Direct numerical simulation of deformable rising bubbles at low Reynolds numbers

We investigate numerically the dynamics of freely rising gas bubbles driven by buoyancy at low Reynolds numbers, focusing on two distinct characteristics: the clustering morphology and the probability density functions (p.d.f.) of the velocity fluctuations for bubbles. A modified Volume-of-fluid (VOF) method is implemented in our direct numerical simulations to circumvent the nonphysical coalescence between bubbles. Four values of the gas fraction are studied: 5%, 10%, 15%, and 20%. The Eotvos number and the Galileo number are fixed at Eo = 2 and Ga = 855, respectively. For a single rising bubble, the Reynolds number according to the terminal velocity and the bubble diameter is around 27, displaying an ellipsoidal shape. For a swarm of bubbles, both irregular and regular clustering configurations are observed in our numerical simulations as we vary the gas fraction, which can only be realized at high Reynolds numbers in the previous experiments due to the low gas fraction limit. Moreover, we find that the p.d.f.s for bubble velocity fluctuations exhibit distinctly different behavior from the high Reynolds number experiments. The horizontal components for these p.d.f.s approach Gaussian distributions only when the gas fraction is high, i.e., α=15% and 20%. It suggests that the strong bubble–bubble interaction through their flow wakes is an efficient way to trigger the flow into turbulent states.