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The Quarterly Journal of Mechanics and Applied Mathematics 1976 29(1):35-60; doi:10.1093/qjmam/29.1.35
© 1976 by Oxford University Press
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CONICAL POTENTIAL FLOW ABOUT BODIES OF REVOLUTION

TOUVIA MILOH

( Department of Fluid Mechanics and Heat Transfer, School of Engineering, Tel-Aviv University Israel )

The method of Green's functions and a formulation in terms of conal functions are used to solve the axisymmetric Laplace equation in a domain bounded externally or internally by conical boundaries. The particular application of interest is to determine the pressure and the velocity distribution about slender bodies lying on the axis of a conical tunnel in an incompressible and irrotational flow.

Expressions are derived for the velocity potential and the stream function of both an isolated source and a ring source in the interior of a conical domain. These basic potential functions are used to formulate Fredholm integral equations of the first and second kinds for the source distribution generating a prescribed slender body in a conical tunnel. The integral equation for the axial source distribution is solved by expanding the solution in terms of a convergent Legendre series. An integral equation which renders directly the surface velocity distribution, by using a surface of a prolate spheroid inside the cone. Both examples involve a radial undisturbed flow. Finally, new expressions for the conal functions, which are more suitable for numerical computations, are also presented together with some numerical results.


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