CFD investigation of sediment-laden flow through Francis turbine guide vanes with clearance gap: Eulerian versus Lagrangian modeling

Hydraulic turbines operating in sediment-laden rivers are continuously exposed to solid particles transported by the water flow. The repeated impacts between sediments and turbine components progressively remove material from their surfaces, causing hydraulic efficiency losses, increased maintenance costs and reduced service life. Among the various turbine components, the guide vane system and its clearance gap represent one of the most critical regions, since the pressure difference between the pressure and suction sides generates a leakage flow capable of transporting sediments into confined regions where erosion is particularly severe. Nowadays, the Eulerian–Lagrangian approach is considered the state-of-the-art numerical methodology for simulating sediment transport and erosion because it provides detailed information on particle trajectories and impact characteristics required by most erosion models. However, its computational cost becomes prohibitive for dense slurry flows, where particle–particle interactions and strong phase coupling significantly increase solution time. These limitations motivate the development of alternative approaches capable of maintaining adequate accuracy while reducing computational effort. The main objective of this Thesis project is the development and qualitative validation of a novel inhomogeneous Eulerian–Eulerian methodology for the simulation of sediment-laden flows inside a Francis turbine guide vane system with clearance gap. Particle transport is modelled through the Kinetic Theory of Granular Flow, while turbulence is reproduced using the homogeneous k-ω SST model. The proposed methodology is validated through a qualitative comparison with a reference Eulerian–Lagrangian model and data available in the literature. The numerical investigation first considers single-phase simulations to characterize the hydraulic behaviour of the guide vane system and the leakage flow through the clearance gap. Multiphase Eulerian–Eulerian simulations are then performed to investigate the influence of sediment concentration, particle diameter and guide vane opening angle on sediment transport. The results demonstrate that the Sediment Volume Fraction and, especially, the Sediment Wall Shear Stress successfully reproduce the qualitative erosion patterns observed on guide vanes and facing plates, confirming their suitability as erosion indicators within the Eulerian framework. A quantitative analysis confirms that the proposed model correctly captures the influence of the main operating parameters on sediment transport. Increasing sediment concentration leads to higher Sediment Wall Shear Stress values, whereas larger particles produce the opposite effect. Although this behaviour differs from trends reported in the literature, additional analyses provide a plausible explanation: larger particles, owing to their greater inertia, are less able to follow the secondary flow structures crossing the clearance gap and therefore reach the most critical surfaces less frequently, reducing both the local sediment concentration and the associated wall shear stress. Finally, the comparison between the Eulerian–Eulerian and Eulerian–Lagrangian approaches demonstrates a generally good agreement in reproducing the dominant transport mechanisms governing sediment-laden flows. The Eulerian methodology provides smoother and more informative erosion-indicator distributions while correctly reproducing the influence of sediment concentration, particle diameter and turbine loading. These findings demonstrate that the proposed methodology represents a promising alternative for the simulation of sediment-laden flows and provides a solid basis for the future development of novel erosion models, based on full Eulerian approach, for hydraulic machinery.