Contribution to single-point closure Reynolds-stress modelling of inhomogeneous flow

Theoretical and Computational Fluid Dynamics

Volumn 17, Issue 5-6, 2004, Pages 407-431

  Gerolymos, G A ^a   Sauret, E ^a   Vallet, I ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

3 D flow; Reynolds stress model; Turbulence; Wall topology independent

Indexed keywords

EID: 5644283025     PISSN: 09354964     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00162-004-0109-5     Document Type: Conference Paper

References (79)

1. Basso, E., Antunes, A.P., Azevedo, J.L.F.: Chimera simulations of supersonic flows over a complex satellite launcher configuration. J. Spacecraft Rockets 40, 345-355 (2003)
2. Batten, P., Craft, T.J., Leschziner, M.A., Loyau, H.: Reynolds-stress transport modelling for compressible aerodynamics applications. AIAA J. 37, 785-797 (1999)
3. Chassaing, J.C., Gerolymos, G.A., Vallet, I.: Efficient and robust Reynolds-stress model computation of 3D compressible flows. AIAA J. 41, 763-773 (2003)
4. Chassaing, J.C., Gerolymos, G.A., Vallet, I.: Reynolds-stress model dual time stepping computation of unsteady 3D flows. AIAA J. 41, 1882-1894 (2003)
5. Chou, P.Y.: On velocity correlations and solutions of equations of turbulent fluctuations. Quart. Appl. Math. 3, 38-54 (1945)
6. Comte-Bellot, G.: Ecoulement turbulent entre 2 parois parallèles. Pub. Scientifiques et Tec. 419, Ministère de l'Air, Paris [F] (1965)
7. Craft, T.J.: Developments in a low-Reynolds-number second moment closure and its application to separating and reattaching flows. Int. J. Heat Fluid Flow 19, 541-548 (1998)
8. Craft, T.J., Launder, B.: A Reynolds-stress model designed for complex geometries. Int. J. Heat Fluid Flow 17, 245-254 (1996)
9. Craft, T.J., Launder, B., Suga, K.: Prediction of turbulent transitional phenomena with a nonlinear eddy-viscosity model. Int. J. Heat Fluid Flow 18, 15-28 (1997)
10. Daly, B.J., Harlow, F.H.: Transport equations in turbulence. Phys. Fluids 13, 2634-2649 (1970)
11. Djenidi, L., Antonia, R.A.: Modelling of the Reynolds-stress transport equation. AIAA J. 35, 450-455 (1997)
12. Dolling, D.S., Murphy, M.T.: Unsteadiness of the separation shock wave structure in a supersonic compression ramp flowfield. AIAA J. 21, 1628-1634 (1983)
13. Doukelis, A., Mathioudakis, K., Papailiou, K.D.: The effect of tip clearance gap size and wall rotation on the performance of a high-speed annular compressor cascade. ASME Paper 98-GT-38 (1998)
14. Durbin, P.A.: A Reynolds-stress model for near wall turbulence. J. Fluid Mech. 249, 465-498 (1993)
15. Favre, A.: Equations des gaz turbulents compressibles - I - formes générales. J. Méc. 4, 361-390 (1965)
16. Favre, A.: Equations des gaz turbulents compressibles - II - méthode des vitesses moyennes; méthode des vitesses moyennes pondérées par la masse volumique. J. Méc. 4, 391-421 (1965)
17. Gerolymos, G.A., Neubauer, J., Michon, G.J.: Analysis and application of chorochronic periodicity for turbomachinery rotor/stator interaction computation. J. Prop. Power 18, 1139-1152 (2002)
18. Gerolymos, G.A., Neubauer, J., Sharma, V.C., Vallet, I.: Improved prediction of turbomachinery flows using the near wall Reynolds-stress model. ASME J. Turbom. 124, 86-99 (2002)
19. Gerolymos, G.A., Sauret, E., Vallet, I.: Influence of inflow turbulence in shock wave/turbulent boundary layer interaction computations. AIAA J. 42, 1101-1106 (2004)
20. Gerolymos, G.A., Sauret, E., Vallet, I.: Oblique shock wave/boundary layer interaction using near wall Reynolds-stress models. AIAA J. 42, 1089-1100 (2004)
21. Gerolymos, G.A., Vallet, I.: Near wall Reynolds-stress 3-D transonic flows computation. AIAA J. 35, 228-236 (1997)
22. Gerolymos, G.A., Vallet, I.: Wall-normal-free near wall Reynolds-stress closure for 3D compressible separated flows. AIAA J. 39, 1833-1842 (2001)
23. Gerolymos, G.A., Vallet, I.: Wall-normal-free Reynolds-stress model for rotating flows applied to turbomachinery. AIAA J. 40, 199-208 (2002)
