Backflow-Induced Negative Cross-Coupled Stiffness—A Numerical Study of Multistage Axial-Flow Impeller Rotordynamic Forces

Rotordynamic forces acting on impellers and turbines in multistage turbomachines can significantly influence rotor critical speeds. In axial-flow pumps with unshrouded impellers, fluid-induced lateral forces are impacted by the unsteady tip leakage flow across the blade tips. This study investigates rotordynamic forces in a helico-axial compression cell, in a multistage configuration. A transient computational fluid dynamics (CFD) approach, employing frame change models, is used to determine fluid-induced forces on the whirling rotor. Whirl angular frequencies from -0.75 to 1.10 times the rotor angular frequency were simulated for two operating conditions: the best effciency point (BEP) and 75% of BEP. The simulations revealed destabilizing forces for negative whirl frequencies and generally stabilizing forces for positive whirl frequencies. Overall, the forces were larger at part-load conditions, relative to those at BEP. Rotordynamic coefficients were derived, showing positive direct stiffness, but near-zero values at part load. Negative tangential rotordynamic forces at small whirl frequencies resulted in significant negative cross-coupled stiffness coefficients, also in BEP. Variations in impeller inlet flow angles, linked to the local rate of backflow, affected each impeller channel's pressure increase, varying by approximately ±3% at 75% of BEP. This results in a net lateral force, ultimately responsible for the negative cross-coupled stiffness coefficients. The study demonstrates how significant rotordynamic forces can arise from hydrodynamic effects linked to impeller backflow.