A critical evaluation of near-wall two-equation models against direct numerical simulation data

Abstract

Abstract Two-equation turbulence models with near-wall corrections are assessed by applying them to calculate plane Couette flow—a flow case where conventional two-equation models and second-order closures fail to give a correct prediction of the spatial distribution of the turbulent kinetic energy—plane channel flow, and flat plate boundary-layer flow. The predictions of 10 near-wall two-equation models, including the k-τ and k-ω models and 5 recently developed asymptotically consistent near-wall k-e models, are compared with data obtained from direct numerical simulations at very low Reynolds numbers. It is found that models that are not asymptotically consistent are incapable of predicting the spatial distribution of k correctly in Couette flows. Instead, they give a fairly uniform distribution of k across a substantial portion of the channel. Of all the models evaluated, the asymptotically consistent k-e models are found to perform the best compared to direct numerical simulation (DNS) data and experimental measurements. Five of the ten models are further validated against DNS data of a backstep flow at low Reynolds number. Similar results as before are obtained. Therefore, the present results lend credence to the hypothesis that an internally consistent and asymptotically correct near-wall model is of crucial importance to the calculations of wall-bounded turbulent flows.