Bubble motion in inclined pipes

Highly nonlinear free-surface flows in vertical, inclined, and horizontal pipes are analyzed. The problem of bubble motion in a vertical pipe is closely related to the Rayleigh-Taylor instability problem. Inclined pipe flows are intensively studied as related to gas and oil transportation. A new theory of motion of large bubbles in pipes is developed. As distinct from previous approaches, which relied on semiempirical methods or numerical fitting, analytical methods of potential theory and complex analysis are used. A careful comparison of 2D and 3D solutions is presented. It is shown that a higher dimensionality may not correspond to a higher bubble velocity. For the first time, free-surface flows in inclined pipes are analyzed by means of direct numerical simulation, which makes it possible to develop a new approach to the Rayleigh-Taylor instability problem (bubbles with wedge-and cone-shaped noses).