Numerical prediction of force on rectangular cylinders in oscillating viscous flow

Numerical results are presented for an oscillating viscous flow past a squa re cylinder with square and rounded corners and a diamond cylinder with squ are corners at Keulegan-Carpenter numbers up to 5. This unsteady flow probl em is formulated by the two-dimensional Navier-Stokes equations in vorticit y and stream-function form on body-fitted coordinates and solved by a finit e-difference method. Second-order Adams-Bashforth and central-difference sc hemes are used to discretize the vorticity transport equation while a third -order upwinding scheme is incorporated to represent the nonlinear convecti ve terms. Since the vorticity distribution has a mathematical singularity a t a sharp corner and since the force coefficients are found in experiments to be sensitive to the corner radius of rectangular cylinders, a grid-gener ation technique is applied to provide an efficient mesh system for this com plex flow. Local grid concentration near the sharp corners, instead of any artificial treatment of the sharp corners being introduced, is used in orde r to obtain high numerical resolution. The elliptic partial differential eq uation for stream function and vorticity in the transformed plane is solved by a multigrid iteration method. For an oscillating flow past a rectangula r cylinder, vortex detachment occurs at irregular high frequency modes at K C numbers larger than 3 for a square cylinder, larger than 1 for a diamond cylinder and larger than 3 for a square cylinder with rounded corners. The calculated drag and inertia coefficients are in very good agreement with th e experimental data. The calculated vortex patterns are used to explain som e of the force coefficient behavior. (C) 1999 Academic Press.