The comparison between the experimental visualizations by Escudier and Hide S.Koyama and numerical simulations of the development procedure of vortex breakdown in laminar swirling flow induced from a rotating endwall is presented. The experimental visualizations by Escudier were the first to reveal the presence of vortex breakdown phenomena in closed cylindrical container with a rotating lid. Afterwards, much experimental and numerical work was done in this research field. The accurate experimental measurements for the recurrence and development of vortex breakdown by Hide S.Koyama then make clear this phenomena. With numerical solution of unsteady axisymmetric Navier Stokes equations, the author accurately reproduces these phenomena. The numerical results are given and compared with experiments.

In the paper the finite control volume integral formulation are derived in three dimensional nonorthogonal coordinates. The curved coordinate velocities on the control volume surface are taken as conveying ones and the Cartesian coordinate velocities at the center of the control volume as the variables of momentum equation. As an example, natural convection are calculated in two and three dimensional domains of eccentric cylinders and spheres.