Blockage effect of oscillatory flow past a fixed cylinder

A numerical study of the effect of the width of the computational domain on viscous oscillatory flow past a circular cylinder has been conducted, for Keulegan–Carpenter numbers ranging between 0.1 and 6 at a fixed frequency parameter equal to 50. The finite element method was used for the solution of the Navier–Stokes equations, in the formulation where the stream function and the vorticity are the field variables. Simulations for blockage ratios in the range between 0.10 and 0.50 were performed assuming frictionless flow at the outer boundaries, the blockage ratio being defined as the cylinder diameter divided by the width of the solution domain. The first set of simulations was carried out for a constant stream function along the horizontal boundaries. Then the procedure was repeated, for stream function values at the outer boundaries derived from the irrotational solution around a circular cylinder. This boundary condition relieves considerably the blockage effect on the flow pattern and on the drag coefficient of the in-line force.