Influence of the radial geometric dimensions on the propagation characteristics of detonation waves in an annular channel

While a detonation wave is confined to propagate within an annular channel, the geometric dimensions have been confirmed to play an important role. Numerical study has been conducted to investigate the influence of radial geometric dimensions on the propagation characteristics of detonation waves in annular channels. The geometric dimensions, i.e., the radial height (h) and the inner radius (r_in), were varied to study the characteristics of the detonation in C₂H₄+3O₂+3N₂ propagating through annular channels. It was observed that as the radial height increases or the inner radius decreases, the velocity deficit at the inner wall increases, leading to the instability in the propagation of the detonation wave. Based on the velocity deficit at the inner wall, the propagation modes were categorized into stable, weakly unstable, and highly unstable modes. For the mentioned mixture at the initial condition of 60 kPa and 300 K, when h < 0.375r_in − 0.5 λ_a* (average cell size), the velocity deficit at the inner wall is within 20%, indicating a stable mode; when 0.375r_in − 0.5 λ_a* < h < 0.375r_in + 0.5 λ_a* , the velocity deficit ranges from 20% to 40%, corresponding to a weakly unstable mode; when h > 0.375r_in + 0.5 λ_a* , the velocity deficit exceeds 40%, indicating a highly unstable mode. It is concluded that the instability for the propagation characteristics of the detonation wave in the annular channel is increased as the increase in the radial height and the decrease in the inner radius. Additionally, the self-sustaining mechanism of the detonation wave propagating in a petal mode has been further explored and revealed.