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Turbulence modelling and turbulent-flow computation in aeronautics

Published online by Cambridge University Press:  04 July 2016

M. A. Leschziner  and
D. Drikakis
M. A. Leschziner
Affiliation:
Imperial College of Science, Technology and Medicine, University of London, UK
D. Drikakis
Affiliation:
Queen Mary, University of London, UK
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Abstract

Competitive pressures and economic constraints are driving aircraft manufacturers towards an ever-increasing exploitation of CFD for design, optimisation and prediction of off-design conditions. Such exploitation is favoured by rapid advances in meshing technology, numerical algorithms, visualisation tools and computer hardware. In contrast, the predictive capabilities of mathematical models of turbulence are limited — indeed, are often poor in regions of complex strain — and improve only slowly. The intuitive nature of turbulence modelling, its strong reliance on calibration and validation and the extreme sensitivity of model performance to seemingly minor variations in modelling details and flow conditions all conspire to make turbulence modelling an especially challenging component of CFD, but one that is crucially important for the correct prediction of complex flows.

Type
Research Article
Information
The Aeronautical Journal , Volume 106 , Issue 1061 , July 2002 , pp. 349 - 384
Copyright
Copyright © Royal Aeronautical Society 2002 

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References

1. Anderson, J.D. A History of Aerodynamics, 1997, Cambridge University Press.Google Scholar
2. Reynolds, O. On the dynamical theory of incompressible viscous fluids and the determination of the critertion, 1894, Phil Trans Roy Soc, 1895, 186, pp 123–164.Google Scholar
3. Mellen, P., Froehlich, J. and Rodi, W. Lessons from the European LESFOIL project on LES of flow around an airfoil, 2002, AIAA 2002-0111.Google Scholar
4. Jones, W.P. and Manners, A. The calculation of the flow through a two-dimensional faired diffuser, Turbulent Shear Flows 6, Andre, J.C. ET AL,(Eds), 1989,pp 18–31, Springer.Google Scholar
5. Lai, Y.G. Computational method of second-moment turbulence closures in complex geometries, J AIAA, 1995,33, pp 1426–1432.Google Scholar
6. Durbin, P. Separated flow computations with the k-ε-v2 model, J AIAA, 1995,33, pp 659–664.Google Scholar
7. Parneix, S., Durbin, PA. and Behnia, M. Computation of 3-D turbulent boundary layers using the V2F model, Flow, Turbulence and Combustion, 1998,60, pp 19–46.Google Scholar
8. Kassinos, S.C., Langer, C.A., Haire, S.L. and Reynolds, W.C. Structure-based modelling for wall-bounded flows, Int J Heat and Fluid Flow, 2000,21, pp 599–605.Google Scholar
9. Cambon, C. and Scott, J.F. Linear and nonlinear models of anisotropic turbulence, Ann Rev Fluid Mech, 1999,31, pp 1–53.Google Scholar
10. Schiestel, R., Multiple time scale modelling of turbulent flows in one point closures, Phys Fluids, 1987,30, pp 722.Google Scholar
11. Wilcox, D.C. Multi-scale model for turbulent flows, AIAA J, 1988, 26, pp 1311–1320.Google Scholar
12. Prandtl, L. Bericht ueber die Enstehung der Turbulenz, Z Angew Math Mech, 1925, 5, pp 136–139.Google Scholar
13. Von Karman, T. Mechanische Aenlichkeit und Turbulenz, 1930, Proc of Third Int Congress App Mech, Stockholm, pp 85-105.Google Scholar
14. Cebeci, T. and Smith, A.M.O. Analysis of turbulent boundary layers, Ser in Appl Math & Mech XV, 1974, Academic Press, London.Google Scholar
15. Baldwin, B.S. and Lomax, H. Thin-layer approximation algebraic model for separated turbulent flows, 1978, AIAA Paper 78-0257.Google Scholar
16. Granville, P.S. Baldwin-Lomax factors for turbulent boundary layers in pressure gradients, J AIAA, 1987,25, pp 1624–1627.Google Scholar
17. Goldberg, U.C. Separated flow treatment with a new turbulence model, J AIAA, 1986,24, pp 1711–1713.Google Scholar
18. Wolfshtein, M. The velocity and temperature distribution in one- dimensional flow with turbulence augmentation and pressure gradient, Int J Heat Mass Transfer, 1969,12, p 139.Google Scholar
19. Norris, L.H. and Reynolds, W.C. Turbulence channel flow with a moving wavy boundary, 1975, Rep FM-10, Dept of Mech Eng, Stanford University.Google Scholar
20. Hassid, S. and Poreh, M. A turbulence energy model for flows with drag reduction, ASME J of Fluids Eng, 1975,97, pp 234–241.Google Scholar
21. Mitcheltree, R.A., Salas, M.D. and Hassan, HA. One equation turbulence model for transonic airfoil flows, J AIAA, 1990,28, pp 1625–1632.Google Scholar
22. Cook, P.H., Mcdonald, MA. and Firmin, M.C.P. Aerofoil 2822 — Pressure distributions, boundary layer and Wake measurements, 1979, AGARD AR-138.Google Scholar
23. Baldwin, B.W. and Barth, T.A. One-equation turbulence transport model for high Reynolds number wall-bounded flows, 1991, AIAA Paper 91-0610.Google Scholar
24. Spalart, P.R. and Allmaras|S.R. A one-equation turbulence model for aerodynamic flows, 1992, AIAA Paper 92-0439.Google Scholar
25. Menter, F.R. Eddy viscosity transport equations and their relation to the k-ε model, ASME J Fluids Eng, 1997, 119, pp 876–884.Google Scholar
26. Goldberg, U.C. Hypersonic flow heat transfer prediction using single equation turbulence models, ASME J Heat Transfer, 2001, 123, pp 65–69.Google Scholar
27. Goldberg, U.C. and Ramakrishnan, S.V., A pointwise version of the Baldwin-Barth turbulene model, Int J Comp Fluid Dynamics, 1994, 1, pp 321–338.Google Scholar
28. Bradshaw, P., Ferris, D.H. and Atwell, N.P. Calculation of boundary layer development using the turbulent energy equation, J Fluid Mech, 1967, 23, pp 31–64.Google Scholar
29. Menter, F. R. Two equation eddy viscosity turbulence models for engineering applications, J AIAA, 1994,32, pp 1598–1605.Google Scholar
30. Jones, W.P. and Launder, B.E. The prediction of laminarisation with a two-equation model of turbulence, Int J Heat and Mass Transfer, 1972, 15, pp 301–314.Google Scholar
31. Johnson, D.A. and King, L.S. A mathematical simple turbulence closure model for attached and separated turbulent boundary layers, 1985, AIAA Paper 84-0175.Google Scholar
32. Coles, D. and Wadcock, AJ. Flying hot-wire study of flow past a NACA 4412 airfoil at maximum lift, J AIAA, 1979,17, pp 321–328.Google Scholar
