Pressure Oscillation in the Leakage Annulus Between a Shrouded Impeller and Its Housing Due to Impeller-Discharge-Pressure Disturbances

Abstract

An analysis is presented for the perturbed flow in the leakage path between a shrouded-pump impeller and its housing caused by oscillations in the impeller-discharge pressure. A bulk-flow model is used for the analysis consisting of the path-momentum, circumferential-momentum, and continuing equations. Shear stress at the impeller and housing surfaces are modeled according to Hirs’ turbulent lubrication model. In the present analysis, perturbations of the impeller discharge pressure are used to excite the fluid annulus. The circumferential variation of the discharge pressure is expanded in a Fourier series up to order n1, where n1 is the number of impeller blades. A precession of the impeller wave pattern in the same direction or opposite to pump rotation is then assumed to completely define the disturbance excitation. Predictions show that the first (lowest-frequency) “centrifugal-acceleration” mode of the fluid within the annulus has its peak pressure amplitude near the wearing-ring seal. Pressure oscillations from the impeller can either be attenuated or (sharply) magnified depending on: (a) the tangential velocity ratio of the fluid entering the seal, (b) the order of the fourier coefficient, and (c) the closeness of the precessional frequency of the rotating pressure field to the first natural frequency of the fluid annulus, and (d) the clearance in the wearing-ring seal.