Solid propellant combustion in the low Mach one-dimensional approximation: from an index-one differential-algebraic formulation to high-fidelity simulations through high-order time integration with adaptive time-stepping - Département de mathématiques appliquées Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

Solid propellant combustion in the low Mach one-dimensional approximation: from an index-one differential-algebraic formulation to high-fidelity simulations through high-order time integration with adaptive time-stepping

Résumé

An unsteady one-dimensional model of solid propellant combustion, based on a low-Mach assumption, is presented and semi-discretised in space via a finite volume scheme. The mathematical nature of this system is shown to be differential-algebraic of index one. A high-fidelity numerical strategy with stiffly accurate singly diagonally implicit Runge-Kutta methods is proposed, and time adaptation is made possible using embedded schemes. High-order is shown to be reached, while handling the constraints properly, both at the interface and for the mass conservation in the gaseous flow field. Three challenging test-cases are thoroughly investigated: ignition transients, growth of combustion instabilities through a Hopf bifurcation leading to a limit cycle periodic solution and the unsteady response of the system when detailed gas-phase kinetics are included in the model. The method exhibits high efficiency for all cases in terms of both computational time and accuracy compared to first and second-order schemes traditionally used in the combustion literature, where the time step adaptation is CFL-or variation-based.
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Dates et versions

hal-02888035 , version 1 (03-07-2020)
hal-02888035 , version 2 (04-01-2024)

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Laurent François, Joël Dupays, Dmitry Davidenko, Marc Massot. Solid propellant combustion in the low Mach one-dimensional approximation: from an index-one differential-algebraic formulation to high-fidelity simulations through high-order time integration with adaptive time-stepping. 2020. ⟨hal-02888035v1⟩
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