Quasi-One-Dimensional Modeling of Internal Ballistics and Axial Acoustics in Solid Rocket Motors

摘要

An unsteady quasi-one-dimensional flow solver for simulating internal ballistics and axial acoustic fluctuations in solid rocket motors is presented in this paper. Higher-order numerical solutions of quasi-one-dimensional governing equations are prone to numerical oscillations due to the nonconservative form of the governing equations and the nonsmooth axial variations of the cross-sectional area. Adding artificial dissipation to a central scheme is found to be inadequate for suppression of such oscillations, and so a simple low dissipation shock-capturing scheme (named SLAU2) is used instead. The inherent numerical dissipation of this scheme is helpful in the proper capturing of steep-fronted acoustic waves (that develop at the onset of triggered instabilities) without undesirable numerical damping of the acoustic waves. Using the new solver, a procedure for computing characteristic frequencies, corresponding mode shapes, and damping rates is proposed and validated for a motor with a cylindrical grain geometry. The quasi-one-dimensional formulation can accommodate either slip or nonslip boundary conditions for axial velocity at grain boundaries and predict damping rates accordingly. The difference in decay rates obtained with these two boundary conditions is shown to be the flow turning contribution.