ROTORDYNAMIC COEFFICIENTS OF INCOMPRESSIBLE-FLOW DAMPING SEALS USING COLEBROOK FORMULA

The basic equations are derived for incompressible flow in an annular seal with large-scale roughness. The flow is assumed to be completely turbulent in the axial and circumferential directions with no separation, and is modeled using Colebrook'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 dynamic coefficients. Results of this analysis are compared with one using Moody's equation and with experimental data for leakage and rotordynamic coefficients.