33. Piccin, O. and Cassoudesalle, D. Etude dans la soufflerie Fl des profils AS239 et AS240, 1987, ONERA Technical Report, PV 73/1685 AYG.Google Scholar
34. Johnson, D.A. and Coakley, TJ. Improvements to a non-equilibrium algebraic turbulence model, J AIAA, 1990,28, pp 2000–2003.Google Scholar
35. Abid, R, Vatsa, V.N., Johnson, D.A. and Wedan, B.W. Prediction of separated transonic wing flows with a non-equilibrium algebraic model, 1989, Paper AIAA 89-0558.Google Scholar
36. Davidov, B.I. On the statistical dynamics of an incompressible turbulent fluid,DoklAkadNaukSSSR, 1961,136, pp 47–50.Google Scholar
37. Rodi, W. and Mansour, N.N. Low Reynolds number k-ε modelling with the aid of direct numerical simulation data, J Fluid Mech, 1993, 250, pp 509–529.Google Scholar
38. Richardson, L.F. Weather Prediction by Numerical Process, 1992, University Press, Cambridge.Google Scholar
39. Harlow, F.H. and Nakayama, P.I. Transport of turbulence energy decay rate, 1968, University of California Report LA-3854, Los Alamos Science Laboratory.Google Scholar
40. Hanjalic, K. Two-Dimensional Asymmetric Flows in Ducts, 1970, PhD Thesis, University of London.Google Scholar
41. Launder, B.E. and Sharma, B.I. Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc, Letters in Heat and Mass Transfer, 1974, l,p 131.Google Scholar
42. Hoffman, G.H. Improved form of low Reynolds-number k-ε turbulence model, Physics of Fluids, 1975,18, pp 309–312.Google Scholar
43. Lam, C.K.G. and Bremhorst, K. A modified form of the k-ε model for predicting wall turbulence, J Fluids Eng, 1981, 103, pp 456–460.Google Scholar
44. Chien, K.Y. 1982, Predictions of channel and boundary-layer flows with a low-Reynolds-number turbulence model, J AIAA, 1982, 20, (1) pp 33–38.Google Scholar
45. Nagano, Y. and Hishida, M. Improved form of the k-ε model for turbulent shear flows, 1987, Trans of ASME, 109, p 156.Google Scholar
46. Myong, H.K. and Kasagi, N. A new approach to the improvement of k-ε turbulence model for wall bounded shear flows, JSME Int J, Series II, 1990,33, pp 63–72.Google Scholar
47. So, R.M.C., Zhang, H.S. and Speziale, C.G. Near-wall modelling of the dissipation rate equation, J AIAA, 1991, 29, pp 2069–2076.Google Scholar
48. Coakley, T.J and Huang, P.G. Turbulence modelling for high speed flows, 1992, Paper AIAA 92-0436.Google Scholar
49. Orszag, S.A., Yakhot, V., Flannery, W.S., Boysan, F., Choudhury, D., Maruzewski|J. and Patel, B. Renormalisation group modelling and turbulence simulations, Near-Wall Turbulent Flows, So, R.M.C., , Speziale, C.G., and Launder, B.E., (Eds), 1993, Elsevier, pp 1031–1046.Google Scholar
50. Kawamura, H. and Kawashima, N. A proposal for a k-ε model with relevance to the near-wall turbulence, Paper IP .l, Proc Int Symp on Turbulence, Heat and Mass Transfer, 1994, Lisbon.Google Scholar
51. Lien, F.S. and Leschziner, M.A. 1994, Modelling the flow in a transition duct with a non-orthogonal FV procedure and low-Re turbulence- transport models, 1994, Proc ASME FED Summer Meeting, Symposium on Advances in Computational Methods in Fluid Dynamics, pp 93-106.Google Scholar
52. Moser, R., Kim, J. and Mansour, N.N. Direct numerical simulation of turbulent channel flow up to Reτ = 590, Physics of Fluids, 1999, 11, pp 943–945.Google Scholar
53. Patel, C.V., Rodi, W. and Scheuerer, G. Turbulence models for near- wall and low Reynolds number flows: A review, J AIAA, 1985, 23, pp 1308–1319.Google Scholar
54. Michelassi, V. and Shih, T-H. LOW Reynolds number two equation modelling of turbulent flows, 1991, Report NASA TM-104368, ICOMP-91-06.Google Scholar
55. Mansour, N.N., Kim, J. and Moin, P. Near-wall k-ε turbulence modeling, J AIAA, 1989,27,pp 1068–1073.Google Scholar
56. Yap, C.R. Turbulent Heat and Momentum Transfer in Recirculating and Impinging Flows, 1987, PhD thesis, University of Manchester.Google Scholar
57. Jakirlic, S. and Hanjalic, K. A second-moment closure for non-equilibrium and separating high- and low-Re-number flows, 1995, Proc 10th Symp on Turbulent Shear Flows, Pennsylvania State University, 23.25.Google Scholar
58. Iacovides, H. and Raisee, M. Computation of flow and heat transfer in 2D rib roughened passages, 1997, Proc 2nd Int Symp on Turbulence, Heat and Mass Transfer, Hanjalic, K. and Peters, T.W.J. (Eds), Delft University Press, pp 21–30.Google Scholar
59. Hanjalic, K. and Launder, B.E. Sensitising the dissipation equation to irrotational strains, ASME J Fluids Eng, 1980, 102, pp 34–40.Google Scholar
60. Yakhot, V., Orszag, S.A. Thangham, S., Gatski, T.B. and Speziale, C.G., Development of turbulence models for shear flows by a double expansion technique, Phys Fluids A4, 1992, p 1510.Google Scholar
61. Kato, M. and Launder, B.E. The modelling of turbulent flow around stationary and vibrating square cylinders, 1993, Proc 9th Symp on Turbulent Shear Flows, Kyoto, 10.4.1-10.4.6.Google Scholar
62. Liou, W.W., Huang, G and Shih, T-H. Turbulence model assessment for shock wave/turbulent boundary-layer interaction in transonic and supersonic flow, Computers and Fluids, 2000,29, pp 275–299.Google Scholar
63. Launder, B.E., Priddin, C.H. and Sharma, B. The calculation of turbulent boundary layers on curved and spinning surfaces, ASME J Fluids Eng, 1977, 98, p 753.Google Scholar
64. Rodi, W. Influence of buoyancy and rotation on equations for the turbulent length scale, 1979, Proc 2nd Symp on Turbulent Shear Flows, London, 10.37-10.42.Google Scholar
65. Rodi, W. and Scheuerer, G. Calculation of curved shear layers with two-equation turbulence models, Physics of Fluids, 1983, 26, p 1422.Google Scholar
66. Leschziner, M.A. and Rodi, W. Calculation of annular and twin parallel jets using various discretisation schemes and turbulence models, ASME J Fluids Eng, 1981, 103, pp 352–360.Google Scholar
67. Wilcox, D.C. 1988, Reassessment of the scale-determining equation for advanced turbulence models, J AIAA, 1988, 26, pp 1299–1310.Google Scholar
68. Wilcox, D.C. Simulation transition with a two-equation turbulence model, J AIAA, 1994, 32, pp 247–255.Google Scholar
69. Speziale, C.G., Abid, R. and Anderson, E.C. Critical evaluation of two-equation models for near-wall turbulence, J AIAA, 1992, 30, pp 324–331.Google Scholar
70. Kalitzin, G., Gould, A.R.B. and Benton, J.J. Application of two-equation turbulence models in aircraft design, 1996, AIAA Paper 96-0327.Google Scholar
