Numerical Determination of the Acoustic Impedance of a Centrifugal Pump

The perturbations generated at the blade-passing frequency and higher harmonics in centrifugal pumps due to the rotor-stator interaction represent a significant contribution to the total load on the machine, which can bring about excessive vibration and noise levels thus limiting the pump performance. These perturbations are in close relation to the pump’s internal geometry and also to the point of operation; in addition, their magnitude is influenced by the acoustic coupling between the pump and the pipelines. The latter can be characterized by the equivalent acoustic impedance; however, the acoustic characterization of the pump is more complex. The usual boundary conditions imposed in numerical simulations of centrifugal pumps (constant outlet velocity, constant static pressure, or pressure loss proportional to squared velocity) induce a particular type of coupling between the pump and the hydraulic network. Hence, the real performance values of the pump are expected to change from those obtained in the simulations if the coupling conditions are modified. The purpose of the present investigation is to obtain a simple 1-D model for the acoustic impedance of a volute-type centrifugal pump from the full 3-D unsteady flow simulations carried out with the code Fluent®. For this purpose, a specific pressure fluctuation is imposed at the outlet port of the pump by means of a user-defined function. The amplitude and frequency of this fluctuation is modified to obtain the response of the pump (i.e., the acoustic impedance) for a series of flow rates. The acoustic 1-D model obtained will allow a quick prediction of the perturbations generated from the acoustic impedance of the network to which the pump is to be coupled.