Turbulence modeling with application to turbomachinery

Progress in Aerospace Sciences

Volumn 32, Issue 6, 1996, Pages 575-624

  Bradshaw, P ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

AERODYNAMICS; COMPRESSIBILITY OF GASES; FORECASTING; GAS TURBINES; TURBOMACHINERY; TURBULENT FLOW;

PREDICTION METHODS;

TURBULENCE;

EID: 0030408820     PISSN: 03760421     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0376-0421(96)00003-6     Document Type: Review

References (157)

1. Abid, R., Valsa, V. N., Johnson, D. A. and Wedan, B. W. (1990) Prediction of separated transonic wing flows with nonequilibrium algebraic turbulence model, AIAA J. 28, 1426.
2. Adams, E. W. and Johnston, J. P. (1984) A mixing-length model for the prediction of convex curvature effects on turbulent boundary layers, J. Gas Turbines Power 106, 142.
3. Anderson, S. and Eaton, J. K. (1987) Experimental study of a pressure-driven, three-dimensional, turbulent boundary layer, AIAA J. 25, 1086.
4. Anon. (1996) Annual research briefs - 1995, Center for Turbulence Research, Stanford University, Stanford, CA.
5. Arcoumanis, C. and Whitelaw, J. H. (1987) Fluid mechanics of internal combustion engines - a review, Proc. Inst. Mech. Engrs 201C1, 57.
6. Baldwin, B. S. and Barth, T. J. (1990) A one-equation turbulence transport model for high Reynolds number wall-bounded flows, NASA TM-102847, and AIAA-91-0610 (1991).
7. Baldwin, B. S. and Lomax, H. (1978) Thin layer approximation and algebraic model for separated turbulent flows, AIAA-78-257.
8. Ballal, D. R. (1988) Combustion-generated turbulence in practical combustors, J. Prop. Power 4, 385.
9. Bandyopadhyay, P. R. (1992) Reynolds number dependence of the freestream turbulence effects on turbulent boundary layers, AIAA J. 30, 1910.
10. Bardina, J., Ferziger, J. H. and Reynolds, W. C. (1983) Improved turbulence models based on large eddy simulation of homogeneous, incompressible turbulent flows, Stanford University Thermosciences Division Reprot TF-19, Stanford, CA.
11. Barlow, R. S. and Johnston, J. P. (1988) Structure of a turbulent boundary layer on a concave surface, J. Fluid Mech. 191, 137.
12. Bell, J. H. and Mehta, R. D. (1993) Effects of imposed spanwise perturbations on plane mixing-layer structure, J. Fluid Mech. 257, 33.
13. Berg, B. v.d., Elsenaar, A., Lindhout, J. P. F. and Wesseling, P. (1975) Measurements in an incompressible three-dimensional turbulent boundary layer under infinite swept-wing conditions, and comparison with theory, J. Fluid Mech. 70, 127.
14. Berg, B. v.d. (1975) A three-dimensional law of the wall for turbulent shear flows, J. Fluid Mech. 70, 149.
15. Bilger, R. W. (1989) Turbulent diffusion flames, Ann. Rev. Fluid Mech. 21, 101.
16. Birch, S. F. and Eggers, J. M. (1972) A critical review of the experimental data for developed free turbulent shear layers, NASA SP-321, p. 11.
17. Blair, M. F. (1983) Influence of free stream turbulence on turbulent boundary layer heat transfer and mean profile development. Parts I and II, J. Heat Transfer 105, 33, 41.
18. Blaisdell, G. A., Mansour, N. N. and Reynolds, W. C. (1993) Compressibility effects on the growth and structure of homogeneous turbulent shear flow, J. Fluid Mech. 256, 443.
19. Bogdanoff, D. W. (1983) Compressibility effects in turbulent shear layers, AIAA J. 21, 926.
20. Bradshaw, P. (1971) Variations on a theme of Prandtl, AGARD Conf. Proc. 93.
21. Bradshaw, P. (1974) The effect of mean compression or dilatation on the turbulence structure of supersonic boundary layers, J. Fluid Mech. 63, 449.
