An implicit fully coupled numerical method for modeling of chemically reacting flows is presented. Favre averaged Navier-Stokes equations of multi-component gas mixture with nonequilibrium chemical reactions using Arrhenius chemistry are applied. A special method of splitting convective fluxes is introduced. This method allows for using spatially second-order approximation in the main flow region and of first-order approximation in regions with discontinuities. To consider the effects of high-speed compressibility on turbulence the author suggests a correction for the model, which is linearly dependent on Mach turbulent number. For the validation of the code the described numerical procedures are applied to a series of flow and heat and mass transfer problems. These include supersonic combustion of hydrogen in a vitiated air, chemically reacting flow through fluid rocket nozzle, afterburning of fluid and solid rocket plumes, fluid dynamics and convective heat transfer in convergent-divergent nozzle. Comparison of the simulation with available experimental data showed a good agreement for the above problems.

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