Structural and Multidisciplinary Optimization

, Volume 55, Issue 1, pp 37–51 | Cite as

Toward design optimization of a Pelton turbine runner

  • Christian Vessaz
  • Loïc AndolfattoEmail author
  • François Avellan
  • Christophe Tournier


The objective of the present paper is to propose a strategy to optimize the performance of a Pelton runner based on a parametric model of the bucket geometry, massive particle based numerical simulations and advanced optimization strategies to reduce the dimension of the design problem. The parametric model of the Pelton bucket is based on four bicubic Bézier patches and the number of free parameters is reduced to 21. The numerical simulations are performed using the finite volume particle method, which benefits from a conservative, consistent, arbitrary Lagrangian Eulerian formulation. The resulting design problem is of High-dimension with Expensive Black-box (HEB) performance function. In order to tackle the HEB problem, a preliminary exploration is performed using 2’000 sampled runners geometry provided by a Halton sequence. A cubic multivariate adaptive regression spline surrogate model is built according to the simulated performance of these runners. Moreover, an original clustering approach is proposed to decompose the design problem into four sub-problems of smaller dimensions that can be addressed with more conventional optimization techniques.


Pelton turbine Bucket shape parameterization Design optimization High-dimension Finite volume particle method 


  1. Anagnostopoulos J S, Papantonis D E (2012) A fast lagrangian simulation method for flow analysis and runner design in pelton turbines. J Hydrodyn Ser B 24(6):930–941. doi: 10.1016/S1001-6058(11)60321-1 CrossRefGoogle Scholar
  2. Andolfatto L (2013) Assistance à l’élaboration de gammes d’assemblage innovantes de structures composites. PhD thesis, École Normale Supérieure de Cachan, FranceGoogle Scholar
  3. Ayachit U (2015) The ParaView guide: a parallel visualization application. KitwareGoogle Scholar
  4. Caniou Y (2012) Global sensitivity analysis for nested and multiscale modelling. PhD thesis, Blaise Pascal University-Clermont II, FranceGoogle Scholar
  5. Falcidieno B, Giannini F, Léon J C, Pernot J P (2014) Processing free form objects within a product development process framework. In: Michopoulos J, Rosen D, Paredis C, Vance J (eds) Advances in computers and information in engineering research, ASME. doi: 10.1115/1.860328_ch13, (to appear in print)
  6. Friedman J H (1991) Multivariate adaptive regression splines. Annals Stat 19(1):1–67. MathSciNetCrossRefzbMATHGoogle Scholar
  7. Halton J H (1964) Algorithm 247: radical-inverse quasi-random point sequence. Commun ACM 7(12):701–702. doi: 10.1145/355588.365104 CrossRefGoogle Scholar
  8. Hietel D, Steiner K, Struckmeier J (2000) A finite-volume particle method for compressible flows. Math Models Methods Appl Sci 10:1363–1382. doi: 10.1142/S0218202500000604 MathSciNetCrossRefzbMATHGoogle Scholar
  9. Iooss B, Boussouf L, Marrel A, Feuillard V (2009) Numerical study of the metamodel validation process. In: First international conference on advances in system simulation, 2009. SIMUL ’09., pp 100–105. doi: 10.1109/SIMUL.2009.8
  10. Jahanbakhsh E, Pacot O, Avellan F (2012) Implementation of a parallel SPH-FPM solver for fluid flows. Zetta – Numer Simul Sci Technol 1:16–20Google Scholar
  11. Jahanbakhsh E (2014) Simulation of silt erosion using particle-based methods. PhD thesis, École polytechnique fédérale de Lausanne, no. 6284. doi: 10.5075/epfl-thesis-6284
  12. Jahanbakhsh E, Vessaz C, Avellan F (2014) Finite volume particle method for 3-D elasto-plastic solid simulation. In: 9th SPHERIC International Workshop. Paris, pp 356–362Google Scholar
  13. Jahanbakhsh E, Vessaz C, Maertens A, Avellan F (2016) Development of a finite volume particle method for 3-D fluid flow simulations. Comput Methods Appl Mech Eng 298:80–107. doi: 10.1016/j.cma.2015.09.013 MathSciNetCrossRefGoogle Scholar
  14. Joṡt D, MeŻnar P, Lipej A (2010) Numerical prediction of a Pelton turbine efficiency. IOP Confe Ser Earth Environ Sci 12(1). doi: 10.1088/1755-1315/12/1/012080
