Numerical investigation on the rotating detonation critical mode for a methane–air mixture in an annular tube using reactive Navier–Stokes equations

Previous experimental studies show that gaseous detonation propagation in an annular tube can be divided into three categories, i.e., stable mode, critical mode and unstable mode. However, the mechanism of detonation propagation with the critical mode is not well understood due to insufficient experimental data. In this paper, detonation propagation with the critical mode in the annular tube was numerically studied for the methane–air mixture based on reactive Navier–Stokes equations, in which the convective term was integrated by the fifth-order weighted essentially non-oscillatory. The numerical results show that the trajectories of the triple points of the shock wave front were drawn to obtain cell structure with “petal” pattern, which is agree with the experimental results. The wall curvature plays an important role for this phenomenon. The outer wall is concave, which can continuously compress the detonation wave and make it stronger. The inner wall is convex, which can produce an isentropic expansion and decouples the reaction front from the shock wave. The transverse shock wave emanating from the triple point moving from the outer wall reignites detonation near the inner wall, which implies that compression of the outer wall plays a key role in the rotating detonation propagation. As the transverse shock wave moves away from the inner wall, the detonation wave near it gradually weakens. Because of the back and forth reflection of the transverse shock wave between the inner and outer walls, the rotating detonation wave can be maintained and its cellular structure presents “petal” pattern. Meanwhile, the averaged detonation velocity at the outer wall is higher than that at the inner wall.