Rigorous Modelling of Two-Equation Heat-Transfer Model Using Direct Simulations. 1st Report. Assessment and Reconstruction of Dissipation-Rate Equations for Temperature Variance.

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, εt, for temperature variance, t2, is completely different from the existing model predictions. In the 1st report, we have performed a critical assessment of existing εt-and εt-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 εt-equation. Comparisons of the present model predictions with the DNS data for a channel flow with heat transfer show an excellent agreement for the profiles of εt itself and the budget in the εt-equation.