Spatio-temporal behaviour in an enclosed corotating disk pair (Q2731179)

The authors present a numerical investigation of the flow between corotating disks in an enclosed corotating disk pair configuration with stationary outer casing. The three-dimensional flow is always unsteady owing to its structure in the radial-tangential plane. Axisymmetric regimes exhibit first a pitchfork bifurcation characteristic of symmetry breaking with respect to inter-disk midplane, and then a Hopf bifurcation occurs. The regime diagrams for these bifurcations are given in the \((Re,G)\)-plane, where \(R\)e is the rotational Reynolds number and \(G\) is gap ratio. For values of \(G\) smaller than a critical value \(G_c\), there exists a range of rotation rates where the motion becomes time-dependent before bifurcating to a steady symmetry breaking regime. It is shown that for \(G>G_c\) the transition to unsteady three-dimensional flow occurs after the pitchfork bifurcation, and the flow structure is characterized by a shift-and-reflect symmetry. The transition to three-dimensional flow is consistent with experimental observations where multiple solutions develop with the presence of quasi-periodic behaviour resulting from successive vortex pairings. On the other hand, for smaller values of gap ratio, the three-dimensional flow shows a symmetry breaking. It is found that the variation of torque coefficient as a function of the rotation rate is the same for both axisymmetric and three-dimensional solutions.