## Abstract

Centrifugal pumps work in a wide range of conditions, often far from the design condition. The flow field can be characterized by large separations, vortex dynamics, and, in general, unsteady turbulent phenomena. Strongly off-design conditions are characterized by large separations that lead to efficiency loss, vibrations, and even to fatigue failure. Therefore, the capability to predict the flow field in these conditions is of great interest and computational fluid dynamics (CFD) can represent a viable solution, which can also complement or substitute experimental measurements. In this context, the Reynolds-averaged Navier–Stokes (RANS) approach allows to accurately simulate attached turbulent flows around complex geometries but it fails the prediction of massively separated flows, crucial for the off-design performance. To overcome this limitation, scale-resolving simulations based on the large eddy simulation (LES) can be used. However, their computational cost is too large for a routine use in industry. In centrifugal pumps, where the typical Reynolds number is in the range $105−106$, the use of a hybrid RANS–LES model or a wall modeled LES approach seems mandatory to improve the RANS accuracy and reduce the LES computational cost. In this work, an improved version of the extra-large eddy simulation (X-LES) model, the delayed X-LES or DX-LES model, is implemented in the open-source tool-box openfoam v.1812 and is assessed in the computation of the flow field through a centrifugal pump impeller, both at the design and one-quarter loads. The results are compared with experimental data and LES results available in literature.

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