Steady simple shear flow past a circular cylinder at moderate Reynolds numbers: a numerical solution

The two-dimensional steady flow of an incompressible viscous fluid past a circular cylinder, placed symmetrically in a simple shear field, has been studied for both the stationary and the freely rotating case by solving numerically the Navier-Stokes equations for values of the Reynolds number R in the range \[ 0.047 \leqslant R \leqslant 70. \] At R = 0·047, the present results are in substantial agreement with the analytic small- R perturbation solution given by Robertson & Acrivos (1970). Inertia effects were found, however, to play a significant role even at R = 1, and hence the calculated flow pattern for R ≥ 1 differs significantly from that of the creeping-flow solution. Specifically, for the freely rotating case, the region of closed streamlines decreases rapidly in extent with increasing R , two symmetrically placed wakes are formed on either side of the cylinder and the dimensionless rotational speed of the freely suspended cylinder decreases as R -½. In fact, for a value of R as low as 70, many of the gross features of the flow are surprisingly similar to those described by an inviscid solution except for the difference in the two sets of pressure profiles and the fact that the numerical results do not as yet exhibit the expected flow separation on the surface of the cylinder.