Counter Gradient Diffusion of Heat Flux in Turbulent Rayleigh Flow

Abstract

The gradient diffusion approximation for the turbulent scalar flux is not valid and counter-gradient diffusion occurs in the turbulent premixed flame. Many processes due to the interaction between the turbulence and the chemical reaction are related to the counter gradient diffusion in the turbulent premixed flame. In this study, we focus on the effects of heat release to the turbulence. To discuss it, we devise and implement the direct numerical simulation of the turbulent Rayleigh flow (TRF), which is generated by isotropic turbulence flowing into Rayleigh flow. We show that the counter-gradient diffusion of the turbulent heat flux occurs in TRF and discuss its mechanism based on the transport equations of turbulent statistical quantities. It is shown that released heat amplifies density-internal energy correlation resulting in the prominent contribution of the pressure gradient effect, which brings counter-gradient diffusion.