22. Bradshaw, P. (1977) Compressible turbulent shear layers, Ann. Rev. Fluid Mech. 9, 33.
23. Bradshaw, P. (1987) Turbulent secondary flows, Ann. Rev. Fluid Mech. 19, 53.
24. Bradshaw, P. and Huang, P. G. (1995) The law of the wall in turbulent flow, Proc. R. Soc. Lond. A 451, 165.
25. Bradshaw, P. and Perot, J. B. (1993) A note on turbulent energy dissipation in the viscous wall region, Phys. Fluids A 5, 3305.
26. Bradshaw, P. and Pontikos, N. S. (1995) Measurements in the turbulent boundary layer on an 'infinite' swept wing, J. Fluid Mech. 159, 105.
27. Bradshaw, P., Mansour, N. N. and Piomelli, U. (1987) On local approximations of the pressure-strain term in turbulence models, Studying Turbulence Using Numerical Simulation Databases, NASA Ames/Stanford Center for Turbulence Research Rept. CTR-S87, p. 159.
28. Bradshaw, P., Launder, B. E. and Lumley, J. L. (1996) Collaborative testing of turbulence models, J. Fluids Engng 118, 24.
29. Broadwell, J. E. and Mungal, M. G. (1991) Large-scale structures and molecular mixing, Phys. Fluids A 3, 1193.
30. Brown, G. L. and Roshko, A. (1974) On density effects and large structures in turbulent mixing layers, J. Fluid Mech. 64, 775.
31. Bussing, T. R. A. and Murman, E. M. (1988) Finite-volume method for the calculation of compressible chemically reacting flows, AIAA J. 26, 1070.
32. Castro, I. P. (1984) Effects of free stream turbulence on low Reynolds number boundary layers, J. Fluids Engng 106, 298.
33. Castro, I. P. (1990) Free-stream turbulence effects on separated shear layers, In: Near-Wall Turbulence - 1988 Zaric Memorial Conf., p. 123 (eds S. J. Kline and N. H. Afgan), Hemisphere, New York.
34. Cebeci, T. and Bradshaw, P. (1977) Momentum Transfer in Boundary Layers, McGraw-Hill Hemisphere, New York.
35. Cebeci, T. and Bradshaw, P. (1984) Physical and Computational Aspects of Convective Heat Transfer, Springer, New York.
36. Cebeci, T. and Smith, A. M. O. (1974) Analysis of Turbulent Boundary Layers, Academic, New York.
37. Choi, K. S. and Lumley, J. L. (1984) Return to isotropy of homogeneous turbulence revisited, In: Turbulence and Chaotic Phenomena in Fluids (ed. T. Tatsumi), North-Holland, Amsterdam.
38. Chow, J. S., Zilliac, G. G. and Bradshaw, P. (1991) Initial roll-up of a wingtip vortex, In: Int. Wake Vortex Symp. Federal Aviation Administration, Washington, DC: see also AIAA J. 33, 1561 (1995).
39. Chow, J. S., Zilliac, G. G. and Bradshaw, P. (1991) Initial roll-up of a wingtip vortex, In: Int. Wake Vortex Symp. Federal Aviation Administration, Washington, DC: see also AIAA J. 33, 1561 (1995).
40. Clemens, N. T. and Mungal, M. G. (1995) Large-scale structure and entrainment in the supersonic mixing layer, J. Fluid Mech. 284, 171.
41. Coakley, T. J. and Huang, P. G. (1992) Turbulence modeling for high speed flows, AIAA-92-0436.
42. Coleman, G. N. and Mansour, N. N. (1991) Simulation and modeling of homogeneous compressible turbulence under isotropic mean compression, In: 8th Symp. on Turbulent Shear Flows, Munich, paper no. 21-3.
43. Coleman, G. N., Kim, J. and Moser, R. D. (1995) A numerical study of turbulent supersonic isothermal-wall channel flow, J. Fluid Mech. 205, 159.
44. Coleman, G N., Kim, J. and Spalart, P. R. (1996) Direct numerical simulation of nonequilibrium three-dimensional boundary layers, AIAA-96-0655.