71. Gibson, M.M. and Dafa’Alla, A.A. Two-equation model for turbulent wall flow, J AIAA, 1995, 33, pp 1514–1518.Google Scholar
72. Goldberg, U.C. Towards a pointwise turbulence model for wall- bounded and free shear flows, ASME J Fluids Eng, 1994, 116, p 72.Google Scholar
73. Benay, R. and Servel, P. Two-equation k-σ turbulence model: application to supersonic base flow, J AIAA, 2001,39, pp 407–416.Google Scholar
74. Apsley, D.D. and Leschziner, M.A. Advanced turbulence modelling of separated flow in a diffuser, Flow, Turbulence and Combustion, 2000, 63, pp 81–112.Google Scholar
75. Menter, F.R. Influence of freestream values on k-ω turbulence model predictions, J AIAA, 1992, 30, pp 1657–1659.Google Scholar
76. Bardina, J.E., Huang, P.G. and Coakley, T.J. Turbulence modelling validation, 1997, Paper AIAA 97-2121.Google Scholar
77. Batten, P., Craft, T.J, Leschziner, M.A. and Loyau, H. Reynolds- stress-transport modelling for compressible aerodynamic flows, J AIAA, 1999,37, pp 785–796.Google Scholar
78. Leschziner, M.A., Batten, P. and Craft, TJ. Reynolds-stress modelling of afterbody flows, Aeronaut J, 2001, 105, (1048), pp 297–306.Google Scholar
79. Apsley, D.D. and Leschziner, M.A. Investigation of advanced turbulence models for the flow in a generic wing-body junction, Flow, Turbulence and Combustion, 2001, 167, pp 25–55.Google Scholar
80. Zeierman, S. and Wolfshtein, M. Turbulent time scale for turbulent flow calculations, J AIAA, 1986, 24, pp 1606–1610.Google Scholar
81. Gilbert, N . and Kleiser, L. Turbulence model testing with the aid of direct numerical simulation results, 1991, Proc 8th Symp on Turbulent Shear Flows, Munich, 26.1.1-26.1.6.Google Scholar
82. Launder, B.E. and Tselepidakis, DP. Contribution to the modelling of near-wall turbulence, Turbulent Shear Flows 8, Durst, F. ET AL (Eds), 1993, Springer Verlag, 81.Google Scholar
83. Hallbaeck, M., Groth, A. and Johansson, A.V. Anisotropic dissipation rate — implications for Reynolds-stress models, Advances in Turbulence, Johansson, A.V., and Alfredson, P.H., (Eds), Springer, pp 414–421.Google Scholar
84. Hanjalic, K. and Jakirlic, S. A model of stress dissipation in second moment closures, Appl Scientific Research, 1993, 51, pp 513–518.Google Scholar
85. Launder, B.E. and Reynolds, W.C. Asymptotic near-wall stress dissipation rates in turbulent flow, Phys of Fluids, 1983,26, p 1157 Google Scholar
86. Hanjalic, K. Advanced turbulence closure models: a view of current status and future prospects, Int J Heat Fluid Flow, 1994, 15, pp 178–203.Google Scholar
87. Oberlack, M. Non-isotropic dissipation in non-homogeneous turbulence, J Fluid Mechanics, 1997, 350, pp 351–374.Google Scholar
88. Rotta, J.C. Statistische theory nichhomogener turbulenz, Zeitschrift der Physik, 1951, 129, p 547.Google Scholar
89. Gibson, M.M. and Launder, B.E. Ground effects on pressure fluctuations in the atmospheric boundary layer, J Fluid Mech, 1978, 86, p 491.Google Scholar
90. Fu, S., Leschziner, M.A. and Launder, B.E. Modelling strongly swirling recirculating jet flow with Reynolds-stress transport closure, 1987, Proc 6th Symposium on Turbulent Shear Flow, Toulouse, 17.6.1.Google Scholar
91. Shir, C.C. A preliminary numerical study of atmospheric turbulent flows in the idealised planetary boundary layer, J Atmos Sci, 1973, 30, p 1327.Google Scholar
92. Craft, T.J. and Launder, B.E. New wall-reflection model applied to the turbulent impinging jet, J AIAA, 1992, 30, p 2970.Google Scholar
93. Launder, B.E. and Shima, N. Second-moment closure for the near-wall sublayer, J AIAA, 1989,27,pp 1319–1325.Google Scholar
94. So, R.M.C., Lai, Y.G., Zhang, H.S. and Hwang, B.C. Second-order near-wall turbulence closures: A review, J AIAA, 1991, 29, pp 1819–1835 Google Scholar
95. Ince, N.Z., Betts, P.L and Launder, B.E. Low Reynolds number modelling of turbulent buoyant flows, 1994, Proc EUROTHERM Seminar 22, Turbulent Natural Convection in Cavities, Delft, Editions europeenes Thermique et Industrie, Paris, Henkes, R.A.W.M. and Hoogendoorn, C.J. (Eds) p 76.Google Scholar
96. Craft, T.J. and Launder, B.E. 1996, A Reynolds stress closure designed for complex geometries, Int J Heat Fluid Flow, 1996, 17, p 245.Google Scholar
97. Durbin, P.A. A Reynolds stress model for near-wall turbulence, J Fluid Mech, 1993, 249, p 465.Google Scholar
98. Shih, T.H. and Lumley, J.L. Modelling of pressure correlation terms in Reynolds-stress and scalar-flux equations, 1985, Report FDA-85-3, Sibley School of Mech. and Aerospace Eng, Cornell University.Google Scholar
99. Fu, S., Launder, B.E. and Tselepidakis, D.P. Accommodating the effects of high strain rates in modelling the pressure-strain correlation, 1987, Report TFD/87/5 Mechanical Engineering Dept, UMIST, Manchester.Google Scholar
100. Speziale, C.G., Sarkar, S. and Gatski, T.B. Modelling the pressure-strain correlation of turbulence: an invariant dynamical systems approach, J Fluid Mech, 1991,227, p 245.Google Scholar
101. Craft, T.J., Graham, L.J.W. and Launder, B.E. Impinging jet studies for turbulence model assessment — II. An examination of the performance of four turbulence models, Int J Heat Mass Transfer, 1993,36, p 2685.Google Scholar
102. Craft, T.J. Developments in a low-Reynolds-number second-moment closure and its application to separating and reattaching flows, Int J Heat and Fluid Flow, 1998, 19, pp 541–548.Google Scholar
103. Pfunderer, D.G., Eifert, C. and Janicka, J. Nonlinear second moment closure consistent with shear and strain flows, J AIAA, 1997, 35, pp 825–831.Google Scholar
104. Jakirlic, S. Reynolds-Spannungs-Modellierung Komplexer Turbulenter Stroemungen, 1997, PhD thesis, University of Erlangen-Nuernberg.Google Scholar
105. Daly, B.J. and Harlow, F.H. Transport equations in turbulence, Phys of Fluids, 1970, 13, pp 2634–2649.Google Scholar
106. Demuren, A.O. and Sarkar, S., Perspective: Systematic study of Reynolds-stress closure models in the computation of plane channel flows, ASME J Fluids Eng, 1993, 115, pp 5–12.Google Scholar
107. Younis, B.A., Gatski, T.B. and Speziale, C.G. Towards a rational model for the triple velocity correlations of turbulence, Proc Royal Soc London A, 2000, 456, pp 909–920.Google Scholar
108. Hanjalic, K. and Launder, B.E. A Reynolds stress model and its application to thin shear flows, J Fluid Mechanics, 1972, 52, pp 609–638.Google Scholar
