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 hydrogenair flame at the burner tip. For both flow problems it is demonstrated that molecular transport is recovered in regions where turbulent mixing vanishes.

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The present work explores the capability of the transported probability density function (PDF) method to predict nitric oxide (NO) formation in turbulent combustion. To this end a hybrid finite-volumelLagrangian Monte Carlo method is implemented into the THETA code ofthe German Aerospace Center (DLR). In this hybrid approach the tr-ansported PDF method governs the evolution of the thermochemical variables, wher-eas the flow field evolution is computed with a Reynolds-averaged Navier-Stokes (RANS) method. The method is used to compute a turbulent hydrogen-air flame and a methaneair flame and computational results are compared to experimental data. In order to assess the advantages of the transported PDF method, the flame computations are repeated with the "laminar chemistry" approach as well as with an "assumed PDF" method, which are both computationally less expensive. The present study reveals that the tr-ansported PDF method provides the highest accwacy in predicting the overall flame structure and nitric oxide formation.