Geometry dependence of the acoustic transmission and reflection properties of centrifugal pumps based on an internal lumped parameter model

Abstract

Abstract As a tool to characterize the acoustic properties of conventional centrifugal pumps, consisting in impeller and vaneless volute casing, a new acoustic lumped parameter model has been developed that simulates the acoustic field induced inside the pumps when subject to low-frequency sound sources. The model is based on a network of nodes distributed through the pump, with local transfer matrices connecting pairs of nodes at neighboring regions, and so it is referred to as an internal transfer matrix model. At the present stage the model has been implemented in a procedure to determine the pump passive acoustic properties, either in terms of a transmission matrix or a scattering matrix, though in a future step the model is to be applied for the characterization of the internal sound sources in centrifugal machinery. This paper presents the assumptions of the model and the resolution approach to calculate transmission or scattering matrices, as well as a summary of results for a reference pump that shows the sensitivity of predictions with respect to several geometrical pump parameters. Finally, a contrast is carried out between experimental data recently reported in the literature on the scattering matrices for five pumps of different geometry and the corresponding predictions obtained from (i) the new lumped parameter model based on internal transfer matrices and (ii) a classical pump model based on an electrical system analogy. The results show that the predictions of the new transfer matrix model are always in reasonable quantitative agreement with measurements, and that, as frequency is increased, its prediction capability clearly outperforms that of the electrical analogy model regardless the pump specific speed or the geometrical features.