Determination of critical conditions for detonation initiation in a finite volume by a converging shock wave

Direct initiation of spherical and cylindrical detonation in a stoichiometric hydrogen–air mixture under normal conditions by a collapsing low-pressure region (cavity) in a space bounded by a rigid shell is considered. The study of the flow with allowance for the actual mechanism of chemical reactions was performed using the finite-difference method based on the Godunov scheme, with a moving computational grid and explicit capturing of the leading shock wave and contact surface. It is established that, for a fixed pressure in the collapsing region and for its radius equal to or exceeding the known critical radius for an unbounded space, there exists a minimum (critical) shell radius, on exceeding which a detonation wave emerges in the flow field under study. In the case of spherical symmetry, the excess internal energy of the spherical layer between the shell and the low-pressure region to be spent on initiation of detonation burning attains a minimum value that far exceeds the critical energy for detonation initiation by a TNT charge in an unbounded space.