Multiphysical effects on high-speed rotordynamics

Abstract

A growing number of research projects focus on the development of rotating machinery on a small scale. These machines generally operate at high speeds and as a result multiphysical effects such as interaction with the surrounding air and thermal effects become significant for the dynamics. Therefore, the multiphysical effects should be modeled and coupled with the structural models in order to perform rotordynamic analysis accurately. This thesis describes modeling approaches for flow-induced forces in moderate flow confinements such as a casing and for temperature increase of fluid in the confinement. Furthermore, a method to couple the flow force model and thermal model with the structural model has been proposed. An experimental setup has been designed and constructed in order to verify the simulations with experimental data. The gap ratio (air gap/rotor radius) in the moderate flow confinement is two orders of magnitude greater than the ones in small air gap geometries such as bearings and seals (0.1 to 0.001). Due to high rotation speeds, the inertia effects become significant as well as the viscous effects. A theoretical model for flow-induced forces in terms of added mass, damping and stiffness was available in the literature for turbulent flow. This model is extended for laminar flow and transition by using the suitable empirical and analytical friction coefficients to model the shear stress. Then a method to implement the flow forces to the rotor finite element model as a spring damper and added mass at each node is proposed. Finite element modeling of the rotor is based on Timoshenko beams (including the flexibility of the rotor shaft) and each element has four degrees of freedom at each node. As the rotation speed increases, the heat loss due to air friction and the temperature increase in the air gap between rotor and stator become more significant. Consequently, the change of air properties due to temperature change in the air gap should be considered when calculating the flow-induced forces. Therefore, a thermal model is established in order to calculate the heat dissipation and as a result, the temperature increase of the air. In this model, the rotor, stator and the gap in between is modeled as lumped thermal networks. The required convective heat transfer coefficients and heat dissipation are calculated by empirical correlations. Afterwards, the new air gap temperature is used to calculate the flow-induced forces with updated air properties. In this way, thermal and fluid effects in medium gap confinements are coupled with the rotordynamic models and their effects on critical speeds and stability are investigated. An experimental setup has been designed to verify the developed models for multiphysical effects on a small scale. The design criteria have been determined such that the rotor size is large enough to make multiphysical effects measurable in the operation range. Flexible supports with changing stiffness are designed to examine the effect of support stiffness. Experiments are performed as spectrum measurements and modal analysis at different support stiffness with and without casing. The developed modeling approach is verified by experimental results. Finally, a simple way to overcome experimentally and theoretically observed instability problems has been presented. Stationary damping is increased by mounting viscoelastic inserts on the support disk. The spectrum and modal analysis experiments are repeated for different viscoelastic materials and significant improvement has been observed. In summary, a method has been developed to couple flow induced forces with structural FE model including the thermal effects. This method can be used for the rotordynamic analysis of high-speed mini rotating machinery with medium gap for both laminar and turbulent flow regimes. In addition, the usage of viscoelastic materials to avoid theoretically and experimentally observed instability is demonstrated.