Rotordynamic Coefficients of Multistepped Annular Seals

Abstract

The basic equations are derived for incompressible flow in multi-stepped annual seals. A 2-D CFD solution is used to verify the model. Exit and entrance loss factors substituted into the bulk flow solution for pressures in the cavity match the 2-D CFD solution. The flow is assumed to be completely turbulent in the axial and circumferential directions with no separation and is modeled using Moody's friction factor relationship. Linearized zeroth- and first-order perturbation equations are developed for small motion about an arbitrary position by an expansion in the eccentricity ratio. The zeroth-order continuity and momentum equations are integrated, yielding the axial and circumferential velocity components and the pressure distribution. The first-order equations are integrated to satisfy the boundary conditions and yield the perturbation pressure distribution. This resultant pressure distribution is integrated along and around the seal to yield the force developed by the seal and the corresponding dynami...