Progress in Favre-Reynolds stress closures for compressible flows

A closure for the compressible portion of the pressure-strain covariance is developed. It is shown that, within the context of a pressure-strain closu re assumption linear in the Reynolds stresses, an expression for the pressu re-dilatation can be used to construct a representation for the pressure-st rain. Additional closures for the unclosed terms in the Favre-Reynolds stre ss equations involving the mean acceleration are also constructed. The clos ures accommodate compressibility corrections depending on the magnitude of the turbulent Mach number, the mean density gradient, the mean pressure gra dient, the mean dilatation, and, of course, the mean velocity gradients. Th e effects of the compressibility corrections on the Favre-Reynolds stresses are consistent with current DNS results. Using the compressible pressure-s train and mean acceleration closures in the Favre-Reynolds stress equations an algebraic closure for the Favre-Reynolds stresses is constructed. Notew orthy is the fact that, in the absence of mean velocity gradients, the mean density gradient produces Favre-Reynolds stresses in accelerating mean flo ws. Computations of the mixing layer using the compressible closures develo ped are described. Favre-Reynolds stress closure and two-equation algebraic models are compared to laboratory data for the mixing layer. Experimental data from diverse laboratories for the Favre-Reynolds stresses appears inco nsistent and, as a consequence, comparison of the Reynolds stress predictio ns to the data is not conclusive. Reductions of the kinetic energy and the spread rate are consistent with the sizable decreases seen in these classes of flows. (C) 1999 American Institute of Physics. [S1070-6631(99)00809-0].