ECCOMAS 2024

A unified two-scale gas-liquid two-fluid model with capillarity and interface regularization through a mass transfer between scales

  • Loison, Arthur (CMAP Ecole Polytechnique)
  • Massot, Marc (CMAP Ecole Polytechnique)
  • Kokh, Samuel (CEA)
  • Pichard, Teddy (CMAP Ecole Polytechnique)

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In this contribution, we derive a gas-liquid two-scale model with capillarity effects along with a novel interface regularization approach. The framework that we consider is able to account for different interface configurations thanks to a unified approach capable of encompassing the interface representation of both separated and disperse regimes as it occurs in atomization processes. Above a preset length threshold, at large-scale, a diffuse interface two-fluid 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 cloud of liquid inclusions with the Geometric Method Of Moments. 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 \textit{via} a relaxation toward a modified Laplace equilibrium such that an inter-scale mass transfer is triggered when the mean curvature is too high. A numerical strategy along with simulations are proposed to assess the properties of the modelling and numerical strategy.