  The objective of this study is to determine the critical conditions for a
detonation 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 experimental
technique is introduced that permits the isolation of this Mach reflection. The
technique is inspired by that of White (1963) and uses a detonation passing
through a bifurcated converging-diverging nozzle to reproducibly generate the
desired shock reflection at its exit, where the two transmitted mis-aligned
incident shocks interact. The collision process was monitored with high-speed
Schlieren videos. The experiments were performed in mixtures of methane-oxygen
and hydrogen-oxygen-argon. Three distinct regimes of transmission were
identified: detonation formation, decaying Mach shock followed by a flame, and
inert Mach shock with no re-ignition. The condition separating the re-ignition
and no re-ignition was very well predicted by the critical decay rate ignition
theory of Eckett et al. On the other hand, the transition between detonation
formation and ignition was found to correlate much better with the critical
curvature 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 in
the literature for these mixtures. For the hydrogen detonations, this criterion
was also in agreement with the critical curvature predicted by ZND theory. For
the methane detonations, order of magnitude disagreement was observed with the
ZND model prediction, further confirming the propensity of irregular cellular
detonations to propagate under higher curvatures than predicted by laminar
detonation theory.
