The present study reports the numerical analyses of lateral jet interaction around a Terminal High Altitude Area Defense-type (THAAD-type) model in hypersonic rarefied flows, with the real gas effect incorporated. The computation approach employed is the recently developed thermochemical non-equilibrium nonlinear coupled constitutive relations (NCCR) model. Regarding the simulation conditions, the flight velocity and height are set to 20 Ma and 80 km, respectively. To disclose the flow mechanism of lateral jet interaction, the complex flowfield characteristics and surface pressure distributions are discussed at length. Additionally, the research explores the impact of two key factors, namely, the jet pressure ratio and the jet Mach number, on the control performance of an in-flight vehicle's reaction control system (RCS). The results demonstrate that the complicated flowfield structures in lateral jet interaction are successfully reproduced by the NCCR model. With an increase in either the jet pressure ratio or the jet Mach number, the force and moment amplification factors decrease, while the absolute value of the normal force coefficient increases. Notably, it is found that the rarefied gas effect captured by the NCCR model against the Navier–Stokes–Fourier solution affects the lateral jet interaction flowfield, e.g., weakening the compressibility of the barrel shock and the expansibility of the Prandtl–Meyer expansion fan, as well as strengthening the jet wraparound effect. Importantly, the rarefied gas effect also exerts a prominent influence on the performance of RCS, with the degree of influence diminishing as the jet Mach number or the jet pressure ratio increases.

A newly heuristic form of second-order slip/jump boundary conditions (BCs) for the Navier–Stokes–Fourier (NSF) equations is proposed from the viewpoint of generalized hydrodynamic equations (GHE) to extend the capability of the NSF equations for moderately rarefied gas flows. The nonlinear Rayleigh–Onsager dissipation function appearing in the GHE, which contains useful information about the nonequilibrium flow fields of interest, is introduced into the proposed BCs named the simplified generalized hydrodynamic (SGH) BCs as a correction parameter. Compared with the classical Maxwell/Smoluchowski (MS) BCs, the SGH BCs may be more sensitive to capture the nonequilibrium information of flows adaptively and produce physically consistent solutions near the wall. Subsequently, the SGH BCs are implemented in the NSF equations for planar micro-Couette gas flows over a wide range of Knudsen numbers. The results indicate that the SGH BCs make impressive improvements against the MS BCs for diatomic and monatomic gases at the slip region and early transition regime, particularly in terms of capturing precisely the temperature and normal heat flux profiles in the flow and the temperature jump on the wall. More importantly, the SGH BCs conducted in NSF equations with less computational cost still can obtain well-pleased results comparable to the non-Newton–Fourier equations, such as several Burnett-type equations and regularized 13-moment equations, and even perform better than these models near the wall compared with direct simulation Monte Carlo data for the Couette flows to some extent.

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.