A numerical study of the charge diameter effect on unsteady detonation

Abstract

A numerical study for the unsteady detonation of an unconfined tetryl charge of small diameter, which is assumed to be homogeneous, was performed by using the two-dimensional Lagrangian hydrodynamic computer code, 2 DL, with the first order Arrhenius equation of reaction rate. Becker-Kistiakowsky-Wilson (BKW) and Kihara-Hikita (KH) equations of state have been applied to the detonation products. In the case of BKW, it is shown that the rarefaction waves propagating inward from the lateral surface make the reaction rate slow and give a curvature to the front. Then after an induction time, a strong initiation occurs in the reaction zone near the lateral surface and higher pressure zone moves to the axis. This higher pressure accelerates the detonation propagation near the lateral surface and the curvature of detonation front is reduced. Then, the reaction at the lateral surface again begins to decay by the rarefaction waves. Such a sequence of process is repeated periodically. The possibility of the occurrence of the strong initiation depends on the pressure and temperature in the shocked zone near the surface. In a small diameter charge, the delayed explosion becomes weaker near the surface, while its frequency increases. No shock interaction occurs because the direction of the particle flow is always divergent. In the case of KH equation of state, the temperature of detonation is higher than that obtained by BKW and the behaviour of instability becomes rather different from the previous result, i.e. in the axis the pressure oscillates repeating the overdriven and underdriven detonation similar with the case of BKW.