Method of characteristics with thermo-chemical non-equilibrium for high Mach number inlet

A method of characteristics (MOC) plays a crucial role in the inviscid design of conventional hypersonic inlets. However, thermo-chemical non-equilibrium effect caused by the high total temperature makes it arduous to accurately predict the flow inside a high Mach number inlet by employing the traditional MOC method. To bridge this gap, this study intends to proposed the method of non-equilibrium characteristics (MONC), a novel approach grounded in the governing equations of inviscid and thermo-chemical non-equilibrium flow. Different from the previous MOC for non-equilibrium flows, the specific heat ratio of translational–rotational energy is derived to execute the solution processes of MONC rather than a frozen specific heat ratio. In addition, the strategy based on a streamline and a Mach line is employed to reduce the errors in the interpolation. As for capturing the shock wave and predicting the vibration relaxation and chemical reactions in the high-temperature flow fields of the high Mach number inlet, the MONC code based on Python language is capable of predicting numerical results with a deviation of less than 2% from computational fluid dynamics (CFD). In the expansion flow of the high-enthalpy nozzle, our MONC code can also well calculate the vibrational temperature, with the maximum error of 1.4% compared to the closest experimental data. Moreover, the MONC method demonstrates a significant improvement in the computational efficiency, being approximately 353 times faster than the CFD method in the case of curve surface compression flow. The MONC demonstrates the outstanding potential for solving shock capture problems in the inviscid flow with the high enthalpy. Thereby, the current study should supply the theoretical tool for the aerodynamic design of the high Mach number inlets.