Predictions of channel boundary-lay er flows with a low-reynolds-number turbulence model. AIAA Journal 1982; 20(1):33-38.
83. So RM, Zhang HS, Speziale CG. Near-wall modeling of the dissipation rate equation. AIAA Journal 1991; 29(12):2069-2076.
84. T. J. Coakley and P. G. Huang, "Turbulence Modeling For High Speed Flows," AIAA Paper 92-0436, 1992.
85. Vuong ST, Coakley TJ. Modeling of turbulence for hypersonic flows with and without separation. AIAA Paper 1987-0286, 1987.
86. T. J. Coakley, C. C. Horstman, J. G. Marvin, J. R. Viegas, J. E. Bardina, P. G. Huang, and M. I. Kussoy, "Turbulence Compressibility Corrections," NASA Technical Memorandum 108827, May 1994.
87. B. Aupoix and S. Viala, "Compressible Turbulent Boundary Layer Modeling," FED-Vol. 224, Transitional and Turbulent Compressible Flows, ASME, 1995.
88. C. C. Horstman, "Prediction of Hypersonic Shock-Wave/Turbulent- Boundary-Layer Interaction Flows," AIAA Paper 87-1367, 1987.
89. C. C. Horstman, "Hypersonic Shock-Wave/Turbulent-Boundary-Layer Interaction Flows," AIAA Journal, Vol. 30, pp. 1480-1481, June 1992.
90. P. G. Huang and T. J. Coakley, "Turbulence Modeling for Complex Hypersonic Flows," AIAA Paper 93-0200, 1993.
91. J. E. Bardina, P. G. Huang, and T. J. Coakley, "Turbulence Modeling Validation, Testing, and Development," NASA TM-110446, April 1997.
92. J. E. Bardina, P. G. Huang, and T. J. Coakley, "Turbulence Modeling Validation," AIAA Paper 97-2121, 1997.
93. T-H Shih, W. W. Liou, A. Shabbir, Z. Yang, and J. Zhu, "A New k-ε Eddy Viscosity Model for High Reynolds Number Turbulent Flows," Computers Fluids, Vol. 24, pp. 227-238, 1995.
94. William W. Liou and P. G. Huang, "Calculations of Oblique Shock Wave/ Turbulent Boundary-Layer Interactions with New Two-Equation Turbulence Models," FED-Vol. 224, Transitional and Turbulent Compressible Flows, ASME 1995.
95. Elfstrom GM. Turbulent hypersonic flow at a wedge-compression comer. Journal of Fluid Mechanics 1972; 53(1):113-127.
96. Robert P. Nance and H. A. Hassan, "Turbulence Modeling of Shock-Dominated Flows with a k-ζFormulation," AIAA Paper 99-0153, January 15-18, 1999.
97. U. Goldberg, P. Batten, S. Palaniswamy, S. Chakravarthy, and O. Peroomian, "Hypersonic Flow Predictions Using Linear and Nonlinear Turbulence Closures," Journal of Aircraft, Vol. 37, pp. 671-675, July-August 2000.
98. Horstman CC. Hypersonic shock-wave/turbulent-boundary-layer interaction flows. AIAA Paper 1991-1760, 1991.
99. Coratekin T, van Keuk J, Ballmann J. Performance of upwind schemes and turbulence models in hypersonic flows. AIAA Journal 2004; 42(5):945-957.
100. Marvin JG, and Coakley TJ. Turbulence modeling for hypersonic flows. NASA TM-101079, 1989.
101. Hillier R, Kirk D, Soltani S. Navier-stokes computations of hypersonic flows. International Journal of Numerical Methods for Heat and Fluid Flow 1995; 5(3):195-211.
102. Mikulla V, Horstman CC. Turbulence measurements in hypersonic shock-wave boundary-layer interaction flows. AIAA Journal 1976; 14(5):568-575.
103. J. E. Bardina and T. J. Coakley, "Three-Dimensional Navier-Stokes Simulation with Two-equation Turbulence Models of Intersecting Shock-Waves/Turbulent Boundary Layer at Mach 8.3," AIAA Paper 94-1905, 1994.
104. N. Narayanswami, C. C. Horstman, and D. D. Knight, "Computation of Crossing Shock/ Turbulent Boundary Layer Interaction at Mach 8.3," AIAA Journal, Vol. 31, pp. 1369-1376, August 1993 (see also AIAA Paper 1993-0779).
