A unified two-scale gas-liquid multi-fluid model with capillarity and interface regularization through a mass transfer between scales
Résumé
In this contribution, we derive a gas-liquid two-scale multi-fluid model with capillarity effects to enable a novel
interface regularization approach for multi-fluid models. As this unified modelling is capable of switching from the
interface representation of a separated to a disperse regime it lays a new way of modelling regime transitions as it
occurs in atomization processes. Above a preset length threshold at large scale, a multi-fluid diffuse interface model
resolves the dynamics of the interface while, at small-scale, a set of geometric variables is used to characterize
the interface geometry. These variables result from a reduced-order modelling of the small-scale kinetic equation
that describes a collection of liquid inclusions. The flow model can be viewed as a two-phase two-scale mixture,
and the equations of motion are obtained thanks to the Hamilton’s Stationary Action Principle, which requires
to specify the kinetic and potential energies at play. We particularly focus on modelling the effects of capillarity
on the mixture’s energy by including dependencies on additional variables accounting for the interface’s geometry
at both scales. The regularization of the large-scale interface is then introduced as a local and dissipative process.
The local curvature is limited via a relaxation toward a modified Laplace equilibrium such that an inter-scale
mass transfer is triggered when the mean curvature is too high. We propose an original numerical method and
assess the properties and potential of the modelling strategy on the relevant test-case of a two-dimensional liquid
column in a compressible gas flow.
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