The counter-rotating shock wave and wave direction control of the hollow rotating detonation combustor with Laval nozzle are studied. The in-house solver BYRFoam, developed on the OpenFOAM platform, is used. The phenomenon and spatial distribution of the counter-rotating shock wave in the combustor are revealed. The result suggests that the closer the location is to the outer wall, the stronger the counter-rotating shock wave is. A method of controlling the wave direction is proposed. It is shown that the intensity of the counter-rotating shock wave is controlled by reducing the total pressure of the inlet, and then the direction of the detonation wave is controlled. The process of detonation wave reversing is divided into four steps, namely, counter-rotating shock waves evolve into detonation waves, several detonation waves are extinguished, detonation waves form again, and detonation waves propagate stably. The mechanism of wave direction control is investigated. The result shows that the fluctuation of the total pressure of the inlet stimulates the positive feedback interaction between the counter-rotating shock wave and the fresh gas, which causes initial detonation waves to be extinguished and the intensity of counter-rotating shock waves to become stronger and stronger, and eventually counter-rotating shock waves evolve into reverse detonation waves.

Recently, with the development of detonation-based propulsion systems, scholars have begun to study how to perform mode control on the rotating detonation combustor (RDC). It is important to figure out the influence of operation mode transition on the RDC. Actually, the essential of different modes is the different multi-wave structures. In this study, two-dimensional numerical simulations of the RDC are conducted to study the multi-wave effect on the stability and performance of the RDC. A uniform inlet condition is adopted in simulations to eliminate the impact of discrepancy mass flow rates, and a mode-locked ignition method is used to induce RDC flow fields with different detonation wave numbers. It is found that the flow field stability and outlet uniformity are improved with increasing detonation counts, and the energy proportion in the flow field is little affected by the multi-wave structure. However, the increase in detonation number will cause a reduction of the mass-averaged total pressure ratio at the exit. Underlying relationship between the unsteady flow field and the total pressure gain is discussed. The total pressure gain is directly linked with the non-uniformity of the circumferential flow field. Then, by utilizing particle trace, the envelope of the thermodynamic cycle is illustrated and the pseudo-thermal efficiency of each case is given. The result implies that the wave number has hardly effect on the thermal efficiency of the combustion chamber. By summarizing the perimeter, axial length, and wave number in the combustor, parameter ξ is carried out and its effects on the uniformity and total pressure ratio in the RDC are concluded.