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, for the general form of the rapid pressure strain rate model of Launder, Reece and Rodi (1975). These equations also represent the slow pressure strain rate and an isotropic dissipation rate tensor of the Rotta model (1951).; Once the algebraic equations have been formulated a standard mathematical program, Mathematica version 4.0, will be used to perform the computations. 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.; At the present moment there are many variations of second order closure turbulence models available. However there is no unique turbulence model exists which can predict satisfactorily all turbulence flows. Each turbulence model applies successfully to some turbulent flows, but predicts unsatisfactorily to others. This present work not only quickens the calculations but also gives a good general prediction to various turbulent flows.