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On the Lagrangian description of unsteady boundary-layer separation. Part 2. The spinning sphere

Published online by Cambridge University Press:  26 April 2006

Leon L. Van Dommelen
Leon L. Van Dommelen
Affiliation:
Department of Mechanical Engineering, FAMU/FSU College of Engineering, PO Box 2175, Tallahasee, FL 32316-2175, USA
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Abstract

A theory to explain the initial stages of unsteady separation has been proposed by Van Dommelen & Cowiey (1990). In the present paper, this theory is verified for the separation process that occurs at the equatorial plane of a sphere or a spheroid which is impulsively spun around an axis of symmetry. A Lagrangian numerical scheme is developed which gives results in good agreement with Eulerian computations, but which is significantly more accurate. This increased accuracy, and a simpler structure to the solution, also allows verification of the Eulerian structure, including the presence of logarithmic terms. Further, while the Eulerian computations broke down at the first occurrence of separation, it is found that the Lagrangian computation can be continued. It is argued that this separated solution does provide useful insight into the further evolution of the separated flow. A remarkable conclusion is that an unseparated vorticity layer at the wall, a familiar feature in unsteady separation processes, disappears in finite time.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 210 , January 1990 , pp. 627 - 645
Copyright
© 1990 Cambridge University Press

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