Research Papers: Flows in Complex Systems

Impact of Blockage on the Hydrodynamic Performance of Oscillating-Foils Hydrokinetic Turbines

[+] Author and Article Information
Etienne Gauthier

Laboratoire de Mécanique des
Fluides Numérique,
Department of Mechanical Engineering,
Laval University,
Quebec City, QC G1V 0A6, Canada
e-mail: etienne.gauthier.4@ulaval.ca

Thomas Kinsey

Laboratoire de Mécanique des
Fluides Numérique,
Department of Mechanical Engineering,
Laval University,
Quebec City, QC G1V 0A6, Canada
e-mail: thomas.kinsey.1@ulaval.ca

Guy Dumas

Laboratoire de Mécanique des
Fluides Numérique,
Department of Mechanical Engineering,
Laval University,
Quebec City, QC G1V 0A6, Canada
e-mail: gdumas@gmc.ulaval.ca

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 22, 2015; final manuscript received March 10, 2016; published online May 26, 2016. Assoc. Editor: Elias Balaras.

J. Fluids Eng 138(9), 091103 (May 26, 2016) (13 pages) Paper No: FE-15-1423; doi: 10.1115/1.4033298 History: Received June 22, 2015; Revised March 10, 2016

This paper describes a study of the impact of confinement on the hydrodynamic performance of oscillating-foils hydrokinetic turbines (OFHT). This work aims to contribute to the development of standards applying to marine energy converters. These blockage effects have indeed to be taken into account when comparing measurements obtained in flumes, towing tanks, and natural sites. This paper provides appropriate correction formula to do so for OFHT based on computational fluid dynamics (CFD) simulations performed at a Reynolds Number Re = 3 × 106 for reduced frequencies between f* = 0.08 and f* = 0.22 considering area-based blockage ratios ranging from ε = 0.2% to 60%. The need to discriminate between the vertical and horizontal confinement and the impact of the foil position in the channel are also investigated and are shown to be of second-order as compared to the overall blockage level. As expected, it is confirmed that the power extracted by the OFHT increases with the blockage level. It is further observed that for blockage ratio of less than ε = 40%, the power extracted scales linearly with ε. The approach proposed to correlate the performance of the OFHT in different blockage conditions uses the correction proposed by Barnsley and Wellicome and assumes a linear relation between the power extracted and the blockage. This technique is shown to be accurate for most of the practical operating conditions for blockage ratios up to 50%.

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Glauert, H. , 1947, The Elements of Aerofoil and Airscrew Theory, 2nd ed., Cambridge University Press, New York.
Maskell, E. C. , 1963, “ A Theory of Blockage Effects on Bluff Bodies and Stalled Wings in Closed Wind Tunnel,” Aeronautical Research Council, London, ARC R&M No. 3400.
Pope, A. , and Harper, J. , 1966, Low-Speed Wind Tunnel Testing, 2nd ed., Wiley, New York.
Bahaj, A. , Molland, A. , Chaplin, J. , and Batten, W. , 2007, “ Power and Thrust Measurement of Marine Current Turbines Under Various Hydrodynamic Flow Conditions in a Cavitation Tunnel and Towing Tank,” Renewable Energy, 32(3), pp. 407–426. [CrossRef]
Barnsley, M. J. , and Wellicome, J. F. , 1990, “ Final Report on the 2nd Phase of Development and Testing of a Horizontal Axis Wind Turbine Test Rig for the Investigation of Stall Regulation Aerodynamics,” Carried Out Under ETSU Agreement No. E.5A/CON5103/1746.
Sørensen, J. N. , Shen, W. Z. , and Mikkelsen, R. , 2006, “ Wall Correction Model for Wind Tunnels With Open Test Section,” AIAA J., 44(8), pp. 1890–1894. [CrossRef]
Betz, A. , 1920, “ Das Maximum der Theoretisch Möglichen Ausnützung des Windes Durch Windmotoren,” Z. Gesamte Turbinenwesen, 26, pp. 307–309.
Lanchester, F. W. , 1915, “ A Contribution to the Theory of Propulsion and the Screw Propeller,” Trans. Inst. Naval Archit., LVII, pp. 98–116.
Garret, C. , and Cummins, P. , 2007, “ The Efficiency of a Turbine in a Tidal Channel,” J. Fluid Mech., 588, pp. 243–251.
Houlsby, G. , Draper, S. , and Oldfield, M. , 2008, “ Application of Linear Momentum Actuator Disc Theory to Open Channel Flow,” Department of Engineering Science, University of Oxford, Report No. OUEL 2296/08.
Whelan, J. , Graham, J. , and Peiró, J. , 2009, “ A Free-Surface and Blockage Correction for Tidal Turbines,” J. Fluid Mech., 624, pp. 281–291. [CrossRef]
Gauthier, E. , Kinsey, T. , and Dumas, G. , 2013, “ RANS Versus Scale-Adaptive Turbulence Modeling for Engineering Prediction of Oscillating-Foils Turbines,” 21th Annual Conference of the CFD Society of Canada, Sherbrooke, Canada, May 6–9, p. CFDSC2013–186.
Kinsey, T. , and Dumas, G. , 2008, “ Parametric Study of an Oscillating Airfoil in a Power Extraction Regime,” AIAA J., 46(6), pp. 1318–1330. [CrossRef]
Kinsey, T. , and Dumas, G. , 2012, “ Computational Fluid Dynamics Analysis of a Hydrokinetic Turbine Based on Oscillating Hydrofoils,” ASME J. Fluids Eng., 134(2), p. 021104. [CrossRef]
Kinsey, T. , and Dumas, G. , 2012, “ Optimal Tandem Configuration for Oscillating-Foils Hydrokinetic Turbine,” ASME J. Fluids Eng., 134(7), p. 031103. [CrossRef]
Kinsey, T. , and Dumas, G. , 2012, “ Three-Dimensional Effects on an Oscillating-Foils Hydrokinetic Turbine,” ASME J. Fluids Eng., 134(7), p. 071105. [CrossRef]
Kinsey, T. , and Dumas, G. , 2014, “ Optimal Operating Parameters for an Oscillating Foil Turbine at Reynolds Number 500 000,” AIAA J., 52(9), pp. 1885–1895. [CrossRef]
Zhu, Q. , and Peng, Z. , 2009, “ Mode Coupling and Flow Energy Harvesting by a Flapping Foil,” Phys. Fluids, 21(3), p. 033601. [CrossRef]
Zhu, Q. , 2011, “ Optimal Frequency for Flow Energy Harvesting of a Flapping Foil,” J. Fluid Mech., 675, pp. 495–517. [CrossRef]
Ashraf, M. , Young, J. , Lai, J. , and Platzer, M. , 2011, “ Numerical Analysis of an Oscillating-Wing Wind and Hydropower Generator,” AIAA J., 49(7), pp. 1374–1386. [CrossRef]
CD-Adapco, 2014, STAR-CCM + V9 User Guide, http://www.cd-adapco.com/products/star-ccm
Menter, F. , 1994, “ Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA J., 32(8), pp. 1598–1605. [CrossRef]
Bullivant, W. K. , 1941, “ Tests of a NACA 0025 and 0035 Airfoils in the Full-Scale Wind Tunnel,” Langley Memorial Aeronautical Laboratory, VA, NACA Report No. 708.
Kinsey, T. , Dumas, G. , Lalande, G. , Ruel, J. , Mehut, A. , Viarouge, P. , Lemay, J. , and Jean, Y. , 2011, “ Prototype Testing of a Hydrokinetic Turbine Based on Oscillating Hydrofoils,” Renewable Energy, 36(6), pp. 1710–1718. [CrossRef]


