Theoretical and experimental study of cylindrical shock and heterogeneous detonation waves

Abstract

A simplified theory of blast initiation of detonations in clouds of fuel in gaseous or droplet form is developed and agrees with the experiments described below. The flow is at first dominated by the strong blast wave but transition from blast to detonation behavior occurs near a critical radius r* where the blast energy and the heat of combustion contained in r r* are equal. The complex flow in this transition region cannot be determined analytically. In the simplified theory the details of the transition region are ignored but the flow is represented by the self-similar solution for a strong blast wave for r r* and by the self-similar detonation solution for r > r*.The development of a sectored shock tube to study cylindrical shock waves and two-phase detonations is described. Data are presented for shock waves as well as for blast initiated detonations of a monodisperse spray of 400 [mu] kerosene droplets in air at standard conditions. Two regimes of propagation were established experimentally: (1) the subcritical energy regime, where decoupling of shock and reaction zone results in a strong blast wave type decay and, (2) the supercritical energy regime, where the initially overdriven cylindrical detonation decays, at some critical radius, to its Chapman-Jouguet state. Experimentally determined critical radii and steady-state detonation velocity agree very well with theoretical predictions. Detonation velocity was found to be constant at the plane C-J value for radius greater than the critical radius.