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

Abstract

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.