Revisiting the Becker-Kistiakowsky-Wilson equation of state

Abstract

The Jones-Wilkins-Lee (JWL) equation of state (EOS) is the most popular equation of state used in hydrocodes to model detonation products thermodynamics resulting from high explosives. However, the JWL EOS presents several major difficulties. Namely, its range of validity and convexity is limited as its parameters are adjusted on a given reference curve. When used in conditions where the thermodynamic state varies significantly, computational failure may happen. It occurs frequently in multiphase flow computations when heat and mass transfers with other phases are present, as the resulting thermodynamic state is far from the reference curve used for adjustment. Moreover, the detonation products composition is absent in the JWL formulation. This is another important limitation when additional physics are involved, such as post-combustion, phase transition, or when dealing with non-ideal explosives. In this work, the Becker-Kistiakowsky-Wilson (BKW) EOS is considered instead. The BKW EOS is widely used in thermochemical codes, as parent EOS to provide the reference data used to fit JWL EOS parameters. The BKW EOS present several advantages. Its formulation considers variable gas species in the detonation products. No specific adjustment is needed for a given explosive, and only the detonation products composition requires computational efforts. Its range of validity is large, as the various parameters have been adjusted for each gas species separately. However, the BKW EOS also present difficulties which limit its application in hydrocodes. These difficulties are the aim of the present work. The BKW EOS is currently restricted to thermochemical codes as its mathematical formulation is computationally expensive. It also requires the gas chemical composition to be computed via an appropriate chemical equilibrium solver. In the present work, the computational cost of the BKW EOS is reduced thanks to the thermodynamic relaxation method of Neron et al. (2023). The variable composition of the detonation products is accounted for through specific relaxation terms computed once, with the help of conventional thermochemical codes. The condensed species, such as solid carbon, are modelled with the Cochran-Chan (CC) EOS, having a simpler thermodynamic formulation and being thermodynamically consistent compared to usual EOSs used for condensed species. This multiphase formulation made of BKW gas mixture with variable composition and condensed phases is considered in temperature and pressure equilibrium. It is embedded in a multiphase flow formulation, with the help of the thermodynamic relaxation method mentioned above. It shows comparable computational cost as the JWL formulation, with significantly enhanced physics capabilities and improved robustness.