Numerical computation of the magnitude and frequency of the lift on a circular cylinder

Abstract

The shear layers bounding the formation region behind a bluff body are modelled by individual elementary vortices. These vortices are free to move under the action of the flow past the body and the velocity field of the vortices. This configuration generates a vortex street. The strengths of the elementary vortices are determined from the velocity calculated at the point at which the vortices are caused to appear. It is essential that this point be downstream of the boundary layer separation point and also that it is allowed to oscillate. The determination of the strengths of the vortices is a crucial point in the calculation and is performed by a careful examination of the flow in the formation region. The basis of this work is to be found in the author’s earlier paper (1966). The independent variables of the model are reduced to a minim um prior to calculation. Calculations have been performed, on a digital computer, with the independent variables corresponding to two flows. At a high subcritical Reynolds number the values of the oscillating velocities, lift force and the scale of the formation region generated by the model agree with experiment. The frequency generated differs from that observed in the way predicted by an assessment of the effect of ignoring turbulent and viscous effects. In the second series of calculations the variables were matched to the flow observed at a Reynolds number of 2000 in the absence of free-stream disturbances. The diminutive values of oscillating quantities observed under these conditions are also generated by the model.