Modelling of the laminar dispersion force in bubbly flows from direct numerical simulations

In a previous study, we have shown that the momentum transfer between phases, which requires modeling in two-fluid models, is partly comprised of a laminar dispersion force connected to surface tension and pressure effects. This dispersion force, which is obtained by stepping away from the particle hypothesis, is important for the prediction of the void fraction distribution and therefore requires modeling. In this article, based on five direct numerical simulations of turbulent bubbly flows in a vertical channel, a model is proposed by using, inter alia, the structure of the pressure field in the vicinity of bubbles. The resulting model shows very positive results. It is expected to be valid through a wide range of flow regimes for spherical and deformable bubbles as long as the drag force closure is accurate. It is ready for use and can be integrated into an Euler-Euler calculation code.