Rotordynamic Coefficients for Partially Roughened Pump Annular Seals

Abstract

The basic equations are derived for incompressible flow in an annular seal with partially roughened surfaces. The flow is assumed to be completely turbulent in the axial and circumferential directions with no separation, and is modeled by Hirs’ turbulent lubrication equations. Linearized zeroth and first-order perturbation equations are developed for small motion about a centered position by an expansion in the eccentricity ratio. The zeroth-order continuity and momentum equations are solved numerically, yielding the axial and circumferential velocity components and the pressure distribution. The first-order equations are reduced to three linear, complex, ordinary, differential equations in the axial coordinate Z. The equations are integrated to satisfy the boundary conditions and yield the perturbated pressure distribution. This resultant pressure distribution is integrated along and around the seal to yield the force developed by the seal from which the corresponding dynamic coefficients are derived. The results of a parametric study on the effect of the rough length/smooth length ratio on the seal leakage and rotordynamic coefficients are presented.