TY - JOUR

T1 - Conical potential flow about bodies of revolution

AU - Miloh, Touvia

PY - 1976/2

Y1 - 1976/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0016918974&partnerID=8YFLogxK

U2 - 10.1093/qjmam/29.1.35

DO - 10.1093/qjmam/29.1.35

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AN - SCOPUS:0016918974

SN - 0033-5614

VL - 29

SP - 35

EP - 60

JO - Quarterly Journal of Mechanics and Applied Mathematics

JF - Quarterly Journal of Mechanics and Applied Mathematics

IS - 1

ER -