Geometric stability of detonation propagation in curved channels

Detonation propagation dynamics in circularly curved channels are investigated using both experimental and geometric modeling approaches. Quasi-two-dimensional curved channels with a range of channel widths and curve radii were tested. Experimentally, three propagation modes were observed: a stable propagation mode featuring a flat detonation front and steady near-CJ propagation, an unstable mode with varying frontal structures and velocity oscillations, and failure to propagate. Experimental data from the current study and those in the literature show that for a given ratio between channel width and detonation cell width, there exists a critical inner-to-outer radius ratio that sets apart the stable and unstable propagation modes. A regime map is proposed in the present work to describe the observed propagation modes. The regime map highlights the competition between the focusing effect of the outer concave boundary (with respect to the transverse waves) and the diverging effect of the inner convex boundary in addition to the effect from the channel-to-cell width ratio. With a reduced channel-to-cell width ratio, the inner-to-outer radius ratio critical to sustained detonation propagation must increase. Geometric modeling results are found to be in agreement with experimental observations. In addition, geometric modeling was used to test channel geometries beyond what has been experimentally tested and to provide a rational explanation for the regime map.