A Model of the Traveling Charge

Abstract : A model is described to permit the theoretical evaluation of the ballistic performance of an end-burning traveling charge. The column of gas between the breech and the regressing propellant surface is analyzed as a one- dimensional, unsteady, inviscid flow with heat loss to the wall. The solid propellant may be represented either as rigid or as unsteady, one-dimensional, viscoplastic continuum which interacts with the tube wall through the action of friction. The combustion of the propellant may be prescribed according to any of several ideal criteria. The reactants may be required to come to rest, to attain a predetermined Mach number or to induce a predetermined pressure on the unreacted side of the interface or a predetermined acceleration of the projectile. Ideal models of such strong deflagration waves are provided so as to enable the assessment of the performance loss associated with a limitation to weak or subsonic deflagrations. The breech may be taken to be gas-permeable and the solution can be continued past muzzle exit in order to study blowdown of the tube. The solution is obtained by means of an explicit two-level finite difference scheme and uses the method of characteristics at the external boundaries and at the interface between the gas and the solid propellant. Sample calculations are provided in order to demonstrate the stability of the method of solution and to benchmark its accuracy. Comparison with a case which admits an exact solution is provided and studies are made of mesh indifference and of the global conservation of mass and energy.