Modeling of unsteady two-phase reactive flow in porous beds of propellant

A model describing reactive two-phase flow through a gas-solid mixture is presented based upon either the concept of continuum mixture or the concept of separated-flow continuum. The resulting governing equations are solved by the method of finite differences. Details of two distinct numerical methods to solve these nonlinear, coupled hyperbolic partial differential equations simultaneously are also presented. In addition, artificial smearing techniques which are generally needed for the shock capturing methods are investigated. The analysis of the transient convective mode combustion process in a highly loaded granular bed of energetic solid propellant indicates a rapidly burning pressure front and an accelerating deflagration front. During the final stages of the burn, the velocity of this deflagration front can range from 1 to 3 mm/μs. A detailed discussion is included which attempts to explain the limits of the theoretical model presented in this study. Assessments are also made regarding the validity of many of the constitutive laws utilized and the assumptions necessary for this analysis. The study concludes with assessment of the modeling effort and how such unsteady flow processes could lead to DDT (deflagration-to-detonation transition) in such porous beds.