Drag force on bubbles in bubble swarms

Direct Numerical Simulations with a Front Tracking model have been used to study the hydrodynamic behavior of bubble swarms for the air/water system. In this work, we focus on the effect of the presence of neighboring bubbles on the drag as a function of the void fraction, especially at higher void fractions. Mimicking bubble swarms with a relatively small number of bubbles in a periodic domain, the number of bubbles was varied while keeping the overall void fraction constant. We have observed a strong hindered rise effect, while bubbles tend to arrange themselves in horizontal clusters. The observed minimum in the drag coefficient as a function of the number of bubbles at a fixed void fraction was related to the maximum number of bubbles that can coordinate themselves in a horizontal plane. The normalized drag coefficient increases for higher void fractions (i.e. hindered rise). Again, significant effects of horizontal bubble clustering on the drag coefficient were found and explained