Two-scale modelling of two-phase flows based on the Stationary Action Principle and a Geometric Method Of Moments

Abstract

In this contribution, we introduce a versatile formalism to derive unified two-phase models describing both the separated and disperse regimes. It relies on the stationary action principle and interface geometric variables. The main ideas are introduced 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 pursues the goal of unifying the modelling of a fully-coupled two-scale flow. It is particularly showed that the resulting dynamics provides closures for the interface area density equation obtained from the averaging approach. The extension to mass transfer from one scale to the other including capillary phenomena, as well as the extension to multiple velocities are possible and proposed in complementary works.

References in corpus (9)

• Symmetric form for the hyperbolic-parabolic system of fourth-gradient fluid model
• A new form of governing equations of fluids arising from Hamilton's principle
• Hyperbolic Models of Homogeneous Two-Fluid Mixtures
• Statistical modeling of the gas-liquid interface using geometrical variables: toward a unified description of the disperse and separated phase flows
• Hamilton's Principle and Rankine-Hugoniot Conditions for General Motions of Mixtures
• High order moment model for polydisperse evaporating sprays towards interfacial geometry
• A hierarchy of simple hyperbolic two-fluid models for bubbly flows
• Validation strategy of reduced-order two-fluid flow models based on a hierarchy of direct numerical simulations
• A unified two-scale gas-liquid multi-fluid model with capillarity and interface regularization through a mass transfer between scales