Nonlinear coupled constitutive relations for hypersonic reacting flows with thermal nonequilibrium effect

The complex interplay between high-temperature and rarefaction effects poses ongoing challenges to model hypersonic nonequilibrium flows, affecting the accurate prediction of aerodynamic and aerothermal loads for hypersonic vehicles. To address this issue, a multispecies Nonlinear Coupled Constitutive Relations (NCCR) model is first derived from the modified Boltzmann equations with vibrational mode. The proposed NCCR model incorporates a thermochemical nonequilibrium suite comprising chemical kinetic packages, Park's two-temperature model, and a modified Landau–Teller energy transfer formula, thereby accounting for the high-temperature effect. Furthermore, an undecomposed algorithm with popular numerical methods is also applied to solve the NCCR model within the finite volume framework. The capability of the NCCR solution to simulate thermochemical nonequilibrium flows was validated through three numerical tests, spanning the continuum to rarefied regimes. The comparative benchmark data were derived from wind tunnel experiments, in-flight tests, and direct simulation Monte Carlo method. It is noteworthy that the results of the NCCR solution show a superior alignment with the benchmark data than those obtained by the Navier–Stokes equations. Moreover, it is found that the rarefaction effect captured by the NCCR solution has a pronounced impact on the energy relaxations and chemical reaction processes in hypersonic thermochemical nonequilibrium flows. These findings underscore the potential of NCCR theory as a valuable tool for simulating thermochemical nonequilibrium flows including rarefaction effects, ultimately shedding light on the prospective development of hypersonic cross-domain vehicles.