45. Crow, S. C. (1968) Viscoelastic properties of fine-grained incompressible turbulence, J. Fluid Mech. 33, 1.
46. Cutler, A. D. and Bradshaw, P. (1993) Strong vortex, boundary layer interactions. Parts I and II, Exp. Fluids 14, 321, 393.
47. Driver, D. M. (1990) Experimental study of a three-dimensional, shear-driven turbulent boundary layer with adverse pressure gradient, NASA TM 102211.
48. Driver, D. M. (1991) Reynolds shear stress measurements in a separated boundary layer flow, AIAA-91-1787.
49. Durbin, P. A. (1991) Near wall turbulence closure modeling without 'damping functions', Theor. Comput. Fluid Dyn. 3, 1.
50. Durbin, P. A. (1993) A Reynolds stress model for near-wall turbulence, J. Fluid Mech. 249, 465.
51. Durbin, P. A. and Zeman, O. (1992) Rapid distortion theory for homogeneous compressed turbulence with application to modeling, J. Fluid Mech. 242, 349.
52. Eibeck, P. A. and Eaton, J. K. (1987) Heat transfer effects of a longitudinal vortex embedded in a turbulent boundary layer, J. Heat transfer 109, 16.
53. Elsenaar, A. and Boelsma, S. H. (1974) Measurements of the Reynolds stress tensor in a three-dimensional turbulent boundary layer under infinite swept conditions, Netherlands NLR TR 74095 U.
54. Favre, A.-J. (1965) The equations of compressible turbulent gases (in French) J. de Mecanique 4, 361: reprinted in Studies in Turbulence (eds T. B. Gatski, S. Sarkar and C. G. Speziale), p. 324, Springer, Berlin (1992).
55. Favre, A.-J. (1965) The equations of compressible turbulent gases (in French) J. de Mecanique 4, 361: reprinted in Studies in Turbulence (eds T. B. Gatski, S. Sarkar and C. G. Speziale), p. 324, Springer, Berlin (1992).
56. Fernando, E. M. and Smits, A. J. (1990) A supersonic turbulent boundary layer in an adverse pressure gradient, J. Fluid Mech. 211, 285.
57. Fernholz, H. (1971) Ein Halbempirisches Gesetz für die Wandreibung in Kompressibilen Turbulenten Grenzschichten bei Isothermer und Adiabatischer Wand, Zeit. für angew. Math. Mech. 51, T146.
58. Fernholz, H. H. and Finley, P. J. (1981) A further compilation of compressible boundary layer data with a survey of turbulence data, AGARDograph 263
59. Ferziger, J. H. and Peric, M. (1996) Computational Methods for Fluid Dynamics, Springer, New York.
60. Ferziger, J. H. Kline, S. J., Avva, R. K., Bordalo, S. N. and Tzuoo, K.-L. (1990) Zonal modelling of turbulent flows - philosophy and accomplishments, In: Near-Wall Turbulence - 1988 Zaric Memorial Conf. (eds S. J. Kline and N. H. Afgan), p. 800. Hemisphere, New York.
61. Fletcher, C. A. J. (1988) Computational Techniques for Fluid Dynamics, Vols 1 and 2, Springer, New York.
62. Fu, S., Launder, B. E. and Tselepidakis, D. P. (1987) Accommodating the effects of high strain rates in modelling the pressure-strain correlation, University of Manchester UMIST TFD/87/5, Manchester.
63. Fu, S., Huang, P. G., Launder, B. E. and Leschziner, M. A. (1988) A comparison of algebraic and differential second-moment closures for axisymmetric turbulent shear flows with and without swirl, J. Fluids Engng 110, 216.
64. Ghosal, S., Lund, T. S., Moin, P. and Akselvoll, K. (1995) A dynamic localization model for large-eddy simulation of turbulent flows, J. Fluid Mech. 286, 229.
65. Gibson, M. M. (1990) Effects of surface curvature on the law of the wall, In: Near-Wall Turbulence - 1988 Zaric Memorial Conf. (eds S. J. Kline and N. H. Afgan), p. 157. Hemisphere, New York.