105. Brian R. Smith, "Prediction of Hypersonic Shock-Wave/Turbulent Boundary-Layer Interactions," Journal of Spacecraft and Rockets, Vol. 33, pp. 614-619, Sept.-Oct. 1996 (also AIAA Paper 95-0232).
106. Alexander Wiedermann, "Blunt-Fin Induced Interaction of Wall Shear Layers in Supersonic Flow," Fluid Dynamics Research, Vol. 21, pp. 221-232, 1997. Also Goldberg [97] has used this flow geometry.
107. D. Barberis and P. Molton, "Shock Wave-Turbulent Boundary Layer Interaction in a Three Dimensional Flow," AIAA Paper 95-0227, January 9-12, 1995.
108. Kussoy MI, Kim K-S, Horstman KC. An experimental study of a three-dimensional shock wave/turbulent boundary-layer interaction at a hypersonic mach number. AIAA Paper 1991-1761, 1991.
109. Bardina J, Coakley T, Marvin J. Two-equation turbulence modeling for 3-d hypersonic flows. AIAA Paper 1992-5064, 1992.
110. M. A. Leschziner, P. Batten, and H. Loyau, "Modeling Shock-Affected Near-Wall Flows with Anisotropy-Resolving Turbulence Closures," Internationaljournal of Heat and Fluid Flow, Vol. 21, pp. 239-251, 2000.
111. Knight DD, Horstman CC, Monson DJ. The hypersonic shock wave-turbulent boundary layer interaction generated by a sharp fin at Mach 8.2. AIAA Paper 1992-0747, 1992.
112. J. R. Edwards and S. Chanda, "Comparison of Eddy Viscosity-Transport Turbulence Models for Three-Dimensional, Shock-Separated Flowfields," AIAA Journal, Vol. 34, pp. 756-763, 1995.
113. J. D. Brown, J. L. Brown, and M. I. Kussoy, "A Documentation of Two- and Three-Dimensional Shock-Separated Turbulent Boundary Layers," NASA TM 101008, July 1988 (also AIAA Paper 87-0553).
114. D. Gaitonde, J. S. Shang, and J. R. Edwards, "The Computed Structure of a 3-D Turbulent Interaction Caused by a Cylinder/Offset Flare Junction," AIAA Paper 95-0230, Jan. 1995.
115. E. R. Van Driest, "Problem of Aerodynamic Heating," Aeronautical Engineering Review, Vol. 15, pp. 26-41, Oct. 1956.
116. Mee DJ. Boundary-layer transition measurements in hypervelocity flows in a shock tunnel. AIAA Journal 2002; 40(8): 1542-1548.
117. Coakley TJ, Viegas JR, Huang PG, Rubesin MW. An assessment and application of turbulent models for hypersonic flows. 9th National Aero-Space Plane Technology Symposium, Paper No. 106, November 1990.
118. G. A. Alexopoulos and H. A. Hassan, "k - ζ(Enstophy) Compressible Turbulence Model for Mixing and Wall Bounded Flows," AIAA Journal, Vol. 35, pp. 1221-1224, 1997.
119. Kimmel, R. L., "Experimental Transition Zone Lengths in Pressure Gradient in Hypersonic Flow," in Transitional and Turbulent Compressible Flows 1993, edited by L. D. Krai and T. A. Zang, FED-Vol. 151, ASME, 1993, pp. 117-127.
120. Kimmel, R. L., "The Effects of Pressure Gradients on Transition Zone Length in Hypersonic Boundary Layers," Journal of Fluids Engineering, Vol. 119, No. 1, 1997, pp. 36-41.
121. Eric S. Warren, Julius E. Harris, and H. A. Hassan, "Transition Model for High-Speed Flow," AIAA Journal, Vol. 33, pp. 1391-1397, 1995.
122. R. D. McDaniel, R. P. Nance, and H. A. Hassan, "Transition Onset Prediction for HighSpeed Flow," Journal of Spacecraft and Rockets, Vol. 37, pp. 304-309, May-June 2000.
123. Daniel C. Reda and John D. Murphy, "Shock Wave/Turbulent Boundary-Layer Interactions in Rectangular Channels," AIAA Journal, Vol. 11, pp. 139-140, Feb. 1973.
124. Daniel C. Reda and John D. Murphy, "Sidewall Boundary Layer Influence on Shock Wave/Turbulent Boundary-Lay er Interactions," AIAA Journal, Vol. 11, pp. 1367-1368, Feb. 1973.
