Fluid-structure interactions in the vibrations of rotating and stationary disks

Anirban Jana, Purdue University

Abstract

This thesis focuses on two fluid-structure interaction effects in thin, flexible disks: the aeroelastic flutter instability of rotating disks in an unbounded fluid, and the hydrodynamic impedances for small vibrations of stationary disks. Rotating disks experience the aeroelastic flutter instability beyond a threshold rotation speed called the flutter speed. To predict the flutter instability, a stability analysis of a rotating Kirchhoff plate coupled to a compressible inviscid fluid is performed, via an eigenvalue perturbation technique combined with a semi-analytical/boundary element solution for the fluid flow. The analysis predicts that a structurally un-damped disk destabilizes at its lowest critical speed. With material damping, the flutter speeds become supercritical and increase with decreasing fluid density. The competing effects of ground-fixed radiation damping into the surrounding fluid and co-rotating disk material damping control the onset of flutter. Experiments on the post-flutter behavior of disks rotating in an unbounded fluid are presented next. The existence of a primary instability at the flutter speed of a reflected traveling wave, followed by secondary instabilities and complicated nonlinear behavior, is observed. A rotating von Kármán plate coupled to a linear rotating damping is employed to quantitatively capture the primary instability branch. This thesis also presents the hydrodynamics of stationary disks vibrating with small amplitudes. A three-dimensional finite element model predicts the viscous impedances, whereas a boundary element method predicts the acoustic impedances. The computed nondimensional impedances, consisting of damping and added mass, encompass disks spanning multiple length scales, operating frequencies and fluidic environments. For a given clamping ratio and vibration mode, the nondimensional viscous impedance depends on the ratio of unsteady fluid inertia to viscous fluid stresses, while the nondimensional acoustic impedance depends on the ratio of structural to acoustic wavelengths. Typically, viscous effects dominate at low frequencies. This suggests that for the low frequency wave destabilized at the flutter speed of a rotating disk, viscous rather than acoustic damping is the dominating fluidic influence causing flutter instability. An alternative spectral solution for the fluid flow around a non-rotating disk is developed. Suggestions are provided to extend it to rotating disks for enhanced flutter prediction.

Degree

Ph.D.

Advisors

Raman, Purdue University.

Subject Area

Mechanics|Mechanical engineering|Plasma physics

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