Boundary condition specification for mobile granular propellant bed combustion processes

In the modeling of transient one-dimensional, two-phase combustion of granular propellants in gun interior ballistics, the boundary conditions at both the breech end and the base of the projectile must be specified adequately. The form and the total number of the boundary conditions required depend upon the relative velocities of the gases and solid particles with respect to the solid boundary and the condition of fluidization. In the study of a simulated gun system, the flow properties at the boundary are obtained by considering 1) the local balances of mass, momentum, and energy over a small control volume adjacent to the boundary; 2) the compatibility relationships along the characteristic lines; and 3) the number of algebraic relationships according to the instantaneous flow conditions. These considerations are necessary to provide the extraneous boundary conditions required for solving the partial differential equations with a second-order numerical scheme. Numerical results were compared and found in agreement with test-firing data.