The Stability of Imploding Detonations

The relative stability of cylindrically imploding shock and detonation waves has been examined using a two-dimensional numerical model. A sequence of increasingly realistic chemistry models is used to explore the effect of model selection on the results. Comparisons with the predictions of the Chester-Chisnell-Whitham (CCW) theory for the acceleration of nonreactive shocks and detonations show quantitative agreement between theory and simulation for symmetrically imploding waves. The influence of structural supports in laboratory experiments on the symmetry of imploding waves is simulated by placing an obstacle in the path of the converging flow. Changes in the convergence time, reductions of the peak pressure at implosion, and deviations from symmetry during the implosion induced by the obstacle are greater for detonations than for the corresponding nonreactive shocks, in qualitative agreement with the linearized CCW theory for shocks and Chapman-Jouguet detonations. These conclusions continue to hold when more sophisticated Zel’dovich-von Neumann-Doering or finite-rate chemistry models are assumed. For these models, a substantial amount of new asymmetrical, dynamical structure is evident in the reaction zone behind the leading shock. The results concur with and extend previous theoretical work suggesting that imploding detonation waves are relatively more unstable than nonreactive shocks.