Flow Between a Smooth Stationary Disk and Grooved Rotating Disk

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Abstract
The radial outflow between a grooved rotating disk and a smooth stationary disk was examined analytically and experimentally with an emphasis on flow rate and drag moment. All investigations were conducted for a zero overall pressure differential across the disk. The analysis was based on an integral method with an area-averaged boundary condition on the grooved rotor. Nondimensionalization of the governing equations revealed that the radial inertia terms cannot in general be neglected. With the exception of the centrifugal acceleration terms, the radial inertia terms are usually neglected in this type of analysis. However, for higher flow rates these terms were found to make a significant contribution. A finite difference scheme was employed in the radial direction and a zero pressure differential across the disk was satisfied by an iterative solution technique. This technique required iteration on both the inlet flow rate to the gap and groove region until compatible flow rates in these two regions were obtained through convergence. The analytical predictions for the smooth rotor, a radially grooved rotor, and a rotor with grooves inclined at ± 20 degree to the radius are compared with experimental data generated using both air and 10 wt. motor oil as test fluids. The agreement between theory and experiment is generally good. A transition regime from laminar to turbulent flow is tentatively identified and plausibility arguments are presented to explain its existence.

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