125. P. Krogmann and E. Schulein, "Documentation of Two-Dimensional Impinging Shock/ Turbulent Boundary Layer Interaction Flow," DLR IB 223-96 A 49, 1996.
126. Nagano, Y., and Hishida, M., "Improved Form of the k-ε Model for Wall Turbulent Shear Flows." Journal of Fluids Engineering, Vol. 109, June 1987, pp. 156-160.
127. Van Driest, E. R., "On Turbulent Flow Near a Wall," Journal of the Aeronautical Sciences, Vol. 23, 1036, Nov. 1956, pp. 1007-1011.
128. J. E. Hopkins, M. W. Rubesin, M. Inouye, E. R. Keener, G. G. Mateer, and T. E. Polek, "Summary and Correlation of Skin-Friction and Heat-Transfer Data for a Hypersonic Turbulent Boundary Layer on Simple Shapes," NASA TN D-5089, 1969 (also AIAA Journal, "Hypersonic Turbulent Skin-Friction and Boundary-Layer Profiles on Nonadiabatic Flat Plates," Vol. 10, Jan. 1972, pp. 40-48.)
129. E. J. Hopkins and M. Inouye, "An Evaluation of Theories for Predicting Turbulent Skin Friction and Heat Transfer on Flat Plates at Supersonic and Hypersonic Mach Numbers," AIAA Journal, Vol. 9, pp. 993-1003, June 1971.
130. P. Bradshaw, B. E. Launder, and J. L. Lumley, "Collaborative Testing of Turbulence Models," Journal of Fluids Engineering, Vol. 118, pp. 243-247, June 1996.
131. S. Catris and B. Aupoix, "Improved Turbulence Models for Compressible Boundary Layers," AIAA Paper 98-2696, June 1998.
132. Wilcox DC. Turbulence Modeling for CFD, 1st Ed., DCW Industries, Inc. 5354 Palm Drive, La Canada, CA 91011, 1988.
133. J. E. Bardina, "Three-Dimensional Navier-Stokes Method with Two-Equation Turbulence Models for Numerical Simulation of Hypersonic Flows," AIAA Paper 94-2950, 1994.
134. T. J. Garrison, G. S. Settles, N. Narayanswami, and D. D. Knight, "Laser Interferometer Skin-Friction Measurements of Crossing-Shock-Wave/ Turbulent-Boundary-Layer Interactions," AIAA Journal, Vol. 32, pp. 1234-1241, June 1994.
135. Doyle D. Knight, T. J. Garrison, G. S. Settles, A. A. Zheltovodov, A. Maksimov, A. M. Shevchenko, and S. S. Vorontsov, "Asymmetric Crossing-Shock-Wave/Turbulent-BoundaryLayer Interaction," AIAA Journal, Vol. 33, pp. 2241-2249, 1995.
136. C. W. Albertson and R. L. Ash, "Compressible Equilibrium Turbulent Boundary Layers at Non Adiabatic Wall Conditions," AIAA Journal, Vol. 29, No. 10, October 1991, pp. 1573-1580.
137. C. W. Albertson, "Evaluation of Equilibrium Turbulence for a Hypersonic Boundary Layer at Nonadabatic Wall Conditions," M.S. Thesis, Old Dominion University, Norfolk, VA, July 1989, also available as NASA TM-101663, Nov. 1989.
138. Alexander Wiedermann, "Blunt-Fin Induced Interaction of Wall Shear Layers in Supersonic Flow," Fluid Dynamics Research, Vol. 21, pp. 221-232, 1997.
139. U. C. Goldberg, "Towards a Pointwise Turbulence Model for Wall-Bounded and Free Shear Flows," ASME Journal of Fluids Engineering, Vol. 116, pp. 72-76, 1994. See Goldberg et al. [97] the cubic eddy viscosity form of this model.
140. Menter, F. R., Grotjans, H., and linger, F., "Numerical Aspects of Turbulence Modeling for the Reynolds Averaged Navier-Stokes Equations," Computational Fluid Dynamics Lecture Series 1997-02, von Karman Institute for Fluid Dynamics, March 3-7, 1997.
141. Roy, C. J., and Blotmer, F. G., "Assessment of One- and Two-Equation Turbulence Models for Hypersonic Transitional Flows," AIAA Paper 2000-0132, January 2000.
142. Roy, C. J., and Blotmer, F. G., "Assessment of One- and Two-Equation Turbulence Models for Hypersonic Transitional Flows," Journal of Spacecraft and Rockets, Vol. 38, No. 5, September-October 2001, pp. 699-710.
