Rotor Dynamic Coefficients for Partially Tapered Annular Seals for Compression Flow

摘要

The basic governing equations are derived, for compressible flow in an annular smooth seal with partially tapered clearance, from Hirs' turbulent bulk-flow model. The flow is assumed to be completely turbulent in the axial and circumferential directions with no separation. Linearized zeroth and first order perturbation equations are developed for small motion about a centred position by an expansion in the eccentricity ratio. The zeroth order continuity, momentum and energy equations are solved to satisfy the boundary conditions and yield the axial and circumferential velocity components, the pressure and the density distribution. The first order equations are integrated to satisfy perturbation boundary conditions and yield the pressure, the density and the components of velocity perturbation. Integration of the pressure perturbation along and around the seal defines the reaction force developed by the seal and the corresponding dynamic coefficients. The model is validated on Scharrer and Nelson geometric model in comparison with Sriti et al. results for an incompressible flow with small difference pressure. The results of a parametric study on the effect of the tapered length on the seal leakage and rotor dynamic coefficients are presented.