Two-dimensional numerical simulation of imploding detonations

Abstract

This study aims to contribute to the understanding of imploding detonations from a numerical perspective, focusing primarily on the detailed transient and wave structures during implosion that are challenging to capture experimentally. An inviscid perfect gas model with a single-step Arrhenius reaction is employed. Imploding detonations are initiated by collisions of multiple small hot spots, and both two-dimensional circular and polygonal implosions are examined, with attention to the effects of obstacles and varying ignition pressures. For circular implosions, a slight acceleration of detonation velocity is observed at ignition, with significant acceleration occurring only in the final stages. Near the implosion center, local wave velocities exceed twice the Chapman–Jouguet velocity, yet the wave front maintains cellular instabilities until the collapse is complete. Additionally, the merging of transverse waves is observed during the implosion. In polygonal cases, a small number of “ignition edges” allows regular reflection, preserving the initial wave front geometry, while increasing the number of ignition lines leads to Mach reflection and the formation of a circular wave front. When obstacles are introduced, the detonation reflects off the obstacle, causing localized delays in the wave front that cannot be fully compensated, as transverse waves are unable to propagate sufficiently in the circumferential direction to smooth out disturbances. Similar effects are noted for implosions with non-uniform ignition pressures. It should be noted that the findings are based on a simplified model and do not account for real gas effects or additional physical processes present in actual detonation implosions.