143. Zoby, E. V., and Sullivan, E. M., "Correlation of Free-Flight Turbulent Heat-Transfer Data from Axisymmetric Bodies with Compressible Flat-Plate Relationships," NASA Technical Note D-3802, Jan. 1967.
144. Zoby, E. V., and Graves, R. A., "Comparison of Turbulent Prediction Methods with Ground and Flight Test Heating Data," AIAA Journal, Vol. 15, No. 7, 1977, pp. 901-902.
145. M. Martin, G. Weits, U. Piomelli, and G. Candler, "Large-Eddy Simulation Over a Hypersonic Elliptical Cross-Section Cone," AIAA Paper 2000-2311, June 19-22, 2000. (do not have this)
146. H. S. Zhang, R. M. C. So, C. G. Speziale, and Y. G. Lai, "Near Wall Two-Equation Model for Compressible Turbulent Flows," AIAA Journal, Vol. 31, pp. 196-199, 1993.
147. T. J. Craft, B. E. Launder, and K. Suga, "Development and Application of a Cubic EddyViscosity Model of Turbulence," Internationaljournal of Heat and Fluid Flow, Vol. 17, pp. 108-115, 1996.
148. D. F. Robinson, J. E. Harris, and H. A. Hassan, "Unified Turbulence Closure Model for Axisymmetric and Planar Free Shear Flows," AIAA Journal, Vol. 33, pp. 2325-2331, 1995.
149. Jeffrey K. Wideman, James L. Brown, John B. Miles, and Oktay Ozcan, "Skin-Friction Measurements in Three-Dimensional, Supersonic Shock-Wave/Boundary-Layer Interaction," AIAA Journal, Vol. 33, pp. 805-811, 1995.
150. . D. F. Robinson and H. A. Hassan, "Further Development of the k - ζ(Enstrophy) Turbulence Closure Model," AIAA Journal, Vol. 36, pp. 1825-1833, 1998.
151. L. D. Kral, "Recent Experience with Different Turbulence Models Applied to the Calculation of Flow Over Aircraft Components," Progress in Aerospace Sciences, Vol. 34, pp. 481-541, 1998.
152. Roger L. Kimmel, Jonathan Poggie and Stephen N. Schwoerke, "Laminar-Turbulent Transition in a Mach 8 Elliptic Cone Flow," AIAA Journal, Vol. 37, pp. 1080-1087, September 1999.
153. M. S. Holden, "Turbulent Boundary Layer Development on Curved Compression Surfaces," Calspan Report No. 7724-1, 1992.
154. B. E. Launder, "The Modeling of Turbulent Flows with Significant Curvature or Rotation," in Modeling Complex Turbulent Flows, Edited by Manuel D. Salas, Jerry N. Hefner, and Leonidas Sakell, Kuwer Academic Publishers, 1999.
155. Horstman and Owen, AIAA Journal
156. Mikulla V, and Horstman CC. The measurement of shear stress and total heat flux in a nonadiabatic turbulent hypersonic boundary layer. AIAA Paper 75-0119, 1975.
157. Mikulla V, and Horstman CC. Turbulence stress measurements in a nonadiabatic hypersonic boundary layer. AIAA Journal, V. 13, No. 12, 1975, pp. 1607-1613.
158. Goldberg U. Hypersonic flow heat transfer prediction using single equation turbulence models. ASME Journal of Heat Transfer, V. 123, Feb. 2001, pp. 65-69.
159. Coleman GT. Hypersonic turbulent boundary layer studies. Ph.D. Thesis, Dept. of Aeronautics, Univ. of London, London, 1973.
160. Rodi W. Experience with two-layer models combining the k-s model with a one-equation model near the wall. AIAA Paper 1991-0216, Jan. 1991.
161. Holden MS, Bergman RC, Harvey J, Duryea GR, Moselle JR. Studies of the structure of attached and separated regions of viscous/inviscid interaction and the effects of combined surface roughness and blowing in high Reynolds number hypersonic flows. AFOSR-89-0033TR, 1988.
162. Holden MS. Experimental database from CUBRC studies in hypersonic laminar and turbulent interacting flows including flowfield chemistry, Prepared for RTO code validation of DSMC and Navier-Stokes code validation studies, Calspan-University at Buffalo Research Center, Buffalo, NY, June 2000, pp. 105-114.
