Analytical representation of the adiabatic equation for detonation products based on statistical mechanics and intermolecular forces

Abstract

A new mathematical form is presented for the equation of state of a detonation product fluid along the adiabat describing its expansion from the Chapman-Jouguet state. The basic ansatz is a rational function form for the adiabatic gamma coefficient in terms of the reduced density V _cj /V as variable, from which the pressure can be derived analytically, and the internal energy by quadrature. Rational approximants of arbitrary order can be fitted by linear least squares to results from an ideal detonation code involving a fundamental equation of state based on statistical mechanics and intermolecular forces. The approximants can be checked for accuracy, and used in hydrodynamic codes. The method is illustrated by application to results for pentaerythritol tetranitrate, and the new equations are compared with the Jones-Wilkins-Lee equation.