Multiscale modeling of solid rocket motors: Computational aerodynamics methods for quasi-steady burning

We consider the problem of efficiently computing the stable burnback of a solid rocket motor when the motor is in the quasi-steady burning regime of operation. When the motor is modeled as a cavity, filled with a compressible fluid with injection from the solid-propellant surface, the problem is a standard one in steady computational aerodynamics. For large rockets, the problem of quasi-steady solid rocket motor core flow is analogous to the steady aerodynamic flow past a large aircraft flying at speeds such that compressible flow effects must be included. One can adopt advanced time-integration strategies that have been applied to commercial or military aircraft to solid rocket motor grain burning to compute a series of steady flows as the grain burns back to near completion. The slow regression of the burning solid-propellant surface is analogous to the motion of control surfaces on the aircraft. With straightforward two-timing, multiscale asymptotic analysis we develop a reduced quasi-steady description of the quasi-steady burning that is extensible to three dimensions. We show how to integrate reduced equations for stable quasi-steady motor burning and use the multigrid method as a representative method to obtain the steady flows in the frozen configurations.