Flow over a thin circular disk at low to moderate Reynolds numbers

Computation of viscous flow over a circular disk of aspect ratio 10 (thickness/ diameter) in the Reynolds number (Re) range of 10 to 300 was performed. The following flow regimes were observed: (I) steady axisymmetric flow when Re < 135, with the presence of a toroidal vortex behind the disk; (II) regular bifurcation with loss of azimuthal symmetry but with planar symmetry and a double-threaded wake, for 135 < Re < 155; (III) three-dimensional flow with periodic shedding of double-sided hairpin-shaped vortex structures and periodic motion of the separation region for 155 < Re < 172; (IV) regular shedding of double-sided hairpin-shaped vortex structures with planar and spatio-temporal symmetry for 172 < Re < 280; (V) periodic three-dimensional flow with irregular rotation of the separation region when Re = 280-300. This transition process for the disk differs from that for the sphere as we observe a loss of the symmetry plane in Regime III due to a twisting motion of the axial vorticity strands in the wake of the disk. The periodic flow was characterized by double-sided hairpin structures, unlike the one-sided vortex loops observed for the sphere. This resulted in the drag coefficient oscillating at twice the frequency of the axial velocity. In Regime IV, the vortex loops were shed from diametrically opposite locations and with equal strength, resulting in the lift coefficient oscillating symmetrically about a zero mean. These results imply the presence of spatio-temporal symmetry.