| This thesis focuses on the numerical studies of a single gas or vapor bubble rising in a viscous fluid. First, coupled with a boundary-fitted grid, a new projection method with second-order accuracy both in space and time is developed for the simulation of axisymmetric free-surface flows. Two variants of this new method are developed by adapting existing algorithms, suitable for prescribed velocity boundary conditions, to the case of normal and tangential stress conditions at the free surface. A normal-mode analysis for a fixed-boundary problem confirms the second-order accuracy of the algorithm in time. The approach is then validated by comparison with a Rayleigh-Plesset solution for an oscillating spherical bubble, with an analysis of shape oscillations, and with existing results for the buoyant rise of a deforming bubble for Reynolds numbers up to 200 and Weber numbers up to 12.;Then, some transient behaviors of the rectilinear rise of a gas bubble in a viscous liquid are studied, and a linear stability analysis is carried out computationally for the instability of the rectilinear path. Contrary to some recently reported experiments, for a bubble released with a spherical, oblate, prolate, or oval shape, it is found that the terminal velocity and final steady shape are independent of the initial shape. This result suggests that the experimental observations may be influenced by uncontrolled effects rather than a genuine multivaluedness of the fluid dynamic solution for a steadily rising bubble. The ascent of a bubble which expands, or contracts, due to a change in the ambient pressure, is also studied. The ensuing behavior of the rise velocity is strongly influenced by added mass effects. For the study of the path instability, the bubble is treated as a fixed-shape spheroid. A millimeter-size gas bubble rises in a zigzag or spiral path in still water. Results of the linear stability calculation show that there is a strong similarity between the instability of flow past a fixed-shape spheroidal bubble and flow past a fixed solid sphere. Mechanism of the planar zigzaging and spiralling can be explained by the instability of m = 1 mode. Furthermore, "frozen" states linear stability calculations show that the amount of vorticity accumulated at the rear of the bubble plays an essential role for the instability. It is also shown that the instability is very sensitive to the deformation of the bubble, but relatively insensitive to the Reynolds number.;Lastly, the behavior of a vapor bubble moving in an infinite fluid is studied through the axisymmetric simulation. The effects of non-sphericity of the vapor bubble are examined by comparing results of the axisymmetric simulation and a spherical model. For a millimeter-size vapor bubble in water, the spherical model is fairly good in predicting the condensation rate despite the large shape deformation of the bubble. Then two other problems, a vapor bubble encountering a superheated or subcooled semi-infinite liquid, or travelling through a liquid layer, are studied. These two processes might provide some control for the vapor bubble. |
