General Burnback Analysis for Anisotropic and Heterogeneous Solid Propellants

Abstract

For several decades, researchers have successfully computed surface burnback to perform complex analyses and simulations related to the combustion of solid propellants. Many of these methods are heuristic or empirical, lacking a rigorous foundation, whereas others introduce numerical issues not related with the involved physics. This paper establishes a common theoretical and numerical core that bases the general study of burnback problems even in the case of designing nonconventional propellants. It starts with Piobert’s statement as a first principle, derives that the eikonal formulation holds for propellants with heterogeneous and anisotropic recession rates, and gives a general mathematical structure for both situations. Then, several configurations found by rocket designers are numerically solved in order to show the efficiency and the accuracy of the theory. The main conclusion is that a direct numerical integration of the eikonal equation using a time marching method is enough in terms of computational efficiency and accuracy to track the combustion surface of any anisotropic and heterogeneous solid propellant.