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Large eddy simulation of compressible channel flow. Arguments in favour of universality of compressible turbulent wall-bounded flows. (English) Zbl 1161.76493
Summary: The present study is a contribution to the analysis of wall-bounded compressible flows, including a special focus on wall modeling for compressible turbulent boundary layer in a plane channel. large eddy simulation (LES) of fully developed isothermal channel flows at \(Re = 3,000\) and \(Re = 4,880\) with a sufficient mesh refinement at the wall are carried out in the Mach number range \(0.3 \leq M \leq 3\) for two different source term formulations: first the classical extension of the incompressible configuration by G. N. Coleman et al. [J. Fluid Mech. 305, 159–183 (1995; Zbl 0960.76517)], second a formulation presently derived to model both streamwise pressure drop and streamwise internal energy loss in a spatially developed compressible channel flow. It is shown that the second formulation is consistent with the spatial problem and yields a much stronger cooling effect at the wall than the classical formulation. Based on the present LES data bank, compressibility and low Reynolds number effects are analysed in terms of coherent structure and statistics. A study of the universality of the structure of the turbulence in non-hypersonic compressible boundary layers (\(M\leq 5\)) is performed in reference to Bradshaw (Annu. Rev. Fluid. Mech. 9:33-54, 1977). An improvement of the van Driest transformation is proposed; it accounts for both density and viscosity changes in the wall layer. Consistently, a new integral wall scaling \((y^{c+})\) which accounts for strong temperature gradients at the wall is developed for the present non-adiabatic compressible flow. The modification of the strong Reynolds analogy proposed by P. G. Huang et al. [J. Fluid Mech. 305, 185–218 (1995; Zbl 0857.76036)] to model the correlation between velocity and temperature for non-adiabatic wall layers is assessed on the basis of a Crocco-Busemann relation specific to channel flow. The key role of the mixing turbulent Prandtl number \(Pr_{m}\) is pointed out. Results show very good agreement for both source formulations although each of them involve a very different amount of energy transfer at the wall.

MSC:
76F65 Direct numerical and large eddy simulation of turbulence
76F50 Compressibility effects in turbulence
76F40 Turbulent boundary layers
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[1] Aupoix, B.: Introduction to turbulence modelling for compressible flows. In: von Karman Lectures Series (2002)
[2] Bradshaw P. (1977). Compressible turbulent shear layers. Annu. Rev. Fluid. Mech. 9: 33–54 · Zbl 0412.76049 · doi:10.1146/annurev.fl.09.010177.000341
[3] Briand, E.: Dynamique des structures cohérentes en couche limite transitionnelle et turbulente étudiée par simulation des grandes échelles. In: PhD Thesis, INPG, Grenoble (1999)
[4] Brun, C., Haberkorn, M., Comte, P.: Compressibility effects in fully developed channel flow up to mach = 5. In: 5th Euromech Fluid Mechanics Conference, Toulouse (2003)
[5] Busemann, A. In: Leipzig Geest, Portig (eds.) Handbuch der physik, Vol. 4 (1931)
[6] Carvin, C., Debiève, J.F., Smits, A.J.: The near wall temperature profile of turbulent boundary layers. AIAA Meeting (1988)
[7] Cebeci T. and Smith J. (1974). Analysis of Turbulent Boundary Layers. Academic Press, New York · Zbl 0342.76014
[8] Coleman G.N., Kim J. and Moser R.D. (1995). A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305: 159–183 · Zbl 0960.76517 · doi:10.1017/S0022112095004587
[9] Comte P. et al. (2001). Dynamics of coherent vortices in large-eddy simulation. In: Geurts, B.J. (eds) Direct and large-eddy simulation IV Ercoftac series., pp 471–480. Kluwer Academic Publischers, Dordrecht
[10] Comte, P., Lesieur, M.: Large-eddy simulations of compressible turbulent flows. In: Advances in turbulence modelling, pp. 77–79. Von Karman Institute, Lecture series 1998–2005 (1998)
[11] Crocco L. (1932). Sulla transmissione del calore da una lamina pilana a un fluido scorrente ad alta velocità (Translated as NACA TM 690). L’Aerotecnica 12: 181–197 · JFM 58.1320.03
[12] Deardorff J.W. (1970). A numerical study of three-dimensional turbulent flow at large Reynolds numbers. J. Fluid Mech. 41: 453–480 · Zbl 0191.25503 · doi:10.1017/S0022112070000691
[13] Debiève J.F., Dupont P., Smith D.R. and Smits A.J. (1997). Supersonic turbulent boundary layer subjected to step changes in wall temperature. AIAA J. 35(1): 51–57 · Zbl 0899.76201 · doi:10.2514/2.86
[14] Ducros F., Comte P. and Lesieur M. (1996). Large-eddy simulation of transition to turbulence in a boundary layer developing spatially over a flat plate. J. Fluid Mech. 326: 1–36 · Zbl 0917.76032 · doi:10.1017/S0022112096008221
[15] Foysi H., Sarkar S. and Friedrich R. (2004). Compressibility effects and turbulence scalings in supersonic channel flow. J. Fluid Mech. 509: 207–216 · Zbl 1066.76035 · doi:10.1017/S0022112004009371
