Diffusion Flame Calculations for Composite Propellants Using a Vorticity-Velocity Formulation

Abstract

A two-dimensional model has been developed to study the flame structure above composite propellants using a vorticity-velocity formulation of the transport equations. This formulation allows for a more stable, robust, accurate, and faster solution method compared with the compressible Navier-Stokes equations in the low Mach flow regime. The model includes mass and energy coupling between the condensed and gas phases. The condensed-phase model is based on previously reported one-dimensional models and includes distributed decomposition and multistepreaction kinetics. The model uses a detailed gas-phase kinetic mechanism consisting of 37 species and 127 reactions. The kinetic mechanism and species diffusion determine the flame structure of the system; no assumptions are made beforehand, aside from appropriate boundary conditions. Numerical studies have been performed to examine the flame structure above an ammonium-perchlorate/hydroxy-terminated-polybutadiene propellant. The predicted flame structure was found to be qualitatively similar to the Beckstead-Derr-Price model with both premixed and diffusion flames present. Results present significant insight into ammonium perchlorate's ability to control a propellant's burning rate and illustrate the importance of the primary diffusion flame in composite propellant combustion.Nomenclature c p = heat capacity, erg=g=K g = gravitational acceleration vector, cm=s 2 h = specific enthalpy, erg=g i = species index M = Mach number r = radial distance, cm r = radial direction T = temperature, K t = time, s v = velocity vector, cm=ŝ v = diffusion velocity, cm=s W = molecular mass, g=mol _ w = chemical production rate, g=cm 3 =s Y = mass fraction z = axial direction = thermal conductivity, erg=s=cm=K = viscosity, poise = density, g=cm 3 = dissipation function ! = vorticity vector, 1=s

Gas phase flame structure of solid propellant sandwiches with different reaction mechanisms

“…3. The simulated temperature contours with a flat burning surface matches qualitatively with those of the simulations in [13] where a flat surface has been adopted. However, when a realistic curved burning surface profile is used for the simulation, the high temperature region tilts towards the middle lamina near the burning surface.…”

“…A gas phase reaction mechanism comprising 45 species and 232 reactions was developed by Beckstead and Pudupakkam [12] for one-dimensional description of gas and condensed phases. Gross et al [13] used a 127-step reaction mechanism with 37 species to study the flame structure of an AP based sandwich with a flat burning surface. In a later work, Gross et al [14] correlated the results of this detailed mechanism to a 4-step global mechanism for the gas phase reactions involving symbolic species which was used in the three-dimensional simulations of actual propellant geometry at affordable computational expense.…”

A Comparison between the OpenFOAM® Toolbox and Custom-built Numerical Solvers for Composite Solid Propellant Combustion Modeling

“…These models successfully predicted a flame structure above an AP/HTPB composite propellant analogous to the theoretical picture predicted by the Beckstead-Derr-Price (BDP) combustion model ( Figure 1). The BDP-flame structure is comprised of a premixed flame formed by the decomposition of AP (1), a primary diffusion flame comprised of a mixture of AP and HTPB decomposition products (2), and a final diffusion flame formed by products from the first two flames (3).…”

“…There have been numerous efforts in recent years to develop a predictive model for the combustion of ammonium perchlorate (AP) and hydroxyl-terminated-polybutadiene (HTPB) solid composite propellants [1][2][3][4][5][6][7][8][9] . These models successfully predicted a flame structure above an AP/HTPB composite propellant analogous to the theoretical picture predicted by the Beckstead-Derr-Price (BDP) combustion model ( Figure 1).…”

Steady-State Combustion Mechanisms of Ammonium Perchlorate Composite Propellants

“…This unique characteristic of AP is due to the flame structure formed above the propellant surface, an artifact of the chlorine and the excess oxygen available in AP. Gross and Beckstead [1] recently calculated the flame structure above an AP/HTPB propellant using a detailed gas-phase kinetic mechanism and species diffusion. In contrast to previous AP composite propellant models, no assumptions were made concerning the flame structure, aside from appropriate boundary conditions; instead, the detailed transport and kinetic processes completely determined the flame structure.…”