Clusterlike instabilities in bubble-plume-driven flows

Continuous release of gas bubbles in large numbers from a localized source in a liquid column, popularly known as "bubble plumes", is very relevant in nature and industries. The bubble plumes morphologically consist of a long continuous stem supporting a dispersed head. Through our direct numerical simulations using two-way coupled Euler-Lagrangian framework, we show that a bubble plume rising in a quiescent liquid column develops clusterlike instabilities for the Grashof numbers, Gr > 145. For levels Gr < 100, the stem is continuous with a small plume head, whereas at high buoyancy (Gr > 350), the plume stem shows intermittently passing puffing instabilities in the form of bubble clusters. The clusters are a group of bubbles localized in space with high concentration that travel upward with speed C-ph = 0.45U(c) and are separated by a distance of at least 5L(0), where U-c is the characteristic velocity and L-0 is the characteristic length based on the injection conditions. The bubble rise Reynolds numbers in the steady state for both the plume head and the stem shows Re proportional to Gr(0.45 +/- 0.03), and the proportionality constant is ten times higher in the plume stem than in the plume head. In the plume core, the spatial acceleration due to the bubble motion generates the turbulent production, whereas, at the plume edge, the small-scale fluctuations generate the mean vorticity. At high Gr, the clusters evolve due to the lift forces acting on the bubbles as a result of increase in the mean vorticity. While rising, bubbles entrain the liquid from the surroundings, and we found that the entrainment rate is not as strong as compared to the classical thermal plumes.