Free surface flows simulations in Pelton turbines using an hybrid SPH-ALE method

Abstract

An Arbitrary Lagrange Euler (ALE) description of fluid flows is used together with the meshless numerical method Smoothed Particle Hydrodynamics (SPH) to simulate free surface flows. The ALE description leads to an hybrid method that can be closely connected to the finite volume approach. It is then possible to adapt some common techniques like upwind schemes and preconditioning to remedy some of the well known drawbacks of SPH like stability and accuracy. An efficient boundary treatment based on a proper upwinding of fluid information at the boundary surface is settled. The resulting SPH-ALE numerical method is applied to simulate free surface flows encountered in Pelton turbines. RÉSUMÉ La méthode numérique sans maillage Smoothed Particle Hydrodynamics (SPH) est modifiée par l'adoption d'une description Arbitrary Lagrange Euler (ALE) des écoulements fluides, dans le but de simuler des écoulements à surface libre. Le formalisme ALE conduit à une méthode numérique hybride s'apparentant sur de nombreux points à une approche volumes finis. Il est alors possible d'adapter des techniques numériques courantes comme les schémas décentrés et le préconditionnement pour résoudre certains défauts majeurs de la méthode SPH, comme la stabilité numérique ou le manque de précision. Par ailleurs, le traitement des conditions limites est réalisé par un décentrement approprié des informations fluides sur les surfaces frontières. La méthode numérique SPH-ALE résultante est appliquée à la simulation d'écoulements à surface libre tels que ceux rencontrés dans les turbines Pelton.

State of the art in numerical modelling of Pelton turbines

“…Being a Lagrangian technique SPH is a promising tool for free surface, multiphase flow modelling as it does not require any mesh. However, even the latest publications on modelling of a Pelton runner using SPH express concerns on the accuracy of the code [62,63] or suggest that the method needs some further validation and development [64]. There is a publication on modelling of Turgo, another impulse turbine, using SPH claiming that it has produced similar results to Fluent in much less time and therefore is a good alternative to Eulerian methods [65].…”

Neighbour lists in smoothed particle hydrodynamics

“…However, this result can be improved in those cases where the loop over particles should be carried out more than once per time step. This is the case, for example, of different improvements in classical SPH formulation as MLS filters [12,36], kernel and kernel gradient corrections [37][38][39][40] or Riemann solvers [41]. In CLL the potential neighbours placed in The improvement is referred to CLL.…”

Development of hydro impulse turbines and new opportunities

“…Therefore considering the strengths and weaknesses of these meshless codes they can be used for the initial design stages [74]. The names of such codes used for Pelton turbine modelling are Smoothed Particle Hydrodynamics (SPH) [81][82][83], Fast Lagrangian Simulation (FLS) [84][85][86], Moving Particle Semi-implicit (MPS) method [87] and Finite Volume Particle Method (FVPM) [88].…”