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Transition to a Rising Core at the Centre of a Vortex. Simplified Analysis for Laminar Flow

Published online by Cambridge University Press:  07 June 2016

M R Head ,
T S Prahlad  and
W R C Phillips
M R Head
Affiliation:
Cambridge University, Engineering Department
T S Prahlad
Affiliation:
Cambridge University, Engineering Department
W R C Phillips
Affiliation:
Cambridge University, Engineering Department
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Summary

A free-vortex flow over a stationary disc produces a boundary layer on the surface which proceeds inwards towards the centre under the action of the imposed radial pressure gradient. Close to the centre the boundary layer leaves the surface to form a rising core. The present paper uses a control-volume approach and earlier calculations of laminar boundary-layer development on the disc to determine the characteristics of the core-formation process.

Type
Research Article
Information
Aeronautical Quarterly , Volume 28 , Issue 3 , August 1977 , pp. 197 - 210
Copyright
Copyright © Royal Aeronautical Society. 1977

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References

1 Legendre, R Lignes de courant d’un écoulement continu. Recherche Aérospatiale, No 105, 1965.Google Scholar
2 Chaussee, D S Numerical simulation of axisymmetric vortex formation normal to a solid boundary. PhD thesis, Iowa State University, 1972. (Available from University Microfilms, Ann Arbor, Michigan.)Google Scholar
3 Serrin, J The swirling vortex. Proc Roy Soc, Vol 271, pp 325–360, 1972.Google Scholar
4 Cooke, J L On Pohlhausen’s method, with application to a swirl problem of Taylor. Journal of the Aerospace Sciences, Vol 19, pp 486–490, 1952.Google Scholar
5 Mack, L M The laminar boundary layer on a disk of finite radius in a rotating flow. Part II: A simplified momentum integral method. Jet Propulsion Laboratory, California Institute of Technology, Report 32-366, 1963.Google Scholar
6 Burggraf, O R Stewartson, K Belcher, R Boundary layers induced by a potential vortex. Physics of Fluids, Vol 14, pp 1821–1833, 1971.CrossRefGoogle Scholar
7 Prahlad, T S Head, M R Numerical solutions for boundary layers beneath a potential vortex. Computersand Fluids, Vol 4, pp 157–169, 1976.Google Scholar
8 Chi, S W Glowacki, W J Applicability of mixing-length theory to turbulent boundary layers beneath intense vortices. Journal of Applied Mechanics, Vol 41, pp 15–19, 1974.Google Scholar
9 Cooke, J C Numerical solution of Taylor’s swirl atomiser problem. RAE Technical Report 66128, 1966.Google Scholar
10 Wei, S N Experimental investigation of the ground boundary layer of a tornado-like vortex. MS thesis, Catholic University of America, Washington, 1970.Google Scholar