24. Gessner, F.B., Emery, A.F.: The numerical prediction of developing turbulent flow in rectangular ducts. ASME J. Fluids Eng. 103, 445-455 (1981)
25. Gibson, M.M., Launder, B.E.: Ground effects on pressure fluctuations in the atmospheric boundary-layer. J. Fluid Mech. 86, 491-511 (1978)
26. Hanjalić, K.: Advanced turbulence closure models: A view of current status and future prospects. Int. J. Heat Fluid Flow 15, 178-203 (1994)
27. Hanjalić, K., Jakirlić, S.: Contribution towards the second-moment closure modelling of separating turbulent flows. Comp. Fluids 27, 137-156 (1998)
28. Hanjalić, K., Launder, B.E.: A Reynolds-stress model of turbulence and its application to thin shear flows. J. Fluid Mech. 52, 609-638 (1972)
29. Hinze, J.O.: Turbulence. McGraw-Hill, [NY, USA], 2nd. ed., ISBN 0-07-029037-7 (1975)
30. Horstman, C.C., Settles, G.S., Vas, I.E., Bogdonoff, S.M., Hung, C.M.: Reynolds number effect on shock-wave turbulent boundary-layer interactions. AIAA J. 15, 1152-1158 (1977)
31. Jakirlić, S., Hanjalić, K.: A new approach to modelling near-wall turbulence energy and stress dissipation. J. Fluid Mech. 459, 139-166 (2002)
32. Lai, Y.G., So, R.M.C.: On near wall turbulent flow modelling. J. Fluid Mech. 221, 641-673 (1990)
33. Lakshminarayana, B.: Turbulence modeling for complex shear flows. AIAA J. 24, 1900-1917 (1986)
34. Laufer, J.: Some recent measurements in a 2D turbulent channel. J. Aero. Sci. 17, 277-287 (1950) [for detailed data cf NACA Tech. Note 2123 (1950) and NACA Rep. 1053 (1950)]
35. Launder, B.E.: Numerical computation of convective heat transfer in complex turbulent flows: Time to abandon wall-functions? Int. J. Heat Mass Transf. 27, 1485-1491 (1984)
36. Launder, B.E.: Second-moment closure: Present ... and future? Int. J. Heat Fluid Flow 10, 282-300 (1989)
37. Launder, B.E., Li, S.P.: On the elimination of wall-topography parameters from 2-moment closure. Phys. Fluids 6, 999-1006 (1994)
38. Launder, B.E., Reece, G.J., Rodi, W.: Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68, 537-566 (1975)
39. Launder, B.E., Sharma, B.I.: Application of the energy dissipation model of turbulence to the calculation of flows near a spinning disk. Lett. Heat Mass Transf. 1, 131-138 (1974)
40. Launder, B.E., Shima, N.: 2-moment closure for the near wall sublayer: Development and application. AIAA J. 27, 1319-1325 (1989)
41. Launder, B.E., Tselepidakis, D.P.: Application of a new second moment closure to turbulent channel flow rotating in orthogonal mode. Int. J. Heat Fluid Flow 15, 2-10 (1994)
42. Le, H., Moin, P., Kim, J.: Direct numerical simulation of turbulent flow over a backward facing step. J. Fluid Mech. 330, 349-374 (1997)
43. Lumley, J.L.: Rational approach to relations between motions of differing scales in turbulent flows. Phys. Fluids 10, 1405-1408 (1967)
44. Lumley, J.L.: Towards a turbulence constitutive relation. J. Fluid Mech. 41, 413-434 (1970)
45. Lumley, J.L.: Computational modeling of turbulent flows. Adv. Appl. Mech. 18, 123-176 (1978)
46. Manceau, R., Hanjalić, K.: Elliptic blending model: A new near-wall Reynolds-stress turbulence closure. Phys. Fluids 14, 744-754 (2002)
47. Manceau, R., Wang, M., Laurence, D.: Inhomogeneity and anisotropy effects on the redistribution term in Reynolds-averaged Navier-Stokes modelling. J. Fluid Mech. 438, 307-338 (2001)
48. Naot, D., Shavit, A., Wolfshtein, M.: Interactions between components of the turbulent velocity correlation tensor due to pressure fluctuations. Israel J. Techn. 8, 259-269 (1970)
49. Naot, D., Shavit, A., Wolfshtein, M.: 2-point correlation model and the redistribution of Reynolds-stresses. Phys. Fluids 16, 738-743 (1973)
50. Pantano, C., Sarkar, S.: A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. J. Fluid Mech. 451, 329-371 (2002)
51. Pennisi, S., Trovato, M.: On the irreducibility of Prof. G. F. Smith's representations for isotropic functions. Int. J. Eng. Sci. 25, 1059-1065 (1987)
52. Pettersson, B.A., Andersson, H.I., Brunvoll, A.S.: Modelling near-wall effects in axially rotating pipe flow by elliptic relaxation. AIAA J. 36, 1164-1170 (1998)
