A detailed quantitative analysis of sparse-Lagrangian filtered density function simulations in constant and variable density reacting jet flows

Abstract

Sparse-Lagrangian filtered density function (FDF) simulations using a generalized multiple mapping conditioning mixing model and density coupling via a conditional form of the equivalent enthalpy method are performed for both constant density and variable density turbulent jet diffusion flames. The consistency between the sparse-Lagrangian FDF for the reactive species and the Eulerian large eddy simulation (LES) for velocity along with the accuracy of the reactive species predictions relative to the exact equilibrium solution are presented in detail. The sensitivity to the number of particles used in the simulations, the mixing localization structure, chemistry and numerical time step are all investigated. The analysis shows that consistency between the FDF and LES fields is relatively insensitive to the sparseness of the particle distributions and other model parameters but that the reactive species are strongly dependent on the degree of mixing localization in the LES mixture fraction space. An algorithm is developed to control the localization for any sparse distribution of particles with inter-particle distances within the inertial range, and it is shown that reactive species predictions are sensitive to the mixing distance in a reference mixture fraction space while there is very low sensitivity to the number of particles used in the simulations.