Modelling of two-phase transient flow and combustion of granular propellants

Gas-permeable solid propellants possess great potential for producing high thrusts during extremely short time intervals. The paper presents a theoretical model describing the important physical phenomena taking place in both gaseous and solid phases in such two-phase, unsteady, reactive-flow systems. The governing equations were derived in the form of coupled, non-linear partial differential equations and the resulting formulation was compared with those used by previous authors. A stable, fast-converging, fully-implicit numerical method, first proposed by Spalding and implemented in a general-purpose computer program, was used to solve the equations, so that effects of importance can be studied. Solutions are presented that predict the pressure wave build-up and accelerating flame front for beds of granulated solid propellants fixed in a rigid enclosure, and in gun barrels with an accelerating projectile. The results show that the flame front accelerates and the rate of pressurization increases substantially in the downstream direction. Some discussion is given of the sensitivity of these predictions to the assumed constitutive relations for interphase heat and momentum transfer and the solid burning-rate law. It is argued that the controversy surrounding the hyperbolicity of the equations, which has delayed progress towards theoretical prediction of two-phase flows, is ill-founded, since the equations are shown to possess unique solutions, as indeed do the physical systems they represent.