The dynamics of dispersed phase flows is rather intricate as a result of the complex momentum and heat transfer between the dispersed phase and the surrounding fluid. In the framework of the PeliGRIFF project, our study is limited to incompressible flows and Reynolds number based on the length scale of a single particle or drop below 1000, which still leaves a large scope of investigation. Hence, the flow might sometimes be considered as turbulent at the level of the flow domain but is often still either laminar or inertial at the level of the drop/particle.
The number of industrial and natural flows that fall into the category of dispersed phase flows is quite large, ranging from solid particles transport in pipelines or rivers to bubble columns in catalyst reactors, as illustrated below.
The key issue of dispersed phase flows is the proper modelling of the momentum exchange between the continuous and dispersed phases:
The elementary sketch above entails the following major issues:
As collectively admitted by the international multiphase flow community as a sound approch, we suggest to employ a three-level multi-scale analysis where the three levels (of scales) corresponds to:
As an illustration, we show below on the problem of solid particles transport what are the typical systems and their size as we apply our 3-level multi-scale approach:
DNS illustrations from Markus Uhlmann's group, KIT, Germany
At the micro scale, both phases are modelled in a direct way and the coupling is achieved via classical interface boundary conditions. In PeliGRIFF, the solution of the fluid conservation equations relies on a Finite Element or Finite Volume scheme and an operator splitting time integration scheme. Depending on the nature of the dispersed phase, we employ:
At the meso scale (this model is considered for solid particles or non-deformable bubbles/drops only), the dispersed phase is still modelled at the micro scale, i.e., in a direct fashion, while the continuous phase (the surrounding fluid) is solved in an average way, which implies that a computational cell is much bigger than a particle/drop/bubble. Therefore, a first closure law is required to account for the hydrodynamic interactions.
Finally, at the macro scale, both phases are described as continuum and a second closure law needs to be introduced to model the dispersed phase behavior.