Random Packs and Their Use in Modeling Heterogeneous Solid Propellant Combustion

Abstract

It isshown thatrandom packsofspheresofvarioussizescan beconstructed thatmodelammonium ‐perchloratein-binder propellants in thesense that both thesize distributions and thepacking fractions of industrial propellant packs can be matched. Strategies for dealing with fractional numbers of large particles are addressed, as are strategies for dealing with a large number of very e ne particles (e ne powder). Fine powder is necessary in a threedimensional pack to achieve the required stoichiometric ratio of ammonium perchlorate to fuel binder, but is not necessary in a two-dimensional (disk) pack. Some preliminary calculations of the two-dimensional combustion e eld supported by a disk pack are presented, in which full coupling between the gas phase, the condensed phase, and the retreating nonplanar propellant surface is accounted for. Nomenclature D1;2 = reaction rate constants dj = mean diameter of particles E1;2 = activation energies L = length of a pack edge N = total number of particles Nj = number of particles in the jth class n j = number fraction of particles in the jth diameter classs n1;2 = pressure exponents Ru = universal gas constant R1;2 = reaction rates rb = surface regression rate T = temperature Vj = volume of particles in the jth class v j = volume fraction of particles in the jth class X = mass fraction of ammonium perchlorate (AP) Y = mass fraction of fuel binder Z = mass fraction of AP decomposition products ´ = surface function A = surface location A = level set function dee ning the pack