  15. Liou M S (1996) A sequel to AUSM: AUSM+. J Comput Phys 129:364–382. doi: 10.1006/jcph.1996.0256 MathSciNetCrossRefzbMATHGoogle Scholar
  16. Mack R, Moser W (2002) Numerical investigation of the flow in a Pelton turbine. In: Proceedings of the 21st IAHR symposium on hydraulic machinery and systems. Lausanne, pp 373– 378Google Scholar
  17. Mack R, Gola B, Smertnig M, Wittwer B, Meusburger P (2014) Modernization of vertical pelton turbines with the help of cfd and model testing. In: IOP Conference series: earth and environmental science, vol 22. IOP Publishing, p 012002Google Scholar
  18. Marongiu J C, Leboeuf F, Caro J, Parkinson E (2010) Free surface flows simulations in Pelton turbines using an hybrid SPH-ALE method. J Hydraul Res 48:40–49. doi: 10.1080/00221686.2010.9641244 CrossRefGoogle Scholar
  19. Michálková K, Bastl B (2015) Imposing angle boundary conditions on B-spline/NURBS surfaces. Comput-Aided Des 62(0):1–9. doi: 10.1016/j.cad.2014.10.002 MathSciNetCrossRefGoogle Scholar
  20. Monaghan J J (2005) Smoothed particle hydrodynamics. Reports Progress Phys 68(8):1703–1759. doi: 10.1088/0034-4885/68/8/R01 MathSciNetCrossRefzbMATHGoogle Scholar
  21. Nestor R M, Basa M, Lastiwka M, Quinlan N J (2009) Extension of the finite volume particle method to viscous flow. J Comput Phys 228(5):1733–1749. doi: 10.1016/ MathSciNetCrossRefzbMATHGoogle Scholar
  22. Pelton LA (1880) Water-wheel., US Patent 233692
  23. Quinlan N J, Nestor R M (2011) Fast exact evaluation of particle interaction vectors in the finite volume particle method. Meshfree Methods Partial Diff Equas V:219–234. doi: 10.1007/978-3-642-16229-9_14
  24. Shan S, Wang G (2010) Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions. Struct Multidiscip Optim 41(2):219–241. doi: 10.1007/s00158-009-0420-2 MathSciNetCrossRefzbMATHGoogle Scholar
  25. Sobieszczanski-Sobieski J, Haftka R (1997) Multidisciplinary aerospace design optimization: survey of recent developments. Struct Optim 14(1):1–23. doi: 10.1007/BF01197554 CrossRefGoogle Scholar
  26. Solemslie B, Dahlhaug O (2012) A reference Pelton turbine design. In: IOP conference series: earth and environmental science, vol 15. IOP Publishing, p 032005, DOI  10.1088/1755-1315/15/3/032005
  27. Sudret B (2008) Global sensitivity analysis using polynomial chaos expansions. Reliab Eng Syst Safety 93 (7):964–979. doi: 10.1016/j.ress.2007.04.002 CrossRefGoogle Scholar
  28. Vessaz C, Tournier C, Münch C, Avellan F (2013) Design optimization of a 2D blade by means of milling tool path. CIRP J Manuf Sci Technol 6:157–166 . doi: 10.1016/j.cirpj.2013.05.002 CrossRefGoogle Scholar
  29. Vessaz C (2015) Finite particle flow simulation of free jet deviation by rotating Pelton buckets. PhD thesis, École polytechnique fédérale de Lausanne, no 6470. doi: 10.5075/epfl-thesis-6470
  30. Vessaz C, Jahanbakhsh E, Avellan F (2015) Flow simulation of jet deviation by rotating pelton buckets using finite volume particle method. J Fluids Eng 137(7):074,501–074,501. doi: 10.1115/1.4029839 CrossRefGoogle Scholar
  31. Xiao Y X, Han F Q, Zhou J L, Kubota T (2007) Numerical prediction of dynamic performance of Pelton turbine. J Hydrodyn Serie B 19:356–364. doi: 10.1016/S1001-6058(07)60070-5 CrossRefGoogle Scholar
  32. Xiao Y X, Cui T, Wang Z W, Yan Z G (2012) Numerical simulation of unsteady free surface flow and dynamic performance for a Pelton turbine. IOP Conf Series: Earth Environ Sci 15(5). doi: 10.1088/1755-1315/15/5/052033
  33. żidonis A, Aggidis G A (2015) State of the art in numerical modelling of Pelton turbines. Renew Sustain Energy Rev 45:135–144. doi: 10.1016/j.rser.2015.01.037 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Christian Vessaz
    • 1
  • Loïc Andolfatto
    • 1
    Email author
  • François Avellan
    • 1
  • Christophe Tournier
    • 2
  1. 1.EPFL, École polytechnique fédérale de LausanneLaboratory for Hydraulic MachinesLausanneSwitzerland
  2. 2.LURPA, ENS Cachan, Univ. Paris-SudUniversité Paris-SaclayCachanFrance

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