Article Dans Une Revue Journal of Fluid Mechanics Année : 2025

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

Résumé

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. (2024). 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.
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Dates et versions

hal-04188956 , version 1 (28-08-2023)
hal-04188956 , version 2 (10-01-2025)

Identifiants

Citer

Arthur Loison, Teddy Pichard, Samuel Kokh, Marc Massot. 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. Journal of Fluid Mechanics, 2025, 1003 (A27), pp.1--42. ⟨10.1017/jfm.2024.1200⟩. ⟨hal-04188956v2⟩
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