Friction behavior of labyrinth seals for fast and reliable design tools based on integro-differential lubrication models

Authors

Robin M. Robrecht  - Chair of Fluid Systems, Technische Universität Darmstadt, Germany
Peter F. Pelz - Chair of Fluid Systems, Technische Universität Darmstadt, Germany

Abstract

Annular seals and journal bearings have significant influence on the design of turbomachines like centrifugal pumps. Firstly, requirements on power density and operational flexibility necessitate precise rotordynamic design of a turbomachine and thus accurate knowledge of forces acting on the rotor. The added mass, damping and stiffness of a seal or bearing influence resonance frequencies and stability. Secondly, the axial leakage flow through such an annulus is of importance for internal pump hydraulics. The leakage does not only have a direct impact on the volumetric efficiency of the machine, but can also be essential for functionality of axial thrust balancing devices or pressure balancing ducts.For the prediction of rotordynamic coefficients and leakage flow, integro-differential lubrication models are generally used. In contrast to CFD, these models are used as fast design tools and for optimization applications. The typical models can generally be divided into three types: one-dimensional bulk flow models, two-dimensional bulk-flow models and Reynolds’ equation (two-dimensional).All three types have shortcomings which can lead to unacceptable prediction uncertainty. One-dimensional bulk flow models are only valid for small eccentricity. In contrast, two-dimensional variants can be used at high eccentricity, too. Nevertheless, the bulk flow averaged inertia terms introduce inaccuracy at low to moderate Reynolds numbers and necessitate the use of purely empirical wall friction models. In case of Reynolds’ equation, extensions exist to incorporate fluid inertia and turbulence. However, the linear differential equation is generally not well suited for superposed axial flow which is usually present in turbomachinery [1].For this reason, the Clearance-Averaged Pressure Model (CAPM) has been developed [1, 2, 3]. The CAPM is a superordinate theory unifying two-dimensional integro-differential models for flow in plain annular gaps covering the full parameter space (laminar and turbulent flow, superposed axial flow, low to high eccentricity). The CAPM has been validated for plain cylindrical geometries at turbulent [2] and laminar flow [1].While the behavior of these plain cylindrical geometries can be predicted reliably, this does not apply to labyrinth or damper seals which are characterized by a structured stator. The change in friction behavior affects leakage and rotordynamic coefficients. In the past, attempts to model labyrinth and damper seals have not been very successful. Thus, in the present paper a generic rectangular seal groove is investigated. The general flow characteristics are analyzed by means of CFD. The applicability of specific friction models is examined. The obtained results can be used to incorporate the effects of arbitrarily structured stators in integro-differential models for plain annuli like the CAPM in a semi-empirical way.[1] Robrecht, R.; Pelz, P.: The Lomakin effect at laminar flow in journal bearings – modeling and simulation. Tribology International, 2022 (under review).[2] Kuhr, M.; Lang, S.; Pelz, P.: Static force characteristic of annular gaps - experimental and simulation results, Journal of Tribology, 2022.[3] Robrecht, R.; Kuhr, M.; Pelz, P.: CAPM vs. Bulk Flow - reliable and efficient prediction of forces and leakage for annular gaps in pumps. Proceedings of the 4th International Rotating Equipment Conference, 2019.