Experimental Study on Three-Dimensional Bubble Rising Behaviours by Virtual Stereo Vision

This study addresses the measurement of three-dimensional (3D) bubble rising behaviour in still water with bubble equivalent diameters ranging from 2.61 mm to 5.11 mm using high-speed imaging and virtual stereo vision technology. The bubble shape, 3D trajectory/velocity, displacement angular frequency and terminal velocity of bubbles are analysed. The bubble equivalent diameter is obtained by the elliptic volume method. The bubbles are divided into small and large bubbles with a critical equivalent diameter of 4.49 mm, according to whether they are accompanied by deformation. The small bubbles (deq<4.49 mm) are spherical or ellipsoid, while the large bubbles (deq >= 4.49 mm) exhibit ellipsoid, mushroom and hat shapes. The 3D trajectory is obtained by 3D reconstruction of bubble centroid coordinates. The rising trajectory of small bubbles shows 3D spiral motion, while the pitch increases gradually with the increase in the equivalent diameter. The trajectory of large bubbles is a two-dimensional (2D) zigzag. The bubble displacement curves in x- and z-directions are evaluated with third-order Fourier fitting. The results show that the bubble displacement frequency in the xand z-directions decreases with the increasing bubble diameter, and the displacement frequency in the xdirection is larger than that in the z-direction. The relative proportions of the viscous force, buoyancy, surface tension and inertial force on bubbles with different equivalent diameters are different, which leads to three trends in the vertical velocity of bubbles within the diameter range of this study. Finally, the bubble terminal velocity in still water is investigated. The terminal velocity first decreases and then increases with the increase in the equivalent diameter. The minimum value is 16.17 cm/s when the diameter of the bubble equivalent diameter is 4.49 mm. Moreover, the applicability of some classical prediction models is discussed.