Numerical analysis of incompressible flow over smooth and grooved circular cylinders

The viscous incompressible how fields around smooth and grooved circular cylinders are simulated by solving two-dimensional time-dependent Navier-Stokes equations. The numerical scheme used is the MAC method in finite-volume discretization with pressure and velocity as variables. New boundary conditions on the grooved cylinder surface are proposed such that the Navier-Stokes solver code, originally developed for smooth cylinder flow, can be slightly modified to simulate the flow field around a grooved cylinder. Detailed comparison between smooth and grooved cylinder flows indicates that the grooves affect the flow characteristics on the cylinder surface as well as the dow structures in space. The phenomena of Strouhal vortex shedding and transition waves in the near wake are predicted. By using spectral analysis, the frequency ratio of the transition wave to the Strouhal vortex of the smooth cylinder flow field is shifted due to the presence of the grooves. The increase in this frequency ratio with Reynolds number at 10(3) less than or equal to Re less than or equal to 5 x 10(3) qualitatively agrees with the experimental results. The interaction processes like vortex pairing and merging in the near wake of both smooth and grooved cylinder flows are also predicted. (C) 1996 Elsevier Science Ltd.