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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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##### References:
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