Sparse Lagrangian Particle Method For The Simulation Of Turbulent Non-Premixed Flame

Probability density function(PDF)method can treat turbulence-chemistry interactions in a precise way and has been successfully used to simulate some laboratory-scale flames.Conventionally,tens of particles are employed per Eulerian grid to approximate the PDF of local physical quantities,and chemical reactions are integrated on those particles.Due to the stiffness of the chemical reactions,the computational cost of PDF method is high.In sparse-Lagrangian filtered density function(sparse FDF)method,significantly fewer particles than the total number of grids are used,therefore the computational cost is much lower.It is expected that sparse particle method yields reliable statistical results.Due to the much reduced number of particles,there are some essential differences between the sparse FDF methods and the conventional intense FDF method.A transient PDF cannot be obtained with the ensemble of particles in one cell.Sparse FDF method solves scalar FDF transport equation,in which,a generalised multiple mapping conditioning(MMC)model is needed to ensure the localness of the mixing.Meanwhile,a new mixing time scale model is needed for scalar mixing model.In addition,the density coupling method for sparse FDF method also needs to be redesigned.In this work,the mixed time scale model in the sparse FDF method and the density coupling method in the reaction flow are studied in depth.A modified density coupling method is proposed,in which the conditional mean source term of equivalent enthalpy is feedback directly as the source term in the filtered equivalent enthalpy transport equation solved by LES.A program to implement sparse FDF method is developed incorporating the large eddy simulation(LES)program.The Sandia flame D/E/F was simulated and the results are compared with the experiments.The simulation results of Sandia flame D/E agree well with the experimental data,which indicate that the new density coupling method is quite reasonable in reducing the numerical errors of LES results.Meanwhile,the good performance validates the sparse FDF method and the program as well.However,the simulation results of Sandia flame F are less satisfactory in the degree of local extinction,which indicates that there is still improvement space of the existing sparse FDF method and model.