66. Gibson, M. M. and Launder, B. E. (1978) Ground effects on pressure fluctuations in the atmospheric boudnary layer, J. Fluid Mech. 86, 491.
67. Goebel, S. G. and Dutton, J. C. (1991) Experimental study of compressible turbulent mixing layers, AIAA J. 29, 538.
68. Goldstein, S. (1972) The Navier - Stokes equations and the bulk viscosity of simple gases, J. Math. Phys. Sci., Univ. Madras 6, 225.
69. Guo, Y. and Adams, N. A. (1994) Numerical investigation of supersonic turbulent boundary layers with high wall temperature, NASA Ames/Standford Center for Turbulence Research, Summer Program 1994, p. 245.
70. Hancock, P. E. and Bradshaw, P. (1983) The effect of free stream turbulence on turbulent boundary layers, J. Fluid Engng 105, 284.
71. Hancock, P. E. and Bradshaw, P. (1989) Turbulence structure of a boundary layer beneath a turbulent free stream, J. Fluid Mech. 205, 45.
72. Hanjalic, K. and Launder, B. E. (1972) A Reynolds stress model of turbulence and its application to thin shear flows, J. Fluid Mech. 52, 609.
73. Hong, S. K. and Murthy, S. N. B. (1986) Effective velocity of transport in curved wall boundary layers, AIAA, J. 24, 361.
74. Hong, S. K. and Murthy, S. N. B. (1986) Pressure-strain correlations in curved wall boundary layers, AIAA J. 24, 971.
75. Horstman, C. C., Kussoy, M. I. and Lanfranc, M. J. (1978) An evaluation of several compressible turbulent boundary layer models - effect of pressure gradient and Reynolds number, AIAA-78-1160.
76. Huang, P. G. (1986) The computation of parabolic turbulent flow with second-moment closure models, Ph.D. thesis, Manchester University, Manchester.
77. Huang, P. G., Bradshaw, P. and Coakley, T. J. (1994) Turbulence models for compressible boundary layers, AIAA J. 32, 735.
78. Huang, P. G., Coleman, G. N. and Bradshaw, P. (1995) Compressible turbulent channel flow: DNS results and modeling, J. Fluid Mech. 305, 185.
79. Jayaram, M. and Smits, A. J. (1985) The distortion of a supersonic turbulent boundary layer by bulk compression and surface Curvature, AIAA-85-0299: see also J. Fluid Mech. 175, 343.
80. Jayaram, M. and Smits, A. J. (1985) The distortion of a supersonic turbulent boundary layer by bulk compression and surface Curvature, AIAA-85-0299: see also J. Fluid Mech. 175, 343.
81. Johnson, D. A. and Coakley, T. J. (1990) Improvements to a nonequilibrium algebraic turbulence model, AIAA J. 28, 2000.
82. Johnson, D. A. and King, L. S. (1985) A mathematically simple turbulence closure model for attached and separated turbulent boundary layers, AIAA J. 23, 1684.
83. Jones, W. P. and Launder, B. E. (1972) The prediction of laminarization with a two-equation model of turbulence, Int. J. Heat Mass Transfer 15, 301.
84. Kader, B. A. and Yaglom, A. M. (1972) Heat and mass transfer laws for fully turbulent wall flows, Int. J. Heat Mass Transfer 15, 2329.
85. Kays, W. M. and Crawford, M. E. (1993) Convective Heat and Mass Transfer, McGraw-Hill, New York.
86. Kline, S. J. and Robinson, S. K. (1990) Quasi-coherent structures in the turbulent boundary layer: part I, status report on a community-wide summary of the data, In: Near-wall Turbulence - 1988 Zaric Memorial Conf. (eds S. J. Kline and N. H. Afgan) p. 200, Hemisphere, New York.
87. Kline, S. J., Cantwell, B. J. and Lilley, G. M. (1982) Proc. 1980-81 AFOSR-HTTM-Stanford Conf. on Complex Turbulent Flows - Comparison of Computation and Experiment, Vols 1-3, Stanford University, Stanford, CA.
