Modeling of heat transfer and differential diffusion in transported PDF methods

Abstract

In order to model the conditional diffusive heat and mass fluxes in the joint probability density function (PDF) transport equation of the thermochemical variables, the diffusive fluxes are decomposed into their Favre mean and fluctuation. While the mean flux appears to be closed, the contributions of fluctuating fluxes are modeled with the interaction by exchange with the mean (IEM) model. Usually, the contribution of the Favre averaged diffusive fluxes is neglected at high Reynolds numbers. Here, however, this term is included to account for molecular mixing in regions, where turbulent mixing is negligible. This model approach is applied in steady state Reynolds Averaged Navier–Stokes (RANS)/transported PDF calculations to simulate the heat transfer of wall bounded flows as well as the stabilization of a hydrogen–air flame at the burner tip. For both flow problems it is demonstrated that molecular transport is recovered in regions where turbulent mixing vanishes. In wall bounded flows this is the case in the viscous sublayer. Heat transfer studies show, that “mixing models” based on the high Reynolds number assumption fail to compute correctly the temperature field and the heat flux close to the wall. A similar situation occurs at the flame root of the investigated turbulent hydrogen-air jet flame, where turbulent mixing is still too weak to achieve a fast mixing of reactants. In this area differential diffusion effects are observed in the experiment, i.e. superequilibrium temperatures and nonlinear relations between the elemental mixture fractions of hydrogen and oxygen. It will be shown, that the presented model can successfully reproduce these effects, which underlines the necessity to include Favre averaged molecular diffusive fluxes in transported PDF methods.