In this paper, we deal with the governing equations of solid-gas two-phase fluid flow and transient combustion processes of granular propellants taking place in a gun chamber with a mobile projectile. We resort to a two-phase fluid dynamics model to model the solid-gas flow field. Due to the projectile motion, it is necessary to make the transformation from the coordinate parallel to the projectile motion to a new coordinate that remains invariant with time. Two sets of transformed basic equations for each phase are analyzed numerically, together with the constitutive equations for the intergranular stress, interphase drag, interphase heat transfer, diffusivity coefficients, and burning rate. In addition, an ignition criterion for the propellant grains must be given. The Noble-Abel equation of state was used for the gas phase in the present analysis, A finite volume method was employed to discretize the basic equations for both the compressible gas phase and propellant solid phase. The derived algebraic equations in a staggered grid system, by using an upwind scheme to approximate total fluxes, were solved iteratively by the newly proposed SIMPLE-COM solution algorithm. In this study, we address the variations of flow structure and physical properties during the ballistic cycle.
Numerical Heat Transfer, Part A: Applications 27(4), pp.395-415