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Potential flow near conical stagnation points

Published online by Cambridge University Press:  20 April 2006

P. G. Bakker ,
W. J. Bannink  and
J. W. Reyn
P. G. Bakker
Affiliation:
Department of Aerospace Engineering, University of Technology, Delft, The Netherlands
W. J. Bannink
Affiliation:
Department of Aerospace Engineering, University of Technology, Delft, The Netherlands
J. W. Reyn
Affiliation:
Department of Mathematics, University of Technology, Delft, The Netherlands
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Abstract

Flow patterns near conical stagnation points in supersonic flow have been investigated on the basis of potential flow. Near the conical stagnation point the nonlinear equation for the conical velocity potential reduces to the equation of Laplace. Solutions of the equation of Laplace for incompressible plane flow are then used as a guide to generate conical stagnation-point solutions. Apart from known types of streamline patterns, such as nodes and saddle points, new types are found. Among them are oblique saddle points, saddle-nodes, topological nodes and topological saddle points. They may be used to clarify certain questions in a number of practical conical-flow problems. The oblique saddle point may be used to describe the inviscid flow associated with flow separation and also certain features of the flow over an external corner. The saddlenode, being structurally unstable, may fall apart into a saddle and a node. It may then be used to interpret the lift-off phenomenon of the singularity in the flow around a circular cone at incidence as a bifurcation. Similarly, this may be done for the appearance of a dividing streamline in the same flow at still higher angles of incidence, where a vortex system is formed at the leeward side of the cone.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 105 , April 1981 , pp. 239 - 260
Copyright
© 1981 Cambridge University Press

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