Interaction of a Vortex Ring With a Single Bubble/Rigid Buoyant Particle: Effect of Particle Shape and Vortex Curvature

Abstract

Multiphase turbulent flows are found in many natural flow settings like plankton and air bubbles in the upper ocean, formation of ice clouds, sediment-laden river flows, vapour bubbles in geysers, and industrial applications like ship hydrodynamics, paper industry, oil transportation, pollutants in the atmosphere, catalytic particles and bubble columns in process technology, to name a few. These flows involve complex and coupled interactions between particles/bubbles and the hairpin vortical structures present in the turbulent boundary layers. However, due to the high number density, multi-scale nature, and unsteadiness of the hairpin vortices, understanding vortex-particle/bubble interactions is challenging, and the dispersed phase makes them more formidable. While bubble deformability further adds to the complexity involved, particle anisotropy makes the problem more interesting, as discussed in recent review articles. In this thesis, we experimentally study an idealisation of multiphase turbulent flow through the interaction of a vortex ring with a rigid buoyant particle/bubble, focusing on the effect of particle shape and the ring's initial aspect ratio on such interactions.

The thesis broadly comprises three main parts. In the first part, we study the interaction of a circular vortex ring with a rigid buoyant particle, as a simplification of particle-laden turbulent flow. The focus of this work is on the effect of particle shape, quantified by the particle shape factor, on the dynamics of both the ring and the particle. An important aspect in multiphase turbulent flow is the vortex curvature, which influences the dynamics of the hairpin vortices. To better understand this, in the second part, we study the interaction of an elliptic vortex ring with a rigid buoyant spherical particle, focusing on the effect of the ring's initial aspect ratio on the ring and particle dynamics. In the third part, we are interested in exploring the effect of vortex curvature on the interaction between a vortex ring and a bubble by considering an elliptic vortex ring, with the vortex curvature varying along the elliptical vortex core axis. In this case, the finite surface tension at the two-phase interface introduces interesting physics.

In the first part, we experimentally studied the interaction of a rigid buoyant particle with a vortex ring in water, focusing on the effect of the particle shape, quantified by the particle shape factor (χ), defined as the ratio of an oblate spheroid's symmetric axis to its normal axis. This gave us a range of particle shapes: disk (χ=0), oblate spheroid (0 < χ < 1), sphere (χ=1), prolate spheroid (χ > 1), and rod (χ → ∞). Laminar, transitional, and turbulent vortex rings were studied by varying the ring Reynolds number (Re_Γ). During the interaction, the particle is entrained into the low-pressure vortex core and settles in a radial equilibrium location. The particle-ring pair continues to move together, while the particle rotates about the toroidal core axis, followed by a reduction in the ring convection speed (ΔU^*). From a particle dynamics perspective, we found that particle alignment, angular velocity, angular deceleration, and rotational kinetic energy vary strongly with the particle shape factor (χ). The particles align with their axis of minimum mass moment of inertia during particle capture. While the disk and oblate spheroid exhibit tumbling motion after capture, the prolate spheroid and rod exhibit spinning motion inside the vortex core. While the disk rotates the slowest, the sphere rotates the fastest. The particle angular acceleration is sensitive to the shape factor (χ) at initial times after capture and becomes nearly insensitive to χ at later times. The initial angular deceleration is maximum for the disk and minimum for the sphere. While the rotational kinetic energy of the disk (χ=0) is the lowest, that of the sphere (χ=1) is the highest. The rod, oblate and prolate spheroids have intermediate values of the above-mentioned quantities. On the ring dynamics, the ring convection speed, azimuthal vorticity, circulation, and enstrophy are strongly influenced by the particle shape factor (χ). This reduction in convection speed is largest for the disk (χ=0) and smallest for the sphere (χ=1), with the other shapes taking intermediate values. As the convection speed is an integral measure, the azimuthal (transverse) vorticity fields yield a more detailed view of the interaction. The particle shape factor (χ) influences the peak azimuthal vorticity and the azimuthal enstrophy. Highest reductions in peak azimuthal vorticity and azimuthal enstrophy are found for the disk, while the reductions are lowest for the sphere. These results show that anisotropic particles are more effective at causing ring disruption than the isotropic sphere, with the disk being the most effective.