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Fig. 1

Imposed heaving h(t) and pitching θ(t) motions. Adapted from Ref. [12].

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Fig. 7

Dependency of the cycle-averaged power coefficient CP*¯ on blockage for different reduced frequencies f*

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Fig. 2

Computational domain and exterior boundary conditions

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Fig. 3

Description of the overset mesh technique and the interface characteristics

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Fig. 4

Characteristics of the mesh shown on a vertical slice at a midspan position for a blockage of ε = 50%

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Fig. 5

Hydrodynamic polar of a NACA 0025 rectangular wing of aspect ratio 6 at a Reynolds number Re = 3.0 × 106 (experimental data from Bullivant [23])

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Fig. 6

Power coefficient (CP*¯) with respect to the reduced frequency for an unconfined NACA 0015 oscillating foil of aspect ratio 7 at Re = 500,000 (xp/c = 0.33, H0/c = 1.0, θ0 = 75 deg)

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Fig. 8

Evolution of vorticity fields (red counterclockwise and blue clockwise) for an unconfined hydrofoil (ε = 0.2%) at reduced frequencies of f* = 0.08 and 0.22

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Fig. 9

Evolution of vorticity fields (red counterclockwise and blue clockwise) at a reduced frequency of f* = 0.12 for an unconfined hydrofoil (ε = 0.2%) and for a blockage of ε = 49.7%

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Fig. 10

Evolution of instantaneous vertical force coefficient CY at f* = 0.08 for ε = 0.2% and ε = 49.7% along with the instantaneous heaving velocity VY /U

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Fig. 11

Mean power coefficient CP*¯ normalized by the mean power coefficient of the unconfined case (CP*¯ε = 0.2%) with respect to blockage ratio for a reduced frequency of f* = 0.18. A linear regression curve for 0% ≤ ε ≤ 40% and an exponential regression curve for 0% ≤ ε ≤ 60% are also presented.

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Fig. 12

Mean power coefficient CP*¯ normalized by the mean power coefficient of the unconfined case (CP*¯ε = 0.2%) with respect to blockage ratio for different reduced frequencies. Linear regression curves are shown for 0% ≤ ε ≤ 50%.

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Fig. 13

Dimensions of the channel cross sections tested

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Fig. 14

Power coefficient evolution for different channel CA and the limit 2D case for ε = 12.4% and f* = 0.18

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Fig. 15

Off-centered turbines

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Fig. 16

Impact of an off-centered turbine on its performance for a blockage ratio of ε = 12% and a reduced frequency of f* = 0.18. (a) Mean streamwise velocity profiles at an upstream distance of x = –2 c from the turbine. (b) Evolution of the instantaneous power coefficient on the oscillating cycle showing the differences on peak values between the downstroke and the upstroke.

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Fig. 17

Blockage correction of Barnsley and Wellicome applied to the present OFHT results CP*¯ (f*; ε) and CD¯ (f*; ε) and the corresponding hypothetical unconfined results CP′¯ ( f ′ ;  ε) and CD′¯ ( f ′ ;  ε)

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Fig. 18

Procedure to correlate the performance of an OFHT for different levels of blockage




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