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 from 0.047 to 70. At R = 0.047, the results obtained are in substantial agreement with the analytic small-R perturbation solution given by Robertson and Acrivos (1970). Inertia effects were found, however, to play a significant role even at R = 1, and hence the calculated flow pattern for R greater than or equal to 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 the reciprocal of the square root of R.