Influence of the bucket geometry on the Pelton performance

The increasing share of hydropower in world electricity production requires the development of standardized and optimized design procedures leading to increasingly higher efficiency values. To date, despite a certain amount of support from computational fluid dynamics, Pelton turbines are still characterized by semiempirical design criteria that do not make it possible to optimize the jet–bucket interaction in order to maximize turbine performance. Based on an analysis of particle flow tracks, this paper presents a hybrid Eulerian–Lagrangian method to investigate the influence of bucket geometry on the Pelton efficiency at two different operating conditions. Jet–bucket interaction was numerically analyzed by means of a traditional mesh-based numerical approach, using a transient multi-phase homogeneous model. Subsequently, the numerical results were integrated using a predictor–corrector algorithm, combining a fourth order Adams-Bashforth method as predictor and a fourth order Adams-Moulton method as corrector, in order to determine the fluid particle trajectories on the rotating buckets. The particle flow tracks were analyzed in detail to evaluate the single-particle performance in terms of discharged kinetic energy, momentum variation, and total energy variation during the jet–bucket interaction. Moreover, on the basis of the particle discharging position, the contribution of the different bucket areas to the total torque of the turbine was investigated to determine the time-depending influence of the bucket geometry on the turbine energy exchange and to suggest possible design solutions for improving bucket performance.