A hybrid scalar model for sooting turbulent flames

A Lagrangian Monte Carlo solution of the joint scalar pdf transport equation for mixture fraction and representative soot properties, coupled with an Eulerian solution for the turbulent flow field and here described as a “hybrid model,” has been developed. The modeling of soot formation and destruction employs an existing description of the key processes based on two soot variables—the soot volume fraction (or mass concentration) and the particle number density. The gas-phase chemistry is introduced through flamelet-state relationships. The simulation strategy is based on tracing the evolution of reactive stochastic particles within the computational domain. The ensemble of these particles at a fixed location and time then describes the joint scalar pdf. Soot rate equations, represented as functions of mixture fraction, soot mass concentration, and number density, are solved exactly in terms of the scalar values of each individual stochastic particle and the associated gas-phase properties derived from laminar flamelet-state relationships. The solution for the turbulent flow field provides the mean velocity and mixing frequency required for the transport of the stochastic particles in both physical and compositional space, while the Monte Carlo simulation returns the computed mean density field to the CFD code. Density-weighted mean values are approximated by ensemble averages over the scalar values of the stochastic particles in individual computational cells. The principal objective of the hybrid model is the improved treatment of nonlinear soot formation and oxidation, in particular, the capture of the intermittency in the oxidation process associated with the noncoexistence of soot and the principal oxidizing species. Significant computational economies accompany the adoption of the laminar flamelet approach for the source terms in the soot rate equations and the reduced number of scalars computed stochastically.