A new numerical calculation method of thermodynamic two-temperature model

The theoretical model for calculating the thermodynamic parameters of high enthalpy gases, widely used in two-temperature model solvers, has the shortcomings such as low program operation efficiency and poor numerical stability in specific applications. A simpler and more effective method for calculating the thermodynamic energy system of the two-temperature model is developed. Drawing on the fitting expressions of the thermodynamic equilibrium energy in the one-temperature model, the representation forms of the internal energy modes are reconstructed to obtain separately a linear energy term characterized by translational temperature and a nonlinear energy term characterized by vibrational temperature. Meanwhile, Chemkin’s fitting polynomials are introduced to characterize and calculate the nonlinear energy term, so as to avoid the potential numerical problems arising from the use of exponential expressions in the theoretical model. Numerical studies indicate that the new method has reliable computational accuracy in predicting thermochemical nonequilibrium flows and their associated aerodynamic characteristics, and has higher computational efficiency compared to the solvers that use the theoretical model. The average time of single step iteration can be reduced by about 12%, and the computational time for convergence can be reduced by more than 10%, which has a positive effect on improving the efficiency of simulation of thermochemical nonequilibrium flows, and has good prospects for engineering applications.