Global Stability Analysis on the Spiral-Vortex Mode in the Confined Cavity Flow Between Rotating and Stationary Disks

Global stability analysis (GSA) is applied to a 3D confined cavity flow between rotating and stationary disks (viz., rotor and stator). The Arnoldi method extended for incompressible viscous flow is used together with the eigenvalue spectrum conversion to solve the eigenvalue problem of the GSA. As a first step, the GSA is conducted in an axisymmetric flow, and circular vortices are obtained as eigen modes. Then, the GSA is applied to a flow with circular vortex at a higher Reynolds number, and eigen vectors of spiral vortex are obtained. The result suggests that the GSA shows unstable flows after transition of the baseflow. However, it is necessary to reconsider the convergence of the eigenvalues for the parameters of Arnoldi method.