Irrotational axisymmetric flow about a prolate spheroid in cylindrical duct

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.