88. Koutmos, P. and McGuirk, J. J. (1991) Isothermal modeling of gas turbine combustors: computational study, J. Prop. Power 7, 1064.
89. Launder, B. E. (1971) An improved algebraic modelling of the Reynolds stresses, Imperial College Mechanical Engineering Report TM/TN/A9, London.
90. Launder, B. E. (1989) Second-moment closure; present ... and future? Int. J. Heat Fluid Flow 10, 282.
91. Launder, B. E. (1995) Modelling the formation and dispersal of streamwise vortices in turbulent flow, Aeronaut. J. R. Aeronaut. Soc. 99, 419.
92. Launder, B. E., Reece, G. J. and Rodi, W. (1975) Progress in the development of a Reynolds-stress turbulence closure, J. Fluid Mech. 68, 537.
93. Launder, B. E., Tselepidakis, D. P. and Younis, B. A. (1987) A second moment closure study of rotating channel flow, J. Fluid Mech. 183, 63.
94. Lele, S. K. (1994) Compressibility effects on turbulence, Ann. Rev. Fluid Mech. 26, 211.
95. Lumley, J. L. (1978) Computational modeling of turbulent flows, Adv. Appl. Mech. 18, 123.
96. Maciejewski, P. K. and Moffat, R. J. (1990) The effects of high free-stream turbulence on heat transfer in turbulent boundary layers, In: Near-Wall Turbulence - 1988 Zaric Memorial Conf. (eds S. J. Kline and N. H. Afgan), p. 640, Hemisphere, New York.
97. Mansour, N. N., Kim, J. and Moin, P. (1987) Reynolds stress and dissipation rate budgets in a turbulent channel flow, J. Fluid Mech. 194, 15.
98. Marvin, J. G. (1983) Turbulence modeling for computational aerodynamics, AIAA J. 21, 943.
99. Marvin, J. G. (1990) Progress and challenges in modeling turbulent aerodynamic flows, In: Engineering Turbulence Modelling Conf., Dubrovnik.
100. Mitcheltree, R. A., Salas, M. D. and Hassan, H. A. (1990) One-equation turbulence model for transonic airfoil flows, AIAA J. 28, 1625.
101. Moin, P., Shih, T.-H., Driver, D. M. and Mansour, N. N. (1990) Direct numerical simulation of a three-dimensional turbulent boundary layer, Phys. Fluids A 2, 1846.
102. Morkovin, M. V. (1962) Effects of compressibility on turbulent flow, In: The Mechanics of Turbulence (ed. A. Favre), p. 367, Gordon and Breach, New York.
103. Müller, U. R. (1982) Measurements of the Reynolds stresses and the mean-flow field in a three-dimensional pressure-driven boundary layer, J. Fluid Mech. 119, 121.
104. Ölçmen, S. M. and Simpson, R. L. (1995) An experimental study of a three-dimensional pressure-driven turbulent boundary layer, J. Fluid Mech. 290, 225.
105. Papamoschou, D. and Roshko, A. (1989) The compressible turbulent shear layer - An experimental study, J. J. Fluid Mech. 197, 453.
106. Pierce, F. J., McAllister, J. E. and Tennant, M. H. (1983) A review of near-wall simularity models in three-dimensional turbulent boundary layers, J. Fluids Engng 105, 251.
107. Poinsot, T. J. (1991) Direct simulation of turbulent combustion, Ames Stanford Center for Turbulence Research, Annual Research Briefs - 1990, p. 91.
108. Pope, S. B. (1978) An explanation of the turbulent round-jet plane-jet anomaly, AIAA J. 16, 279.
109. Pope, S. B. (1987) Turbulent premixed flames, Ann. Rev. Fluid Mech. 19, 237.
110. Pope, S. B. (1990) Computations of turbulent combustion: progress and challenges, In: Proc. 23rd Symp. (Int.) on Combustion, The Combustion Institute, Pittsburgh, p. 591.
