RIGOROUS FORMULATION OF TWO-EQUATION HEAT TRANSFER MODEL OF TURBULENCE USING DIRECT SIMULATIONS

Abstract

A rigorous two-equation heat transfer model has been constructed with the aid of the most up-to-date direct numerical simulation (DNS) data for wall turbulence with heat transfer. The DNS data indicate that the near-wall profile of the dissipation rate, ϵ1, for the temperature variance, kt (= t2¯ /2), is completely different from the existing model predictions. In this study, we performed a critical assessment of existing ϵ1 and ϵ1, equations for both two-equation and second-order closure models. Based on these assessments, we propose a new dissipation rate equation for temperature variance, taking into account all the budget terms in the exact ϵ1 equation. Also, the proposed ϵ1 equation is linked with a similarly refined kt equation to constitute a new two-equation heat transfer model. Comparisons of the present model predictions with the DNS data for a channel flow with heat transfer have shown excellent agreement for the profiles of kt and ϵ1 themselves and of the budget in the kt and ϵ1 equations. The model is also tested in turbulent boundary-layer flows with five different wall thermal conditions. Agreement with the experimental data is quite satisfactory.