Interaction of wavy cylindrical Couette flow with endwalls

Abstract

The finite length of a Taylor–Couette cell introduces endwall effects that interact with the centrifugal instability and the subsequent wavy vortex flow. We investigate the interaction between the endwall Ekman boundary layers and the wavy vortices in a finite-length cavity via direct numerical simulation using a three-dimensional spectral method. To analyze the nature of the interaction between the vortices and the endwall layers, we consider three endwall boundary conditions: fixed endwalls, endwalls rotating with the inner cylinder, and stress-free endwalls. Near the endwalls, the waviness is diminished, primarily due to the effect of the flatness of the endwall rather than as a result of the no-slip boundary condition at the endwall. However, the waviness is present just one or two vortices away from the endwalls, indicating that the effect of the endwall on waviness does not penetrate far from the endwall. The interaction of the waviness with the endwall Ekman layer does not appear to result in disorder in the flow, either in the endwall vortex or farther from the endwall. Likewise, the waviness does not significantly alter Ekman layer thickness from that predicted based on theory.