Cavitation in Vortex and Mixing in Stratified Fluids

Pranav Mohan, Purdue University

Abstract

Cavitation is ubiquitous in nature and scientific application where it might hinder through noise, vibration or erosion which eventually leads to reduced performance. Similarly, rising bubbles are employed in several industrial applications to homogenize the fluid. This thesis sheds light on special applications of these two phenomena. Once a bubble has been captured by a vortex core, the low (sometimes negative) pressure in the core causes the cavitation bubble to elongate axially while the radius of the bubble oscillates with time. Three dimensional compressible Navier-Stokes equations with surface tension are numerically solved using an all-mach solver on Basilisk software. The bubble dynamics can be categorised into separate stages: spherical growth, pinching, elongation and fragmentation. As the cylindrical bubble grows, it increases the vortex core radius. The flow and the bubble dynamics are strongly coupled. The effect of changing cavitation number and bubble to vortex size ratio has been explored. The bubble sizes and dynamics at different time steps have also been recorded. When the pressure in the core is negative, the bubble continues to grow axially forming a long tube, which is also observed in experiments. In oceans, density varies with depth due to varying salinity and temperature gradient, which prevents the vertical exchange of heat, carbon, dissolved oxygen, and nutrients as well as blooms the population of harmful bacteria such as cyanobacteria. The rising motion of a single or cluster of bubbles creates an upflow that can cause homogenization or destratification. Confined bubble columns are used for microelectronic cooling as well as in chemical reactors for mixing stratified fluids without any mechanical agitation or power. To begin realizing this complex multi-phase flow system to better understand mixing, we start with a simplified problem of a single air bubble rising in a confined Hele-Shaw channel. We performed a time-resolved stereoscopic Particle Image Velocimetry (PIV) measurement to characterize the bubble wake. Pure water and varying salt concentration were used to achieve a linear density stratification corresponding to Froude numbers (Fr) ranging from 22.1 to 40.7. Due to the large velocity dynamic range for PIV, we enhanced the signal to noise ratio of our correlation planes with pyramid correlation. We found a significant out of plane velocity component in both homogenous and stratified fluid in the vicinity of the bubble, which was assumed to be negligible in previous studies with confined fluid. The wake of the bubble carries the higher density fluid to the top, which later releases from the wake to form the reverse jet. This buoyant jet has been characterized for different Fr. Eulerian coherent structures are also considered to describe the flow. The rising bubble generates vortices that shed downstream and decay with varying timescales for different Fr. The difference in the coherent structures and decay coefficient leads to a different level of mixing with Fr. The scope of this research is in applications homogenizing the stratified flow using rising bubbles.

Degree

M.Sc.

Advisors

Ardekani, Purdue University.

Subject Area

Fluid mechanics|Mechanics|Microbiology

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