The dynamics of the hairpin-shaped vortical structures in turbulent boundary layers are known to be influenced by the vortex curvature, which further complicates the behaviour of these vortices in the presence of the dispersed phase. In the second part of this thesis, we explored the effect of vortex curvature on the interaction by considering an elliptic vortex ring and a rigid buoyant sphere, where the ring's initial aspect ratio (AR₀) is a critical parameter. Two elliptic vortex rings (AR₀=0.4 and 0.6) were investigated to contrast their behaviour with the well-studied circular ring (AR₀=1), for a range of particle sizes (D_p) and ring Reynolds numbers (Re). Using high-speed visualisations, we measure quantities related to the dynamics of both the ring and the particle, such as the ring's axis-switching time period, trajectory, and convection speed, as well as the particle's angular velocity. While the non-interacting (base) ring's initial aspect ratio (AR₀) influences the relation between its trajectory (and hence its convection speed) and the input piston impulse used to generate the ring, AR₀ does not significantly affect the behaviour of the reduction in ring convection speed (ΔU^*) with particle size. This could happen because the input piston impulse (I) directly affects only the initial convection speed (U₀). Since ΔU^* is dependent on the ratio of speeds, the initial convection speed (U₀) and thus the piston impulse (I) are not vital quantities that affect the reduction of convection speed itself. However, the ring's axis-switching time period is delayed by the presence of the particle during their interaction. On the dynamics of the particle, its angular velocity (Ω_p) varies across AR₀ at lower ring Reynolds numbers (Re), while at higher ring Reynolds numbers, AR₀ has a negligible effect on Ω_p.

In the third part, as the introduction of finite surface tension to the two-phase interface leads to additional interesting physics, such as bubble deformation, oscillation, coalescence, and break-up, we investigate the effect of vortex curvature on the interaction between a vortex ring and a bubble, with the bubble representing a deformable dispersed phase. We quantify the vortex curvature by an elliptic vortex ring's initial aspect ratio (AR₀), where AR₀<1 represents elliptic vortex rings of different vortex curvatures and AR₀=1 represents a circular vortex ring. The study is carried out at three aspect ratios, namely, AR₀=0.4, 0.6, and 1. High-speed visualisations are performed to measure the vortex ring dynamics and bubble dynamics from the top and side views. In the first part, we explore the effect of the bubble capture angle (θ_c) for the elliptic ring with AR₀=0.6, where we find that θ_c has a strong influence on the probability of bubble capture, the final number of daughter bubbles (N_b) and the reduction in the ring's convection speed (ΔU^*). Bubble capture at the high-curvature ends of the elliptic vortex axis is more probable than that at the low-curvature ends. The number of broken bubbles is larger at the high-curvature ends, corresponding to a larger reduction in the ring convection speed. We also attempt to elucidate distinct bubble breakup modes for the extreme values of the capture angle. Additionally, the bubble capture and elongation delay the ring's axis switching time period. In the second part of the elliptic ring-bubble interaction study, we explore the effect of AR₀ on the interaction dynamics for a range of Weber number (We) values. The ring's initial aspect ratio is found to influence the bubble occupancy, the final number of daughter bubbles, and the reduction in the ring's convection speed, at higher We. The most elliptic ring (AR₀=0.4) is found to cause a relatively lower bubble occupancy, a lower number of daughter bubbles, and a higher reduction in the ring's convection speed. Although these results could have implications for bubbly turbulent flows, additional factors, such as background shear and a multitude of hairpin vortices and bubbles, render the situation more complex. However, the current study helps us gain insight into the behaviour of these hairpin vortices and bubbles in an idealised scenario.