The accurate modelling of two-phase flows is a very active research field with significant implications for space applications, defense technologies, and geophysical phenomena. The derivation of models capable of describing the wide range of scales or the non-equilibrium effects that naturally arise in such flows, especially in the case of compressible high-velocity flows involving shocks, is still an open question.
The main goal of this presentation is to present a modelling strategy that allows for a systematic derivation of two-phase models within a variational framework. The strategy relies on two stages. First, the non-dissipative part of the model is derived by means of the Stationary Action Principle. A generic Eulerian framework, compatible with an underlying Lagrangian description, will be presented. The framework ensures that the resulting model admits a supplementary conservation law thus providing a coherent thermodynamic structure. The second stage introduces dissipative effects in accordance with the Second Principle of thermodynamics.
We will illustrate the application of this framework through several examples. After an introductory case to build familiarity, we will discuss the derivation of multi-fluid models which include a coupling between the relative velocity and velocity fluctuations. We will present a two-scale model which allows for the separated-to-disperse phase transition based on an interfacial energy budget that occurs in atomization processes. Finally, as a follow-up on the presentation of disperse two-phase flows, we will show how different levels of descriptions for the spray can naturally be integrated in the two-scale model.