Irrotational axisymmetric flow about a prolate spheroid in cylindrical duct
Abstract
A solution to the problem of potential flow about a prolate spheroid placed axially symmetric in a circular duct has been derived. The solution is in the form of a distribution of vortex rings over the surface of the spheroid. The vortex strength is expressed in terms of an infinite series of Legendre polynomials and the analysis yields an infinite set of equations for determining the coefficients of this series. An expression for the velocity distribution on the surface of the spheroid as well as the longitudinal added mass coefficients of the spheroid are derived in terms of the coefficients of the Neumann series expansion of the vortex sheet strength. Numerical results are presented for various spheroids and different blockages. Also given is a comparison between the present method and few available approximate methods.
 Publication:

Journal of Engineering Mathematics
 Pub Date:
 October 1974
 DOI:
 10.1007/BF02353498
 Bibcode:
 1974JEnMa...8..315M
 Keywords:

 Axisymmetric Flow;
 Ducted Flow;
 Flow Velocity;
 Potential Flow;
 Prolate Spheroids;
 Velocity Distribution;
 Entire Functions;
 Flow Equations;
 Flow Theory;
 Inviscid Flow;
 Legendre Functions;
 Polynomials;
 Vortex Rings;
 Fluid Mechanics and Heat Transfer;
 Vortex;
 Vortex Ring;
 Prolate;
 Approximate Method;
 Legendre Polynomial