On the Jones-Wilkins-Lee equation of state for high explosive products

The Jones-Wilkins-Lee (JWL) model is a widely used Equation Of State (EOS) in the literature to model high explosive products. It is based on exponentially decaying isentropes in the pressure-volume diagram, completed by an additional term meant to recover an ideal-gas behavior for large expansions where exponential terms are negligible. A step-by-step analysis of the EOS is proposed. Starting from the main isentrope, the constant Grüneisen, and constant isochoric heat capacity, the JWL expressions of pressure, temperature, sound speed, specific internal energy, specific entropy and specific enthalpy are derived. For a specific set of JWL parameters meant to model HMX products, various thermodynamic fields are investigated in pressure–volume and temperature–volume planes. The positivity of pressure and temperature, the convexity, the thermodynamic stability, and the monotonicity along an Hugoniot are investigated in order to characterize the JWL domain of validity. For each of these constraints, different regions of validity are found. Besides presenting a study of the JWL model and its limits, this work also provides a standalone presentation and derivation containing the necessary materials for the understanding and for the use of the JWL EOS in reactive hydrodynamic simulations of condensed phase explosives.