163. Smith BR. A near wall model for the k-l two equation turbulence model. AIAA Paper 1994-2386, June 1994.
164. Marvin JG, Horstman CC, Rubesin MW, Coakley TJ, and Kussoy MI. An experimental and numerical investigation of shock-wave induced turbulent boundary-layer separational hypersonic speeds," AGARDograph-CPP-168, May 1975.
165. Fluent 6.1 User's Guide, Vols. 1-3, 2003.
166. Oberkampf, WL, and Aeschliman, DP. Joint computational/experimental aerodynamics research on a hypersonic vehicle, part 1: experimental results. AIAA Journal, V. 9, No. 3, 1995, pp. 432-437.
167. P. G. Huang, P. Bradshaw, and T. J. Coakley, "Turbulence Models for Compressible Boundary Layers," AIAA Journal, Vol. 32, pp. 735-740, April 1994
168. P. R. Spalart, "Trends in Turbulence Treatments," AIAA 2000-2306, June 19-22, 2000.
169. Sebastein Deck, P. Duveau, P. d'Espiney, and P. Guillen, "Development and Application of Spalart-Allmaras One Equation Turbulence Model to Three-Dimensional Supersonic Complex Configurations," Aerospace Science and Technology, Vol. 6, pp. 171-183, 2002.
170. H. H. Femholz and P. J. Finley, "Incompressible Zero-pressure- Gradient Turbulent Boundary Layer: Assessment of the a Data," Progress in Aerospace Sciences, Vol. 32, pp 245-311, August 1996.
171. F. K. Hill, "Boundary-Layer Measurements in Hypersonic Flow," J. of the Aeronautical Sciences, Vol. 23, pp. 35-42, Nov.-Dec. 1956. (F&F 5901)
172. F. K. Hill, "Turbulent Boundary Layer Measurements at Mach Number 8 to 10," Physics of Fluids, Vol. 2, 1959, pp. 668-680,
173. . E. M. Winkler and M. H. Cha, "Investigation of Flat Plate Hypersonic Turbulent Boundary Layers With heat Transfer at a Mach Number of 5.2," NOL NAVORD Report 6631, 1959; also Trans. ASME, Series E, Vol. 83, pp. 323-329, 1961.
174. D. R. Moore, "Velocity Similarity in the Compressible Turbulent Boundary layer With Heat Transfer," University of Texas Defence Research Laboratory, Report DRL 480, 1962.
175. D. R. Moore and J. Harkness, "Experimental Investigation of the Compressible Turbulent Boundary layer at Very High Reynolds Numbers," AIAA Journal. Vol. 3, No. 4, April 1965, pp. 631-638
176. R. D. Watson, J. E. Harris, and J. B. Andeps, "Measurements in a Transitional/Turbulent Mach 10 Boundary layer at High Reynolds Numbers," AIAA Paper 73-165, 1973.
177. R. D. Watson, "Characteristics of Mach 10 Transitional and Turbulent Boundary Layers," NASA TP-1243, Nov. 1, 1978, also "Wall Cooling Effects on Hypersonic Transitional/Turbulent Boundary Layers at High Reynolds Numbers," AIAA Journal, Vol. 15, pp. 1455-1461, Oct. 1977.
178. A. J. Laderman and A. Demetriades, "Mean and Fluctuating Flow Measurements in the Hypersonic boundary Layer Over a Cooled Wall," Journal of Fluid Mechanics, Vol. 63, pp. 121144, 1974, (F&F 7403) also "Investigation of the Structure of a Cooled Wall Turbulent Supersonic Boundary Layer," Aeronautics Publication No. U-6370.
179. J. E. Hopkins, and E. R. Keener, "Studies of Surface Pitots for Measuring Turbulent Skin Friction at Supersonic Mach Numbers," NASA TN D-3478, 1966.
180. E. J. Hopkins, E. R. Keener, "Pressure-Gradient Effects on Hypersonic Turbulent SkinFriction and Boundary-Layer Profiles," AIAA Journal, Vol. 10, pp. 1141-1142, Sept. 1972.
181. F. K. Owen, C. C. Horstman, "On the Structure of Hypersonic Turbulent Boundary Layers," Journal of Fluid Mechanics, Vol. 53, pp. 611-636, June 1972.
182. C. C. Horstman and F. K. Owen, "Turbulent Properties of a Compressible Boundary Layer," AIAA Journal, Vol. 10, pp. 1418-1424, Nov. 1972.
183. F. K. Owen, C. C. Horstman, and M. I. Kussoy, "Mean and Fluctuating Flow Measurements on a Fully-Developed, Non-Adiabatic Hypersonic Boundary Layer," Journal of Fluid Mechanics, Vol. 70, No. 2, pp. 393-413, 1975.
