Skip to main content
Top
Published in:
Cover of the book

2019 | OriginalPaper | Chapter

Simple Models for Cross Flow Turbines

Authors : Esteban Ferrer, Soledad Le Clainche

Published in: Recent Advances in CFD for Wind and Tidal Offshore Turbines

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Using a high order discontinuous Galerkin numerical method with sliding meshes, we simulate one, two and three bladed cross-flow turbines to extract statistics of the generated wakes (time averaged velocities and Reynolds stresses). Subsequently, we compare the wakes resulting from simple models (a circular cylinder and an actuator disc) to the time averaged cross-flow turbine wakes. Additionally, we provide results for a reduced order model based on dynamic mode decomposition (Le Clainche and Ferrer, Energies, 11(3), 2018, [1]). Whilst simplified models find difficulties in capturing wake asymmetries characteristic of cross-flow turbines, our proposed reduced order model captures mean values and Reynolds stresses with good accuracy, showing the potential of the last technique to speed up the simulation of cross-flow turbine statistics.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Footnotes
1
Airfoil aerodynamics and hydrofoil hydrodynamics are equivalent nomenclatures for foils operating in air or water environments. Since this work encompasses both wind and tidal turbine applications, from this point onwards, “foils” will denote either “airfoils” or “hydrofoils”. In addition, the term “aerodynamic” can always be replaced by “hydrodynamic” in this work.
 
