Unsteady Dynamic Variables Method for Heterogeneous Solid Propellant Burning

An extension of the vortex ‐stream function method is developed for solving two-dimensional gas e ows at low Mach numbers (M <0:1) near localized heat release regions. The method allows simulation of the locally heated unsteady gas e ows for a wide range of density changes in the computational domain. Based on the developed method, a two-dimensional gasdynamic model for a multicomponent burning process is presented. The coupled, two-dimensionalNavier ‐Stokesequations,withtheconservationofenergyandspeciesandtheconservationofmass, comprisethemodel. Temperaturedependenciesforthegas thermophysical propertiesaretakeninto accountin the rangeof500‐3000K.Solutionsusingthevortex ‐streamfunctionmethodarepresentedthatdescribethemicroe ame structuresfor the combustion of a prescribed array of ammonium perchlorateoxidizer and a hydroxyl-terminated polybutadiene binder, the fuel. HE main objective of the paper is to establish a new method forthe numericalsimulation of unsteadye owsofviscous compressible gas at essentially subsonic speeds but with large changes density. Although the solution of the Navier ‐Stokes equations with chemicalreactionsisroutinelydone, 1;2 intheunsteadyproblemconsidered here, the complications of the coupled heat transfer to the solids and surface pyrolysis leads to the need to resolve wide ranges of timescales for both the acoustic and gasdynamic processes. The general idea of our method is to solve the gasdynamic equations using dynamic variables (vortex‐stream function ), where pressure is excluded from the motion equations. It has been established for some steady-state problems that methods using dynamicvariablesmaybemoreefe cientinsomecasesthanmethods using primitive variables (velocity‐pressure variables ), especially for the two-dimensional problems. 1i3 However, as is well known, dynamicvariablescannotbeemployedwhenunsteadycompressible gas movement is considered. Theproposedmethod,unsteadydynamicvariables (UDV),allows one to stay within the framework of an approach that implements vortex‐stream function variables and to preserve its higher efe ciency.Itwillbe shown that this can beachieved by the introduction of a new function, which required an additional transfer equation to be solved.