Unified Prediction of Hydrodynamic Forces in Plain Annular Seals and Journal Bearings by means of an Analytically Derived Design Tool

Annular seals and journal bearings are essential parts of rotating machinery and share comparable geometries characterized by narrow annuli between rotor and stator. Both machine elements exert hydrodynamic forces on the rotor that must not be neglected during the design process. Accurate prediction of these forces by means of fast and reliable design tools is required to optimize the rotordynamic shaft design within short time.

The paper deals with the analytical development of a unified design tool to predict the hydrodynamic forces for both annular seals and hydrodynamic bearings in rotating machinery. The requirements on such a unified tool are discussed in terms of various flow regimes that are to be expected in thin film flows in rotating machinery. Following that, the analytic derivation of our ‘Clearance-Averaged Pressure Model’ (CAPM) is described. All simplifications applied can be justified by means of the characteristic geometries of the narrow annuli. Especially, no further assumptions regarding the flow regime (laminar/turbulent), the role of fluid inertia or the friction modeling were applied. The CAPM provides a clear interface to the vast knowledge about friction modeling that has been accumulated in hydrodynamic lubrication research. Thus, the CAPM serves as a generalized modeling framework for all typical thin film flows in rotating machinery and includes both Reynolds’ differential equation and the bulk-flow model as special cases. Hence, user-specific uncertainties on the applicability of a specific design tool for a specific application are reduced.

The accuracy of the current state of our model is assessed by means of comparisons to Computational Fluid Dynamics (CFD) results. We applied both the CAPM and CFD to test cases typically representing geometrical and operational characteristics of annular seals within a parameter study. The predicted hydrodynamic radial forces agreed well for all operating points considered. In contrast to that, the predicted tangential forces agreed well only if the flow number φ is small or if the preswirl is close to Γ=0.5. The observed differences are discussed by means of the different roles of velocity profile development throughout the annulus.