53. Pope, S.B.: Turbulent Flows. Cambridge Uni. Press, Cambridge [UK], ISBN 0-521-59125-2 (2000)
54. Poroseva, S.V., Kassinos, S.C., Langer, C.A., Reynolds, W.C.: Structure-based turbulence model: Application to rotating pipe flow. J. Phys. Fluids 14, 1523-1532 (2002)
55. Ristorcelli, J.R., Lumley, J.L., Abid, R.: A rapid pressure covariance representation consistent with the Taylor-Proudman theorem materially frame indifferent in the 2D limit. J. Fluid Mech. 292, 111-152 (1995)
56. Rogers, S.E., Roth, K., Cao, H.V., Slotnick, J.P., Whitlock, M., Nash, S.M., Baker, M.D.: Computation of viscous flow for a Boeing 777 aircraft in landing configuration. J. Aircraft 30, 1060-1068 (2001)
57. Rotta, J.: Statistische Theorie nichthomogener Turbulenz - 1. Mitteilung. Z. Phys. 129, 547-572 (1951)
58. Rotta, J.: Statisfische Theorie nichthomogener Turbulenz - 2. Mitteilung. Z. Phys. 131, 51-77 (1951)
59. Sarkar, S., Erlebacher, G., Hussaini, M.Y., Kreiss, H.O.: The analysis and modelling of dilatational terms in compressible turbulence. J. Fluid Mech. 227, 473-493 (1991)
60. Sellig, M.S., Andreopoulos, J., Muck, K.C., Dussauge, J.P., Smits, A.J.: Turbulence structure in a shock-wave/turbulent boundary layer interaction. AIAA J. 27, 862-869 (1989)
61. Settles, G.S., Dodson, L.J.: Supersonic and hypersonic shock/boundary layer interaction database. AIAA J. 32, 1377-1383 (1994)
62. Settles, G.S., Vas, I.E., Bogdonoff, S.M.: Details of a shock separated turbulent boundary layer at a compression comer. AIAA J. 14, 1709-1715 (1976)
63. Shima, N.: A Reynolds-stress model for near wall and low Reynolds number regions. ASME J. Fluids Eng. 110, 38-44 (1988)
64. Shima, N.: Prediction of turbulent boundary layer flows with a 2-moment closure - Part 1 - Effects of periodic pressure gradient, wall transpiration, and free-stream turbulence. ASME J. Fluids Eng. 115, 56-63 (1993)
65. Shima, N.: Prediction of turbulent boundary layer flows with a 2-moment closure - Part 2 - Effects of streamline curvature and spanwise rotation. ASME J. Fluids Eng. 115, 64-69 (1993)
66. Shima, N.: Low Reynolds number second moment closure without wall reflection redistribution terms. Int. J. Heat Fluid Flow 19, 549-555 (1998)
67. Shir, C.C.: A preliminary numerical study of atmospheric turbulent flows in the idealized planetary boundary layer. J. Atm. Sci. 30, 1327-1339 (1973)
68. Smith, G.F.: On isotropic functions of symmetric tensors, skew-symmetric tensors and vectors. Int. J. Eng. Sci. 9, 899-916 (1971)
69. Smits, A.J., Dussauge, J.P.: Turbulent Shear Layers in Supersonic Flow. AIP Press, Woodbury [NY, USA], ISBN 1-56396-260-8 (1996)
70. So, R.M.C., Lai, Y.G., Zhang, H.S., Hwang, B.C.: 2-order near wall turbulence closures: A review. AIAA J. 29, 1819-1835 (1991)
71. So, R.M.C., Yuan, S.P.: Near wall 2-equation and Reynolds-stress modelling of backstep flow. Int. J. Eng. Sci. 36, 283-298 (1998)
72. So, R.M.C., Yuan, S.P.: A geometry independent near wall Reynolds-stress closure. Int. J. Eng. Sci. 37, 33-57 (1999)
73. Spalding, D.B.: A single formula for the law of the wall. ASME J. Appl. Mech. 28, 455-458 (1961)
74. Speziale, C.G.: On nonlinear k - ℓ and k - ε models of turbulence. J. Fluid Mech. 178, 459-475 (1987)
75. Speziale, C.G.: Analytical methods for the development of Reynolds-stress closures in turbulence. Ann. Rev. Fluid Mech. 23, 107-157 (1991)
76. Speziale, C.G., Gatski, T.B.: Analysis and modelling of anisotropies in the dissipation rate of turbulence. J. Fluid Mech. 344, 155-180 (1997)
77. Speziale, C.G., Sarkar, S., Gatski, T.B.: Modelling the pressure-strain correlation of turbulence: An invariant dynamical systems approach. J. Fluid Mech. 227, 245-272 (1991)
78. 60. J. Aircraft 37, 361-367 (2000)
79. Younis, B.A., Gatski, T.B., Speziale, C.G.: Towards a rational model for the triple velocity correlations of turbulence. Tech. Mem. TM-1999-209134, NASA, Langley Research Center, Hampton [VA, USA] (1999)