A geometry independent near-wall Reynolds-stress closure

Abstract

Models proposed for high-Reynolds-number Reynolds–stress closures are, in general, geometry independent. Therefore, they are most suitable for flows with complex geometries. With the advent of supercomputers, the near-wall flow can be calculated with greater efficiency to give more accurate results on surface properties. However, with modifications made to the various models to account for near-wall behavior, the closures are no longer geometry independent. The cause is the presence of wall distance and wall unit normals in the proposed corrections for either the velocity–pressure-gradient correlation tensor, the dissipation rate tensor, the dissipation rate equation, or all of them. In this paper, a proposal is put forward where the modifications made to these tensors and equation are free of wall distance and wall unit normals. The closure is validated against a wide variety of simple flows and good agreement with data is obtained. Further, the closure is applied to calculate backstep flows and developing square duct flows. The results are compared with direct numerical simulation and experimental data. In addition, they are also compared with the calculations of another near-wall Reynolds–stress closure with wall unit normal dependence and is known to give good correlations with backstep flow and square duct flow data. The present closure is found to yield results that are in good agreement with the data and the calculations of the model with wall unit normals. As a result, a viable geometry independent near-wall Reynolds–stress closure is available.