Flow Field Instability and Rotordynamic Impedances for an Open Impeller Centrifugal Pump in Transient Four-Quadrant Regimes

The American Petroleum Institute (API) level 2 rotordynamic stability analysis requires determination of all possible destabilization forces on a compressor or pump impeller. Dynamic forces in transient regimes are often excluded although a turbomachine impeller may experience transient operation intentionally or accidentally. The centrifugal pump head, flow direction, rotation and torque can be both positive and negative in transient regimes. Theoretically, 16 combinations of fluid head, flow direction, rotation and torque can exist. For example, in a renewable energy application, pump flow direction and rotation are reversed to generate power from the imposed fluid head. The complete characteristics of a centrifugal pump correspond to all four quadrants (4Q) of operation, to encompass all possible operating conditions. Pump manufacturers typically provide only performance curves for normal pump operations (1Q). It may be required to understand centrifugal pump impeller dynamic forces and rotordynamic responses for all 4Q for design, fault diagnostic, instability analysis, upset conditions (water hammer, surge etc.) and for reliable operation of high energy density machines. There are very limited data for impeller head and pump efficiency for transient 4Q operations. In the open literature, whirling impeller rotordynamic analyses appear only for normal pump operation. Centrifugal pump dynamic forces, rotordynamic impedances and flow instabilities of an open impeller are reported for 4Q operating regimes in this paper. A transient Computational Fluid Dynamics (CFD)-based model is implemented which is applicable to nonaxisymmetric turbomachinery components, such as with a volute and/or vaned diffuser. The model includes all components of a centrifugal pump flow path/stage including suction, impeller, diffuser, volute, outlet and seal. Whirling motion of the impeller is modeled by imposing mesh deformation at the impeller walls. Phase modulated multi-frequency displacements are imposed via mesh deformation. Then rotordynamic impedance of the impeller for a particular flow coefficient and eccentricity ratio is extracted from a single simulation run using a multi-frequency mesh deformation model. Reynolds Averaged Navier-Stokes (RANS) equations with the Shear Stress Transport (SST) turbulence model are employed for the CFD solution. A transitional bypass turbulence model was used in the numerical simulation to accurately capture flow transition and stall cells involved in the unsteady flow of the whirling impeller in 4Q operation. The results show the underlying flow field instability and stall cells responsible for the impedance shapes. The model is employed for determining the dependence of the outputs on specific speed to extract rotordynamic forces more efficiently. 4Q impedances mapped over specific speed are applicable to a wide range of open impellers for prediction of rotordynamic responses. Impeller dynamic forces are found to scale with the size of the impeller for the same eccentricity ratio and the same flow coefficient. Strength of impeller rotating stalls has dependence on whirl frequency ratio.