109. Lumley, J.L. 1978, Computational modelling of turbulent flows, Adv Appl Mech, 18, pp 123–176.Google Scholar
110. Shima, N. A Reynolds-stress model for near-wall and low-Reynolds- number regions, ASME J of Fluids Engineering, 1988, 110, pp 38–44.Google Scholar
111. Lien, F.S. and Leschziner, M.A. Modelling 2D and 3D separation from curved surfaces with variants of second-moment closure combined with low-Re near-wall formulations, 1993, Proc 9th Symposium Turbulent Shear Flows, Kyoto, 13.1.1-13.1.6.Google Scholar
112. Lien, F.S. and Leschziner, M.A. A pressure-velocity solution strategy for compressible flow and its application to shock/boundary-layer interaction using second-moment turbulence closure, J of Fluids Engineering, 1993, 115, pp 717–725.Google Scholar
113. Lien, F.S. Computational Modelling of 3D Flow in Complex Ducts and Passages, 1992, PhD thesis, University of Manchester.Google Scholar
114. Leschziner, M.A. and Ince, N.Z. Computational modelling of three- dimensional impinging jets with and without cross flow using second- moment closure, Computers and Fluids, 1995, 24, pp 811–832.Google Scholar
115. Hanjalic, K., Hadzic, I. and Jakirlic, S. Modelling the turbulent wall flows subjected to strong pressure variations, ASME J of Fluids Engineering, 1999, 121, pp 57–64.Google Scholar
116. Rodi, W. A new algebraic relation for calculating the Reynolds stresses, Z Angew Math Mech, 1976, 56, pp 219–221.Google Scholar
117. Pope, S.B. A more general effective-viscosity hypothesis, J Fluid Mech, 1975, 72, pp 331–340.Google Scholar
118. Launder, B.E., Reece, G.J. and Rodi, W. Progress in the development of Reynolds-stress turbulence closure, J Fluid Mech, 1975, 68, pp 537–566.Google Scholar
119. Fu, S., Leschziner, M.A. and Launder, B.E. Modelling strongly swirling recirculating jet flow with Reynolds-stress transport closure, 1987, Proc 6th Symposium on Turbulent Shear Flow, Toulouse, 17.6.1- 17.6.6Google Scholar
120. Girimaji, S.S. A Galilean invariant explicit algebraic Reynolds stress model for turbulent curved flows, Physics of Fluids, 1997, pp 1067–1077.Google Scholar
121. Rumsey, C.L., Gatsky, T.L. and Morrison, J.H. Turbulence model predictions of extra strain rate effects in strongly curved flows, 1999, Paper AIAA 99-157.Google Scholar
122. Wallin, S. and Johansson, A.V. Modelling of streamline curvature effects on turbulence in explicit algebraic Reynolds stress turbulence models, 2001, Proc Second Int Symp on Turbulence and Shear Flow Phenomena, Stockholm, pp 223-228.Google Scholar
123. Jongen, T. and Gatski, T.B. General explicit algebraic stress relations and best approximation for three-dimensional flows, 1998, Int J of Engineering Science, 36, pp 739–763.Google Scholar
124. Wallin, S. and Johansson, A.V. An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows, 2000, J Fluid Mech, 403, pp 89–132.Google Scholar
125. Xu, X-H. and Speziale, C.G. Explicit algebraic stress model of turbulence with anisotropic dissipation, J AIAA, 1996, 34, pp 2186–2189.Google Scholar
126. Johansson, M.C., Knoell, J. and Taulbee, D.B. Monlinear stress- strain model accounting for dissipation anisotropics, J. AIAA, 2000, 38, pp 2187–2189.Google Scholar
127. Saffman, P.G. Results of a two-equation model for turbulent and development of a relaxation stress model for application to straining and rotating flows, Proc Project SQUID Workshop on Turbulence in Internal Flows, Murthy, S. (Ed), 1977, Hemisphere Press, pp 191–231.Google Scholar
128. Wilcox, D.C. and Rubesin|M.W. Progress in turbulence modelling for complex flow field including effects of compressibility, 1980, NASA TP1517.Google Scholar
129. Speziale, C.G. On nonlinear K-l and K-E models of turbulence, J Fluid Mech, 1987, 178, pp 459–475.Google Scholar
130. Yoshizawa, A. Statistical analysis of the derivation of the Reynolds stress from its eddy-viscosity representation, Phys of Fluids, 1987, 27, pp 1377–1387.Google Scholar
131. Shih, T-H., Zhu, J. and Lumley, J.L. A realisable Reynolds stress algebraic equation model, 1993, NASA TM105993.Google Scholar
132. Rubinstein, R. and Barton, J.M. Non-linear Reynolds stress models and the renormalisation group, Phys Fluids A, 1990, 2, pp 1472–1476.Google Scholar
133. Gatski, T.B. and Speziale, C.G. On explicit algebraic stress models for complex turbulent flows, J Fluid Mech, 1993, 254, pp 59–78.Google Scholar
134. Craft, T.J., Launder, B.E. and Suoa, K. Development and application of a cubic eddy-viscosity model of turbulence, Int J Num Meth in Fluids, 1996, 17, pp 108–115.Google Scholar
135. Lien, F.S. and Durbin, P.A. 1996, Non-linear k-v2 modelling with application to high-lift, Proc Summer Prog, Centre For Turbulence Research, Stanford University, pp 5–22.Google Scholar
136. Lien, F.S., Chen, W.L. and Leschziner, M.A. Low-Reynolds-number eddy-viscosity modelling based on non-linear stress-strain/vorticity relations, Engineering Turbulence Modelling and Measurements 3, Rodi, W. and Bergeles, G. (Eds), 1996, Elsevier, pp 91–100.Google Scholar
137. Taulbee, D.B., Sonnenmeier, J.R. and Wall, K.M. 1993, Application of a new non-linear stress-strain model to axisymmetric turbulent swirling flows, Engineering Turbulence Modelling and Experiments 2, Rodi, W. and Martelli, F.A. (Eds), 1993, Elsevier, pp 103–112.Google Scholar
138. Wallin, S. and Johansson, A.V. 1997, A new explicit algebraic Reynolds stress turbulence model for 3D flows, Proc 1 1th Symp. on Turbulent Shear Flows, DURST, F.et al, (Eds), 1997, Grenoble, 13.13-13.17.Google Scholar
139. Rung, T., Fu, S., , and Thiele, , On the realisability of non-linear stress- strain relation for Reynolds-stress closures, Flow, Turbulence and Combustion, 1999,60, pp 333–359.Google Scholar
140. Apsley, D.D. and Leschziner, M.A. A new low-Reynolds-number nonlinear two-equation turbulence model for complex flows, Int J Heat and Fluid Flow, 1998,19, pp 209–222.Google Scholar
141. H. Loyau, H., Batten, P. and Leschziner, M.A. Modeling shock/boundary-layer interaction with nonlinear eddy-viscosity closures, Flow, Turbulence and Combustion, 1998,60, pp 257–282.Google Scholar
142. Tavoularis, S. and Corrsin, S. 1981, Experiment in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient, Part I, J Fluid Mech, 1981, 104, pp 311–347.Google Scholar
