On the behaviour of steamwhirl and nonlinear rotor-bearing systems

The problem of steamwhirl is the technological limit which now prohibits the development of power generating turbomachinery substantially above 1 GW. Due to the steam flow, self excited vibrations develop at high loads, above the onset of instability of the linearized system, in the form of stable limit cycles which, at even higher loads, deteriorate to chaotic vibration. The bearing nonlinearity is introduced in the form of high order coefficients of a Taylor expansion of the perturbation forces for fixed-arc slider bearing and employing non-linear pad functions for the tilting pad bearings. The flow excitation is introduced in the form of radial and tangential force gradients related to the flow and power generated. The study of stable and unstable limit cycles and stability of the system in the large, beyond the linear analysis currently utilized, is done analytically for the DeLaval 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 limit cycles permit the operation at loads much higher than the ones which correspond to the onset of instability of the linearized system. The conditions for the limit cycle deterioration into chaotic orbit is studied. Analytical expressions have been obtained for the different thresholds for the DeLaval rotor.