Moment coefficients of incompressible-flow seals with conically whirling rotors

Abstract

A computational model is developed to investigate the dynamic behavior of a rotor that is in contact with a fluid, to infinitesimally small disturbance modes. The rotor here is that of an annular seal, commonly used in turbomachinery applications, with an incompressible flow in the annular clearance gap. Under consideration is an angular excitation of the rotor axis, coupled with a whirling motion around the housing centerline at a finite whirl frequency. The fluid response in this case is quantified in the form of direct and cross-coupled moment coefficients, which constitute a measure of the stiffness, damping and inertia effects of the rotor/fluid interaction. Uniqueness of the computational model stems from the manner in which the rotor eccentricity is physically perceived and subsequently incorporated. It is first established that the fluid reaction components are the result of infinitesimally small deformations of varied magnitudes that are experienced by an assembly of finite elements in the rotor-to-housing gap as the gap becomes distorted due to the rotor virtual eccentricity. The idea is then cast into a perturbation model in which the perturbation equations emerge from the flow-governing equations in their discrete finite-element form, as opposed to the differential form, which is traditionally the case. The computational model is potentially applicable to a wide range of rotor-to-housing pasage configurations where ellipticity of the passage flow field is too significant to ignore. The numerical results are compared to those obtained through an existing bulk-flow model which is particularly suited for the leakage passage in annular seals and other similarly simple passage configurations.