143. Huang, P.G. Bradshaw, P. and Coakley, TJ. Turbulence models for compressible boundary-layers, J AIAA, 1994, 32, pp 735–740.Google Scholar
144. Marvin, J.G. and Huang, P.G. Tubulence modelling — progress and future outlook, 1996, Proc of 15th Conf on Numerical Methods in Fluid Dynamics, Monterey, California.Google Scholar
145. Morkovin, M.V. 1962, Effects of compressibility on turbulent flows, Mecanique de la Turbulence, Favre, A. (Ed), Gordon and Breach, NY, pp 367–380.Google Scholar
146. Huang, P.G., Coleman, G.N. and Bradshaw, P. Compressible turbulent channel flows — DNS results and modelling, J Fluid Mech, 1995, 305, pp 185–218.Google Scholar
147. Zeman, O. Dilatation disspation: the concept and application in modelling compressible mixing layers, Phys Fluids, 1990,2, pp 178–188.Google Scholar
148. Sarkar, S., Erlebacher, G., Hussaini, MY. and Kreiss, H.O. The analysis and modelling of dilatational terms in compressible turbulence, J Fluid Mech, 1991, 227, pp 473–493.Google Scholar
149. Wilcox, D.C. Turbulence Modelling for CFD, 1993, DCW Industries, La Canada, California.Google Scholar
150. Fauchet, G., Sho, L., Wunenberger, R. and Bertoglio, J.P. An improved two-point closure for weakly compressible turbulence and comparison with large-eddy simulations, Appl Sci Research, 1997, 57, pp 165–194.Google Scholar
151. Aupoix, B., Blaisdell, G.A., Reynolds, W.C. and Zeman, O. Modelling the turbulent kinetic energy equation for compressible homoge-neous turbulence, J AIAA, 1986, 24, pp 437–443.Google Scholar
152. Sarkar, S. The pressure-dilatation correlation in compressible flows, Phys Fluid, 1992, 282, pp 163–186.Google Scholar
153. Zeman, O. New model for super/hypersonic turbulent boundary layers, 1993, Paper AIAA 93-0897.Google Scholar
154. El Baz, A.M. and Launder, B.E. Second-moment modelling of compressible mixing layers, Engineering Turbulence Modelling and Experiments 3,1993, Elsevier, pp 63–70.Google Scholar
155. Coakley, T.J., Horstman, C.C., Marvin, J.G., Viegas, J.R, Bardina, J.E., Huang, P.G. and Kussoy, M.I. Turbulence compressibility corrections, 1994, NASA TM-108827.Google Scholar
156. Huang, P.G. Modelling hypersonic boundary layers with second moment closure, 1990, CTR, University of Stanford, Annual Research Briefs, pp 1-13.Google Scholar
157. Friedrich, R. and Bertolotti, F. Ompressibility effects due to turbulent fluctuations, Appl Sci Research, 1997, 57, pp 165–194.Google Scholar
158. Coleman, G.N., Kim, J. and Moser, R.D. A numerical study of turbulent supersonic isothermal wall channel flow, J Fluid Mech, 1995, 30, pp 159–183.Google Scholar
159. Sarkar, S. The stabilising effect of compressibility in turbulent shear flow, J Fluid Mech, 1995, 282, pp 163–186.Google Scholar
160. Harlow, F.H. and Welch, J.E. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys Fluids, 1965,8,pp 2182–2189.Google Scholar
161. Patankar, S.V. and Spalding, D.B. Heat and Mass Transfer in Boundary Layers, 1970, Second Edition, Intertext, London.Google Scholar
162. Chorin, J. Numerical solution of the Navier-Stokes equations, Mathematics of Computation, 1968, 22, pp 745–762.Google Scholar
163. Chorin, J. A numerical method for solving incompressible flow problems, J Comput Phys, 1967,2, pp 12–26.Google Scholar
164. Chorin, A.J. and Marsden, G. A Mathematical Introduction to Fluid Mechanics, 1993, Springer-Verlag.Google Scholar
165. Rogers, S.E., Kwak, D. and Kiris, C. Steady and unsteady solutions of the incompressible Navier-Stokes equations, J AIAA, 1991. 29, pp 603–610.Google Scholar
166. Merkle, C.L. and Athavale|M. Time-accurate unsteady incompressible flow algorithms based on artificial compressibility, 1987, AIAA Paper 87-1137.Google Scholar
167. Drikakis, D. Uniformly high-order methods for unsteady incompressible flows, In Godunov Methods: Theory and Applications, Toro, E.F. (Ed), 2001, Kluwer Academic Publishers, pp 263–283.Google Scholar
168. Barakos, G. and Drikakis, D. Implicit-coupled implementation of two-equation turbulence models in compressible Navier-Stokes methods, Int J Num Meth Fluids, 1998, 28, pp 73–94.Google Scholar
169. Drikakis, D. and Goldberg, U. Wall-distance-free turbulence models applied to incompressible flows, Int J of Comput Fluid Dyn, 1998, 10, pp 241–253.Google Scholar
170. Kunz, R.F. and Lakshminarayama, B. Explicit Navier-Stokes computation of cascade flows using the turbulence model, J AIAA, 1992, 30, pp 13–22.Google Scholar
171. Liou, W.W. and Shih, T.H. Transonic turbulent flow predictions with two-equation turbulence models, NASA, Lewis, CR, ICOMP (1996).Google Scholar
172. Sahu, J. and Danberg, J. Navier-Stokes computations of transonic flows with a two equation turbulence model, J AIAA, 1986, 24, pp 1744–1751.Google Scholar
173. Gerolymos, G.A. and Vallet, I. Implicit computation of three-dimensional compressible Navier-Stokes equations using k-ε closure, J AIAA, 1996,34, pp 1321–1330.Google Scholar
174. LIN, etal. Google Scholar
175. Chakravarthy, S.R. High resolution upwind formulations for the Navier-Stokes equations, 1988, VKI Lecture Series, Comp Fluid Dyns, 1988-05.Google Scholar
176. Eberle, A. 3D Euler calculations using characteristic flux extrapolation, 1985, Paper AIAA-85-0119.Google Scholar
177. Zoltak, J. and Drikakis, D. Hybrid upwind methods for the simulation of unsteady shock-wave diffraction over a cylinder, Computer Methods in Appl Mech & Eng, 1998, 162, pp 165–185.Google Scholar
178. Schmatz, M.A., Brenneis, A. and Eberle, A. Verification of an implicit relaxation method for steady and unsteady viscous flow problems, 1988, AGARD CP 437,15.1-15.33.Google Scholar
179. Drikakis, D and Durst, F. Investigation of flux formulae in transonic shock wave/Turbulent boundary layer interaction, Int J Num Meth Fluids, 1994, 18, pp 385–413.Google Scholar
180. Chen, J.P. and Whitfield, D.L. Navier-Stokes calculations for the unsteady flowfield of turbomachinery, 1993, Paper AIAA-93-0676.Google Scholar
181. Eberle, A., Rizzi, A. and Hirschel, E.H. Numerical solutions of the Euler equations for steady flow problems, Notes on Numerical Fluid Mechanics, 1992,34, Vieweg Verlag.Google Scholar
182. Drikakis, D. Schreck, E., and Durst, F. Performance analysis of viscous flow computations on various parallel architectures, ASME J of Fluids Eng, 1994, 116, pp 835–841.Google Scholar