Literature
1.
go back to reference Le Clainche S, Ferrer E (2018) A reduced order model to predict transient flows around straight bladed vertical axis wind turbines. Energies 11(3) Le Clainche S, Ferrer E (2018) A reduced order model to predict transient flows around straight bladed vertical axis wind turbines. Energies 11(3)
2.
go back to reference Gretton GI, Bruce T (2005) Preliminary results from analytical and numerical models of a variable-pitch vertical-axis tidal current turbine. In: 6th European wave and tidal energy conference, Glasgow, UK, September 2005 Gretton GI, Bruce T (2005) Preliminary results from analytical and numerical models of a variable-pitch vertical-axis tidal current turbine. In: 6th European wave and tidal energy conference, Glasgow, UK, September 2005
3.
go back to reference Gretton GI, Bruce T (2006) Hydrodynamic modelling of a vertical-axis tidal current turbine using a Navier–Stokes solver. In: Proceedings of the 9th world renewable energy congress, Florence, Italy, 2006 Gretton GI, Bruce T (2006) Hydrodynamic modelling of a vertical-axis tidal current turbine using a Navier–Stokes solver. In: Proceedings of the 9th world renewable energy congress, Florence, Italy, 2006
4.
go back to reference Ferrer E, Willden RHJ (2015) Blade-wake interactions in cross-flow turbines. Int J Mar Energy 11:71–83CrossRef Ferrer E, Willden RHJ (2015) Blade-wake interactions in cross-flow turbines. Int J Mar Energy 11:71–83CrossRef
5.
go back to reference Montlaur A, Giorgiani G (2015) Numerical study of 2D vertical axis wind and tidal turbines with a degree-adaptive hybridizable discontinuous Galerkin Method. In: Ferrer E, Montlaur A (eds) CFD for wind and tidal offshore turbines, Chap 2. Springer Tracts in Mechanical Engineering. Springer, Cham pp 13–26 Montlaur A, Giorgiani G (2015) Numerical study of 2D vertical axis wind and tidal turbines with a degree-adaptive hybridizable discontinuous Galerkin Method. In: Ferrer E, Montlaur A (eds) CFD for wind and tidal offshore turbines, Chap 2. Springer Tracts in Mechanical Engineering. Springer, Cham pp 13–26
6.
go back to reference Somoano M, Huera-Huarte FJ (2017) Flow dynamics inside the rotor of a three straight bladed cross-flow turbine. Appl Ocean Res 69:138–147CrossRef Somoano M, Huera-Huarte FJ (2017) Flow dynamics inside the rotor of a three straight bladed cross-flow turbine. Appl Ocean Res 69:138–147CrossRef
7.
go back to reference Bachant P, Wosnik M (2015) Characterising the near-wake of a cross-flow turbine. J Turbul 16(4):392–410CrossRef Bachant P, Wosnik M (2015) Characterising the near-wake of a cross-flow turbine. J Turbul 16(4):392–410CrossRef
8.
go back to reference Islam M, Ting DSK, Fartaj A (2008) Aerodynamic models for Darrieus-type straight-bladed vertical axis wind turbines. Renew Sustain Energy Rev 12(4):1087–1109CrossRef Islam M, Ting DSK, Fartaj A (2008) Aerodynamic models for Darrieus-type straight-bladed vertical axis wind turbines. Renew Sustain Energy Rev 12(4):1087–1109CrossRef
9.
go back to reference Newman BG (1983) Actuator-disc theory for vertical-axis wind turbines. J Wind Eng Ind Aerodyn 15(1–3):347–355CrossRef Newman BG (1983) Actuator-disc theory for vertical-axis wind turbines. J Wind Eng Ind Aerodyn 15(1–3):347–355CrossRef
10.
go back to reference Araya DB, Colonius T, Dabiri JO (2017) Transition to bluff-body dynamics in the wake of vertical-axis wind turbines. J Fluid Mech 813:346–381MathSciNetCrossRef Araya DB, Colonius T, Dabiri JO (2017) Transition to bluff-body dynamics in the wake of vertical-axis wind turbines. J Fluid Mech 813:346–381MathSciNetCrossRef
11.
go back to reference Ferrer E (2012) A high order Discontinuous Galerkin - Fourier incompressible 3D Navier–Stokes solver with rotating sliding meshes for simulating cross-flow turbines. PhD thesis, University of Oxford, 2012 Ferrer E (2012) A high order Discontinuous Galerkin - Fourier incompressible 3D Navier–Stokes solver with rotating sliding meshes for simulating cross-flow turbines. PhD thesis, University of Oxford, 2012
12.
go back to reference Ferrer E, Willden RHJ (2011) A high order discontinuous Galerkin finite element solver for the incompressible Navier–Stokes equations. Comput Fluids 46(1):224–230MathSciNetCrossRef Ferrer E, Willden RHJ (2011) A high order discontinuous Galerkin finite element solver for the incompressible Navier–Stokes equations. Comput Fluids 46(1):224–230MathSciNetCrossRef
13.
go back to reference Ferrer E, Willden RHJ (2012) A high order discontinuous Galerkin - Fourier incompressible 3D Navier–Stokes solver with rotating sliding meshes. J Comput Phys 231(21):7037–7056MathSciNetCrossRef Ferrer E, Willden RHJ (2012) A high order discontinuous Galerkin - Fourier incompressible 3D Navier–Stokes solver with rotating sliding meshes. J Comput Phys 231(21):7037–7056MathSciNetCrossRef
14.
go back to reference Ferrer E, Moxey D, Willden RHJ, Sherwin S (2014) Stability of projection methods for incompressible flows using high order pressure-velocity pairs of same degree: continuous and discontinuous Galerkin formulations. Commun Comput Phys 16(3):817–840CrossRef Ferrer E, Moxey D, Willden RHJ, Sherwin S (2014) Stability of projection methods for incompressible flows using high order pressure-velocity pairs of same degree: continuous and discontinuous Galerkin formulations. Commun Comput Phys 16(3):817–840CrossRef
15.
go back to reference Ferrer E (2017) An interior penalty stabilised incompressible discontinuous Galerkin - Fourier solver for implicit large eddy simulations. J Comput Phys 348:754–775MathSciNetCrossRef Ferrer E (2017) An interior penalty stabilised incompressible discontinuous Galerkin - Fourier solver for implicit large eddy simulations. J Comput Phys 348:754–775MathSciNetCrossRef
16.
go back to reference Wang ZJ, Fidkowski K, Abgrall R, Bassi F, Caraeni D, Cary A, Deconinck H, Hartmann R, Hillewaert K, Huynh HT, Kroll N, May G, Persson PO, van Leer B, Visbal M (2013) High-order CFD methods: current status and perspective. Int J Numer Methods Fluids 72(8):811–845MathSciNetCrossRef Wang ZJ, Fidkowski K, Abgrall R, Bassi F, Caraeni D, Cary A, Deconinck H, Hartmann R, Hillewaert K, Huynh HT, Kroll N, May G, Persson PO, van Leer B, Visbal M (2013) High-order CFD methods: current status and perspective. Int J Numer Methods Fluids 72(8):811–845MathSciNetCrossRef
17.
go back to reference Ferrer E, de Vicente J, Valero E (2014) Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools. Int J Numer Methods Fluids 76(3):169–184MathSciNetCrossRef Ferrer E, de Vicente J, Valero E (2014) Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools. Int J Numer Methods Fluids 76(3):169–184MathSciNetCrossRef
18.
go back to reference Gonzalez LM, Ferrer E, Diaz-Ojeda HR (2017) Onset of three-dimensional flow instabilities in lid-driven circular cavities. Phys Fluids 29(6):064102CrossRef Gonzalez LM, Ferrer E, Diaz-Ojeda HR (2017) Onset of three-dimensional flow instabilities in lid-driven circular cavities. Phys Fluids 29(6):064102CrossRef
19.
go back to reference Ferrer E, Le Clainche S (2015) Flow scales in cross-flow turbines. In: Ferrer E, Montlaur A (eds) CFD for wind and tidal offshore turbines, Chap1. Springer tracts in mechanical engineering. Springer, Cham, pp 1–11 Ferrer E, Le Clainche S (2015) Flow scales in cross-flow turbines. In: Ferrer E, Montlaur A (eds) CFD for wind and tidal offshore turbines, Chap1. Springer tracts in mechanical engineering. Springer, Cham, pp 1–11
20.
go back to reference Oler JW, Strickland JH, Im BJ, Graham GH (1983) Dynamic stall regulation of the Darrieus turbine. Technical report, Sandia Report SAND83-7029 UC-261 Oler JW, Strickland JH, Im BJ, Graham GH (1983) Dynamic stall regulation of the Darrieus turbine. Technical report, Sandia Report SAND83-7029 UC-261
21.
go back to reference Ouro P, Runge S, Luo Q, Stoesser T (2018) Three-dimensionality of the wake recovery behind a vertical axis turbine. Renew Energy Ouro P, Runge S, Luo Q, Stoesser T (2018) Three-dimensionality of the wake recovery behind a vertical axis turbine. Renew Energy
22.
go back to reference Kou J, Le Clainche S, Zhang W (2018) A reduced-order model for compressible flows with buffeting condition using higher order dynamic mode decomposition with a mode selection criterion. Phys Fluids 30(1):016103CrossRef Kou J, Le Clainche S, Zhang W (2018) A reduced-order model for compressible flows with buffeting condition using higher order dynamic mode decomposition with a mode selection criterion. Phys Fluids 30(1):016103CrossRef
23.
24.
go back to reference Le Clainche S, Vega J (2017) Higher order dynamic mode decomposition to identify and extrapolate flow patterns. Phys Fluids 29(8):084102CrossRef Le Clainche S, Vega J (2017) Higher order dynamic mode decomposition to identify and extrapolate flow patterns. Phys Fluids 29(8):084102CrossRef
Metadata
Title
Simple Models for Cross Flow Turbines
Authors
Esteban Ferrer
Soledad Le Clainche
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-030-11887-7_1