A center-averaged two-fluid model for wall-bounded bubbly flows

In a bubbly flow, the presence or absence of the dispersed phase (gas) at a given instant and a given point in space depends on two factors, namely: (a) the forces acting on the bubble (or, more generally the dispersed particle) as a whole and responsible for its movement, and (b) the shape (geometry) of the bubble, which contributes to define if the spatial point in question lays inside or outside the bubble at that instant.Based on that point of view, we propose herein a two-fluid model that involves a particle-center-averaging procedure for the disperse phase, and a re-interpretation and post-processing of the results obtained. This center-averaged approach averages the disperse phase (bubbles) based on a particle center indicator function, while retaining standard phase indicator averaging for the continuous phase (liquid). The solution fields obtained are then post-processed to introduce the geometry of the bubbles in order to recover the values that are representative of the measured fields. The key idea here is to separate the geometric aspect from the dynamic aspect of the problem into two independent, successive steps. Tracking the bubble centers makes it possible to model the wall-induced forces more accurately. We take advantage of this fact to propose models for the wall normal force for very small Weber numbers and for Weber numbers of order unity. The additional tangential drag induced by the wall is also examined in light of recent experimental evidence. The resultant two-fluid model may be easily incorporated into existing two-fluid model codes. Results obtained with the new model showing agreement with experimental data are also presented.