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

Laurent François (1, 2) , Joël Dupays (1) , Dmitry Davidenko (1) , Marc Massot (2)

1 DMPE, ONERA, Université Paris Saclay (COmUE) [Palaiseau]
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

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.

Mots clés: shooting method; solid propellant combustion; dynamical system; nonlinear surface pyrolysis; travelling wave solution

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Milieux fluides et réactifs; Mécanique des fluides [physics.class-ph]; Dynamique des Fluides [physics.flu-dyn]

Laurent François, Joël Dupays, Dmitry Davidenko, Marc Massot. Travelling wave mathematical analysis and efficient numerical resolution for a one-dimensional model of solid propellant combustion. Combustion Theory and Modelling, 2020, 24 (5), pp.775-809. ⟨10.1080/13647830.2020.1752943⟩. ⟨hal-02418793v2⟩