Large-eddy simulation (LES) of reacting multi-phase flows in practical combustor geometries is essential to accurately predict complex physical phenomena of turbulent mixing and combustion dynamics. This necessitates use of Lagrangian particle-tracking methodology for liquid phase in order to correctly capture the droplet evaporation rates in the sparse-liquid regime away from the fuel injector. Our goal in the present work is to develop a spray-atomization methodology which can be used in conjuction with the standard particle-tracking schemes and predict the droplet-size distribution accurately. The intricate process of primary atomization and lack of detailed experimental observations close to the injector requires us to model its global effects and focus on secondary breakup to capture the evolution of droplet sizes. Accordingly, a stochastic model for LES of atomizing spray is developed. Following Kolmogorov's idea of viewing solid particle-breakup as a discrete random process, atomization of liquid blobs at high relative liquid-to-gas velocity is considered in the framework of uncorrelated breakup events, independent of the initial droplet size. Kolmogorov's discrete model of breakup is represented by Fokker-Planck equation for the temporal and spatial evolution of droplet radius distribution. The parameters of the model are obtained dynamically by relating them to the local Weber number. A novel hybrid-approach involving tracking of individual droplets and a group of like-droplets known as parcels is developed to reduce the computational cost and maintain the essential features and dynamics of spray evolution. The present approach is shown to capture the complex fragmentary process of liquid atomization in idealized and realistic Diesel and gas-turbine combustors.
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