Jones-Wilkins-Lee (JWL) reaction product equations of state for overdriven PETN detonation waves

Abstract

The Jones-Wilkins-Lee (JWL) equation of state (EOS) has long been used to accurately calculate the Chapman - Jouguet (C-J) state of condensed phase explosive detonation waves and the subsequent expansion of the reaction products as they do work on surrounding materials. In many applications, the states of the reaction products must also be known at higher pressures and temperatures than the C-J state. Such states occur in overdriven detonation waves supported by high velocity impacts, reflected waves, and converging waves. When the states attained in overdriven detonations were first measured experimentally, the initial JWL EOS's based only on expansion data were found to be too compressive. This problem was resolved 30 years ago by modifying the two exponential terms in the JWL EOS to yield less compressible states at higher pressures, while still matching C-J state and product expansion states at lower pressures. The experimental data on overdriven detonation waves in Pentaerythritol tetranitrate (PETN) is used to develop accurate JWL EOS's using three methods. The first method is to use the analytical formulas of Urtiew and Hayes, who used the experimental C-J detonation velocity, C-J pressure, and the heat of reaction to develop JWL EOS's that fit high and low pressure data. The second method is to use the CHEETAH chemical equilibrium code to calculate: the C-J state; the adiabatic expansion of the products; and a JWL EOS fit to its predicted expansion states. The accuracy of the CHEETAH calculated PETN C-J detonation velocities was checked against experimental detonation velocities measured at several initial densities ranging from 0.27 g/cm3 to 1.764 g/cm3. The third method is to use the CHEETAH code to calculate the overdriven Hugoniot states based on its C-J calculation. This method accounts for the changes in reaction product concentrations as the shock pressures and temperatures increase. Excellent agreement with the experimental shock pressures and densities approaching 120 GPa and 3.6 g/cm3 was obtained using all three methods.