Numerical Study on Viscous Shear Flow past a Circular Cylinder

Numerical solutions of the unsteady Navier-Stokes equations are presented for a two-dimensional flow past a circular cylinder immersed in a uniform shear flow. Several values of the shear parameter K defined as Ga/U∞ is the oncoming velocity at the center of the cylinder. The Reynolds number Re based on 2a and U∞ is assumed to be 40 and 80. Although a pair of steady standing vortices is formed in a uniform flow when Re=40, it is found that a periodic vortex shedding occurs at the same Reynolds number in the case of a shear flow with a shear parameter K=0.2, however, the vortex shedding is suppressed even in the case of a shear flow revealing a clearly asymmetric flow pattern with respect to the geometrical center line of the cylinder. The same tendency is also observed in the flow of the Reynolds number Re=80. The time-averaged lift force acts in the direction towards the high-velocity side of the shear flow and its magnitude is approximately proportional to the shear parameter.