Secondary Motion and Turbulence in Circular Couette Flow

Abstract

The flow in an annular space between two separately rotating cylinders of finite length is investigated. It is found that when the outer cylinder rotates faster than, and in the same direction as, the inner cylinder, the fluid moves largely in solid body rotation with the outer cylinder. In order to understand the dynamics of this type of flow, a laminar theory is formulated. The equations of motion are linearized by developing the solution as a perturbation of the state of solid body rotation. The theory predicts tangential velocities which are independent of the axial co-ordinate in the interior region. It also predicts the streamline pattern of the secondary motion in that region. The observed tangential velocities at mid-height in the annular space, using water and air, are in good agreement with the predicted velocities from the theory. Hot wire anemometers are used for the measurement of turbulence intensities in air. In light of these measurements the agreement with the theory is somewhat surprising, since the flow is observed to be turbulent in all the experiments. The turbulence intensities near the inner cylinder wall are found to be of the same order of magnitude as those found near the wall in pipe flow.