Bulk-Flow Model for the Transition to Turbulence Regime in Annular Pressure Seals

An analysis for the prediction of the dynamic force response for annular seals in the transition regime to flow turbulence is presented. A heuristic curve fit connects the laminar friction factor to Moody's turbulent friction factor curve in the transition regime from laminar to fully developed turbulent flows. A universal friction factor model is provided and included in the bulk-flow equations (zeroth- and first-order) governing the flow for small amplitude rotor motions about an equilibrium position. General equations are presented for the shear coefficients and their derivatives required in the bulk-flow model. Flow rates, drag torque and rotordynamic force coefficients are compared with those from traditional analyses for an annular seal experiencing wear and increased clearances leading to off-design operating conditions. Predicted seal force coefficients show physically sound, smooth variations while passing through the transition zone and demonstrate a marked improvement over simpler models which predict sharp discontinuities.