Ocean Dynamics

, Volume 66, Issue 1, pp 41–57 | Cite as

Determining tidal turbine farm efficiency in the Western Passage using the disc actuator theory

  • Shivanesh RaoEmail author
  • Huijie Xue
  • Min Bao
  • Simon Funke
Part of the following topical collections:
  1. Topical Collection on the 6th International Workshop on Modeling the Ocean (IWMO) in Halifax, Nova Scotia, Canada 23-27 June 2014


Tidal power potential is determined across the Western Passage in Passamaquoddy Bay using the Finite Volume Community Ocean Model (FVCOM). The tidal turbines are implemented in FVCOM using the disc actuator theory method to determine the power potential for different densities and arrangements of tidal turbines. At the most efficient setting for 10 turbines across the Western Passage, the optimal turbine drag coefficient is 2.0 and the average power output, in a 2-week period, is ∼819 kW. Results suggest that for a single row of turbines, the addition of turbines decreases the efficiency of the turbine farm, but this decrease in efficiency is less than 7 %. A parallel distribution of turbines in an array diminishes the average power for turbines in the shadow of other turbines, while staggered distribution in an array increases the average power extraction for some turbines, due to the speed gains in the gaps between turbines. A simple tidal farm optimization using the OpenTidalFarm (OTF) model suggests a similar tidal farm distribution.


Tidal power Tidal turbine efficiency Disc actuator theory Tidal turbine farms Western passage Bay of Fundy Farm optimization 



The authors would like to thank Steve Cousins from the University of Maine for his assistance in coding and setting up our numerical experiments. The work is supported by the Department of Energy award number DE-EE0000298 and Argonne National Laboratory contract number 3F-30543 to the University of Maine.


