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Spin-up from rest of a compressible fluid in a rapidly rotating cylinder

Published online by Cambridge University Press:  26 April 2006

Jae Min Hyun  and
Jun Sang Park
Jae Min Hyun
Affiliation:
Department of Mechanical Engineering, Korea Advanced Institute of Science & Technology, P.O. Box 150, Chong Ryang, Seoul, Korea
Jun Sang Park
Affiliation:
CAD/CAM, R & D Center, Sam Sung Electro-Mechanics, Suweon, Korea
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Abstract

Spin-up flows of a compressible gas in a finite, closed cylinder from an initial state of rest are studied, The flow is characterized by small reference Ekman numbers, and the peripheral Mach number is O(1). Comprehensive numerical solutions have been obtained for the full, time-dependent compressible Navier-Stokes equations. The details of the flow, temperature, and density evolution are described. In the early phase of spin-up, owing to the thermoacoustic disturbances caused by the compressible Rayleigh effect, the flows are oscillatory, and this oscillatory behaviour is pronounced at higher Mach numbers. The principal dynamical role of the Ekman layer is dominant over moderate times of orders of the homogeneous spin-up timescales. Owing to the density stratification in the radial direction, the Ekman layer is thicker in the central region of the interior. The interior azimuthal flows are mainly uniform in the axial direction. As the Mach number increases, the rate of spin-up in the interior becomes slower, and the propagating shear front is more diffusive. Explicit comparisons with the results for an infinite cylinder are made to ascertain the contributions of the endwall disks. In contrast to the usual incompressible spin-up from rest, the viscous effects are relatively more important for the case of a compressible fluid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 237 , April 1992 , pp. 413 - 434
Copyright
© 1992 Cambridge University Press

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