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The objective of this study is to determine the critical conditions for adetonation wave formation following a Mach reflection of two incident shocks.This problem is central to the propagation mechanism of cellular detonations,where such periodic reflections occur continuously. A new experimentaltechnique is introduced that permits the isolation of this Mach reflection. Thetechnique is inspired by that of White (1963) and uses a detonation passingthrough a bifurcated converging-diverging nozzle to reproducibly generate thedesired shock reflection at its exit, where the two transmitted mis-alignedincident shocks interact. The collision process was monitored with high-speedSchlieren videos. The experiments were performed in mixtures of methane-oxygenand hydrogen-oxygen-argon. Three distinct regimes of transmission wereidentified: detonation formation, decaying Mach shock followed by a flame, andinert Mach shock with no re-ignition. The condition separating the re-ignitionand no re-ignition was very well predicted by the critical decay rate ignitiontheory of Eckett et al. On the other hand, the transition between detonationformation and ignition was found to correlate much better with the criticalcurvature concept of quasi-steady curved detonations of Kasimov and Stewart.Both mixtures were found in excellent agreement with this criterion,established on the basis of experimental velocity-curvature data available inthe literature for these mixtures. For the hydrogen detonations, this criterionwas also in agreement with the critical curvature predicted by ZND theory. Forthe methane detonations, order of magnitude disagreement was observed with theZND model prediction, further confirming the propensity of irregular cellulardetonations to propagate under higher curvatures than predicted by laminardetonation theory.

The critical conditions for the re-ignition and detonation formation from Mach reflections of curved decaying shocks