Compressibility effects in the solenoidal dissipation rate equation: A priori assessment and modeling

Several attempts have been made in the literature to improve the ability of statistical models to predict turbulent compressible flows. As yet, it is not possible to accurately predict both free and wall-bounded flows with the same model under a variety of conditions. One drawback in these attempts has been the lack of sufficiently reliable data with which to assess the various terms arising in the compressible turbulent transport equations. In this study, the exact terms of the solenoidal dissipation rate equation are calculated for the first time in both a compressible channel flow and a turbulent mixing layer. This data is then used to assess both the exact and modeled form of this equation. In its exact form, terms explicitly dependent on dilatation fluctuations and density and viscosity gradients appear. In addition, the terms that are also present in the incompressible equation now may vary differently under increased compressibility conditions. This latter effect can be either an indirect one, that is compressibility modifies mean quantities and Reynolds stresses, or a direct one, that is the processes in the solenoidal dissipation rate equation are themselves modified by compressibility. In order to separate the indirect and direct effects, it is assumed that the processes in the solenoidal dissipation rate equation are properly described by the available incompressible functional forms. The model coefficients are then determined by a priori tests. Direct effects appear if the coefficients depend on compressibility. These effects have then to be modeled additionally.