Rotordynamic Moment on the Backshroud of a Francis Turbine Runner Under Whirling Motion

Abstract

This paper addresses the rotordynamic instability of an overhung rotor caused by a hydrodynamic moment due to whirling motion through the structural coupling between whirl and precession modes. First, the possibility of instability is discussed based on a vibration model in which the hydrodynamic forces and moments are assumed to be smaller than structural forces with the structural coupling being represented by a structural influence factor. Then, the fundamental characteristics of rotordynamic moment on the backshroud of a Francis turbine runner under whirling motion were studied using model tests and numerical calculations. The runner is modeled by a disk positioned close to a casing with a small radial clearance at the outer periphery. The moment is caused by an inward leakage flow that is produced by an external pump in the model test. The experiments were designed to measure the rotordynamic fluid force moments under various leakage flow rates with various preswirl velocities and various axial clearances between the backshroud and casing. The computation was carried out based on a bulk flow model. It was found that the fluid force moment is generally destabilizing, except for a small region of positive whirling speed ratios.

Rotordynamic Instabilities Caused by the Fluid Force Moments on the Backshroud of a Francis Turbine Runner

“…The second order component is stabilizing except for F 2 at smaller ω/ω n . This is because the destabilization by the whirl moment occurs through the structural coupling as shown in [10] between linear ( ε% ) and angular ( α % ) displacements as shown in Fig. 12(b).…”

“…The angular velocity ratio Ω/ω was varied from -1.2 to 1.2. For the detailed experimental facility and the measurement of the fluid force moments, refer to [10,11]. Figure 4 shows the normalized whirl moments m n_W ≡M n_W /(ρπR T…”

“…In order to study the rotordynamic problem of the Francis turbine runner as reported in [6], the authors have measured the rotordynamic force moments on a whirling and precessing disk simulating the backshroud of a Francis turbine runner, respectively [10,11]. In [10], it was shown by a simplified vibration analysis that the moment on the rotor caused by the whirl can cause whirl instability through structural coupling for the case of an overhung rotor.…”

“…In [10], it was shown by a simplified vibration analysis that the moment on the rotor caused by the whirl can cause whirl instability through structural coupling for the case of an overhung rotor. The purpose of the present study is to verify this result with a more elaborate vibration analysis including both whirl and precession modes.…”

“…In addition, the relative importance of whirl and precession moments is examined. The rotordynamic moment coefficients were determined from the fluid force moments measured in [10] and [11]. The stability analysis of a cantilevered rotor is carried out by using a lumped parameter model.…”