Elliptic relaxation second moment closure for turbulent heat flux

The present contribution describes the development of near-wall second moment turbulent heat flux closure and its application to turbulent flows rotating with heat transfer to test the performance of the model. The second-moment models for turbulent heat fluxes are proposed on the basis of elliptic concept. The new models satisfy the near-wall balance between viscous diffusion, viscous dissipation and temperature-pressure gradient correlation, and also have the characteristics of approaching its respective conventional high Reynolds number model far away from the wall. In order to develop the new heat flux models, first of all, the velocity field variables are supplied from the DNS data, and the differential equations only for the mean temperature and the scalar flux are solved by the present calculations with constant wall heat flux and constant wall temperature boundary conditions respectively. And then, the rotating channel and square duct flows with heat transfer have been simulated by the present heat flux models. The predictions in rotating and non-rotating flows show that the behavior of the turbulent heat transfer in the whole flow region is well captured by the present models.