Flow-Excited Turbine Rotor Instability

The problem of steam whirl is one of the technological limits that now prohibit the development of power-generating turbomachinery substantially above 1 GW. Due to steam flow, self-excited vibrations develop at high loads in the form of stable limit cycles that, at even higher loads, deteriorate to chaotic vibration of high amplitude. A mathematical model is developed for stability analysis and for the development of a rational stability criterion to be used at the design stage. The bearing nonlinearity is introduced in the form of high-order coefficients of a Taylor expansion of the perturbation forces for fixed-arc slider bearings and employing nonlinear pad functions for the tilting pad bearings. The flow excitation is introduced in the form of follower force gradients related to the flow and the power generated. The study of the stable and unstable limit cycles, and the stability of the system in the large, beyond the linear analysis currently utilized, is done analytically for the De Laval rotor and numerically with finite element analysis of typical turbomachinery rotors. The range of loads for which limit cycles exist was found to be substantial. This is important for the operation of large machinery because such cycles permit the operation at loads much higher than the ones that correspond to the onset of instability of the linearized system. The conditions for the limit cycle deterioration into chaotic orbit are investigated. Analytical expressions have been obtained for the different stability thresholds for the De Laval rotor.