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A finite-rate method is used to simulate the three-dimensional combustion process in a plasma generator with CH4 as the fuel. The simulation was run with RNG k-ε model to simulate turbulence, with eddy-dissipation-concept (EDC) model to simulate the combustion and with discrete ordinates model to simulate radiation. The numerical results show that the flow field characteristics and the parameter distributions are under the condition of rich fuels, and these results provide valuable information when optimizing the plasma generator design and organizing its flow fields.