Regression fronts in random sphere packs: Application to composite solid propellant burning rate

Abstract

The burning rate of a composite solid propellant may be estimated by global modeling, such as the widely used BDP model. The backbone of such models is the “mixture law” that links the propellant burning rate r p with the burning rate of its own components, i.e., oxidizer r ox and binder r b. However, different laws are available in literature which all read: 1/ r p = q( ξ)/ r ox + (1 − q( ξ))/ r b, with q( ξ) a function of oxidizer volume fraction ξ. This work attempts in analyzing numerically the validity of those empirical formulations by surface regression computation. Composite propellants are modeled by a random packing of monomodal spheres and the evolution of the regression front is computed via the resolution of Hamilton–Jacobi equations. It is shown that the popular choice q( ξ) = ξ is fairly valid but only provided that burn rate ratio Z = r ox/ r b is about 1. When Z > 1, combustion surface is no longer plane and global burning rate deviates from postulated laws. A special regime is also noticed for high rate ratio Z (typically Z > 5) because combustion then preferentially takes place through adjacent oxidizer particles. Computed results occur to be correctly modeled by percolation theory. This hints that percolation is a common feature of propellant combustion and a critical percolation threshold on volume fraction is numerically found to be about ξ c ∼ 0.2. First validations show encouraging correlations with experimental data.