Analysis of Eccentric Annular Incompressible Seals: Part 1—A New Solution Using Fast Fourier Transforms for Determining Hydrodynamic Force

Abstract

A new analysis procedure is presented which solves for the flow variables of an incompressible-flow annular pressure seal in which the rotor has a large static displacement from the centered position. The analysis begins with a set of governing equations based on a turbulent bulk-flow model and Moody’s friction equation. No simplification of these bulk-flow equations are required for the solution procedure. Perturbation of the flow variables yields a set of zeroth and first-order equations. The zeroth-order equations (which model the large static displacement) are integrated by means of an efficient new method which employs Fast Fourier Transforms. Further integration of the zeroth-order pressures yields the hydrodynamic reactive force. Predictions for the hydrodynamic forces from this analysis procedure are in excellent agreement with available experimental results.