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.
Origine | Fichiers produits par l'(les) auteur(s) |
---|