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Axisymmetric flow of a viscous fluid near the vertex of a body

Published online by Cambridge University Press:  11 April 2006

Shoichi Wakiya
Shoichi Wakiya
Affiliation:
Faculty of Engineering, Niigata University, Nagaoka, Japan
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Abstract

Axially symmetric motion of a viscous fluid in a cone is considered on the basis of the Stokes assumption. Near the apex of the cone the solution obtained reveals features quite similar to those of that near a sharp corner in two dimensions, which has been discussed already. An infinite sequence of eddies is induced near the apex for values less than about 80·9° of the semi-angle of the cone, which is measured from the symmetry axis lying in the fluid. The solution found by Pell & Payne for a spindle in a uniform stream offers a good illustration of the general discussion. Special attention is paid to the angle 120° for the spindle as well as the cone. The limiting case of zero angle of the cone corresponds to the flow occurring in a circular cylinder.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 78 , Issue 4 , 22 December 1976 , pp. 737 - 747
Copyright
© 1976 Cambridge University Press

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References

Bourot, J. M. 1974 J. Fluid Mech. 65, 513.
Fitz-Gerald, J. M. 1972 J. Fluid Mech. 51, 463.
Moffatt, H. K. 1964 J. Fluid Mech. 18, 1.
Payne, L. E. 1959 J. Math. & Phys. 38, 145.
Payne, L. E. & Pell, W. H. 1960 J. Fluid Mech. 7, 529.
Pell, W. H. & Payne, L. E. 1960 Quart. Appl. Math. 18, 257.
Pironneau, O. 1973 J. Fluid Mech. 59, 117.
Schubert, G. 1967 J. Fluid Mech. 27, 647.
Stasiw, D. M., Cook, F. B., Detraglia, M. C. & Cerny, L. C. 1974 Quart. Appl. Math. 32, 351.
Takagi, H. 1973 J. Phys. Soc. Japan, 35, 1225.
Wakiya, S. 1975 J. Phys. Soc. Japan, 39, 1113.