Diffusion flames in condensed-phase energetic materials: Application to Titanium–Boron combustion

Abstract

The characteristics of a steady diffusion flame that arises at the interfaces of two condensed phase reactant streams that form an opposed counterflow are discussed. We assume that the flow is due to deformation from compaction or local heating and thermal expansion processes in the microscale environment of composite energetic materials. As a representative example of high temperature combustion of metal/intermetallic reactants, the overall reaction of titanium and boron to create titanium diboride products is considered under near isobaric conditions. The multi-component diffusion description uses a generalized Fick formulation with coefficients related to the binary diffusivities defined in the Maxwell–Stefan relations. A fairly simple depletion form with Arrhenius temperature dependent coefficients is used to describe the reaction rate. Several types of analyses are carried out at increasing levels of complexities: an asymptotic analysis valid in the limit of low strain rates (high residence time in the reaction zone), a constant mixture density assumption that simplifies the flow description, diffusion models with equal and unequal molecular weights for the various species, and a full numerical study for finite rate chemistry, composition-dependent density and strain rates extending from low to moderate values. All are found to agree remarkably well in describing the flame structure, the flame temperature and the degree of incomplete combustion. Of particular importance is the determination of a critical strain rate beyond which steady burning may no longer be observed. The analysis has a general character and can be applied to other condensed phase energetic material systems, where reaction and diffusion occur in the presence of flow and material deformation.