Fully resolved DNS of droplet array combustion in turbulent convective flows and modelling for mixing fields in inter-droplet space

The combustion of droplets in turbulent convective flows is simulated using direct numerical simulations (DNS). The liquid-vapour interface between kerosene droplets and the surrounding air is fully resolved with realistic boundary conditions for mass conservation, heat conduction and species diffusion. The study focuses on the characterisation of the mixing process between the evaporating fuel and the surrounding gas in regions that are dominated by small turbulent scales. For inertial droplets, these regions are characterised by Kolmogorov time scales and the mean relative velocity between droplets and the surrounding gas phase. Scaling laws for quantities of interest that require sub-grid modelling for LES, such as mixture fraction, its conditional scalar dissipation and probability density functions (PDF), are presented and assessed by comparisons with the DNS data. The scaling laws provide satisfactory estimates and are validated for different inflow Reynolds numbers, turbulence intensities and integral length scales, droplet diameters, inter-droplet distances, droplet combustion regimes and various instants of the transient evaporation process. Suitable modelling parameters are extracted from the DNS and functional dependencies of the parameters are suggested. This study demonstrates that the scaling laws are suitable to serve as sub-grid scale models for mixture fraction based approaches such as flamelet, conditional moment closure (CMC) or multiple mapping conditioning (MMC) methods.