Evaluation of thermodynamic closure models for partially reacted two-phase mixture of condensed phase explosives

One of the key fundamental issues that is crucial in the continuum modeling of reactive flow phenomena is the thermodynamically consistent description of reaction mixture properties. To define the mixture properties, thermodynamic closure rules that relate the properties of the individual reaction components to the mixture properties are required. In the context of reactive two-phase modeling approaches, various strategies to define the thermodynamic closures have been adopted such as pressure temperature (PT) equilibrium between the individual reaction components, pressure (specific) volume (PV) equilibrium, etc. The choice of closure rules determines the relative distribution of specific volume and energy across the reaction components that comprise the mixture. Therefore, depending on the choice of the closure, the mixture thermodynamic behavior can vary. The present work examines the effect of different closure approaches on the thermodynamic properties of the reaction mixture. The analysis is performed for a condensed phase HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) based plastic bonded explosive (PBX) 9501 explosive using four different thermodynamic closures, viz., PT equilibrium, PV equilibrium, volume temperature (VT) equilibrium, and pressure (P) equilibrium with reactants on an isentrope. Furthermore, the relative variations in the thermodynamic properties of the mixture are analyzed and compared under both compression and expansion loading regimes. It is shown that out of the four closure models, only PT equilibrium and P equilibrium closures lead to a thermodynamically accurate description of the mixture under both compression and expansion.