Dynamic Instability and it's Mechanism in a Rotating Flexible Disk Subjected to Swirling Fluid Flow. Instability Analysis of Nondissipative System.

Abstract

This paper deals with a theoretical instability analysis of a rotating flexible disk subjected to swirling fluid flow in a confined fluid, and an instability mechanism governing the unstable vibration where the dissipation effect of structural damping and fluid viscosity are disregarded. In the instability analysis, the basic equations of swirling fluid flow around the rotating disk are derived by integrating Navier-Stokes equations 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-Love plate model neglecting structural damping. 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 deflections of the disk near the equilibrium state, and the solution of these equations is obtained by using the multimodal expansion approximation and applying Galerkin's method. Instability is defined as the condition of a negative imaginary part of complex eigenvalues in the characteristics equation. The instability mechanism governing the unstable vibration is sufficiently understood. It is found that the characteristics of the unstable vibration are dependent on the added mass parameter.