Unsteady flamelet progress variable modeling of reacting diesel jets

Accurate modeling of turbulence/chemistry interactions in turbulent reacting diesel jets is critical to the development of predictive computational tools for diesel engines. The models should be able to predict the transient physical and chemical processes in the jets such as ignition and flame lift-off. In the first part of this work, an existing unsteady flamelet progress variable (UFPV) model is employed in Reynolds-averaged Navier-Stokes (RANS) simulations and large-eddy simulations (LES) to assess its accuracy. The RANS simulations predict that ignition occurs toward the leading tip of the jet, followed by ignition front propagation toward the stoichiometric surface, and flame propagation upstream along the stoichiometric surface until the flame stabilizes at the lift-off height. The LES, on the other hand, predicts ignition at multiple points in the jet, followed by flame development from the ignition kernels, merger of the different flames and then stabilization. The UFPV model assumes that combustion occurs in thin zones known as flamelets and turbulent strain characterized by the scalar dissipation rate modifies the flame structure. Since the flamelet is thinner than the smallest grid size employed in RANS or LES, the effect of the turbulence is modeled through probability distribution functions of the independent variables. The accuracy of the assumptions of the model is assessed in this work through direct numerical simulations (DNS) which resolves the flame. The DNS is carried out in turbulent mixing layers since the combustion in a diesel jet occurs in the fuel/air mixing layer surrounding the jet. The DNS results show that the flamelet model is applicable but that its implementation in the UFPV model is flawed because the effects of expansion due to heat release and increase in diffusivity due to rise in temperature are not accounted for in the formulation of the scalar dissipation rate. A new diffusivity-corrected flamelet model is proposed which leads to an improved prediction of flame development. Furthermore, it is shown that the most commonly used approach to calculate the scalar dissipation rate in LES of reacting flows leads to large errors when the LES grid size is large. The DNS results are used to determine the best model for the filtered scalar dissipation rate and its PDF under diesel engine conditions. A new model is derived for the variance of the scalar dissipation rate. The DNS results are also used to compare the performance of the UFPV model with the Perfectly Stirred Reactor (PSR) model predictions. It is shown that the UFPV model performance is superior for turbulent intensities and grid sizes encountered in diesel engine applications