184. J. E. Hopkins, E. R. Keener, and P. T. Louie, "Direct Measurements of Turbulent Skin Friction on a Non-Adiabatic Flat Plate at Mach Number 6.5 and Comparisons with Eight Theories," NASA TN D-5675, 1969.
185. C. W. Albertson and R. L. Ash, "Compressible Equilibrium Turbulent Boundary Layers at Non Adiabatic Wall Conditions," AIAA Journal, Vol. 29, No. 10, October 1991, pp. 15731580.
186. C. W. Albertson, "Evaluation of Equilibrium Turbulence for a Hypersonic Boundary Layer at Nonadabatic Wall Conditions," M.S. Thesis, Old Dominion University, Norfolk, VA, July 1989, also available as NASA TM-101663, Nov. 1989.
187. M. S. Holden, "Turbulent Boundary layer Development on Curved Compression Surfaces," Calspan report No. 7724-1, 1992.
188. H. Yan, D. Knight, and A. A. Zheltovodov, "Large Eddy Simulation of Supersonic Flat Plate Boundary Layer Using MILES Technique," Journal of Fluid Engineering, Vol. 124, No. 4, pp. 868-875, 2002 (also H. Yan, D. Knight, and A. A. Zheltovodov, "Large Eddy Simulation of Supersonic Flat Plate Boundary Layer Part I," AIAA 2002-0132, January 14-17, 2002).
189. M. P. Martin, "Preliminary DNS Database of Hypersonic Turbulent Boundary Layers," AIAA 2003-3726, June 22-26, 2003.
190. E. R. Van Driest, "The Turbulent Boundary layer With Variable Prandtl Number," in 50 Jahre Grenzschichtforschung, Edited by H. Gortler and W. Tollmien, Friedr. Vieweg & Sohn, Braunschweig, 1955.
191. . A. J. Smits and Jean-Paul Dussauge, Turbulent Shear layers in Supersonic Flow, American Institute of Physics, Woodbury, N. Y., 1996.
192. Dean R. Chapman and R. H. Kester, "Measurements of Turbulent Skin friction on Cylinders in Axial Flow at Subsonic and Supersonic Velocities,"
193. R. K. Lobb, E. M. Winkler, J. Persh, "Experimental Investigation of Turbulent Boundary layers in Hypersonic Flow," U.S. Naval Ordnance Laboratory, Report 3380, 1955 also Journal of the Aeronautical Sciences, Vol 22, 1955, pp. 1-9, 1955.
194. D. Coles, "Measurements in the Boundary Layer on a Smooth Flat Plate Boundary-Layer at Jet Propulsion Laboratory," Jet Propulsion Lab., California Institute of Technology, Pasadena, CA, Report 20-71, 1953; also Journal of the Aeronautical Sciences," Vol. 21, No. 7, July. 1955, pp. 433-448.
195. S. C. Sommer and B. J. Short, "Free-Flight Measurements of Turbulent Boundary-Layer Skin Friction in the Presence of Severe Aerodynamic Heating at Mach Numbers from 2.8 to 7.0," NACA TN 3391, 1955; also Journal of the Aeronautical Sciences, Vol. 23, No. 6, June 1956, pp. 536-542.
196. R. H. Korkegi, "Transition Studies and Skin-Friction Measurements on an Insulated Flat Plate at a Mach Number of 5.8," Journal of the Aeronautical Sciences," Vol. 23, No. 2, Feb. 1956, pp. 97-107.
197. J. B. Peterson, Jr., A Comparison of Experimental and Theoretical Results for the Compressible Turbulent-Boundary-Layer Skin Friction with Zero Pressure Gradient, NASA Technical Note D-1795, March 1963
198. F. W. Matting, D. R. Chapman, T. R. Nyholm, and A. G. Thomas, "Turbulent Skin Friction at High Mach Numbers and Reynolds Numbers in Air and Helium," NASA TR R-82, 1961
199. R. E. Wilson, "Turbulent Boundary-Layer Characteristics at Supersonic Speeds - Theory and Experiments," Journal of the Aeronautical Sciences, Vol. 17, pp. 585-594, September 1950.
200. J. E. Wallace and E. J. McLaughlin, "Experimental Investigation of Hypersonic Turbulent Flow and Laminar Leeward-Side Flow on Flat Plates," Cornell Aeronautical Lab., Buffalo, N.Y., Technical Report AFFDL-TR-66-63, Vol. 1, July 1966.