111. Pope, S. B. (1991) Application of the velocity-dissipation probability density function model to inhomogeneous turbulent flows, Phys. Fluids A 3, 1947.
112. Pope, S. B. (1994) Lagrangian PDF Methods for turbulent flows, Ann. Rev. Fluid Mech. 26.
113. Povinelli, L. A., Liou, W. W., Shabbir, A. and Shih, T.-H. (eds.) (1992) Workshop on engineering turbulence modeling, NASA Conf. Pub. 10088.
114. Prandtl, L. (1961) Einfluß Stabilisierender Kräfte auf die Turbulenz, In: Ludwig Prandtl Gesammelte Abhandlungen (eds W. Tollmien, H. Schlichting and H. Görtler), p. 775, Springer, Berlin.
115. Purtell, L. P. (1992) Turbulence in complex flows - a selected review, AIAA-92-0435.
116. Ristorcelli, J. R. (1995) A pseudo-sound constitutive relationship and closure for the dilatational covariances in compressible turbulence: an analytical theory, IC ASE Report 9-22.
117. Rizk, J. K. and Mongia, H. C. (1991) Three-dimensional analysis of gas turbine combustors, J. Prop. Power 7, 445.
118. Rodi, W. (1976) A new algebraic relation for calculating the Reynolds stress, Z. Angew. Math. 56, 219.
119. Rodi, W. (1988) Recent developments in turbulence modelling, In: 3rd Int. Symp. on Refined Flow Modelling and Turbulence Measurements, Tokyo.
120. Rotta, J. C. (1951) Statistische Theorie Nichthomogener Turbulenz, Z. für Physik, 129, 547 and 131, 51.
121. Rotta, J. C. (1951) Statistische Theorie Nichthomogener Turbulenz, Z. für Physik, 129, 547 and 131, 51.
122. Samimy, M., Elliott, G. S. and Reeder, M. F. (1991) Compressibility effects on large structures in free shear flows, In: 8th Symp. on Turbulent Shear Flows, Munich, paper no. 23-3.
123. Sarkar, S. (1995) The stabilizing effect of compressibility in turbulent shear flow, J. Fluid Mech. 282, 163.
124. Sarkar, S. and Lakshmanan, B. (1991) Application of a Reynolds stress turbulence model to the compressible shear layer, AIAA J. 29, 743.
125. Sarkar, S., Erlebacher, G. and Hussaini, M. Y. (1992) Compressible and homogeneous shear - simulation and modeling, In: Turbulent Shear Flows 8 (eds F. Durst, B. E. Launder, F. W. Schmidt and J. H. Whitelaw), p. 249, Springer, Berlin.
126. Schwarz, W. R. and Bradshaw, P. (1994) Term-by-term tests of stress-transport turbulence models in a three-dimensional boundary layer, Phys. Fluids 6, 986.
127. Schwarz, W. R. and Bradshaw, P. (1994) Turbulence structural changes for a three-dimensional boundary layer in a 30 ≤ bend, J. Fluid Mech. 272, 183.
128. Selig, M. S. and Smits, A. J. (1990) The dynamic behavior of a shock-wave turbulent boundary layer interaction, In: Near-Wall Turbulence - 1988 Zaric Memorial Conf. (eds S. J. Kline and N. H. Afgan), p. 190, Hemisphere, New York.
129. Settles, G. S. and Dodson, L. J. (1993) Hypersonic turbulent boundary-layer and free shear database, NASA CR 177610.
130. Shih, T. H., Mansour, N. N. and Chen, J. Y. (1987) Reynolds stress models of homogeneous turbulence, Studying Turbulence Using Numerical Simulation Databases. NASA Ames/Stanford CTR-S87, p. 191.
131. Shizawa, T. and Eaton, J. K. (1992) Interaction of a longitudinal vortex with a three-dimensional, turbulent boundary layer, AIAA J. 30, 1180.
132. Soteriou, M. C. and Ghoniem, A. F. (1995) Effects of the free-stream density ratio on free and forced spatially developing shear layers, Phys. Fluids 7, 2036.
