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Flow of an inviscid fluid past a sphere in a pipe

Published online by Cambridge University Press:  28 March 2006

Wei Lai
Wei Lai
Affiliation:
Rensselaer Polytechnic Institute, Troy, New York
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Abstract

The problem of flow of an inviscid, incompressible fluid inside a circular pipe, with a sphere on the axis of the pipe, has been studied by Lamb (1936) (irrotational flow), Long (1953) and Fraenkel (1956) (swirling flow). Because of the difficulty of satisfying all the boundary conditions in the problem, only approximate solutions, valid for spheres of small diameter (compared with that of the pipe) have been obtained. In this paper, it is found that by introducing a vortex sheet over a segment of the diameter of the sphere, flow patterns can be obtained by an inverse method for the case of large spheres. Four different types of flow are considered: (1) irrotational flow, (2) swirling flow with constant axial and angular velocities far upstream, without lee waves, (3) swirling flow with constant axial and angular velocities far upstream, with lee waves, and (4) rotational flow with a paraboloidal velocity distribution far upstream.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 18 , Issue 4 , April 1964 , pp. 587 - 594
Copyright
© 1964 Cambridge University Press

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References

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