201. F. L. Young and E. J. McLaughlin, "Experimental Investigation of the Effects of Surface Roughness on Compressible Turbulent Boundary Layer Skin Friction and heat Transfer," Defence Research Lab., University of Texas, Austin, Texas, Report DRL-532, CR-21, 1965.
202. L. Neal Jr., "A Study of the Pressure, Heat transfer, and Skin Friction on Sharp and Blunt Flat Plates at Mach Number 6.8," NASA TN D-3312, 1966.
203. S. Catris and B. Aupoix, "Density Corrections for Turbulence Models," Aerospace Science Technology, Vol. 4, pp. 1-11, 2000.
204. A. L. Kistler, "Fluctuation Measurements in Supersonic Turbulent Boundary Layers," Ballistic Research Laboratories, Report 1052, 1958 and Physics of Fluids, Vol. 2, 1959.
205. . R. C. Hasting and W. G. Sawyer, "Turbulent Boundary Layers on a Large Flat Plate at M = 4," R.A.C., Technical Report 70040 and R&M 3678, 1970.
206. D. G. Mabey, H. U. Meier, and W. G. Sawyer, "Experimental and Theoretical Studies of the Boundary layer on a Flat Plate at Mach Numbers from 2.5 to 4.5," RAE TR 74127, 1974.
207. D. G. Mabey, "Some Observations on the Wake Component of the Velocity Profiles of Turbulent Boundary Layers at Subsonic and Supersonic Speeds," RAE TR 77-004.
208. R. L. Richmond, "Experimental Investigation of Thick, Axially Symmetric Boundary Layers on Cylinders at Subsonic and Hypersonic Speeds," Guggenheim Aeronautics Lab., Cal Tech, Pasadena, CA, Hypersonic Research Project Memo 39, 1957.
209. J. L. Sims, Tables for Supersonic Flow Around Right Circular Cones, NASA SP-3004, Jan. 1, 1964.
210. C. B. Rumsey and D. B. Lee, Measurements of Aerodynamic Heat Transfer and Boundary-Layer Transition on a 15 Degree Cone in Free Flight at Supersonic Mach Numbers Up to 5.2, NASA Technical Note D-888, August 1961.
211. C. F. Merlet and C. B. Rumsey, "Supersonic Free-Flight Measurement of Heat Transfer and Transition on a 10 Degree Cone Having a Low Temperature Ratio, NASA Technical Note D951, August 1961.
212. R. L. Wright and E. V. Zoby, Flight Boundary-Layer Measurements on Slender Cone at Mach 20, AIAA Paper 77-719, June 1977.
213. P. C. Stainback, M. C. Fischer, and Wagner, Effects of Wind-Tunnel Disturbances on Hypersonic Boundary Transition, AIAA Paper Number 72-181, January 17-19, 1972
214. Kuei-Yuan Chien, Hypersonic, Turbulent Skin-Friction and Heat-Transfer Measurements on a Sharp Cone, AIAA Journal, Vol. 12, pp. 1522-1526, Nov. 1974
215. K. F. Stetson, Mach 6 Experiments of Transition on a Cone at Angle of Attack, J. Spacecraft, Vol. 19, pp. 397-403, September-October 1982.
216. K. F. Stetson, E. R. Thompson, J. C. Donaldson, and L. G. Siler, Laminar Boundary Layer Stability Experiments on a Cone at Mach 8, Part 1: Sharp Cone, AIAA Paper 83-1761, July 12-14, 1983.
217. P. A. Deman, J. K. Harvey, and R. Hillier, Hypersonic Boundary Layer and Base Flow Workshop Test Problem 1 and 2, pp. 43-56 in Reference [52].
218. S. G. Mallinson, R. Hillier, A. P. Jackson, D. C. Kirk, S. Soltani, and M. Zanchetta, Gun Tunnel Flow Calibration: Defining Input Conditions for Hypersonic Flow Computations, Shock Waves, Vol.10, pp. 313-322, 2000.
219. S L. Lawrence, Hypersonic Cone Flow Predictions Using an Implicit Upwind SpaceMarching Code, pp. 75-91.
220. Same as 100 S. P. G. Dinavahi, Comparison of Two Transition Models, in Instability and Transition, Edited by M. Y. Hussaini and R. G. Voigt, Springer-Verlag, 1989.
