Progress in Favré–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 closure assumption linear in the Reynolds stresses, an expression for the pressure-dilatation can be used to construct a representation for the pressure-strain. Additional closures for the unclosed terms in the Favré–Reynolds stress equations involving the mean acceleration are also constructed. The closures accommodate compressibility corrections depending on the magnitude of the turbulent Mach number, the mean density gradient, the mean pressure gradient, the mean dilatation, and, of course, the mean velocity gradients. The effects of the compressibility corrections on the Favré–Reynolds stresses are consistent with current DNS results. Using the compressible pressure-strain and mean acceleration closures in the Favré–Reynolds stress equations an algebraic closure for the Favré–Reynolds stresses is constructed. Noteworthy is the fact that, in the absence of mean velocity gradients, the mean density gradient produces Favré–Reynolds stresses in accelerating mean flows. Computations of the mixing layer using the compressible closures developed are described. Favré–Reynolds stress closure and two-equation algebraic models are compared to laboratory data for the mixing layer. Experimental data from diverse laboratories for the Favré–Reynolds stresses appears inconsistent and, as a consequence, comparison of the Reynolds stress predictions 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.