On the applicability of internal ballistics closure relations in compressible two-phase flow models

Nearly all mathematical models of propellant combustion, which are based on the standard geometric burning model and applied under typical internal ballistic conditions (such as in a barrel system or solid-fuel engine), treat the propellant as an incompressible medium. This assumption is generally justified by the range of parameters considered in these problems. However, for a number of energetic applications, burning regimes, such as convective burning or low-speed detonation, are of interest. These regimes are characterized by combustion waves propagating at elevated pressures, where the compressibility of the solid phase becomes significant. This paper addresses the issue of burning grained propellants in a closed vessel, using the Baer-Nunziato model. The model assumes compressibility of both phases and pressure non-equilibrium. We propose three modifications to the classical model of propellant combustion: (1) adjusting the heat release by the internal energy of the propellant, (2) adding a term to the equation for the relative thickness of the burning layers of the propellant grain to account for compressibility effects, and (3) implementing a procedure to adjust the burning coefficient to ensure that the impulse of the burnt gases' pressure matches experimental data. These corrections are validated through the example of burning a single-channel pyroxylin powder charge in a closed vessel.