The Explicit Algebraic Reynolds Stress Models for Turbulent Flows

The explicit algebraic Reynolds stress models are obtained from second-order closure models that are valid for three-dimensional turbulent flows in non-inertial frames. The purpose of this present research is to simplify the development of the Reynolds stress anisotropy tensor. This anisotropy stress tensor has seven scalar coefficients and has seven tensor polynomial groups that are the integrity basis for the functions of both symmetric and antisymmetric tensors. This research will also explicitly determine the six independent invariants of the mean strain rate tensor and of the mean rotation rate tensor. The resulting algebraic equation for the anisotropy tensor depends on the choice of the model that is used to determine the dissipation rate and pressure-strain correlation. These equations also represent the slow pressure strain rate and an isotropic dissipation rate tensor of the Rotta model. The results of present research can be compared with the results of Gatski and Speziale that give the complete expression for a traceless symmetric second order tensor which depended on the symmetric and the antisymmetric tensor that involved ten tensor polynomial groups with five independent invariants. The present work reduces the ten tensor polynomial groups down to seven groups which drastically decreases computational time.