# Gravels and stones impact

Gravels and stones found in streams can become a severe nuisance to the operation of a hydropower plant. In the case of a Pelton turbine, the momentum of stones impacting one or many of its buckets can cause them to crack or break, which indeniably leads to the immediate cease of operations of the concerned turbine and hence to a great economic loss for the exploiting company. Determining the nature of the phenomenon leading to a Pelton turbine’s demise can be quite an ardous task, many times leading to disputes between the manufacturer and the operator of the turbine. In order to predict the nature and extent of the damage that stones on a jet stream can induce on a Pelton’s bucket, the current subject aims to numerically simulate this phenomenon by using cutting-edge numerical methods for the simulation of the fluid and solid subdomains along with coupling algorithms which allow to more accurately capture the physics behind this problem.

A Smothed-Particle-Hydrodynamics expressed in an Arbitrary-Lagrangian-Eulerian framework (SPH-ALE) approach will be used to simulate the water flow through the injectors and into the Pelton turbine. This revolutionary mesh-less technique allows to simulate free-surface flows while more accurately representing the fluid flow repartition upon the impact of the jet on the bucket. ASPHODEL, an internally developed SPH-ALE solver by Andritz Hydro, will be used throughout the whole project for the simulation of fluid flows.

For the simulation of the Pelton turbine bucket and rocks in the jet stream, a classical Finte-Element approach will be implemented. The robustness and maturity of this method make it the ideal choice as the problem at hand aims at accurately describing complex non-linear behaviors that this method is known to handle well. Different solvers, either commercial or developed internally, will be used to carry out the simulation of solid structures.

Finally, in order to couple the fluid and solid solvers, an algorithm that ensures energy conservation at the interface will be implemented. This algorithm, besides being able to accurately represent the fundamental laws of physics, allows to put the SPH-ALE and Finite-Element formulations under a common formalism. The coupling algorithm used throughout this project was developed internally during previous doctoral works, however several features are being added to it to make it more efficient. These features include the adaptability of the algorithm to any given geometry, the possibility of solving problems where the solid and fluid subdomains have different time steps, the inclusion of more efficient output/input formats and the nesting of the algorithm within ASPHODEL’s source code.

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