On the motion of long bubbles in inclined tubes

This thesis is concerned with the motion of long bubbles in inclined tubes with circular cross-sections. In general, the bubble moves through an open pipe, with non-zero average liquid flow at infinity. An important sub-class, however, comprises phenomena where the tube is closed at one end with the liquid at rest there. The latter case, being simpler, and of basic interest, has received most attention in the past, and is rather well understood. The main topics of this thesis therefore concern the former general problem, which is also of increasing importance in applications, particularly in connection with two-phase oil and gas transport in pipelines. The thesis consists of two papers which are closely connected: 'An experimental investigation of the motion of long bubbles in inclined tubes'. Accepted for publication in the International Journal of Multiphase Flow, 1983. and 'On the motion of long bubbles in vertical tubes'. Preprint Series, Appl. Math. No 3, University of Oslo, 1983. The first paper deals with the effects of inclination angle and liquid motion at infinity on bubble propagation rates, experimentally. The use of phototransistors and diodes in a specially designed instrumentation, based on the difference in refractive properties of gas and liquid with respect to infrared light, significantly increases the accuracy of the bubble velocity measurements. A correlation between bubble and average liquid velocities from a least squares fit to the data is suggested. An interesting dynamic phenomenon, the bubble turning process, to our knowledge reported herein for the first time, was observed in down-flow systems. This is characterized by a change in relative bubble propagation direction, from counter - to co-current liquid with a corresponding sharp increase in bubble speed at a given liquid velocity. In the second paper potential flow theory has been applied to determine the speed and shape of an infinitely long bubble in vertical tubes with axis-symmetry. An analytic formula for the bubble propagation rate is proposed, and, together with other predictions, tested against experiments reported. (author)