Journal Article10.1017/S0022112087000430
On rotating disk flow
John F. Brady,Louis J. Durlofsky +1 more
120
TL;DR: In this paper, the relationship of axisymmetric flow between large but finite coaxial rotating disks to the von Karman similarity solution is studied by means of a combined asymptotic- numerical analysis.
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Abstract: The relationship of the axisymmetric flow between large but finite coaxial rotating disks to the von Karman similarity solution is studied. By means of a combined asymptotic – numerical analysis, the flow between finite disks of arbitrarily large aspect ratio, where the aspect ratio is defined as the ratio of the disk radii to the gap width separating the disks, is examined for two different end conditions: a ‘closed’ end (shrouded disks) and an ‘open’ end (unshrouded or free disks). Complete velocity and pressure fields in the flow domain between the finite rotating disks, subject to both end conditions, are determined for Reynolds number (based on gap width) up to 500 and disk rotation ratios between 0 and – 1. It is shown that the finite-disk and similarity solutions generally coincide over increasingly smaller portions of the flow domain with increasing Reynolds number for both end conditions. In some parameter ranges, the finite-disk solution may not be of similarity form even near the axis of rotation. It is also seen that the type of end condition may determine which of the multiple similarity solutions the finite-disk flow resembles, and that temporally unstable similarity solutions may qualitatively describe steady finite-disk flows over a portion of the flow domain. The asymptotic – numerical method employed has potential application to related rotating-disk problems as well as to a broad class of problems involving flow in regions of large aspect ratio.
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References
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William G. Cochran
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TL;DR: In this paper, the steady motion of an incompressible viscous fluid due to an infinite rotating plane lamina was considered, and it was shown that the equations of motion and continuity are satisfied by taking
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K. Stewartson
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TL;DR: In this article, the steady motion of a viscous fluid confined between two coaxial rotating disks is discussed both experimentally and theoretically, and it is found experimentally that when the disks rotate in the same sense, the main body of the fluid rotates as well, but if they rotate in opposite senses, the fluid is almost at rest.
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