183. Drikakis, D. and Durst, F. Parallelisation of inviscid and viscous flow solvers, Int J of Comp Fluid Dyn, 1994,3, pp 101–121.Google Scholar
184. Barakos, G. and Drikakis, D. An implicit unfactored method for unsteady, turbulent compressible flows with moving boundaries, Computers & Fluids, 1999, 28, pp 899–921.Google Scholar
185. Morrison, J.H. A compressible Navier-Stokes solver with two-equation and Reynolds stress closure models, 1992, NASA CR 4440.Google Scholar
186. Vallet, I. Aerodynamique Numerique 3D Instationnaire avec Fermature bas-Renolds au Second Ordre, 1995, Doctoral Thesis, Universite Paris 6.Google Scholar
187. Batten, P., Leschziner, M.A. and Goldberg, U.G. Average state Jacobians and implicit methods for compressible viscous and turbulent flows, J Comput Phys, 1997, 137, pp 38–78.Google Scholar
188. Liu, F. Multigrid Solution of the Navier-Stokes Equations with a two- equation turbulence model, Frontiers of Computational Fluid Dynamics, Caughey, D.A. and Hafez, M.M. (Eds), 1994, John Wiley and Sons, pp 339–359.Google Scholar
189. Liu, F. and Zheng, X. A staggered finite volume scheme for solving cascade flow with a two-dimensional model of turbulence, 1993, Paper AIAA 93-1912.Google Scholar
190. Merci, B., Steelant, J., Vierendeels, J., Riemslagh, K. and Dick, E. Computation treatment of source terms in two-equation turbulence models, J AIAA, 2000,38, pp 2085–2093.Google Scholar
191. Bachalo, W.D. and Johnson, D.A. 1986, Transonic turbulent boundary layer separation generated on an axisymmetric flow model, J AIAA, 24, pp 437–443.Google Scholar
192. Johnson, D.A., Horstman, C.C. and Bachalo, W.D. Comparison between experiment and prediction for a transonic turbulent separated flow, J AIAA, 1982, 20, pp 737–744.Google Scholar
193. Kline, S.J., Cantwell, B.J. and Lilley, G.M. Proc 1980-81 AFSOR- HTTM-Stanford Conference on Complex Turbulent Flows, 1981, Stanford University, Stanford, California.Google Scholar
194. Barakos, G., and Drikakis, D. Investigation of non-linear eddy- viscosity models in shock/boundary-layer interaction, AIAA J, 2000,38, pp 461–469.Google Scholar
195. Delery, J.M. Experimental investigation of turbulence properties in transonic shock/boundary-layer interactions, J AIAA, 1983, 21, pp 180– 185.Google Scholar
196. Karki, K.C. and Patankar, S.V. A pressure-based calculation procedure for viscous flows at all speeds in arbitrary configurations, J AIAA, 1989,27, pp 1167–1174.Google Scholar
197. Mcguirk, J.J and Page, G.J. Shock-capturing using a pressure-correction method, 1989, AIAA Paper, 27th Aerospace Sciences Meeting, Reno.Google Scholar
198. Kobayashi, M.H. and Peirera, J.C.F. Prediction of compressible viscous flows at all Mach numbers using pressure correction, collocated primitive variables and non-orthogonal meshes, 1992, Paper AIAA-92- 0548.Google Scholar
199. Lien, F-S. and Leschziner, M.A. A general non-orthogonal finite volume algorithm for turbulent flow at all speeds incorporating second-moment closure. Part I: Numerical implementation, Comput Meth Appl Mech Eng, 1994, 114, pp 123–148.Google Scholar
200. Shyy, W., Chen, M-H and Sun, C-S. A pressure-based FMG/FAS algorithm for flow at all speeds, 1992, Paper AIAA-92-0426.Google Scholar
201. Klein, R. Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics, J Comput. Phys, 1995, 121, pp 213–237.Google Scholar
202. Sesterhenn, J., Mueller, B. and Thomann, H. On the cancellation problem in calculating compressible low Mach number flows, J Comput Phys, 1999, 151, pp 597–615.Google Scholar
203. Drikakis, D. and Bagabir, A. On Godunov-type methods for low Mach number flows, 2000, CD-ROM Proceedings of the ECCOMAS 2000 Conference, Barcelona.Google Scholar
204. Leschziner, M.A. and Lien, F-S. Numerical aspects of applying second-moment closure to complex flows, Closure Strategies for Turbulent and Transitional Flows, 2001, Launder, B.E. and Sandham, N.D. (Eds), Cambridge University Press.Google Scholar
205. Huang, P.G. and Leschziner, M.A. Stabilisation of recirculating flow computations performed with second-moment closure and third-order discretisation, 1985, Proc 5th Symp on Turbulent Shear Flow, Cornell University, 20.7-20.12.Google Scholar
206. Lien, F.S. and Leschziner, M.A. Modelling 2D separation from highlift aerofoils with a non-linear eddy-viscosity model and second-moment closure, Aeronaut J, 1995,99, pp 125–144.Google Scholar
207. Lien, F.S. and Leschziner, M.A. 1997, Computational modelling of separated flow around streamlined body at high incidence, Aeronaut J, 1997, 101, pp 269–275.Google Scholar
208. Hasan, R.G.M. and Mcguirk, J.J. Assessment of turbulence model performance for transonic flow over an axisymmetric bump, Aeronaut J,2001,105, pp 17–31.Google Scholar
209. Hasan, R.G.M., Apsley, D.D., Mcguirk, J.J. and Leschziner, M.A. A turbulence model study of separated 3D jet/afterbody flow, submitted to Aeronaut J, 2002. Google Scholar
210. Haase, W., Brandsma, F., Elsholz, E., Leschziner, M.A. and Schwamborn, D. (Eds). Euroval — A European Initiative on Validation of CFD Codes — Results of the EC/BRITE-EURAM Project EUROVAL, 1990-1992, Notes on Numerical Fluid Mechanics, 1993, 42, Vieweg Verlag.Google Scholar
211. Haase, W., Chaput, E., Elsholz, E., Leschziner, M.A. and Muller, U.R. (Eds) ECARP: European Computational Aerodynamics Research Project. II: Validation of CFD Codes and Assessment of Turbulent Models, Notes on Numerical Fluid Mechanics, 1996, 58, Vieweg Verlag.Google Scholar
212. Dervieux, A., Braza, F. and Dussauge, J-P. (Eds), Computation and Comparison of Efficient Turbulence Models for Aeronautics - European Research Project ETMA, Notes on Numerical Fluid Mechanics, 1998,65, Vieweg Verlag.Google Scholar
213. Delery, J. Investigation of strong turbulent boundary-layer interaction in 2D flows with emphasis on turbulence phenomena, 1981, Paper AIAA 81-1245.Google Scholar
214. Horseman, C.C. Prediction of hypersonic shock wave/turbulent boundary layer interaction flows, 1987, Paper AIAA 87-1367.Google Scholar
215. Dolling, D.S. High-speed turbulent separated flows: consistency of mathematical models and flow physics, J AIAA, 1998, 36, pp 725–732.Google Scholar
216. Menter, F.R., Performance of popular turbulence models for attached and separated adverse pressure gradient flows, J AIAA, 1992, 30, pp 2066–2072.Google Scholar
