An efficient and accurate numerical strategy for two-way coupling in unsteady polydisperse moderately dense sprays: application to Solid Rocket Motor instabilities

François Doisneau (1, 2) , Alaric Sibra (1, 2) , Joel Dupays (2) , Angelo Murrone (3) , Frédérique Laurent (1) , Marc Massot (1)

1 EM2C - Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion
2 ONERA - The French Aerospace Lab [Palaiseau]
3 ONERA - The French Aerospace Lab [Châtillon]

The accurate simulation of polydisperse sprays strongly coupled to unsteady gaseous flows at sufficiently high mass loading is a major issue for solid rocket motor optimization. The Eulerian Multi-Fluid method (MF) has proven to account for polydispersity efficiently, considering conservation equations for moments of the spray distribution in droplet size intervals. This describes droplet size sorted "fluids" which are all coupled to the gas through drag and heat transfer source terms. The potential of this model to deal with polydisperse spray-acoustics two-way interactions has not been addressed, which is an issue regarding both physics and code quality evaluation. Such an interaction is described through two strongly coupled systems of equations, which involve a large spectrum of scales in both time and space and require specific numerical methods in order to reach a good level of accuracy and predictability with an acceptable computational cost. In this paper, we define the physics and key issues of polydisperse spray-acoustics two-way interactions, identify physically relevant test cases and investigate the ability of MF systems to predict such a physics; in particular, we describe the numerical peculiarities related to the strong coupling, at high mass loading, of polydisperse sprays in unsteady gaseous flow fields. The case of small droplets and related very short time scales is carefully studied. We finally introduce, thoroughly study, and adapt to an industrial-oriented code a new numerical strategy for polydisperse moderately dense sprays with a high level of flexibility, which can be adapted to accuracy needs. The method is tested on an unsteady polydisperse solid rocket motor case to prove the feasibility and the efficiency of the approach for two-way coupling in a supersonic nozzle, which is representative of the difficulties encountered in a wide range of unsteady flows.

Mots clés: Polydisperse moderately dense spray; Eulerian Multi-Fluid; Two-way coupling; Two-phase acoustics; Splitting strategy; Solid rocket motor

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Analyse numérique [math.NA]; Physique Numérique [physics.comp-ph]; Milieux fluides et réactifs; Acoustique [physics.class-ph]; Acoustique [physics.class-ph]

François Doisneau, Alaric Sibra, Joel Dupays, Angelo Murrone, Frédérique Laurent, et al.. An efficient and accurate numerical strategy for two-way coupling in unsteady polydisperse moderately dense sprays: application to Solid Rocket Motor instabilities. 2012. ⟨hal-00745991v1⟩