A velocity-entropy invariance theorem for the Chapman-Jouguet detonation

TL;DR

This paper proves a velocity-entropy invariance property for CJ detonations, enabling new calculations of detonation states from velocity alone, with validation through numerical simulations and discussion of physical limitations.

Contribution

It introduces a new invariance theorem for CJ detonation parameters, allowing state calculations without detailed equations of state, and explores its implications and limitations.

Findings

Invariance holds within 0.01% for gaseous explosives.

Predicted CJ pressures for liquids are about 20% higher than measurements.

The invariance may reflect a general property of hyperbolic systems.

Abstract

The velocity and specific entropy of the Chapman-Jouguet (CJ) equilibrium detonation are shown to be invariant under the same variations of initial temperature with initial pressure. This leads to additional CJ relations, for example, for calculating the CJ state -- including the adiabatic exponent -- from the only CJ velocity, without using an equation of state for the detonation products. For gaseous stoichiometric explosives with ideal products, numerical calculations with detailed chemical equilibrium confirm the invariance theorem to $\mathcal{O}(10^{-2}$\% and the additional CJ properties to $\mathcal{O}(10^{-1}$\%. However, for four liquid carbon explosives, the predicted CJ pressures are about 20\% higher than the measurements. The analysis emphasizes the limited physical representativeness of the hydrodynamic framework of the modelling, i.e. single-phase inviscid fluids at equilibrium for the initial and final states of the explosive. This invariance may illustrate a general feature of hyperbolic systems and their characteristic surfaces.