Two-size moment Eulerian multi-fluid method describing the statistical trajectory crossing: modeling and numerical scheme

Matthieu Boileau (1, 2) , Julien Lagarde (3) , Valentin Dupif (3, 4, 5) , Frédérique Laurent (3, 4) , Marc Massot (4, 3)

1 TONUS - TOkamaks and NUmerical Simulations
2 IRMA - Institut de Recherche Mathématique Avancée
3 EM2C - Laboratoire d'Énergétique Moléculaire et Macroscopique, Combustion
4 FR3487 - Fédération de Mathématiques de l'Ecole Centrale Paris
5 ONERA - The French Aerospace Lab [Palaiseau]

High fidelity modeling and simulation of turbulent dispersed two-phase flows is still a major challenge for many applications. Eulerian approaches are well suited for high performance computations of such flows. Recently, hybrid Eulerian methods that combine the multi-fluid approach-where the size is discretized-and the moment method were developed. On the one hand, in order to capture efficiently the size-polydispersion, two size moments were used on each interval of the size discretization (Two Size Moment method). On the other hand, the Anisotropic Gaussian (AG) velocity closure has been introduced as a relevant model to describe velocity dispersion occurring when the particles from the disperse phase have a significant inertia compared to the time scales of the flow, leading to particle trajectory crossings. The purpose of this contribution is to develop a model able to describe size and velocity dispersion, coupling the two-size moment Eulerian multi-fluid method and the anisotropic velocity closure. Adapted numerical schemes based on a relaxation method are provided. This new model (AG-TSM) is then evaluated on various test cases relevant to rocket propulsion and two-phase combustion.

Mots clés: polydisperse spray; two-size moment Multi-Fluid model; moment method; particle trajectory crossing; relaxation scheme

Domaines: Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Matthieu Boileau, Julien Lagarde, Valentin Dupif, Frédérique Laurent, Marc Massot. Two-size moment Eulerian multi-fluid method describing the statistical trajectory crossing: modeling and numerical scheme. 9th International Conference on Multiphase Flow, May 2016, Firenze, Italy. ⟨hal-01543507⟩