Spray combustion is commonly employed in propulsion engineering with the most widespread application in internal combustion engines. Numerical simulations of spray combustion are usually performed in the Euler-Lagrange context, where the governing equations of the continuous (carrier) phase are solved in the Eulerian framework, whereas the dispersed phase is modelled by discrete (Lagrange) particles. Some common combustion models for LES, such as flamelet and CMC, rely on the existence of a characteristic variable such as mixture fraction and the strong correlation of the reacting species on this variable. For dilute reacting sprays, the sub-grid mixture fraction conditional scalar dissipation and its PDF are usually modelled by expressions that have been derived and tested for single phase non-premixed combustion. Appropriate modelling for the LES of combustion in relatively dense sprays is less certain since droplet-turbulence-chemistry interactions are not well understood, but may strongly affect the sub-grid quantities. Our scope is to quantify these sub-grid scale interactions and to provide suitable and accurate closures for quantities such as the mixture fraction distribution (i.e. its PDF) and its conditional scalar dissipation for the entire mixture fraction space, ranging from the LES filtered cell mean to the value at the droplet surface. To this end, direct numerical simulations of evaporation and combustion in moderately dense sprays are performed and results are compared to scaling laws for spray combustion.
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