Two-dimensional oblique detonation wave (ODW) propagations in partially prevaporized n-heptane sprays are numerically simulated with a skeletal chemical mechanism. The influences of the droplet diameter and total equivalence on oblique detonation are considered. The initiation length is found to increase first and then decrease with increasing initial droplet diameter, and the effect of droplet size is maximized when the initial droplet diameter is approximately $10\ \mathrm {\mu } {\rm m}$ . As the initial droplet diameter varies, unsteady and steady ODWs are observed. In the cases of unsteady ODWs, temperature gradients and non-uniform distributions of the reactant mixture due to droplet evaporation lead to formation of unsteady detonation propagation, therefore leading to fluctuations in the initiation length. The fluctuations in initiation length decrease as the pre-evaporation gas equivalence ratio increases for the unsteady cases. The results further suggest that the relationship between the evaporation layer thickness along the streamline and the corresponding theoretical initiation length can be used to identify an unsteady or steady ODW in cases with large droplets that evaporate behind an oblique shock wave or ODW under the effects of different initial droplet diameters.

In experimental studies, single-wave mode and two counter-rotating wave mode are often observed in rotating detonation combustors. To investigate the mechanism behind different propagation modes, high-resolution numerical simulations of two-dimensional detonation in hydrogen/air mixtures are conducted by solving the reactive Navier–Stokes equations with a detailed chemical mechanism. The numerical results show that the occurrence of the dual-wave detonation propagation mode is positively influenced by an increase in both the channel width and the initial pressure. The dual-wave modes are observed when increasing the channel width, and it is found that the dual-wave modes are caused by increasing the residual premixed gas height near the inner wall. When increasing the initial pressure, the initial peak detonation heat release increases, which leads to the increase in the hot spot intensity formed, and it is found that the dual-wave modes are mainly caused by the interactions between the initial detonation wave and the inner wall. However, the initial equivalent ratio appears to have a relatively minor impact on the detonation propagation mode due to a relatively narrow range variation of physical properties. The peak heat release rate exerts a greater influence on the change of the propagation mode than the induction time does through a wider range test on rotating detonation engines' working condition. Moreover, the velocities and the cell sizes of detonation waves propagating in different directions with different channel widths are also analyzed, revealing that the characteristics of the detonation waves propagating in different directions are nearly the same.

During a lunar module landing, the gas extended from the engine nozzle impinges on the lunar surface. A recirculation bubble could form beneath the surface shock wave, which alters the flow pattern close to the surface, thus affecting the surface soil transportation process. This study conducted numerical simulations to investigate the flow characteristics, formation mechanism, and effects of this recirculation bubble on surface soil erosion using direct simulation Monte Carlo method or solving the Navier–Stokes equations. It is found that during the descent, the recirculation zone under the surface shock wave first disappears and then reappears. The shock wave systems in the plume at different lander heights is analyzed, revealing that the formation of the recirculation bubble can be attributed to the total pressure loss due to gas crossing different wave structures. When the lander descends to a close proximity to the lunar surface, the recirculation bubble can even expand into the nozzle. Furthermore, this study investigated the effects of the recirculation bubble on lunar soil transportation by a gas–solid two-phase solver. It is shown that the recirculation bubble at low landing altitude will entrain the lunar dusts and result in a high ejection angle of the latter, thus aggravating the obstruction of surface observation for the safe landing.