217. Robinson, D. P. and Hasan, H.A. Further developments of the k-ζ , (enstrophy) turbulence closure model, J AIAA, 1998, 36, pp 1825–1833.Google Scholar
218. Jang, Y-J., Temmerman, L. and Leschziner, M.A. Investigation of anisotropy-resolving turbulence models by reference to highly-resolved LES data for separated flow, 2001, CD-ROM proc ECCOMAS 2001 conf, Swansea.Google Scholar
219. Huang, P.G. Validation of turbulence model - uncertainties and measures to reduce them, 1997, Proc ASME FED Summer Meeting, June 22-26,1997.Google Scholar
220. Driver, D.M. Reynolds shear stress measurements in a separated boundary layer, 1991, Paper AIAA 91-1787.Google Scholar
221. Rung, T., Luebke, H., Franke, M., Xue, L., Thile, F. and Fu, S. Assessment of explicit algebraic stress models in transonic flows, Engineering Turbulence Modelling and Experiments 4, 1999, Rodi, W., and Laurence, D., (Eds), Elsevier, 659–668.Google Scholar
222. Schmitt, V. and Charpin, F. Pressure distributions on the ONERA M6 wing at transonic Mach numbers, AGARD AR-138 (179).Google Scholar
223. Obi, S. Aoki, K. and Masuda, S. (1993), Experimental and computational study of turbulent separated flow in an asymmetric diffuser, Proc 9th Symp on Turbulent Shear Flows, Kyoto, pp 305-307.Google Scholar
224. Barakos, G. and Drikakis, D. Assessment of various low-Re turbulence models in shock boundary layer interaction, Computer Methods in Applied Mechanics and Engineering, 1998, 160, pp 155–174.Google Scholar
225. Barakos, G., Drikakis, D. and Lefebre, W. Improvement to numerical predictions of aerodynamic flows using experimental data assimilation, Journal of Aircraft, 1999,36, (3), pp 611–614.Google Scholar
226. Abid, R., Rumsey, C and Gatski, T.B. Prediction of non-equilibrium turbulent flows with explicit algebraic stress models, J AIAA, 1995, 33, pp 2026–2031.Google Scholar
227. Abid, R., Morrison, J.H., Gatski, T.B. and Speziale, C.G., Prediction of aerodynamic flows with a new explicit algebraic stress model, J AIAA, 1996,34, pp 2632–2635.Google Scholar
228. Haidinger, F.A. and Friedrich, R. Computation of shock wave/ boundary layer interactions using a two-equation model with compressibility corrections, Appl Scientific Research, 1993,51, pp 501–505.Google Scholar
229. Haidinger, F.A. and Friedrich, R. Numerical simulation of strong shock/turbulent boundary layer interaction using a Reynolds stress model, Zeitschrift der Flugwissenschaften und Weltraumforschung, 1995,19, pp 10–18.Google Scholar
230. Coratekin, T. Schubert, A. and Ballmann, J. Assessment of eddy- viscosity models in 2D and 3D shock/boundary-layer interactions, Engineering Turbulence Modelling and Experiments 4, Rodi, W. and Laurence, D. (Eds), Elsevier, pp 649–658.Google Scholar
231. Zhou, G., Davidson, L. and Olsson, E. Turbulent transonic airfoil flow simulation using a pressure-based algorithm, J AIAA, 1995, 33, pp 42–47.Google Scholar
232. Srinivasan, G.R., Ekaterinaris, J.A. and Mccroskey, W.J. Dynamic stall of an oscillating wing, 1993, Part 1: Evaluation of turbulence models, Paper AIAA 93-3403.Google Scholar
233. Ekaterinaris, J.A. and Menter, F.R. Computation of oscillating airfoil flows with one and two-equation turbulence models. J AIAA, 1994, 32, pp 2359–2365.Google Scholar
234. Leschziner, M.A., Loyau, H. and Apsley, D.D. Prediction of shock/boundary-layer interaction with non-linear eddy-viscosity models, 2000, CD-ROM Proc European Congress on Computational Methods in Applies Sciences and Engineering, ECCOMAS 2000, Barcelona.Google Scholar
235. Wu, X. and Squires, K.D. Prediction of the three-dimensional turbulent boundary layer over a swept bump, J AIAA, 1998,36, pp 505–514.Google Scholar
236. Vandromme, D. and Haminh, H. Physical analysis for turbulent boundary-layer/shock-wave interactions using second-moment closure predictions, Turbulent Shear-Layer/Shock-Wave Interactions, Delery, J. (Ed), 1985, Springer, pp 127–136.Google Scholar
237. Benay, R., Coet, M.C. and Delery, J. A study of turbulence modelling in transonic shock-wave/boundary-layer interactions, 1987, Proc of 6th Symp on Turbulent Shear Flows, Toulouse, 8.2.1-8.2.6.Google Scholar
238. Leschziner, M.A., Dimitriadis, K.P. and Page, G. Computational modelling of shock wave/boundary layer interaction with a cell-vertex scheme and transport models of turbulence, Aero J, 1993, 97, pp 43–61.Google Scholar
239. Morrison, J.H., Gatski, T.B., Sommer, T.P. and So, R.M.C. Evaluation of a near-wall turbulent closure model in predicting compressible ramp flows, Near-Wall Turbulent Flows, So, R.M.C, Speziale, C.G. and Launder, B.E. (Eds), 1993, Elsevier, pp 239–250.Google Scholar
240. Chenault, C.F. and Beran, P.S. K-E and Reynolds stress turbulence model comparisons for two-dimensional injection flows, J AIAA, 1998, 36,pp 1401–1412.Google Scholar
241. Chenault, C.F., Beran, P.S. and Bowersox, R.D.W. Numerical investigation of supersonic injection using a Reynolds-stress turbulence model, JAIAA, 1999,37, pp 1257–1269.Google Scholar
242. Gerolymos, G.A. and Vallet, I. Near-wall Reynolds-stress three- dimensional transonic flow computation, J AIAA, 1997, 35, pp 228–236.Google Scholar
243. Drikakis, D. and Barakos, G. Numerical developments in unsteady aerodynamic flows, 2000, CD-ROM Proc ECCOMAS Conference, Forum: CFD in Aeronautics, Industrial Technology Session organised by EU, Barcelona, 2000.Google Scholar
244. Huang, P.G. and Coakley, T.J. Modelling hypersonic flows with second-moment closure, Near-Wall Turbulent Flows, So, R.M.C, Speziale, C.G. and Launder, B.E. (Eds), 1993, Elsevier, pp 199–208.Google Scholar
245. Meier, H.U., Kreplin., H.P., Landhauser, A. and Baumgarten, D. Mean velocity distribution in 3D boundary layers developing on a 1:6 prolate spheroid with artificial transition, 1984, DFVLR Report IB 222-84 All.Google Scholar
246. Davidson, L. Reynolds stress transport modelling of shock induced separated flow, Computers & Fluids, 1995,24, pp 253–268.Google Scholar
247. Pot, T., Delery, J. and Quelin, C. Interaction choc-couche limite dans un canal tridimensionnel — nouvelles experiences en vue de la validation du code CANARI, 1991, ONERA TR-92/7078 AY.Google Scholar
248. Leschziner, M.A., Batten, P. and Loyau, H. Modelling shock-affected near-wall flows with anisotropy-resolving turbulence closures, Int J Heat and Fluid Flow, 2000,21, pp 239–251.Google Scholar
