Sparse-Lagrangian Particle Methods for Spray Combustion

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Stochastic particle methods shall be developed for the modelling of turbulent spray combustion. Stochastic particle methods are suited for the modelling of two-phase flows if one phase can be understood as a continuum and the other phase can be represented by discrete droplets. These conditions hold in most combustion chambers after primary spray breakup, and a Lagrangian method can be used for the modelling of the droplets’ conservation equations. In addition, we use a particle-based Monte Carlo method for the approximation of the joint probability density function (PDF) of the chemical composition of the gas phase. Every Monte Carlo (PDF) particle represents an instantaneous, local solution of a fluid element, the closure problems of classical moment methods can be avoided, and the chemical source term is given in closed form. Particle methods are therefore ideally suited for the modelling of reactive two-phase flows. The conservation equations for the velocity field are solved in an Eulerian framework with the aid of large-eddy simulations (LES). The novelty of the proposed work is the use of a sparse particle method for the computation of the gas phase composition PDF. Conventional particle methods require between 20 and 50 particles per LES cell and their numerical solution can be extremely costly. The particle number can be lowered to less than 1 particle per 10 LES cells when using sparse methods, and simulation times can be reduced by up to 2 orders of magnitude for cases with complex chemistry. The modelling of mass and heat transfer across the phase interface, i.e. the transfer between the disperse liquid droplets and the PDF (gas phase) particles is, however, a significant challenge and requires novel modelling approaches. Closures cannot easily be adapted from conventional (dense) particle methods. A variety of alternative closures has been investigated in the first funding period using direct numerical simulations (DNS) of a droplet laden double shear layer configuration. Only DNS allows for an explicit (and isolated) analysis of particle pairing (i.e. selection of the gas phase particle to receive the mass from the droplet) and the speed of the mixing between (i.e. the mixing time scale) between the two phases, and this isolation of certain physical processes facilitates the development of new closures. MMC-LES of laboratory spray flames continue, however, to feature distinct deviations from experimental data since real spray flames are unlikely to burn entirely within the non-premixed combustion regimes and droplets may not be dispersed everywhere. In the second funding period, the models shall therefore be extended to cover a variety of process and flame conditions such as partially premixed flames and dense spray flames, and they will then be validated with the aid of available experimental data.