Analysis of Bubble Motion in Sinusoidal Wavy Channel By Immersed Boundary Based Cut Cell Method

Abstract

Dynamics of bubble rising is area of research for many researchers since centuries. The main reason it covers wide range of diverse application. Such as heat and mass transfer in natural, electrification of atmospheric air by sea bubble, Bubble column reactors, flow of foam in carbon sequestration, flow of bubble in blood veins etc. Bubble rising in the channel is complex phenomena. For simple case of bubble rising in a straight channel, the parameters that affect the bubble dynamics are density and viscosity of bubble and surrounding fluid, Surface tension, gravitational acceleration and bubble radius. As complexity increases more and more number of parameters has to be introduced and studied. In case of inclined channel, angle of inclination is additional parameter. Since we are performing analysis in the wavy channel, parameters such as Amplitude and Phase angle difference between two wall is added. Conventionally the effect of Reynolds number and Bond number on the dynamics is studied. When we talk about the study of dynamics in bubble rising paradigm, we actually determined the effect of various parameters on terminal velocity, steady state shape, aspect ratio, wobbling and path instability etc. Immersed Boundary based cut cell method is used to analyze the dynamics of the phenomena. Effect of various non-dimensional parameters is studied. As following the conventional way, first of all for different combination of Reynolds number and Bond number steady state shape is obtained and with help of this data shape regime is plotted. Then for different shapes the effect of Reynolds number and Bond number is analyzed. These non-dimensional numbers combine three primary forces that has significant effect on the dynamics of phenomena – Surface tension force, Buoyant force and Viscous force. The surface tension force is the key force that defines the surface area of the bubble. As surface tension decreases (increment in Bond number), the shape of the bubble would change in such a way that surface area of the bubble would increases. So, for the continuous increment of the Bond number shape of the bubble evolves from ellipsoidal to skirted through dimple ellipsoidal and spherical cap shape. The buoyant force is reason of the bubble motion. As buoyant force increases (increment in Bond number), the terminal velocity of the bubble increases. The effect of viscous force is quite less as compared to the other two forces. It is the resistive force, and it would try to reduce the terminal velocity of bubble. The effect of non-dimensional amplitude on the dynamics of the phenomena is studied. It is found that the increment of amplitude leads to instability, but its effect drastically depends upon the shape regime of the bubble. For the ellipsoidal bubble, surface tension force is quite large, it is a stabilizing force and trys to overcome the instability introduced by the increment of amplitude, so in this regime if we aspect ratio, terminal velocity with respect to time, periodic oscillation is observed. In case of regime of spherical cap, skirted where bond number is high, the stabilizing force is not enough to overcome the instability. Hence, in this regions chaos is observed. The one of the most unique characteristic of ellipsoidal bubble is, it shows path instability which is also known as wobbling. The effect of amplitude on wobbling is studied. It is found that as amplitude decreases, the wobbling region shifts downwards in the regime map. So, we can infer that as amplitude decreases, wobbling is observed at the lower Reynolds number. The detailed discussion of each non-dimensional parameter on dynamics of rising bubble is presented in the following sections of Thesis.