The Effect of Curvature on Detonation Speed

Abstract

This is the second in a series of papers describing a program for the numerical modeling of detonation waves. In this paper, the validity of an asymptotic theory, developed by Jones (“The spherical detonation,” Adv. Appl. Math., to appear), for the correction to detonation wave speed due to the curvature of an expanding detonation wave is established. Expanding cylindrically symmetric undriven detonation waves are taken as test problems. Comparisons of the quasisteady-state theory of Jones are made with random choice computations in which the reaction zone is resolved and in which operator splitting is applied to both the geometrical and chemical source terms. A computation employing a rate law and equation of state modeling a real explosive is also presented. It is shown numerically that Jones’ equations supply the correction to detonation wave speed due to the curvature of the front to lowest order in inverse radius and that the form of the correction depends on the order of the reaction in the rate law employed.This result, in combination with the result of the previous paper in this series, will enable the computation of the transition from strong detonations to weak detonations of two-dimensional curved detonations in the near future. The implementation of this result in the context of front tracking computations is discussed.