| An unsteady three-dimensional potential flow model was developed. The panel method (a surface singularity technique), as developed by Hess and Smith, formed the basis for this model. Instantaneous and time-averaged dynamic fluid forces, acting on whirling centrifugal impellers, were computed. Unbounded impellers and impellers bounded by a volute were analyzed. Inertial, damping, and stiffness matrices were presented for both types of impellers.; For the unbounded impeller, the radial and tangential forces remained constant in time. Therefore, the rotordynamic matrices possessed skew-symmetry. When bounded impellers were operated at design flows and beyond, the rotordynamic matrices could be approximated by skew-symmetry matrices.; For both the unbounded and bounded impeller analyses,the panel method correctly predicted radial force trends with increasing flow. However, for negative whirl speed ratios, the radial force predictions were underestimated. The radial force predictions were offset below the experimental data, yielding poor estimates for the primary stiffness terms.; In the case of the unbounded impeller, cross-coupling stiffness coefficients were accurately predicted at design flows and above. The destabilizing cross-coupling stiffness coefficients, which were found experimentally at flows below the design point, were not predicted by the panel method.; In the case of the bounded impeller, a low flow instability was predicted in the region 0 {dollar}<{dollar} {dollar}Omega{dollar}/{dollar}omega{dollar} {dollar}<{dollar} 0.3. The experimental instability region was somewhat larger, extending to whirl speed ratios as great as 0.5. Correct trends with increasing flow were predicted. Cross-coupling stiffness coefficients were predicted with the correct sign. The magnitude of these coefficients were underpredicted by a factor of two at low flows. This underprediction grew to a factor of four at flows beyond the design point.; The computational technique developed in this study has the capability of assessing dynamic fluid forces acting on a single stage centrifugal pump. It provides analytical verification of the existence of a subsynchronous whirl instability region for centrifugal pumps bounded by a volute. |
