Two-dimensional steady-state detonation waves

Abstract

Exact relationships have been derived for the steady-state Zeldovich-von Neumann-Doering flow in a cylindrically symmetric detonation behind a curved shock. The equations of motion are integrated along the axis of symmetry without approximating the radial particlevelocity gradient to obtain conservation relationships as generalized Rankine-Hugoniot equations. The Chapman-Jouguet (C-J) condition is formulated with these relationships for a polytropic equation of state to obtain exact expressions for C-J parameters on the axis of symmetry. An inverse method is developed for constructing exact solutions for the axial reaction zone, as the diameter of the charge increases from its critical value to infinity and the flow becomes one dimensional. A particular solution is constructed and examined to demonstrate the dependence of the reaction zone on flow divergence in two-dimensional detonation.