Abstract
This work presents analytical estimates for various flow scales encountered in cross-flow turbines (i.e. Darrieus type or vertical axis) for renewable energy generation (both wind and tidal). These estimates enable the exploration of spatial or temporal interactions between flow phenomena and provide quantitative and qualitative bounds of the three main flow phenomena: the foil scale, the vortex scale and wake scale. Finally using the scale analysis, we show using an illustrative example how high order computational methods prove beneficial when solving the flow physics involved in cross-flow turbines.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 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.
- 2.
β < 1 for unblocked cases but may exceed 1 if blockage leads to accelerated flow through the turbine.
References
Abbott I, Von-Doenhoff A (1959) Theory of wing sections: including a summary of airfoil data. Dover, New York
Anderson JD (2005) Fundamentals of aerodynamics, 4th edn. McGraw-Hill, New York
Burton T, Jenkins N, Sharpe D, Bossanyi E (2001) Wind energy handbook. Wiley, New York
Consul CA, Willden RHJ, Ferrer E, McCulloch MD (2009) Influence of solidity on the performance of a cross-flow turbine. In: Proceedings of the 8th European wave and tidal energy conference
Draper S (2011) Tidal stream energy extraction in coastal basins. Ph.D. thesis, University of Oxford
Eriksson S, Bernhoff H, Leijon M (2008) Evaluation of different turbine concepts for wind power. Renew Sust Energ Rev 12(5):1419–1434
Ferrer E (2012) A high order Discontinuous Galerkin-Fourier incompressible 3D Navier-Stokes solver with rotating sliding meshes for simulating cross-flow turbines. Ph.D. thesis, University of Oxford
Ferrer E, Willden RHJ (2011) A high order discontinuous Galerkin finite element solver for the incompressible Navier–Stokes equations. Comput Fluids 46(1):224–230
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):7037–7056
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):817–840
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
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
Houlsby GT, Draper S, Oldefield MLG (2008) Application of linear momentum actuator disc theory to open channel flows. Technical report, Oxford University Engineering Library Report
Howell R, Qin N, Edwards J, Durrani N (2010) Wind tunnel and numerical study of a small vertical axis wind turbine. Renew Energ 35(2):412–422
McAdam R (2011) Studies into the technical feasibility of the transverse horizontal axis water turbine. Ph.D. thesis, University of Oxford
Newman BG (1983) Actuator-disc theory for vertical-axis wind turbines. J Wind Eng Ind Aerodyn 15(1–3):347–355
Paraschivoiu I (2002) Wind turbine design with emphasis on Darrieus concept. Polytechnic International Press, Montreal
Savage A (2007) Tidal power in the UK - tidal technologies overview, Technical Report Sustainable Developement Commission, 2007
Schlichting H (1979) Boundary layer theory. McGraw-Hill, New York
Strickland JH (1975) Darrieus turbine: a performance prediction model using multiple streamtubes. Technical report. Report No. SAND-75-0431, Sandia Labs
Templin RJ (1974) Aerodynamic performance theory for the NRC vertical-axis wind turbine. NASA STI/Recon Technical Report N, 76
Vermeer LJ, Sørensen JN, Crespo A (2003) Wind turbine wake aerodynamics. Prog Aerosp Sci 39(6–7):467–510
Whelan J, Thomson M, Graham JMR, Peiró J (2007) Modelling of free surface proximity and wave induced velocities around a horizontal axis tidal stream turbine. In: 7th European wave and tidal energy conference, Porto
Whelan JI, Graham JMR, Peiro J (2009) A free-surface and blockage correction for tidal turbines. J Fluid Mech 624:281–291
Wilson RE, Lissaman PBS (1974) Applied aerodynamics of wind power machines. NASA STI/Recon Technical report 75:22669
Acknowledgements
EF would like to acknowledge the financial support of the John Fell OUP fund and the European Commission (ANADE project under grant contract PITN-GA-289428).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
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. Springer Tracts in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-16202-7_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-16202-7_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16201-0
Online ISBN: 978-3-319-16202-7
eBook Packages: EngineeringEngineering (R0)