Numerical study of detonation wave propagation modes in annular channels

Modes of detonation wave propagation in annular channels were investigated numerically by using the adaptive mesh refinement technique. Two-dimensional, reactive Euler equations with a detailed hydrogen/oxygen reaction model were adopted in the computations to simulate the detonation dynamics in the annular geometry. Considering both the decoupling of the detonation wave front and the development of the Mach-stem in reflection, the propagation is divided into unstable and stable propagation modes with different Mach-stem evolutions, namely, a growing, steady, or decaying type. The numerical observations indicate that in the unstable propagation mode, velocity loss and oscillation occur near the inner wall, while the wave front shape and velocity evolution are steadier for the stable propagation mode. The overdriven degree near the outer wall increases as the Mach-stem strength attenuates. The propagation mode diagrams demonstrate that an increase in the initial pressure and wall curvature radius can extend the range of the stable propagation mode, and the Mach-stem is transformed from a growing to steady, and finally a decaying type with the increase in the initial pressure or the decrease in the wall curvature radius to channel width ratio. The limit of wall curvature radius separating the unstable and stable modes is independent of the channel width for the Mach-stem steady and decaying types, while they are positively correlated for the Mach-stem growing type. Finally, a qualitative procedure is proposed to help distinguish different propagation modes based on the formation mechanism of each propagation dynamics.