Hydrodynamics and shape reconstruction of single rising air bubbles in water using high-speed tomographic particle tracking velocimetry and 3D geometric reconstruction

Abstract

Abstract Time-resolved tomographic particle tracking velocimetry (TR-3D-PTV), also called 4D-PTV, is used here to obtain the instantaneous 3D liquid flow field information in the wake of a single rising bubble in water. Simultaneously, the bubble shape, size and velocity are determined by tomographic reconstruction of the 3D bubble shape. Both, tracer particles for PTV and bubbles, are imaged in a shadow mode with background illumination. The Lagrangian method used in this paper, especially combined with the shake the box algorithm, has big advantages compared to particle image velocimetry, in situations, where only low particle per pixel values can be obtained. In this research, single air bubbles of different sizes, with diameters of around 2.4 mm, 4.0 mm, 6.0 mm and 9.6 mm, were injected into stagnant de-ionized water. Their shape was reconstructed in 3D, and an equivalent bubble diameter was determined from this reconstruction. Compared to conventionally used 2D shadow imaging, this diameter is about 13% smaller. The 3D bubble trajectory can be analysed and decomposed into a sinusoidal function curve lateral projection and an ellipsoidal shape vertical projection. As the bubble diameter increases, the radius of the spiral trajectory is decreasing as well as the amplitude of vertical sinusoidal oscillation. The wake structure in the liquid behind the bubbles is also changing with bubble size: from simple vortex pairs for smaller bubbles to an intertwined structure of several twisted vortices for the bigger ones. Graphical abstract Three-dimensional bubble reconstruction (grey surface) and liquid stream lines coloured with velocity magnitude around an ascending air bubble in de-ionized water.