Numerical Analyses Concerning the Spatial Dynamics of an Initially Plane Gaseous ZDN Detonation.

Abstract

The investigation of detonation dynamics and cellular structure is important to find criteria for the establishment and failure of a detonation. Recent large-scale experiments have shown that scale and geometric effects strongly influence the ability of a fuel/air mixture to propagate or sustain a detonation and the chance that a deflagration will undergo a transition to detonation. The starting point of the used numerical code is a steady, choked flow correspondding to a Chapman-Jouguet detonation. The implementation of realistic reaction kinetics leads by means of numerical integration to the well-known Zeldovich-Doring-von Neumann (ZDN) steady detonation structure. In this paper we will show by methods of numerical analysis that the ZDN structure based on themochemical equilibrium turns out to be catastropically unstable. In a reference system fixed to the detonation front, the applied numerical scheme yields a spontaneous establishment of the transverse wave structure. The influence of the channel width and the initial pressure on the transverse spacing is studied and compared with experimental outcomes. The eigenvalue character of the cell size and its channel width dependence are demonstrated. From the numerical results a correspondence principle can be derived, which expresses the vanishing influence of the channel width on the characteristic spacing with an increasing number of acoustic modes. Copyright © 1988 by Government of West Germany. Permission to be published by American Institute of Aeronautics and Astronautics. All rights reserved. * Research Assistant, Department of Mechanical Engineering t Professor, Department of Mechanical Engineering 4 S. U. SCHOFFEL AND F. EBERT