Near-wall two-equation and Reynolds-stress modeling of backstep flow

Abstract

Most near-wall two-equation turbulence models fail to predict the wall shear stress along the step wall of a plane backstep flow and the error could become very large downstream of the reattachment point. This failure was usually attributed to the use of an eddy viscosity damping function that depends on the wall friction velocity and the fact that the near-wall correction depends on the wall normal coordinate. The present paper examines the underlying reasons for this failure and suggests that the major cause is the lack of asymptotic consistency in the near-wall region. Several asymptotically consistent models are analysed and their predictions are compared with direct numerical simulations (DNS), with conventional model results and with Reynolds-stress model calculations. Three Reynolds-stress models are compared; two of which do not depend on wall normals. It is shown that asymptotically consistent models with or without dependence on wall normal coordinate and with a damping function not dependent on friction velocity give fairly accurate predictions of the plane backstep flow considered. Furthermore, these calculations are in good agreement with that given by a near-wall Reynolds-stress model with no damping functions. In many respects, the predictions agree better with DNS data than those given by the Reynolds-stress models. The presence of wall normals does not significantly affect the performance of the Reynolds-stress model for this particular flow.