Eigenvalue Analysis and Calculations for the Deflagration of Porous Energetic Materials in the Merged-Flame Regime*

Abstract

Analytical and numerical calculations of the structure and burning rate of a deflagrating porous energetic material are presented for the limiting case of merged condensed and gas-phase reaction zones. The reaction scheme is modeled by a global two-step mechanism, applicable to certain types of degraded nitramine propellants and consisting of sequential condensed and gaseous steps. Taking into account important effects due to multiphase flow and exploiting the limit of large activation energies, a theoretical analysis may be developed based on activation-energy asymptotics. For steady, planar deflagration, this leads to an eigenvalue problem for the inner reaction-zone, the solution of which determines the burning rate. Numerical solutions give a reasonably complete description of the dependence of the structure and burning rate on the various parameters in the problem, and show excellent agreement with analytical results that are obtained in a more limited parameter regime in which most of the heat release is produced by the condensed-phase reaction and the porosity of the solid is small. These calculations indicate the significant influences of two-phase flow and the multiphase, multi-step chemistry on the deflagration structure and the burning rate, and thus serve to define an important parameter regime that supports the intrusion of the primary gas flame into the two-phase condensed decomposition region at the propellant surface.

Keywords:

• Porous energetic materials
• burning-rate eigenvalue
• deflagration
• two-phase flow

Notes

*Work supported by the U. S. Department of Energy under Contract DE-AC04-94AL85000.