Resolvent analysis of flow inside a centrifugal pump*

The near-tongue region of a centrifugal pump where the impeller and the volute meet plays a critical role in determining its overall performance and efficiency. The flow in this region is characterized by its complex unsteady behavior including flow separation and vortex shedding, which impact the pump operation.  In this study, we employ resolvent analysis to investigate the unsteady flow dynamics in the near-tongue region of a centrifugal pump. Resolvent analysis allows us to identify the input and output modes about the baseflow. Here, the baseflow is taken to be the time-averaged turbulent flow in a two-dimensional centrifugal pump at $Re =\mathcal{O}$.  Our findings reveal the existence of key modes and frequencies that govern the flow behavior in the near-tongue region. At below-nominal flow rate, the primary resolvent forcing and response modes appear inside of the tongue. On the other hand, when the flow rate is above nominal flow rate, the modal structures reside outside of the tongue.  The identification of the resolvent modes and their frequencies has implications for potential design modification near the tongue.