Numerical study is carried out to investigate the impact of the non-uniform filling of the fresh mixture on the detonation wave propagating in the disk-shape and hollow rotating detonation combustor. The propagation characteristics in the two-dimensional curved channel with lateral expansion on the inner side are analyzed by fixing the virtual inner wall radius at 65 mm and radial height at 15 mm while varying the incomplete filling distance, initial pressure, dilution ratio and temperature of combustion products. Considering the coupled effects of axial and radial expansions, simulations are also conducted in the three-dimensional channel by varying the axial filling height of the fresh mixture. In the two-dimensional channel where only the lateral expansion effect exists, four propagating modes are observed, i.e., stable mode, weakly unstable mode, strongly unstable mode, and deflagration mode, based on the velocity deficit and whether the detonation wave degenerates into a deflagration wave. As the temperature of the residual combustion products increases, the acoustic impedance ratio between the residual combustion products and the fresh mixture decreases, causing the oblique shock within the combustion products region to advance ahead of the detonation wave along the propagation direction. On the one hand, the pressure rise behind the oblique shock directly suppresses the detonation deficit induced by radial expansion. On the other hand, when the interaction between the oblique shock and the detonation front satisfies the Mach reflection condition, the formation of a Mach stem results in a stable wave system, can further promote the stable self-sustained propagation of the detonation wave. Critical criteria for mode transition among the stable mode, the weakly unstable mode, the highly unstable mode, and the deflagration mode have been established in terms of the incomplete filling distance and the average cell size. In the three-dimensional condition where the detonation wave undergoes the radial and axial expansion simultaneously, a linear decay coefficient of the maximum pressure is defined to quantify the sensitivity of the detonation wave to pressure loss in the axial direction. As the axial filling height increases or the radial position approaches the outer wall, the linear decay coefficient of the maximum pressure exhibits a decreasing trend, indicating an increased resistance to the inward development of pressure loss and an enhanced ability of the detonation wave to endure lateral expansion.

In the disk-shaped rotating detonation chamber with injection from the outer side, the detonation wave propagates in a curved channel without the constraint of the inner wall. Actually, both the channel curvature and the radial expansion have a great influence on the propagation of detonation waves. To clarify the propagation characteristics in curved channels under the radial expansion on the inner side, this study has been carried out utilizing a mixture of ethylene, oxygen, and nitrogen. First, the effects of the equivalence ratio on the propagation characteristics in both confined and semi-confined curved channels are focused on in this study. Then, the formation mechanism of the inflection structure in the radial expansion region is revealed by numerical simulations. The results show that the curvature of the detonation wave front decreases under the influence of radial expansion, and the wave velocity along the wave front is reduced when introducing the radial expansion near the inner wall which is below 0.7 times theoretical C-J velocity. However, the circumferential wave velocity increases near the outer wall. Under the fuel-lean and fuel-rich conditions, the intensity of detonation waves in the expansion region decreases, and the expansion angle increases rapidly. Three propagation modes are observed after the stable detonation waves enter the curved channels, i.e., a stable mode, a critical mode, and an unstable mode. Finally, the critical conditions for the stable mode are clarified with the influence of the radial expansion on the inner side. The critical inner radius is 19.01 times the average cell width, and meanwhile, the minimum mixture height is equivalent to 8.77 times the average cell width.

When detonation waves propagate in curved channels, they will be influenced by the curvature of the channel. Both the compression effect near the outer wall and the diffraction effect near the inner wall cause the detonation wave front to exhibit a certain degree of curvature, making the propagation more unstable due to decoupling between the shock wave and the chemical reaction. To clarify the propagation characteristics of detonation waves in curved channels, this study investigated the effects of the equivalence ratio and the dilution ratio on the propagation of stable detonation waves by using a mixture of ethylene, oxygen, and nitrogen. The results show that in curved channels, there are differences in the decoupling mechanism between the fuel-lean and fuel-rich conditions. Under fuel-rich conditions, as the dilution ratio varied from 0.4 to 0.6, detonation waves transitioned from the regular reflection mode to the Mach growth mode. By comparing the wave velocity on the inner wall with 0.8 times the C-J velocity, three propagation modes were observed after stable detonation waves entered the curved channel, i. e., a stable mode, a critical mode, and an unstable mode. Under fuel-lean conditions, the dilution ratio had a more significant impact on the detonation propagation mode. The critical condition of the stable detonation mode was clarified to be that the critical inner radius should be 18.6–24.2 times of the average cell sizes.