Use of Algebraic-Stress Model for determination of near-wall Reynolds-Stresses in turbulent flow over a flat plate

Abstract

The algebraic stress model (ASM) is investigated for the problem of spatially developing zero-pressure-gradient boundary layer for the steady state turbulent flow of air over a 2D flat plate. For a region very close to the wall, the convection and diffusion transport terms of the governing equations for the Reynolds stresses can be approximated with simpler terms, and therefore, there would no longer be a need to solve the transport equations. The system of highly coupled non-linear algebraic equations is then solved for all of the Reynolds stress components in the near-wall region. Different versions of the pressure-strain term will be considered, e.g., with and without the wall effect, and compact vs. complete form of the pressure strain formulation arising from the presence of the mean rate of strain, as well as the explicit ASM. MATLAB software package is used in order to solve the system of algebraic equations for Reynolds stresses. The initial guesses for all of the Reynolds stresses are obtained by solving the turbulent flow in the domain of interest using the Reynolds Stress turbulence model in ANSYS Fluent for a few iterations. The estimates for mean velocity gradients, and turbulent dissipation rate are taken from Fluent as well. The ASM calculations are carried out at positions with the Reynolds number Rex of 3.2e6 and 4e6 along the plate and for all of the grid points sufficiently close to the plate. Based on the current results, the Reynolds stresses predicted by ASM and RSM are quite similar, and they are both close to the well accepted published experimental data. More investigation on benefits of ASM has to be carried out, before extending its use to more complicated geometries.