  1. Bao M (2013) Tidal Turbine Array Optimization - using the Quoddu regions as an example, PhD thesis, Ocean University of ChinaGoogle Scholar
  2. Betz A (1920) Das maximum der theoretisch mglichen ausnutzung des windes durch windmotoren. Z Gesamte Turbinewesen 17:307–309Google Scholar
  3. Blanchfield J, Garrett C, Rowe A, Wild P (2008) Tidal stream power resource assessment for Massett Sound, Haida Gwaii. J Power Energy 222(5):485–492CrossRefGoogle Scholar
  4. Brooks DA (2006) The tidal-stream energy resource in Passamaquoddy-Cobscook Bays: a fresh look at an old story. Renew Energy 31(14):2284–2295CrossRefGoogle Scholar
  5. Cameron M (2012) Flow field measurements for cross-field turbines. Master’s thesis, University of MaineGoogle Scholar
  6. Chen C, Beardsley R (2003) An unstructured grid, finite-volume, three-dimensional, primitive equations ocean model: application to coastal ocean and estuaries. J Atmos Ocean Technol 20:159–186CrossRefGoogle Scholar
  7. Chen C, Cowles G, Beardsley R (2006) An unstructured grid, finite volume coastal ocean model: FVCOM user manual 2nd edn. Technical report, SMAST/UMASSD Technical Report -06-0602Google Scholar
  8. Chen C, Huang H, Beardsley RC, Liu H, Xu Q, Cowles G (2007) A finite volume numerical approach for coastal ocean circulation studies: comparisons with finite difference models. Journal of Geophysical Research: Oceans 112(C3):n/a–n/a. C03018CrossRefGoogle Scholar
  9. Chen C, Huang H, Beardsley RC, Xu Q, Limeburner R, Cowles GW, Sun Y, Qi J, Lin H (2011) Tidal dynamics in the gulf of Maine and New England shelf: an application of FVCOM. Journal of Geophysical Research: Oceans 116(C12):n/a–n/a. C12010CrossRefGoogle Scholar
  10. Defne Z, Haas KA, Fritz HM (2011) Numerical modeling of tidal currents and the effects of power extraction on estuarine hydrodynamics along the Georgia Coast, {USA}. Renew Energy 36(12):3461–3471CrossRefGoogle Scholar
  11. Dupont F, Hannah CG, Greenberg D (2005) Modelling the sea level of the upper Bay of Fundy. Atmosphere-Ocean 43(1):33–47CrossRefGoogle Scholar
  12. Funke S, Farrell P, Piggott M (2014) Tidal turbine array optimisation using the adjoint approach. Renew Energy 63:658–673CrossRefGoogle Scholar
  13. Garrett C, Cummins P (2004) Generating power from tidal currents. J Waterw Port Coast Ocean Eng 130(3):114–118CrossRefGoogle Scholar
  14. Garrett C, Cummins P (2007) The efficiency of a turbine in a tidal channel. J Fluid Mech 588:243–251Google Scholar
  15. Greenberg DA, Shore JA, Page FH, Dowd M (2005) A finite element circulation model for embayments with drying intertidal areas and its application to the Quoddy region of the Bay of Fundy. Ocean Model 10(12):211–231. The Second International Workshop on Unstructured Mesh Numerical Modelling of Coastal, Shelf and Ocean FlowsCrossRefGoogle Scholar
  16. Hasegawa D, Sheng J, Greenberg D, Thompson K (2011) Far-field effects of tidal energy extraction in the Minas Passage on tidal circulation in the Bay of Fundy and Gulf of Maine using a nested-grid coastal circulation model. Ocean Dyn 61(11):1845–1868CrossRefGoogle Scholar
  17. Karsten RH, McMillan JM, Lickley MJ, Haynes RD (2008) Assessment of tidal current energy in the Minas Passage, Bay of Fundy. Proc IME A J Power Energy 222(5):493–507CrossRefGoogle Scholar
  18. Lynch DR, Naimie CE (1993) The M2 tide and its residual on the outer banks of the Gulf of Maine. J Phys Oceanogr 23:2222–2253CrossRefGoogle Scholar
  19. McMillian J, Lickley M (2008) The potential of tidal power from the Bay of Fundy. Society of Industrial and Applied Mathematics Google Scholar
  20. Mellor GL, Yamada T (1982) Development of a turbulence closure model for geophysical fluid problems. Rev Geophys 20(4):851–875CrossRefGoogle Scholar
  21. Plew DR, Stevens CL (2013) Numerical modelling of the effect of turbines on currents in a tidal channel—Tory Channel, New Zealand. Renew Energy 57:269–282CrossRefGoogle Scholar
  22. Roc T, Conley DC, Greaves D (2013) Methodology for tidal turbine representation in ocean circulation model. Renew Energy 51:448–464CrossRefGoogle Scholar
  23. Smagorinsky J (1963) General circulation experiments with the primitive equations. Mon Weather Rev 91:99CrossRefGoogle Scholar
  24. U.S. EIA (2014) Annual energy outlook. Technical report, U.S. Energy Information AdministrationGoogle Scholar
  25. Vennell R (2010) Tuning turbines in a tidal channel. J Fluid Mech 663:253–267CrossRefGoogle Scholar
  26. Vennell R (2011) Tuning tidal turbines in-concert to maximise farm efficiency. J Fluid Mech 671:587–604CrossRefGoogle Scholar
  27. Vennell R (2012) Realizing the potential of tidal currents and the efficiency of turbine farms in a channel. Renew Energy 47:95–102CrossRefGoogle Scholar
  28. Vennell R (2013) Exceeding the Betz limit with tidal turbines. Renew Energy 55:277–285CrossRefGoogle Scholar
  29. Xu D, Xue H (2011) A numerical study of horizontal dispersion in a macro tidal basin. Ocean Dyn 61(5):623–637CrossRefGoogle Scholar
  30. Xu D, Xue H, Greenberg D (2006) A numerical study of the circulation and drifter trajectories in Cobscook Bay, chapter 11, pp 176–195. American Society of Civil EngineersGoogle Scholar
  31. Xue H, Bao M, Bao X, Cameron M (2013) A numerical study of tidal farm efficiency in the Western Passage, US and Canada. In: OCEANS - Bergen, 2013 MTS/IEEE, pp 1–10Google Scholar
  32. Yang Z, Wang T, Copping AE (2013) Modeling tidal stream energy extraction and its effects on transport processes in a tidal channel and bay system using a three-dimensional coastal ocean model. Renew Energy 50:605–613CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Shivanesh Rao
    • 1
    Email author
  • Huijie Xue
    • 1
  • Min Bao
    • 2
  • Simon Funke
    • 3
  1. 1.School of Marine SciencesUniversity of MaineOronoUSA
  2. 2.State Key Laboratory of Satellite Ocean Environment Dynamics2nd Institute of OceanographyHangzhouChina
  3. 3.Center for Biomedical ComputingSimula Research LaboratoryFornebuNorway

Personalised recommendations