Discussion of a Simple Treatment of Detonation Waves
Authors: Groves T.K. 
Published: December 2007

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
This paper was prepared for the 42nd Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houston, Tex., Oct. 1–4, 1967. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made.
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Abstract
The behavior of an air blast wave in the region close to an explosive charge is strongly affected by the shape of the charge, by its loading density and by its chemical nature. The physical nature of the unexploded charge is of less importance.
Computation of the spatial variation of variables behind the detonation front is readily accomplished once the adiabatic originating at the Chapman-Jouguet point has been calculated. The latter step, however, requires considerable computation if a theoretically defensible equation of state is used. Since the calculated spatial distribution of properties behind the detonation front is rather insensitive to the equation of state assumed, a constant adiabatic exponent relation may be assumed in order to derive a family of variable-space curves behind the detonation front approximating behaviour in a variety of explosives. The errors and implications of so doing are examined.

Introduction
The aim of this paper is to provide some evidence of the implications and errors in assuming that the products of detonation in explosives obey the simple adiabatic relation
dlnp/dlnp= = con st = CJ..(1.1)
where gamma CJ is the value of the adiabatic exponent at the Chapman-Jouguet (CJ) surface at the rear end of the reaction zone at the head of a detonation wave. This exponent is obtainable from the observed relation between detonation wave speed and loading density. Methods of computing the spatial distribution of variables behind the detonation wave front are well known. One method is presented in the interest of completeness.
Some Implications of the Assumption gamma = const.
The assumption gamma = const in the detonation products allows the very simple computations to be described. These require little computer time and relatively few storage locations. In contrast, if an equation of state is used which does not depend on observed detonation wave properties, the computation of the spatial distribution of variables behind the detonation wave front becomes much more laborious. The determination of conditions at the wave front is particularly costly both in time and in computer storage.