249. Barakos, G. and Drikakis, D. Unsteady separated flows over manouvring lifting surfaces, Phil Trans Royal Soc London. A, 2000, 358, pp 3279–3291.Google Scholar
250. Putnam, L.E. and Mercer, CE. Pitot-pressure measurements in flow fields behind a rectangular nozzle with exhaust jet for free-stream Mach numbers of 0,0-6 and 1-2. 1986, NASA TM 88990.Google Scholar
251. Fleming, J.L., Simpson, R.L., Cowling, J.E. and Devenport, W.J. An experimental study of wing-body junction and wake flow, Experiments in Fluids, 1993,14, pp 366–378.Google Scholar
252. Rumsey, C.L., Gatsky, T.B., Ying, S.X. and Bertelrud, A. Prediction of high-lift flows using turbulent closure models, J AIAA, 1998, 36, pp 765–774.Google Scholar
253. Cousteix, J. and Houdeville|R. Effects of unsteadiness on turbulent boundary layers, 1983, von Karman Inst for Fluid Dynamics, Lecture Series 1983-03.Google Scholar
254. Power, G.D., Verdon, J.M. and Kousen, K.A. Analysis of unsteady compressible viscous layers, Tran ASME J Turbomachinery, 1991, 133, pp 644–653.Google Scholar
255. Mankbadi, R.R. and Mobarak, A. Quasi-steady turbulence modelling of unsteady flows, Int J Heat and Fluid Flow, 1991,12, pp 122–129.Google Scholar
256. Justesen, P. and Spalart, P.R. Two-equation turbulence modelling of oscillating boundary layers, 1990, Paper AIAA 90-0496.Google Scholar
257. Fan, S., Lakshminarayana, B. and Barnett, M. Low-Reynolds- number k-ε model for unsteady turbulent boundary layers, J AIAA, 1993, 31, pp 1777–1784.Google Scholar
258. Dafa'Alla, A.A., Juntasaro, E. and Gibson, M.M. Calculation of oscillating boundary layers with the q-ζ , turbulence model, Eng Turbulence Modelling and Experiments, 1996,3,pp 141–150.Google Scholar
259. Shima, N. Prediction of turbulent boudary layers with a second-moment closure: Part l,Tran ASME J Fluids Eng, 1993, 115, pp 56–63.Google Scholar
260. HA Minh, H., Viegas, J.R., Rubesin, M.W., Vandromme, D.D. and Spalart, P. Physical analysis and second-order modelling of an unsteady turbulent flow: The oscillating boundary layer on a flat plate, 7th Symp on Turbulent Shear Flows, Stanford, CA, (1989), 11.5.1- 11.5.6.Google Scholar
261. Hanjalic, K., Jakirlic, S. and Hadzic, I. Computation of oscillating turbulent flows at transitional Reynolds number, 1993, 9th Symp on Turbulent Shear Flows, Kyoto, Japan, 1.4.1 - 1.4.6.Google Scholar
262. Spalart, P.R. and Baldwin, B.S. Direct numerical simulation of turbulent oscillating boundary layer, Turbulent Shear Flows, 1989, Springer, pp 417–440.Google Scholar
263. Kani, A.R. Investigation of Turbulence Models in Oscillating Turbulent Flows, 2000, PhD dissertation, Queen Mary, University of London.Google Scholar
264. Jensen, B.L., Sumer, B.M. and Fredsoe, J. Turbulent oscillating boundary layers at high Reynolds numbers, J Fluid Mech, 1989, 206, pp 265–297.Google Scholar
265. Hino, M., Kashiwayanagi, M. Nakayama, A. and Hara, T. Experiments on the turbulence statistics and the structure of a reciprocating oscillatory flow, J Fluid Mech, 1983, 133, pp 363–400.Google Scholar
266. Barakos, G. and Drikakis, D. Numerical simulation of transonic buffet flows using various turbulence closures, Int J Heat and Fluid Flow, 2000, 21, pp 620–626.Google Scholar
267. Telionis, D.P. Unsteady boundary layers, separated and attached, paper 16, AGARD CP-227, Unsteady Aerodynamics, 1977, Ottawa.Google Scholar
268. Mehta, U.B. and Lavan, Z. Starting vortex, separation bubbles and stall: A numerical study of laminar unsteady flow around an airfoil, J FluidMechs, 1975,67, pp 227–256.Google Scholar
269. Gulcat, U. Separate Numerical Treatment of Attached and Detached Flow Regions in General Viscous Flows, 1981, PhD thesis, Georgia Institute of Technology, Atlanta, Georgia.Google Scholar
270. Mccroskey, W.J., Mcalister, K.W, Carr, L.W., Lambert, O. and Indergrand, R.F. Dynamic stall of advanced airfoil sections, J American Helicopter Soc, 1991, pp 40–50.Google Scholar
271. Wu, J.C, Wang, CM. and Tuncer, I.H. Unsteady aerodynamics of rapidly pitched airfoil, 1986, Paper AIAA 86-1105.Google Scholar
272. Tuncer, I.H., Wu, J.C. and Wang, CM. Theoretical and numerical studies of oscillating airfoils, J AIAA, 1990,28, pp 1615–1624.Google Scholar
273. AGARD Advisory Report No 702, Compendium of Unsteady Aerodynamic Measurements, 1982.Google Scholar
274. Mccroskey, W.J., Mcalister, K.W, Carr, L.W. and Pucci, S.L. An experimental study of dynamic stall on advanced airfoil sections, 1982 Vol. 1: Summary of the experiment, NASA-TM-84245-VOL-l.Google Scholar
275. Carr, L.W. Progress in analysis and prediction of dynamic stall, J Aircraft, 1988,25, pp 6–17.Google Scholar
276. Visbal, M.R. Effect of compressibility on dynamic stall, 1988, Paper AIAA Paper 88-0132.Google Scholar
277. Piziali, R.A. An experimental investigation of 2D and 3D oscillating wing aerodynamics for a range of angle of attack including stall, 1993, NASA-TM-4632.Google Scholar
278. Guo, W.H., Fu, D.X. and Wa, Y.W. Numerical investigation of dynamic stall of an oscillating aerofoil, Int J for Num Methods in Fluids, 1994,19, pp 723–734.Google Scholar
279. Mcdevitt, J.B. and Okuno, A.F. Static and dynamic pressure measurements on a NACA 0012 airfoil in the Ames High Reynolds Number Facility, 1985, NASA-TP-2485, NASA Ames, CA.Google Scholar
280. Mcdevitt, J.B., Levy, L.L. and Deiwert, G.S. Transonic flow about a thick circular-arc airfoil, J AIAA, 1976,14, pp 606–613.Google Scholar
281. Sofialidis, D. and Prinos, P. Development of a non-linear strain-sensitive k-ω turbulence model, 1997, Proc of the 1 1th TSF-11 Conference, Grenoble, France, 2-89 - 2-94.Google Scholar
282. Rider, W. and Drikakis, D. High resolution methods for computing turbulent flows, Turbulent Flow Computation, Drikakis, D., and Geurts, B., (Eds), 2002, Kluwer Academic Publisher, 2002, to appear.Google Scholar
283. Oran, E.S. and Boris, J.P. Numerical Simulation of Reactive Flow, 2001,Elsevier.Google Scholar
284. Drikakis, D. Numerical issues in very large eddy simulation. CD-ROM, 2001, Proc of the ECCOMAS CFD 2001 Conference, Swansea, UK.Google Scholar
285. Spalart, P.R., Jou, W-J, Strelets, M. and Allmaras, S.R. Comments on the feasibility of LES for wings and on the hybrid RANS/LES approach, 1997, Advances in DNS/LES, 1st AFOSR Int Conf on NDS/LES, Greden Press.Google Scholar