Thesis: Turbulent Rayleigh Benard Convection (RBC) with and without rotation and (ii) Path instability of a rising bubble

PhD defense: Viswa Maitreyi Moturi

Title: Turbulent Rayleigh Benard Convection (RBC) with and without rotation and (ii) Path instability of a rising bubble

Team: MecaFlu

Abstract: The aim of this thesis is to study instabilities of flow in two fluid dynamics problems namely (i) Turbulent Rayleigh Benard Convection (RBC) with and without rotation and (ii) Path instability of a rising bubble.

(i) Turbulent Rayleigh Benard Convection :

The convection between a hot bottom surface and cold top surface is called Rayeligh Benard Convection (RBC). RBC is ubiquitous in nature and has applications in earth mantle convection, convection in the oceans, convection inside household kettle, convection inside power plants..etc. Under no rotation and in slow rotation, the Rayleigh Benard Convection has a large scale flow structure formed due to the rising and falling plumes. Beyond a critical rotation rate, the RBC changes its flow structure from domain filling large scale circulation to vertical column due to Ekman pumping. At further high rotation rate, the interaction between the vertical columns is constrained and heat transfer begins to decrease. To analyze the flow inside the RBC in the rotation unaffected and rotation affected regime, we conduct two experiments such as Particle Image Velocimetry (PIV) and Laser Induced Fluorescence (LIF). We study the transition from the large scale circulation to the vertical columns in the mid vertical plane of cylindrical RBC cell and compare the flow behavior near the bottom and top surfaces. From our experimental results we found that the columns begin to form for rotation rate of Rossby number < 2. We also found that the vorticity developed near the boundary layers inside the columns decreases from the bottom and top surfaces to the center of the cell. It also changes direction near the center of the cell causing the columns to rotate in opposite directions near the top and bottom surfaces. From LIF experiment, the temperature flow field is studied and it was found that the hot and cold plumes alternatively rise and fall in the vertical extent of RBC cell.

(ii) Path instability of rising bubbles

Bubble dynamics is present in many natural phenomena like aerosol transfer from sea, oxygen dissolution in lakes and in industrial applications such as bubble column reactors, petroleum industry, multi phase heat exchangers and many other. The path instability of rising bubbles has been studied since centuries, yet the transitional regime from rectilinear path to oscillating path is not clearly understood. Small bubbles rise in straight path, where as, beyond a critical size, the bubbles begin to oscillate. Until recently, it was believed that the wake behind the bubble is solely responsible for the path instability. But recent studies have shown that the path instability does not always result from a wake instability. The deformation of the bubble also plays an important role in determining the threshold of transition from a straight to an oscillatory path. The instability of bubble path is studied using two non dimensional numbers such as Galileo number and Bond number. In the present work, the path instability of a bubble is studied experimentally in de-mineralized water and silicon oil of different viscosity (5cst, 10cst) in a square cross section column. A solenoid valve and a pressurized tank are used to inject bubbles of various sizes in the bottom of the column. In our studies, we have observed the transition from straight path to various flow regimes such as helical or zig-zag path. Our experimental results allowed us to obtain three points of the marginal stability curve. In the case of water and 5cst silicon oil, a very good agreement with numerical results of Zhou Wei, (PhD thesis) 2017 is obtained. Our observation yield a lower critical Galileo number for the 10cst silicon oil. The experiment results show a parabolic increase of the amplitude of oscillation with sqrt(Ga), as well as a super critical Hopf bifurcation.

The jury comprises of:

• Dr. Denis Funfschilling (Directeur de thèse)
• Dr.Christel Metivier (Rapporteur)
• Dr.Olga Shishkina (Rapporteur)
• Prof. Jan Dusek (Examinateur)
• Prof. Yannick Hoarau (Examinateur)
• Dr. Stephan Weiss (Examinateur)
• Dr. Nicolas Rimbert (Examinateur)
• Prof. Robert Mose (Examinateur)

The defense will be held in English on 30 September 2019 at 09:30 am at the "Salle seminaire" (4 rue Boussingault, 67000 Strasbourg).