Modelling and analysis of multiphysical interactions in hydropower rotor systems

Abstract: In this thesis the objective is to develop rotordynamical models of hydropower units, where coupling between mechanical, electromagnetic and fluid dynamical system systems is of certain interest. Both fluid-rotor and electromechanical interactions are known to change the system coefficients of the rotor system, which affects eigenfrequencies, damping, stability and response. In addition, external forces from the magnetic field and the hydraulic system can excite the rotor system. Both system coefficients and external excitations are important considerations during design and operation of a hydropower unit, in order to obtain reliable design and operations. Hydropower rotor systems differ from other rotating systems because they rotate with comparably low rotational speed and the total mass of the rotor system is high. The relative airgap in the generator is small compared to a turbo generator, which results in larger electromagnetic forces. Detailed electromechanical force models of large synchronous generators are a missing part of the scientific literature and there is an industrial need for better models. When including hydraulic forces in a rotordynamical model of a hydropower system, industrial rules of thumb are normally used. Hence, there is a need for better multi-physical models in rotordynamical models of hydropower rotor systems. The electromechanical model of synchronous generators for hydropower has been developed, from only considering radial electromagnetic forces to considering both radial and tangential force. The latter is induced due to a change in the magnetic field when the rotor is in an eccentric position, which induces current in the damper winding of the rotor and changes the magnitude and direction of the electromagnetic force. The current in the damper winding is dependent on whirling, eccentricity and change of eccentricity; hence, the electromagnetic forces are significantly dependent on the motion of the rotor. The electromagnetic forces are implemented as stiffness and damping matrices in the mechanical model, leading to significant changes in the system's eigenfrequency and damping. Computational fluid dynamics (CFD) has been used to analyse fluid forces and moments acting on the turbine runner. Since rotordynamical analysis is normally carried out for a small model during a long simulation time and CFD-models normally has a large degree of freedom, it is of certain interest to develop models that are computationally efficient. The influence of the details on the upstream flow in the inlet boundary conditions have been analysed in order to obtain computationally efficient boundary conditions. It is shown that the obtained forces and moments increase from an insignificant size for a boundary condition with a perfectly distributed inlet flow to a significant size for a boundary condition, based on more information from the upstream domain. CFD has also been used to determine torsional system coefficients, such as added polar inertia and damping, due to the flow through a hydraulic turbine. It is shown that these coefficients have a significant effect and that it decreases the eigenfrequency and increases the damping ratio of the mechanical system. In addition to the numerical work, two different approaches to identify sources of excitations and the system's eigenfrequencies at industrial units have been suggested. The first approach uses a simplified mathematical model for the electromagnetic forces that occur due to shape deviations in the airgap of the generator, together with an assumption of the frequency content of the fluid forces on the turbine runner. The calculated frequency content at the bearings is compared with on-site measurements and an idea of the possible sources of vibrations is given. The other approach uses the changes in electromagnetic forces at a sudden loss of the magnetic field in the generator to excite the system's eigenfrequencies. It is shown that a few of the eigenfrequencies can be identified with this method. However, when the torque of the generator suddenly decreases due to the loss of magnetic field, the control system of the turbine decreases the mass flow through the turbine, leading to more separations of the flow and a broad-banded excitation that perturbs the measurements. The general conclusion of this thesis states the importance of including multi-physical interactions in a rotordynamical model for analysis of design and operation. It is further concluded that the electromagnetic forces of a synchronous generator show similar characteristics to the ones presented for asynchronous generators with both radial and tangential components, and not only a radial force component as earlier research stated. The damper winding for an asynchronous whirling acts as a damper for all the motion simulated in this thesis, since as the whirling deviates from syncronous whirl, the currents in the damper winding will change and induce a force that dampens the motion. The boundary conditions of a CFD- model of a hydraulic turbine have a large effect on the obtained resulting rotordynamical forces and moments. Hence, it is important to consider accurate inlet boundary conditions in a CFD-model for calculation of rotordynamical forces and moments. The added polar inertia and damping due to the flow through the turbine in a torsional dynamic model have a large effect on the system characteristics of the torsional system, which is an important consideration. The suggested methods for on-site measurements are concluded to be useful. However, they require a better modelling of both the electromagnetic forces (especially the model of shape deviations of the generator airgap) and the fluid-rotor interactions (especially at part discharge and transient operation). There are still several topics concerning rotordynamics in hydropower units that are of interest for further research; for example, continuing development of fluid-rotor interactions of hydraulic turbines and electromagnetic forces. Further research regarding accurate modelling of vertical bearings, as well as models for transient analysis of the whole system, are also suggested.