A unified model of gaseous fuel and air mixing is applied here to study the use of shock waves for enhancement of mixing between methane and air. The model uses fuel mass fraction within infinitesimal fluid elements and the total derivative of this fraction with respect to time to measure the degree and rate of mixing, respectively. The model is accurate only for low-pressure combustors since it is based on the ideal gas law. The model is also limited to gaseous fuels that contain single chemical specie, or those that behave like single specie. The model presented here can be applied to any combustor geometry or operational conditions. Results show that mixing can be completed within the narrow region of the shock wave and therefore in a negligibly short time, if pressure, temperature, and velocity distributions within this region are optimized. Furthermore, the combined effects of air preheat and shock waves can enhance both mixing mechanisms with air penetration into the fuel and with fuel dispersion into the surrounding air. These results provide important guidelines for the mixing in supersonic combustors that are required to provide high efficiency and high intensity, while maintaining low levels of pollutants emission.

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