Numerical Modelling of Sediment–Laden Flows in Hydraulic Machines: A Critical Review of Multiphase Approaches, Erosion Models, and Computational Challenges

The accurate prediction of sediment–laden flows and the resulting erosion in hydraulic machines remains a challenging problem that involves the coupling of multiphase fluid dynamics and solid–surface interaction models. This work aims to provide a critical and systematic assessment of the numerical methodologies developed for this purpose. The review focuses on the mathematical and computational frameworks used to represent the dispersed solid phase and its erosive action on machine components, analysing in detail both Eulerian and Lagrangian formulations. A comprehensive survey of the available literature was performed, covering numerical studies on Pelton, Francis and Kaplan turbines, as well as centrifugal pumps. Each publication was examined with respect to its modelling approach, governing equations, coupling strategy, erosion model, and computational setup. The collected data were organised into comparative tables that enable a structured evaluation of model complexity, numerical assumptions, mesh characteristics, and validation procedures. The objective of this review is to clarify the modelling strategies currently available for simulating sediment transport and erosion, to highlight the mathematical assumptions underlying each approach, and to identify the open challenges that still hinder model calibration, standardisation and broader applicability. The paper provides a methodological framework intended to guide future developments toward reliable and computationally efficient multiphase models for sediment–laden hydraulic flows.