Oscillatory drag, lift, and torque on a circular cylinder in a uniform flow

Abstract

Numerical solutions of the equations governing time-dependent, viscous, incompressible fluid flow past a circle are presented for Reynolds numbers 100, 400, and 1000. These solutions show the dramatic rise of the drag coefficient during the development of the Kármán vortex street and reveal the oscillatory character of the drag, lift, and torque that are experienced by the circle. Contour plots of the vorticity and stream function are compared with histories of the pressure distribution, drag, lift, torque, and separation angles. These comparisons show how the pressure distribution, drag, lift, and torque on the circle are intimately and logically related to the well-known flow pattern of the Kármán street. A new method is described for implementing the infinity conditions. The use of this technique makes it possible to observe the motion of the upstream stagnation streamline and relate this effect to the lift on the circle. The fact that the drag is larger for the oscillatory wake than the symmetric wake is interpreted as a tendency toward an equilibrium state of maximum energy dissipation. Comparisons are made with experimental results. These comparisons suggest that the present results are a valid description of flow past a circular cylinder for Reynolds numbers in the range from 40 to 400. Copyright © 1972 by the American Institute of Physics.