Evaluation of Reynolds Stress Turbulence Closures in Compressible Homogeneous Shear Flow

Direct numerical simulation data bases for compressible homogeneous shear ow are used to evaluate the performance of recently proposed Reynolds stress closures for compressible turbulence. Three independent pressure-strain models are considered along with a variety of explicit compressible corrections that account for dilatational dissipation and pressure-dilatation e ects. The ability of the models to predict both time evolving elds and equilibrium states is systematically tested. Consistent with earlier studies, it is found that the addition of simple dilatational models allows for the prediction of the reduced growth rate of turbulent kinetic energy in compressible homogeneous shear ow. However, a closer examination of the equilibrium structural parameters uncovers a major problem. None of the models are able to predict the dramatic increase in the normal Reynolds stress anisotropies or the signi cant decrease in the Reynolds shear stress anisotropy that arise from compressible e ects. The physical origin of this de ciency is attributed to the neglect of compressible terms in the modeling of the deviatoric part of the pressure-strain correlation. This research was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19480 while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23681-0001.