Abstract:

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.

Key words: rotating detonation, non-uniform filling, lateral expansion, detonation wave, propagation characteristics