Theoretical Instability Analysis of a Flexible Disk Subjected to Swirling Fluid Flow.

Abstract

The paper deals with a theoretical instability analysis of a rotating flexible disk subjected to swirling fluid flow, resulting in the generation of a strong coupling between the flexible disk vibration and swirling fluid flow around it, and a possible mechanism governing unstable vibration. In the instability analysis, the basic equations of swirling fluid flow around the rotating disk are based on Navier-Stokes equations integrated over the gap width between the rotating disk wall and the shroud wall. The structural vibration equation of the rotating flexible disk is based on the Kirchhoff plate model. The equations of coupled fluid-structure motion take into account the moving boundary conditions with respect to both the rotating disk and the fluid flow. These equations were linearized for small deflection of the disk near the equilibrium state, and the solution of these equations is obtained using the multimodal expansion approximation and applying the Garlerkin method. Instability is defined as the negative imaginary part of complex eigenvalues for the characteristics equation. The unstable vibration mode shapes and the frequencies are in good qualitative agreement with the experimental results.