Date of Award

1984

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mechanical Engineering

Abstract

The rise of a large gas bubble, or slug, through a closed, vertical, liquid-filled channel of infinite length has been investigated by means of potential flow theory. Three channel geometries are considered: (1) the circular tube, (2) the two-dimensional rectangular channel and (3) the three-dimensional rectangular slot. The effect of inter- facial surface tension is explicitly accounted for by application of the Kelvin-LaPlace equation, thus making the bubble shape an integral part of the solution. For the circular tube of radius R and diameter D, the solution is expressed in terms of the Stokes Stream Function which consists of an infinite Bessel Function series. The resultant equations have been solved numerically for the first six terms in the series. For negligible surface tension and ideal liquid, the bubble rise velocity is given by U(,s) = 0.352 SQRT.(gD) and the radius of curvature at the bubble nose R(,c) = 0.75R. For air/water and D = 2.54 cm, the inclusion of surface tension gives U(,s) = 0.346 SQRT.(gD) and R(,c)/R = 0.71. It is also shown for the tube case that the potential flow solution may be applied with good results to liquids of moderate viscosity if an effective tube radius R(,eff) (TBOND) R - (nu)(delta) is used, where (nu) is a function of the liquid properties and (delta) is the laminar wall film thickness. For rectanguar channels, the solution is expressed in terms of the velocity potential function which consists of an infinite series of trigonometric functions. In the case of a two-dimensional rectangular channel, of finite length 2L and infinite width, the solution does not converge as rapidly as for the tube case. For a three-dimensional rectangular slot of length 2L and width 2W, the solution converges even more slowly than the two-dimensional channel case, especially at large aspect ratios and significant surface tension. For negligible surface tension, the theoretical solution compares well with measured data for aspect ratios up to 6. For a square channel and negligible surface tension, a value of Fr = 0.333 is calculated compared to the measured value of 0.330. Including surface tension in the three-dimensional solution decreases the maximum aspect ratio at which the solution gives good agreement with data, for the same number of terms in the series expansion. For a 7.62 cm square channel and an air/water system, a value of Fr = 0.330 is calculated compared to the measured value of 0.330. (Abstract shortened with permission of author.).

Pages

310

DOI

10.31390/gradschool_disstheses.4024

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