A PERFORMANCE COMPARISON OF THE STANDARD k-ϵ MODEL AND A DIFFERENTIAL REYNOLDS STRESS MODEL FOR A BACKWARD-FACING STEP

Abstract

A differential Reynolds stress model (RSM) based on Launder, Reece, and Rodi (LRR) is formulated with appropriate wall Junctions and applied to predict the backward-facing step problem of Driver and Seegmiller. Numerical prediction obtained with the LRR, with and without “wall reflection” terms in the pressure strain model, are compared with the results of standard k-e model of Launder and Spalding for the step problem. The results demonstrate that both LRR models, i.e., with and without wall reflection terms, are capable of capturing the secondary bubble near the step, as observed in the experiment, whereas the standard k-ϵ model fails to predict the secondary bubble. In addition, the mean velocity profiles obtained with the LRR models agree better with the experimental data than those by the k-ϵ model, particularly inside the recirculating flow region. It also emerges from the present study that, with proper wall functions, LRR model is capable of predicting recirculating flows at least as well as the original LRR model does without the “wall reflection” terms.