Fluid-Structure Interaction Forces at Pump-Impeller-Shroud Surfaces for Axial Vibration Analysis

Abstract

Solutions are presented for the dynamic axial forces developed by pump-impeller-shroud surfaces. A bulk-flow model of the leakage path between the impeller and the housing is used for the analysis consisting of the path-momentum, circumferential-momentum, and continuity equations. Shear stresses at the impeller and housing surfaces are modeled according to Hirs’ turbulent lubrication model. The governing equations were developed earlier to examine lateral rotordynamic forces developed by impellers. A perturbation expansion of the governing equations in the eccentricity ratio yields a set of zeroth and first-order governing equations. The zeroth-order equations define the leakage rate, velocity distributions, and the pressure distribution for a centered impeller position. The first-order equations define the perturbations in the velocity and pressure distributions due to axial motion of the impeller. Integration of the perturbed pressure and shear-stress distribution acting on the rotor yields the reaction forces acting on the impeller face. Calculated results yield predictions of resonance peaks of the fluid within the annulus formed by the impeller shroud and housing. Centrifugal acceleration terms in the path-momentum equation are the physical origin of these unexpected predictions. For normalized tangential velocities at the inlet to the annulus, uθo(0) = Uθo(0)/Riω of 0.5, the phenomenon is relatively minor. As uθo(0) is increased to 0.7, sharper peaks are predicted. The fluid modes are well damped in all cases. Numerical results are presented for a double-suction single-stage pump which indicate that the direct stiffness of the perturbed impeller shroud forces are negligible. Small but appreciable added-mass and damping terms are developed which have a modest influence on damping and peak-amplitude excitation frequency. The forces only became important for pumps with very low axial natural frequencies in comparison to the running speed, viz., ten percent of the running speed or lower.