[16] Gaviglio J. (1987). Reynolds analogies and experimental study of heat transfer in the supersonic boundary layer. J. Heat. Mass Transf. 30(5): 911–926 · Zbl 0623.76068 · doi:10.1016/0017-9310(87)90010-X
[17] Guarini S., Moser R., Shariff K. and Wray A. (2000). Direct numerical simulation of a supersonic turbulent boundary layer at mach 2.5. J. Fluid Mech. 414: 1–33 · Zbl 0983.76039 · doi:10.1017/S0022112000008466
[18] Haberkorn, M.: Simulation des grandes echelles en canal plan turbulent: effets de compréssibilité et propagation acoustique. PhD Thesis. Institut de Mécanique des Fluides et des Solides, Strasbourg (2004)
[19] Huang P.G. and Coleman G.N. (1995). van driest transformation and compressible wall-bounded flows. AIAA J. 305: 185–218 · Zbl 0857.76036
[20] Huang P.G., Coleman G.N. and Bradshaw P. (1995). Compressible turbulent channel flows: Dns results and modelling. J. Fluid Mech. 305: 185–218 · Zbl 0857.76036 · doi:10.1017/S0022112095004599
[21] Kim, J.: Physics and control of wall turbulence. In: Direct and Large-Eddy Simulation VI. Poitiers, France (2005)
[22] Kim J., Moin P. and Moser R. (1987). Turbulence statistics in fully developed channel flow at low reynolds number. J. Fluid Mech. 177: 133–166 · Zbl 0616.76071 · doi:10.1017/S0022112087000892
[23] Kovasznay L.S.G. (1953). Turbulence in supersonic flow. J. Aeronaut. Sci. 20: 657
[24] Lechner R., Sesterhenn J. and Friedrich R. (2001). Turbulent supersonic channel flow. J. Turbul. 2: 01–25 · Zbl 1001.76510 · doi:10.1088/1468-5248/2/1/001
[25] Lele K. (1994). Compressibility effects on turbulence. Annu. Rev. Fluid. Mech. 26: 211–254 · Zbl 0802.76032 · doi:10.1146/annurev.fl.26.010194.001235
[26] Lenormand E. and Sagaut P. (2000). Subgrid-scale models for large-eddy simulations of compressible wall bounded flows. AIAA J. 38: 1340–1350 · doi:10.2514/2.1133
[27] Lenormand E., Sagaut P. and Ta Phuoc L. (2000). Large-eddy simulation of subsonic and supersonic channel flow at moderate reynolds number. Int. J. Num. Meth. Fluids 32: 369–406 · Zbl 0981.76046 · doi:10.1002/(SICI)1097-0363(20000229)32:4<369::AID-FLD943>3.0.CO;2-6
[28] Lesieur M. and Comte P. (2001). Favre filtering and macro-temperature in large-eddy simulations of compressible turbulence. C. R. Acad. Sci. 329(IIb): 363–368 · Zbl 1032.76027
[29] Lesieur M., Métais O. and Comte P. (2005). Large-Eddy Simulations of Turbulence. Cambridge University Press, Cambridge · Zbl 1101.76002
[30] Maeder T., Adams N. and Kleiser L. (2001). Direct simulation of turbulent supersonic boundary layers by an extended temporal approach. J. Fluid Mech. 429: 187–216 · Zbl 1007.76031 · doi:10.1017/S0022112000002718
[31] Métais O. and Lesieur M. (1992). Spectral large-eddy simulation of isotropic and stably stratified turbulence. J. Fluid Mech. 239: 157–194 · Zbl 0825.76272 · doi:10.1017/S0022112092004361
[32] Michel, R.: Aerodynamique Experimentale. Rebuffet, Vol. 1 (1962)
[33] Michel, R., Quemard, C., Durand, R.: ONERA. N.T. (1969)
[34] Morinishi Y., Tamano S. and Nakabayashi K. (2004). Direct numerical simulation of compressible turbulent channel flow between adiabatic and isothermal walls. J. Fluid Mech. 502: 273–308 · Zbl 1134.76363 · doi:10.1017/S0022112003007705
[35] Morkovin, M.V.: Effects of compressibility on turbulent flows. In: Favre, A.J. (ed) Mécanique de la Turbulence, pp. 367–380. CNRS (1961)
[36] Normand X. and Lesieur M. (1992). Direct and large-eddy simulation of transition in the compressible boundary layer. Theor. Comp. Fluid Dyn. 3: 231–252 · Zbl 0825.76370 · doi:10.1007/BF00417915
[37] Pirozzoli S., Grasso F. and Gatski T.B. (2004). Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M = 2.25. Phys. Fluids 11(4): 943–945 · Zbl 1186.76423
[38] Poinsot T.J. and Lele S.K. (1992). Boundary conditions for direct simulations of compressible viscous flows. J. Comp. Phys. 103: 16–42 · Zbl 0759.65006 · doi:10.1016/0021-9991(92)90324-R
[39] Rubesin, M.: Extra compressibility terms for favre-averaged two-equation models of inhomogeneous turbulent flows. In: NASA CR-177556, NASA Ames (1990)
[40] Salinas Vázquez M. and Métais O. (2002). Large-eddy simulation of the turbulent flow through a heated square duct. J. Fluid Mech. 453: 201–238 · Zbl 1141.76414
[41] Schlichting H. (1968). Boundary-Layer Theory, 3rd English edn. McGraw-Hill, New York · Zbl 0096.20105
[42] Smits, A., Dussauge, J.: Turbulent shear layers in supersonic flows. American Institute of Physics (1996)
[43] Spina A.J., Smits I.J. and Robinson S.K. (1994). The physics of supersonic turbulent boundary layers. Annu. Rev. Fluid. Mech. 26: 287–319 · doi:10.1146/annurev.fl.26.010194.001443
[44] Van Driest E. (1951). Turbulent boundary layer in compressible fluid. J. Aeronaut. Sci. 18(3): 145–160 · Zbl 0045.12903
[45] White F.M. (1974). Viscous Fluid Flow. Mc Graw-Hill, New York · Zbl 0356.76003
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