Numerical study of laminar near-wake vortices behind a circular cylinder

Abstract

The unsteady incompressible Navier-Stokes equations are solved for the laminar flow past a circular cylinder in the Reynolds number range 50-200 to investigate the behavior of the vortices in the near-wake. The Euler explicit finite difference scheme is used for the vorticity equation and the direct elliptic solver (SEVP) for the stream function equation. An integral-series method is newly developed for accurate evaluation of the stream function on the far boundary of a finite two-dimensional flow domain. For the stationary cylinder, present results indicate that the so-called Berger``s ``low-speed mode`` and ``basic mode`` in the Strouhal number-Reynolds number relation are the same thing when the turbulence effect is absolutely eliminated from the vortex phenomenon. The two different shedding mechanisms experimentally observed, the wake instability and the direct voirtex shedding, are also numerically obtained in the present study with their inter-transition Reynolds number at about 80. For the heated or cooled cylinder, purely periodic flows at Re=100 was found to degenerate abruptly into a steady twin vortices at the critical Grashof number 1500, confirming an earlier experimental observation identified by the name ``breakdown of the Karman vortex street.`` Various other buoyancy effects associated with the heating or cooling of the cylinder have been discussed in terms of flow patterns, Nusselt number and drag coefficient. For the oscillated cylinder, the phenomenon of so-called ``lock-is`` in examined. The change of amplitude and frequency causes the vortex shedding pattern to have dual types. The generation of secondary vortices has been investigated in detail in the lock-in range.