Bubble cloud configuration effect on the added mass

Understanding the mechanisms that control the dynamics of bubble clouds is essential to many industrial processes in the energy and chemical realms. Due to the complexity of the two-phase flow configurations, modeling the physics of the phenomena driving the mixing of bubbles within a liquid matrix is still a major challenge. One of the weaknesses of most existing two-phase flow models is due to the incomplete handling of bubble dispersion. This difficulty comes from the fact that dispersion can be driven by numerous complex phenomena, such as turbulence, local pressure distribution, bubble to bubble interaction, etc. In this study, we introduce the effect of added mass fluctuations on the dispersion of small bubbles. Existing models based on the Euler–Euler approach do not take into account local flow variations due to bubble distributions. Therefore, these models do not correctly describe fine dispersion features. Solving the potential flow around N bubbles allows to take into account the effect of the added mass on bubble cloud distributions. To this aim, a complete added mass model, which includes local bubble configurations via the void fraction gradient, is developed. The void fraction gradient allows us to account for the asymmetry of the bubble cloud around a single central bubble. Consequently, the proposed model can only represent regular and irregular bubble cloud distributions. This methodology results in a more consistent consideration of the added mass effects as well as Meshchersky's force, which should be included in hydrodynamic two-phase flow models. The proposed approach can be implemented in Euler–Euler models intended to consider the dispersion of bubbles caused by the effect of added mass.