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

Random Packs and Their Use in Modeling Heterogeneous Solid Propellant Combustion

Nonsteady burning of periodic sandwich propellants with complete coupling between the solid and gas phases

On the combustion of heterogeneous AP/HTPB composite propellants: A review

H ETEROGENEOUS solid energetic materials are widely used in the aerospace and defense industries in rockets, explosives, and diverse pyrotechnic devices. Their basic microstructure consists of oxidizer particles embedded in a polymeric binder. Two important classes of energeticmaterials are solid propellants and plastic bonded explosives. A typical composite solid propellant is composed ammonium perchlorate (AP) particles embedded in a polymer such as hydroxyl-terminated polybutadiene (HTPB) or polybutadiene acrylonitrile. A common variation is the addition of metal particles (e.g., aluminum) to raise the combustion temperature. Plastic bonded explosives consist of a heterogeneous mixture of high-explosive crystals (such as cyclotetramethylenetetranitramine or cyclotrimethylenetrinitramine) and a polymeric binder. Here, the discussion is restricted to composite solid propellants. The intent of the present survey is to provide a highlighted discussion of relevant work on the multidimensional computational simulation of heterogeneous solid propellant combustion. Routine numerical simulations are now being carried out, in which many of the physical characteristics of real propellants are mimicked, including random packing of oxidizer particles in a fuel binder, unsteady three-dimensional heat conduction within the solid, unsteady regressionof thenonplanar propellant surface, andcoupling with an unsteady three-dimensional combustion field sustained by reactantfluxes from the surface. Such computations require the use of massively parallel supercomputers, and even then there are limitations onwhat physics can be included. The ultimate goal is to develop a truly predictive simulation tool that can assist in design and optimization of propellant microstructures and propellant grain designs for internal solid rocket motors. Modeling and simulation of composite propellants will remain a vital task because solid rocket motors are critical to national defense, communications, space exploration, and eventually space tourism. The value of computational combustion is eloquently presented in a recent review paper [1]. II. Modeling

Modeling of Heterogeneous Propellant Combustion: A Survey

OpenMP is a relatively new programming paradigm, which can easily deliver good parallel performance for small numbers (

/pdf/producing-scalable-performance-with-openmp-experiments-with-4mw4qvehus.pdf

Producing scalable performance with OpenMP: experiments with two CFD applications

We examine a surface which mimics that of a heterogeneous propellant and through which passes distributed fluxes of oxidizer and fuel. The three-dimensional flames supported by these fluxes we calculated using a simple model. An elementary propellant packing model defines a variety of flux distributions according to the level of the slice through the propellant which defines the surface, and the effect of the different distributions on the combustion field and on the heat flux to the surface is discussed. An important geometric effect is identified. The more likely that arbitrary surface area fractions contain both ammonium perchlorate (AI) and binder fluxes, the greater will be the total heat flux to the surface from the AP/binder flames. The likelihood, and therefore the heat flux, is maximized for fuel-rich slices. This work is part of an ongoing study whose goal is a sophisticated numerical model of three-dimensional heterogeneous propellant burning.

J. Hoeflinger

Papers

Three-dimensional flames supported by heterogeneous propellants