Prediction of turbulent wall shear flows directly from wall

Abstract

AbstractThe fully elliptic Reynolds‐averaged Navier–Stokes equations have been used together with Lam and Bremhorst's low‐Reynolds‐number model, Chen and Patel's two‐layer model and a two‐point wall function method incorporated into the standard k‐ϵ model to predict channel flows and a backward‐facig step flow. These flows enable the evaluation of the performance of different near‐wall treatments in flows involving streamwise and normal pressure gradients, flows with separation and flows with non‐equilibrium turbulence characteristics. Direct numerical simulation (DNS) of a channel flow with Re =3200 further provides the detailed budgets of each modelling term of the k and ϵ‐transport equations. Comparison of model results with DNS data to evaluate the performance of each modelling term is also made in the present study. It is concluded that the low‐Reynolds‐number model has wider applicability and performs better than the two‐layer model and wall function approaches. Comparison with DNS data further shows that large discrepancies exist between the DNS budgets and the modelled production and destruction terms of the ϵ equation. However, for simple channel flow the discrepancies are similar in magnitude but opposite in sign, so they are cancelled by each other. This may explain why, even when employing such an inaccurately modelled ϵ‐equation, one can still predict satisfactorily some simple turbulent flows.