A fast Lagrangian simulation method for flow analysis and runner design in Pelton turbines

In the present work, an alternative numerical methodology is developed for a fast and effective simulation and analysis of the complex flow and energy conversion in Pelton impulse hydro turbines. The algorithm is based on the Lagrangian approach and the unsteady free-surface flow during the jet-bucket interaction is simulated by tracking the trajectories of representative fluid particles at very low computer cost. Modern regression tools are implemented in a new parameterization technique of the inner bucket surface. Key-feature of the model is the introduction of additional terms into the particle motion equations to account for various hydraulic losses and the flow spreading, which are regulated and evaluated with the aid of experimental data in a Laboratory Pelton turbine. The model is applied to study the jet-runner interaction in various operation conditions and then to perform numerical design optimization of the bucket shape, using a stochastic optimizer based on evolutionary algorithms. The obtained optimum runner attains remarkably higher hydraulic efficiency in the entire load range. Finally, a new small Pelton turbine (150 kW) is designed, manufactured and tested in the Laboratory, and its performance and efficiency verify the model predictions.