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

Abstract

Hydrodynamics and shape reconstruction of single rising air bubbles in water using high-speed tomographic particle tracking velocimetry and 3D geometric reconstructionTime-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 (STB), has big advantages compared to particle image velocimetry (PIV), in situations, where only low particle per pixel (ppp) 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. Lensless Particle Image VelocimetryThe application of lensless imaging to particle image velocimetry (PIV) is demonstrated. Lensless PIV eliminates the need for imaging lenses to measure flow fields near a surface. Only the camera sensor, a thin mask, and computations are required to image particles in a flow field and to compute the velocity field. The small form factor could enable embedded sensors for near-wall measurements. Flow field measurements are obtained simultaneously for a lensless system and lens-based 2D PIV system, and several different reconstruction techniques are demonstrated. The reconstructed particle images and computed velocity fields compare well for both a uniform and shear flow. The potential for stereo and 3D volumetric PIV with a single camera sensor is demonstrated through different image reconstruction approaches.