A nonlinear low-Reynolds number heat transfer model for turbulent separated and reattaching flows

A nonlinear low-Reynolds number heat transfer model is developed to predict turbulent flow and heat transfer in separated and reattaching flows. The k-ε-f(μ) model of Park and Sung (T.S. Park, H.J. Sung, A new low-Reynolds-number model for predictions involving multiple surface, Fluid Dynamics Research 20 (1997) 97-113) is extended to a nonlinear formulation, based on the nonlinear model of Gatski and Speziale (G.B. Gatski, C.G. Speziale, On explicit algebraic stress models for complex turbulent flows, J. Fluid Mech. 254 (1993) 59-78). The limiting near-wall behavior is resolved by solving the f(μ) elliptic relaxation equation. An improved explicit algebraic heat transfer model is proposed, which is achieved by applying a matrix inversion. The scalar heat fluxes are not aligned with the mean temperature gradients in separated and reattaching flows; a full diffusivity tensor model is required. The near-wall asymptotic behavior is incorporated into the f(λ) function in conjunction with the f(μ) elliptic relaxation equation. Predictions of the present model are cross-checked with existing measurements and DNS data. The model performance is shown to be satisfactory. (C) 2000 Elsevier Science Ltd. All rights reserved.