Numerical analysis on acoustic coupling of spinning detonation in a square tube

We investigate spinning detonations propagating in a square tube using numerical simulations based on three-dimensional compressible Euler equations and the two-step-reaction model proposed by Korobeinikov et al. The dynamics of the simulation results is used to understand how spinning detonations propagate. The track angles calculated from soot-track images of the square-tube walls are numerically reproduced for various initial pressures and channel length. The results show that the numerically obtained track angles are consistent with those of the previous reports. The spinning detonation maintains its propagation when the rotating transverse detonation completely consumes any unburned gas. Transverse detonation is important for the propagation of spinning detonations. We also discuss acoustic coupling between the transverse detonation and the acoustic wave that propagates along the wall. The rotating transverse detonation propagates with successive reflections off the walls, and acoustic waves are generated at the reflections. When the spinning detonation maintains its propagation, the rotating transverse detonation couples with the acoustic wave traveling between the walls. We analyze the maximum and minimum track angles that allow the coupling and propagation of a spinning detonation in a square tube to be maintained and find that the simulated track angles fall within the estimated maximum and minimum track angles. This result indicates that acoustic coupling is important for maintaining propagation of a spinning detonation in a square tube.