Direct numerical simulation and CMC (conditional moment closure) sub-model validation of spray combustion

Direct numerical simulation (DNS) is used to study spray combustion in a slab layer configuration. The gas phase is simulated in an Eulerian way, while the droplets are tracked with a Lagrangian method. The coupling between the two phases is considered. A fourth-order explicit Runge–Kutta method for time integration and an eighth-order central differencing scheme for spatial discretization are used to solve the fully compressible Navier–Stokes (N–S) equation system. One-step reaction mechanism for heptane is adopted. Several cases with different droplet diameters, global equivalence ratios and turbulence intensities are investigated. The general characteristics of spray combustion are described. It is shown that ignition is always found in low scalar dissipation rate regions. Equivalence ratio has the most significant effect on the evolution of spray combustion, while turbulence intensity only has a limited effect. The presumed beta PDF (probability density function) for the mixture fraction is studied, and excellent agreement is found for the predictions and the DNS results. It is demonstrated that the beta PDF is more accurate without evaporation. Conditional moment closure (CMC) sub-models are validated for the scalar dissipation rate, evaporation rate and reaction rate. The scalar dissipation rate is modeled using the amplitude mapping closure (AMC) model. The AMC model has the ability to predict the dissipation rate well except in the rich side. A linear model for evaporate rate captures the correlations of the conditional averaged evaporation rate and the mixture fraction very well for the stoichiometric and fuel-rich cases. Finally, the first-order closure for the reaction rate is examined. It is found that the predictions qualitatively agree with the DNS results at all the timings. The discrepancy is mainly attributed to ignition and extinction in the spray region.