Travelling wave mathematical analysis and efficient numerical resolution for a one-dimensional model of solid propellant combustion

TL;DR

This paper develops a mathematical and numerical framework for analyzing a one-dimensional solid propellant combustion model, establishing existence of travelling waves and introducing an efficient shooting method validated against CFD simulations.

Contribution

It extends dynamical system tools to prove existence of travelling waves in solid propellant combustion and introduces a novel shooting method for efficient numerical resolution.

Findings

Successful proof of travelling wave existence and uniqueness.

The shooting method efficiently solves the model without space discretisation.

Comparison shows the method's effectiveness against CFD results.

Abstract

We investigate a model of solid propellant combustion involving surface pyrolysis coupled to finite activation energy gas phase combustion. Existence and uniqueness of a travelling wave solution are established by extending dynamical system tools classically used for premixed flames, dealing with the additional difficulty arising from the surface regression and pyrolysis. An efficient shooting method allows to solve the problem in phase space without resorting to space discretisation nor fixed-point Newton iterations. The results are compared to solutions from a CFD code developed at ONERA, assessing the efficiency and potential of the method, and the impact of the modelling assumptions is evaluated through parametric studies.