Effect of entrained bubbles on the structure of vortex rings

Abstract

The effect of entrained bubbles on the structure of a vortex ring is studied using particle image velocimetry. Quantitative information on the velocity and vorticity distribution within the vortex core is obtained from multiple images recorded with two 65 frames per second, 35 mm cameras. Bubble trajectories and velocities are also determined from these images. It is demonstrated that for certain combinations of vortex strengths and bubble diameters, a few microscopic bubbles, at very low overall void fraction, shift and macroscopically deform the structure of the vortex. For example, five 512 μm diameter bubbles, entrained by a vortex with core diameter of 2 cm and strength of 160 cm² s⁻¹, displace the core by 3.5 mm and fragment the core into two regions with peak vorticities that are 20% higher than the original maximum vorticity. The same phenomenon is observed with laminar, transitional and turbulent vortices. Dimensional analysis along with the experimental data show that the distortion is maximum when the bubbles settle, following entrainment by the vortex, in a region located between 20% and 40% of core radius. The governing dimensionless parameters and trends are identified and discussed. The vortex distortions are explained in terms of changes to the liquid momentum caused by the entrainment of the bubbles. It is argued and proven in detail in Appendix A that the change to the liquid momentum due to the presence of the bubble is equal to the bubble volume multiplied by the local stresses that exist in the absence of the bubble. These stresses include the gravity-induced (buoyancy) and hydrodynamic pressure gradients as well as viscous stresses. The buoyancy displaces the core of the vortex upward whereas the force due to hydrodynamic pressure gradients reduces the core size and as a result increases the vorticity. Estimated distortions agree with the experimental data.