221. R. Abgrall and J. A. Desideri, M. Mallet, J. Periaux, P. Perrier, and B. Stoufflet, The European Hypersonic Data Base: A New CFD Validation Tool for the Design of Space Vehicles, AIAA Paper 93-3045, July 6-9, 1993
222. G. G. Mateer and H. K. Larson, "Unusual Boundary-Layer Transition Results on Cones in Hypersonic Flow," AIAA Journal, Vol. 7, pp. 660-666, April 1969.
223. G. G. Mateer, Effects of Wall Cooling and Angle of Attack on Boundary-Layer Transition on Sharp Cones at Mach = 7.4, NASA Technical Note D-6908, August 1972.
224. G. G. Meeter, The Effect of Angle of Attack on Boundary-Layer Transition on Cones, AIAA Journal, Vol. 10, August 1972.
225. M. S. Holden, D. Bower, and K. Chadwick, Measurements of Boundary Layer Transition on Cones at Angle of Attack for Mach Numbers from 11 to 13, AIAA 95-2294, June 19-22, 1995.
226. F.-J. Chen, M. R. Malik, and I. E. Beckwith, Boundary-Layer Transition on a Cone and Flat Plate at Mach 3.5, AIAA Journal, Vol. 27, pp. 687-693, 1989.
227. J. T. Lachowicz, N. Chokani, and S. P. Wilkinson, Hypersonic Boundary-Layer Stability Over a Flared Cone in a Quiet Tunnel, AIAA Paper number 96-0782, 1996.
228. J. T. Lachowicz, N. Chokani, and S. P. Wilkinson, Boundary-Layer Stability Measurements in a Hypersonic Quiet Tunnel, AIAA Journal, Vol. 34, pp. 2496-2500, December 1996.
229. C. D. Pruett and C-L Chang, Spatial Direct Numerical Simulation of High-Speed Boundary-Layer Flows Part II: Transition on a Cone in Mach 8 Flow, Theoretical and Computational Fluid Dynamics, Vol. 7, pp. 397-424, 1995.
230. C. D. Pruett, Direct Numerical Simulation of Hypersonic Boundary-Layer Flow on a Flared Cone, Theoretical and Computational Fluid Dynamics, Vol. 11, pp. 49-67, 1998.
231. Alvin Seiff, Examination of the Existing Data on the Heat Transfer of Turbulent Boundary Layers at Supersonic Speeds From the Point of View of Reynolds Analogy, NACA Technical Note 3284, August 1954.
232. Eli Reshotko and M. Tucker, "Approximation Calculation of the Compressible Turbulent Boundary Layer With Heat Transfer and Arbitrary Pressure Gradient," NACA TN 4154, December 1957.
233. M. H. Bertram and L. Neal, Recent Experiments in Hypersonic Turbulent Boundary Layers, NASA Technical Memorandum X-56335, 1965.
234. Neal Tetervin, "A Transformation Between Axisymmetric and Two-Dimensional Turbulent Boundary Layers," AIAA Journal, Vol. 8, pp. 985-987, May 1970.
235. F. M. White, R. C. Lessmann and G. H. Christoph, "Analysis of Turbulent Skin Friction in Thick Axisymmetric Boundary Layers," AIAA Journal, Vol. 11, pp. 821-825, June 1973.
236. A. D. Young, Boundary Layers, AIAA Education Series, AIAA, Washington D. C., 1089.
237. E. V. Zoby, J. N. Moss, and K. Sutton, Approximate Convective-Heating Equations for Hypersonic Flows, J. Spacecraft, Vol. 18, pp. 64-70, January-February 1981.
238. F. Seiler, U. Werner, and G. Patz, Ground Testing Facility for Modeling Real Projectile Flight Heating in Earth Atmosphere, Journal of Thermophysics and Heat Transfer, Vol. 16, pp. 101-108, January-March 2002.
239. S. P. G. Dinavahi, "Comparison of Two Transition Models," pages 453-462 in Instability and Transition (Volume II), Editors M. Y. Hussaini and R. G. Voigt, Springer-Verlag, 1989.
240. S. A. McKeel, R. W. Walters, and K. M. Chadwick, Investigation into Transition Modeling, AIAA Paper 95-1746, In AIAA CFD Conference Papers, pp 1126-1138, June 19-22, 1995.
241. P. E. Rodi and D. S. Dolling, "An Experimental/Computational Study of Sharp Fin Induced Shock Wave/Turbulent Boundary Layer Interactions at Mach 5," AIAA Paper 92-0749, Jan. 1992