Thermally induced non-equilibrium gas flows have been simulated in the present study by coupling kinetic and extended thermodynamic methods. Three different types of thermally induced gas flows, including temperature-discontinuity- and temperature-gradient-induced flows and radiometric flow, have been explored in the transition regime. The temperature-discontinuity-induced flow case has shown that as the Knudsen number increases, the regularised 26 (R26) moment equation system will gradually loss its accuracy and validation. A coupling macro- and microscopic approach is employed to overcome these problems. The R26 moment equations are used at the macroscopic level for the bulk flow region, while the kinetic equation associated with the discrete velocity method (DVM) is applied to describe the gas close to the wall at the microscopic level, which yields a hybrid DVM/R26 approach. The numerical results have shown that the hybrid DVM/R26 method can be faithfully used for the thermally induced non-equilibrium flows. The proposed scheme not only improves the accuracy of the results in comparison with the R26 equations, but also extends their capability with a wider range of Knudsen numbers. In addition, the hybrid scheme is able to reduce the computational memory and time cost compared to the DVM.

Variable-thrust liquid rocket engines are essential for precision landing in deep-space exploration, reusable launch vehicle recovery, high-accuracy orbital maneuvers, and emergency obstacle evasions of space drones. However, with the increasingly complex space missions, challenges remain with the development of different technical schemes. In view of these issues, this paper systematically reviews the technology’s evolution through mechanical throttling, electromechanical precision regulation, and commercial space-driven deep throttling. Then, the development of key variable thrust technologies for liquid rocket engines is summarized from the perspective of thrust regulation and control strategy. For instance, thrust regulation requires synergistic flow control devices and adjustable pintle injectors to dynamically match flow rates with injection pressure drops, ensuring combustion stability across wide thrust ranges—particularly under extreme conditions during space drones’ high-maneuver orbital adjustments—though pintle injector optimization for such scenarios remains challenging. System control must address strong multivariable coupling, response delays, and high-disturbance environments, as well as bottlenecks in sensor reliability and nonlinear modeling. Furthermore, prospects are made in response to the research progress, and breakthroughs are required in cryogenic wide-range flow regulation for liquid oxygen-methane propellants, combustion stability during deep throttling, and AI-based intelligent control to support space drones’ autonomous orbital transfer, rapid reusability, and on-demand trajectory correction in complex deep-space missions.

Hypersonic unmanned flight vehicles have complex dynamic characteristics, such as nonlinearity, strong coupling, multiple constraints, and uncertainty. Operating in highly complex flight environments, hypersonic unmanned flight vehicles must not only contend with uncertainties and disturbances such as parameter perturbations and noise but also deal with complex task scenarios such as interception and no-fly zone avoidance. These factors collectively pose great challenges on the control performance of the vehicle. To address the challenges of trajectory tracking for the vehicles under complex constraints, this paper proposes a trajectory tracking control method based on model predictive control (MPC). Firstly, a nonlinear dynamic model for hypersonic unmanned flight vehicles is established. Then, a robust model predictive controller is designed and the optimal control law is derived to address the trajectory tracking control problem under complex constraints such as parameter perturbations. Finally, simulation experiments are designed under the conditions of aerodynamic parameter changes in the longitudinal plane and lateral no-fly zone avoidance. The simulation results demonstrate that the vehicle is capable of accurately and rapidly tracking the reference despite aerodynamic parameter perturbations and large-scale lateral maneuvers, thereby validating the effectiveness of the controller.

In the present study, the performance of the moment method, in terms of accuracy and computational efficiency, was evaluated at both the macro- and microscopic levels. Three different types of non-equilibrium gas flows, including the force-driven Poiseuille flow, lid-driven and thermally induced cavity flows, were simulated in the slip and transition regimes. Choosing the flow fields obtained from the Boltzmann model equation as the benchmark, the accuracy and validation of Navier–Stokes–Fourier (NSF), regularized 13 (R13) and regularized 26 (R26) equations were explored at the macroscopic level. Meanwhile, we reconstructed the velocity distribution functions (VDFs) using the Hermite polynomials with different-order of molecular velocity moments, and compared them with the Boltzmann solutions at the microscopic level. Moreover, we developed a kinetic criterion to indirectly assess the errors of the reconstructed VDFs. The results have shown that the R13 and R26 moment methods can be faithfully used for non-equilibrium rarefied gas flows in the slip and transition regimes. However, as indicated from the thermally induced case, all of the reconstructed VDFs are still very close to the equilibrium state, and none of them can reproduce the accurate VDF profile when the Knudsen number is above 0.5.

Thermally induced oscillatory rarefied gas flow inside a two-dimensional rectangular cavity is investigated based on the hybrid macro-/mesoscopic scheme. The effects of the Knudsen (Kn) numbers and the oscillation frequency of lid temperature on the flow parameters are analyzed. The Shakhov model equation is solved numerically based on the mesoscopic approach in the near-wall region, and the macroscopic approach is adopted in the bulk flow region to reduce the computational cost. To close the numerical iteration procedure, the velocity distribution functions serving as the pseudo boundary between macroscopic and mesoscopic methods are reconstructed using the high-order Hermite polynomials. Numerical simulations demonstrate that the temperature profile at the central vertical of the cavity predicted by the hybrid method is in good agreement with results from the mesoscopic method, with a maximum error of 0.23%. In addition, the computational memory cost can be saved up to about 69.91%. The hybrid approach is able to capture the nonlinear phenomenon in the thermally induced oscillatory rarefied gas flow under high Kn numbers, where the horizontal velocity no longer obeys the law of periodic oscillating cosine function, and the rise time of the horizontal velocity is much longer than the fall time. The thickness of the viscous penetration layer and the disturbed region increases as the Kn number increases and decreases as the Strouhal number increases.