Characteristics of Incompressible Free Shear Flows and Implications for Turbulence Modeling

Abstract

It is shown that in self-preserving incompressible free shear flows governed by the boundary-layer equations, a region must exist in which the Reynolds-stress anisotropies are constant. The theoretical result is confirmed by an analysis of well-established experimental data for the plane jet, the axisymmetric jet, and the plane mixing layer. The values of the corresponding Reynolds-stress anisotropies are determined, revealing differences between the corresponding eigensystems of these flows. While the shape of the corresponding tensor surfaces is similar, the corresponding principal axes have varying inclinations with respect to the flow-aligned coordinate system. Hence, the shear-stress anisotropy differs even in the case of almost identical eigenvalues or invariants of the anisotropy tensor. Numerical predictions can be improved by a calibration of the pressure-strain correlation of a Reynolds-stress model using the observed anisotropies in the constant layer. For an industrial application, this will require an automatic adjustment of model coefficients according to the local flow type, although a self-adaptive model that can switch automatically between the respective sets of tailored coefficients for each local flow type is still being sought.