133. Spalart, P. R. and Allmaras, S. R. (1994) A one-equation turbulence model for aerodynamic flows, La Recherche Aéro. 1, 5 and AIAA-92-0439 (1992).
134. Speziale, C. G., Sarkar, S. and Gatski, T. B. (1991) Modelling the pressure-strain correlation of turbulence - an invariant dynamical systems approach, J. Fluid Mech. 227, 245.
135. Spina, E., Smits, A. J. and Robinson, S. K. (1994) The physics of supersonic turbulent boundary layers, Ann. Rev. Fluid Mech. 26, 287.
136. Stretch, D., Guezennec, Y. and Kim, J. (1990) Heat and momentum exchange mechanism in turbulent channel flow, Bull. Am. Phys. Soc. 35, 2304.
137. Teitel, M. and Antonia, R. A. (1993) A step change in wall heat flux in a turbulent channel flow, Int. J. Heat Mass Transfer 36, 1707.
138. Thomas, N. H. and Hancock, P. E. (1977) Grid turbulence near a moving wall, J. Fluid Mech. 82, 481.
139. Townsend, A. A. (1956) The Structure of Turbulent Shear Flow, University Press, Cambridge.
140. Trouve, A. (1991) Simulation of flame-turbulence interactions in premixed combustion. Stanford Ames Center for Turbulence Research, Annual Research Briefs, p. 273.
141. Van Driest, E. R. (1956) The problem of aerodynamic heating, Aero. Engng Rev. 15, 15.
142. Van Driest, E. R. (1956) On turbulent flow near a wall, J. Aero. Sci. 23, 1007.
143. Viegas, J. R. and Rubesin, M. W. (1991) A comparative study of several compressibility corrections to turbulence models applied to high-speed shear layers, AIAA-91-1783.
144. Viegas, J. R., Rubesin, M. W. and Horstman, C. C. (1985) On the use of wall functions as boundary conditions for two-dimensional separated flows, AIAA-85-0180.
145. Vreman, A. W., Sandham, N. D. and Luo, K. H. (1995) Compressible mixing layer growth rate and turbulence characteristics, Queen Mary College, London, Report QMW-EP-1105.
146. Westphal, R. V., Eaton, J. K. and Pauley, W. R. (1987) Interaction between a vortex and a turbulent boundary layer in a streamwise pressure gradient, In: Turbulent Shear Flows 5 (eds F. Durst, B. E. Launder, F. W. Schmidt and J. H. Whitelaw), p. 266, Springer, New York.
147. Wilcox, D. C. (1988) Reassessment of the scale determining equation for advanced turbulence models, AIAA J. 29, 1299.
148. Wilcox, D. C. (1988) Multiscale model for turbulent flows, AIAA J. 29, 1311.
149. Wilcox, D. C. (1991) Progress in hypersonic turbulence modeling, AIAA-91-1785.
150. Wilcox, D. C. (1992) The remarkable ability of turbulence model equations to describe transition, In: 5th Symp. on Numerical and Physical Aspects of Aerodynamic Flows, Long Beach, CA.
151. Wilcox, D. C. (1992) Dilatation-dissipation corrections for advanced turbulence models, AIAA J. 30, 2639.
152. Wilcox, D. C. (1993) Turbulence modeling for CFD, DCW Industries, La Cañada.
153. Wilson, G. J. and MacCormack, R. W. (1992) Modeling supersonic combustion using a fully implicit numerical method, AIAA J. 30, 1008.
154. Winter, K. G., Rotta, J. C. and Smith, K. G. (1968) Studies of the turbulent boundary layer on a waisted body of revolution in subsonic and supersonic flow, British Aero. Res. Council R. and M. 3633.
155. Zeman, O. (1990) Dilatation dissipation - the concept and application in modeling compressible mixing layers, Phys. Fluids A 2, 178.
156. Zeman, O. (1991) The role of pressure-dilatation correlation in rapidly compressed turbulence and in boundary layers, NASA Ames/Stanford Center for Turbulence Research Annual Research Briefs, p. 105.
157. Zeman, O. (1993) A new model for super/hypersonic turbulent boundary layers, AIAA-93-0897.