Purdue University Graduate School
thesis_final_M3.pdf (21.24 MB)


Download (21.24 MB)
posted on 2021-04-30, 16:23 authored by Maathangi GaneshMaathangi Ganesh
Mixing of stratified fluids due to motion of bubble swarms can happen through two major mechanisms. The first is the capture and transport of heavier liquid into the lighter layers by the bubble wake. The second is the mixing due to turbulent dispersion. Stratification also affects bubble dynamics in various ways, namely by reducing the horizontal and vertical bubble fluctuations and extent, altering the drag experienced by rising bubbles, and changing the wake dynamics. The objective of this study is to understand these explained phenomena by decoupling their effects from each other and studying them individually. CFD offers powerful capabilities to achieve the decoupling and perform in-depth analysis of the fluid flow.

Firstly, the study of mixing induced in stratified fluids by bubbly flow in a Hele-Shaw Cell will be performed. Simulations are run for a range of void fractions and Froude numbers. The confinement prevents turbulence production, and mixing occurs primarily due to transport of colder liquid into the hotter layers by the bubble wake. Bubbles move in a zigzag motion attributed to the periodic vortex shedding in their wake. We report the formation of horizontal clusters and establish a direct correlation between the size of clusters and the rise velocity of the bubbles. We report an increase in the buoyancy flux across the isopycnals as the void fraction increases. The fraction of energy production due to the buoyancy flux increases with the strength of stratification, giving rise to a higher mixing efficiency. At the same time, cross isopycnal diffusion is higher at weaker stratification strengths.

Subsequently, direct numerical simulations of up to 146 bubbles rising in unbounded stratified fluids are performed. Both the bubble dynamics and destratification effects caused by the bubble motion are analyzed. The importance of bubble deformability and bubble Reynolds numbers on the induced background mixing are studied by varying the $E\ddot{o}tv\ddot{o}s$ number in the range 1.55 to 4.95 and Reynolds number in the range 25 to 200. Highly deformable, high Reynolds number bubbles undergo path instabilities and give rise to higher levels of mixing. Liquid and bubble velocity fluctuations and pseudo-turbulence caused by the bubble motion in the unconfined setting are examined and are seen to play an important role in mixing statistics. An increase in turbulent kinetic energy (TKE) levels with void fraction is noted. TKE levels are seen to decrease slightly as the stratification strength is increased, indicating increasing stability and resistance to destratification. Regardless of the stratification strength, a kinetic energy spectrum slope value between $-3 \sim -3.25$ is reported depending on Reynolds number. The dependence of mixing parameters on the void-fraction of bubbles and stratification strength of the liquid is also presented.

Next, the study of buoyancy driven motion of a single air bubble in stratified liquid is undertaken. A range of parameters including Froude number, Reynolds number and Bond number are explored. The Reynolds and Bond numbers will be maintained at values where the bubble motion and wake can be assumed to be axisymmetric. Wake dynamics and drift-volumes associated with the bubble rising in the stratified fluid are analyzed. The presence of secondary and tertiary vortices, which are alternating in direction, in the wake of the bubble due to the negative buoyant force experienced by the isopycnals is reported. The isopycnals oscillate before coming back to their stable state and the frequency of oscillations increases with stratification strength. The dependence of drag coefficient, determined by an unsteady force balance, and steady state bubble velocities, on the above mentioned parameters are studied. Analysis of bubble rise in partial stratification reveals the differences between homogeneous and stratified mediums.

Since most stratified bubbly flows occur near the free surface, an attempt is made at modeling the bubble rise up-to the free surface and subsequent bubble bursting. A brief study of in-line bubble coalescence is also attempted and potential future work for bubbly flows with topological changes is discussed.


Degree Type

  • Doctor of Philosophy


  • Mechanical Engineering

Campus location

  • West Lafayette

Advisor/Supervisor/Committee Chair

Sadegh Dabiri

Additional Committee Member 2

Ivan C. Christov

Additional Committee Member 3

Martin A. Lopez-De-Bertodano

Additional Committee Member 4

Jun Chen

Usage metrics



    Ref. manager