Modeling approaches for strongly non-homogeneous two-phase flows

In some situations, two-phase flows exhibit strongly non-homogeneous behaviors like the one where the flow domain is divided into a bubbly region and a droplet region separated by a free surface. In such a situation, the gas bubbles in the bubbly region and the gas sky in the droplet region can exhibit very different fields of velocity and temperature. The same observation can be made for the liquid droplets and the continuous liquid in the bubbly region. The classical ‘two-fluid model’ can be too limited in its capabilities to correctly predict such types of flow, especially in the region around the free surface. In this paper, we analyze three different models more adapted to this kind of situation. The first one is a four-field model where one set of balance equations is written for each of the four fields: continuous liquid, continuous gas, liquid droplets and gas bubbles. This model is particularly heavy since it basically contains 12 balance equations. Therefore, two simplified two-field models have been written by summing the equations of the four-field model two by two, in two different ways. In the first two-field model, the equations are summed by region, giving three balance equations for the bubbly mixture and three balance equations for the droplet mixture. In the second two-field model, the equations are summed by phase, giving a model analogous to the usual two-fluid model, but with additional terms coming from the different fields interactions. The closure problem is discussed for each model and the three models are compared according to several criteria.