An anisotropic modification of the Reynolds stresses for algebraic models of turbulence

The development of an anisotropic modification of linear and nonlinear models of turbulence is presented. This modification departs from the observation that there are some regions of fluid domains in which the Reynolds stresses do not depend on the magnitude of the mean flow gradients. The model is based on the hypothesis that actions of fluctuating motion on mean motion are almost exclusively due to large turbulent eddies, and that the latter contain the same kinetic energy of the small eddies of mean flow. The contribution of large turbulent eddies to the Reynolds stresses is then modeled by a linear combination of an iso-tropic term and an anisotropic term. The latter is obtained by multiplying a quote of the turbulent kinetic energy by a normalized redistribution tensor. The performance of the model is tested by calculating the Reynolds stresses in a fully developed turbulent channel flow and simulating the separated turbulent flow over a backward-facing step, and a fully developed turbulent flow in a squared duct. The results show that the modified models improve the prediction of the normal Reynolds stresses in a bidimensional channel and of the reattachment point in a backward-facing step. On the other hand, these models do not improve the prediction of secondary flows in a squared duct.