The Multiple Mapping Conditioning/Large Eddy Simulation (MMC-LES) model is extended for the first time to high-speed, compressible flow conditions and validated against non-reacting and reacting experimental data from a model supersonic combustor. The MMC-LES method solves the subgrid joint composition filtered density function through a Monte Carlo approach, and it permits a low-cost numerical implementation using a sparse distribution of stochastic Lagrangian particles. The sensitivity of results to the particle resolution is examined, and similar to past low-speed applications of MMC-LES, that sensitivity is found to be low. In comparison to the model equations for subsonic turbulent combustion conditions, the pressure work and viscous heating effects have been incorporated here to account for the effects of compressibility. As expected, the viscous heating effects are small for this flow case and can be ignored, while the pressure work is not negligible and makes a significant contribution at expansion fans and shock fronts where the magnitude of the pressure derivative term in non-reacting/reacting cases is as much as 23.8%/24.5% and 19.2%/18.6% of the stochastic particle standardized enthalpy, respectively. The MMC-LES predictions show good quantitative agreement with the available experimental data for the mean and root-mean-square of axial velocity, mean temperature, and wall pressure. Good qualitative comparison to the data is also observed for major flow characteristics, including location and size of shocks, expansion fans, and recirculation zone, and combustion characteristics such as flame lift-off distance. Although the effects of the pressure work on the mean flame lift-off distance are negligible, they have a significant influence on the predicted spatial fluctuations of the flame base.

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