Bubble Motion in a Rotating Liquid Body
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BUBBLE MOTION IN A ROTATING LIQUID BODY
P. ANNAMALAI, R. S. SUBRAMANIAN, AND R. COLE Department of Chemical Engineering, Clarkson College of Technology, New York 13676
Potsdam,
ABSTRACT Single bubble behavior inside a rotating liquid-filled sphere is studied both experimentally and theoretically. In the limit of small values of the Taylor number, a quasi-static theoretical description of the motion of the bubble is developed. The analytical result thus obtained is compared with experiment and predicts the bubble trajectory as well as its asymptotic location which, in the presence of gravity, is not exactly on the axis of rotation.
INTRODUCTION In a space laboratory, rotation of liquid bodies containing gas bubbles can bring the bubbles to the axis of rotation. Such a possibility is of interest in the formation of the hollow glass spheres required in inertial confinement fusion experiments. Furthermore, rotation can play a supporting role in the thermocapillary fining of glass melts. One of the studies in our NASA sponsored Space Shuttle flight program [1] will involve acoustic rotation as one of a number of possible bubble centering procedures. The experiments and analysis briefly described in this presentation are part of ongoing ground-based investigations initiated to aid in the design and interpretation of our shuttle experiments. EXPERIMENT AND DATA ANALYSIS The experimental apparatus shown schematically in figure 1, consisted of a spherical glass shell of diameter in the range 40-70 mm, filled with silicone oil and containing a small gas bubble. The shell, which was directly connected to the shaft of a variable speed d.c. motor, was spun about a horizontal axis. The resulting motion of the bubble toward the rotation axis was recorded on film by means of a Bolex H8 motion picture camera. The processed film was analyzed on a Vanguard Motion Analyzer interfaced to an IBM keypunch. The apparent bubble trajectory relative to an inertial frame of reference was obtained by reading out the X and Y coordinates of the bubble center at convenient time intervals. The apparent trajectory was later transformed to actual bubble trajectory by means of appropriate optical correction equations [2]. ANALYSIS In order to interpret the experimental data, it is helpful to have some theoretical understanding of the migration process. In an earlier analysis [21, the virtual mass concept and the equations of particle dynamics were used to write an equation for the bubble motion within a liquid field undergoing rigid body rotation. Numerical solutions of these equations yielded good agreement with the experimental migration data when secondary flows resulting from the spin-up process were negligible. A very simplified analysis leading to an
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BEARING SUPPORT ASS SPHERE
D.C.
CAMERA--.%
METAL BLOCK Fig.
1.
Schematic of experimental apparatus.
analytical solution was developed to aid in correlating the observed migration times, but was not successful in predicting the bubble trajectory. Subsequently an attempt has bee
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