A one-dimensional code for the analysis of internal ballistic problems

This paper presents a 1D code to assist in the analysis of internal ballistic problems. This is based on a conservative formulation of the model proposed by Gough in the seventies. This is formed by a set of seven partial differential equations corresponding to the balances of mass, momentum, and energy of each phase and a constitutive law for the surface regression length of the solid phase. The authors have chosen an Eulerian approach based on a finite volume approximation in which the conserved variables are determined explicitly. A splitting technique is applied solving the system of equations in several steps. This consists of solving separately the convective part of the homogeneous system and after the system of ODEs which includes the source terms. For the convective part, numerical fluxes are evaluated by means of approximate Riemann solvers. Rusanov scheme and AUSM family of schemes are extended for their use in this context. Source terms are calculated explicit and implicitly making the model quite robust for the type of problems studied so far. The constitutive equations used are briefly studied; namely interfacial drag, interfacial heat transfer and combustion law. Solid phase is considered incompressible and Nobel-Abel equation of state is used to characterize the Thermodynamic state of the gas phase. These are satisfactory approaches for this type of problems. The robustness of the model proposed to analyze internal ballistic problems is shown by studying some experimental tests.