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Small-scale interface dynamic modelling based on the geometric method of moments for a two-scale two-phase flow model with a disperse small scale

Published online by Cambridge University Press:  20 January 2025

Arthur Loison Open the ORCID record for Arthur Loison [Opens in a new window] ,
Teddy Pichard Open the ORCID record for Teddy Pichard [Opens in a new window] ,
Samuel Kokh Open the ORCID record for Samuel Kokh [Opens in a new window]  and
Marc Massot Open the ORCID record for Marc Massot [Opens in a new window]
Arthur Loison*
Affiliation:
Institut Polytechnique de Paris, CMAP, CNRS, École polytechnique, Palaiseau 91120, France
Teddy Pichard
Affiliation:
Institut Polytechnique de Paris, CMAP, CNRS, École polytechnique, Palaiseau 91120, France
Samuel Kokh
Affiliation:
Service de Génie Logiciel pour la Simulation, Université Paris-Saclay, CEA, 91191 Gif-sur-Yvette, France
Marc Massot
Affiliation:
Institut Polytechnique de Paris, CMAP, CNRS, École polytechnique, Palaiseau 91120, France
*
†Email address for correspondence: [email protected]
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Abstract

In this contribution, we develop a versatile formalism to derive unified two-phase models describing both the separated and disperse regimes as introduced by Loison et al. (Intl J. Multiphase Flow, vol. 177, 2024, 104857). It relies on the stationary action principle and interface geometric variables. This contribution provides a novel method to derive small-scale models for the dynamics of the interface geometry. They are introduced here on a simplified case where all the scales and phases have the same velocity and that does not take into account large-scale capillary forces. The derivation tools yield a proper mathematical framework through hyperbolicity and signed entropy evolution. The formalism encompasses a hierarchy of small-scale reduced-order models based on a statistical description at a mesoscopic kinetic level and is naturally able to include the description of a disperse phase with polydispersity in size. This hierarchy includes both a cloud of spherical droplets and non-spherical droplets experiencing a dynamical behaviour through incompressible oscillations. The associated small-scale variables are moments of a number density function resulting from the geometric method of moments (GeoMOM). This method selects moments as small-scale geometric variables compatible with the structure and dynamics of the interface; they are defined independently of the flow topology and, therefore, this model allows the coupling of the two-scale flow with an inter-scale transfer. It is shown, in particular, that the resulting dynamics provides partial closures for the interface area density equation obtained from the averaging approach.

JFM classification

Mathematical Foundations: Hamiltonian theory Multiphase and Particle-laden Flows: Gas/liquid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1003 , 25 January 2025 , A27
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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