Modeling of complex internal flows with reynolds stress algebraic equation model

Different three-dimensional flows, including effects of swirl and separation are studied with an algebraic Reynolds stress equation model, using a new explicit equation for the Reynolds stresses based on the invariant theory of continuum mechanics. The formulation of the model is Galilean and tensorially invariant and satisfies realizability conditions, following recent developments of Shih and Lumley. Quadratic Reynolds stress-mean strain polynomials allow to obtain better predictions of the anisotropy effects in comparison with the predictions from eddy-viscosity closure. A modification of the coefficients of the polynomial is introduced in order to model the influence of the streamline curvature on the turbulence characteristics. Comparisons with experimental results for swirling flow in a conical diffuser, flow in a 90°-bend rectangular duct, and in an S-shaped circular diffuser show improvement in the Reynolds stress prediction obtained with these additional modifications.