Multi-Scale Modeling of Solid Rocket Motors: Time Integration Methods from Computational Aerodynamics Applied to Stable Quasi-Steady Motor Burning

Abstract

Here we consider the problem of e‐ciently computing the stable burn-back of a solid rocket motor when the motor is in the quasi-steady burning regime of operation. When themotorismodeledasacavitythatisfllledwithacompressible∞uidwithnormalmass, momentumandenergyinjectionfromthesolidpropellantsurface,theproblemposedisa standard one in steady computational aerodynamics. For large rockets such as the space shuttlesolidrocketbooster,theproblemofquasi-steadysolidrocketmotorballistic∞owis analogoustothesteadyaerodynamic∞owpastalargeaircraftsuchasaBoeing575orF15 ∞ying at speeds such that compressible ∞ow must be fully accounted for. One can adopt advanced time integration strategies developed for application to commercial or military aircrafttothesolidrocketmotorgrainburningtocomputeaseriesofrealizationsofsteady ∞owsasthegrainburnsbacktonearcompletion. Theslowregressionoftheburningsolid propellantsurfaceisanalogoustothemotionofcontrolsurfacesontheaircraftasitmoves through a controlled maneuver. Through the use of straightforward two-timing multiscale asymptotic analysis we develop the reduced quasi-steady description of the quasisteady burning regime for a model problem that is extensible to a full three-dimensional rocket. Wediscusstheapplication ofnow standardtime integration methodsfrom steady computationalaerodynamicstothetime-resolvedcomputationofstablequasi-steadymotor burning.