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Flows in Complex Systems

Computational Fluid Dynamics Analysis of a Hydrokinetic Turbine Based on Oscillating Hydrofoils

[+] Author and Article Information
Thomas Kinsey

Laboratoire de Mécanique des Fluides Numérique,Department of Mechanical Engineering,  Laval University, Quebec City, Quebec G1V 0A6, Canadathomas.kinsey.1@ulaval.ca

Guy Dumas

Laboratoire de Mécanique des Fluides Numérique,Department of Mechanical Engineering,  Laval University, Quebec City, Quebec G1V 0A6, Canadagdumas@gmc.ulaval.ca

J. Fluids Eng 134(2), 021104 (Mar 19, 2012) (16 pages) doi:10.1115/1.4005841 History: Received December 28, 2010; Revised September 19, 2011; Published March 19, 2012; Online March 19, 2012

The performance of a new concept of hydrokinetic turbine using oscillating hydrofoils to extract energy from water currents (tidal or gravitational) is investigated using URANS numerical simulations. The numerical predictions are compared with experimental data from a 2 kW prototype, composed of two rectangular oscillating hydrofoils of aspect ratio 7 in a tandem spatial configuration. 3D computational fluid dynamics (CFD) predictions are found to compare favorably with experimental data especially for the case of a single-hydrofoil turbine. The validity of approximating the actual arc-circle trajectory of each hydrofoil by an idealized vertical plunging motion is also addressed by numerical simulations. Furthermore, a sensitivity study of the turbine’s performance in relation to fluctuating operating conditions is performed by feeding the simulations with the actual time-varying experimentally recorded conditions. It is found that cycle-averaged values, as the power-extraction efficiency, are little sensitive to perturbations in the foil kinematics and upstream velocity.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Front view of the rectangular extraction plane of the oscillating hydrofoils turbine compared to the classical rotor blade design. Note that the schematic is indicative and not representative of actual distances to the seabed and free surface.

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Figure 2

Heaving and pitching motions (φ = 90°). The foil pitching center is located at xp  = c/3. d = 2.55c when H0  = c and θ0  = 75° (adapted from Ref. [15]).

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Figure 3

2D URANS mesh details for the single oscillating hydrofoil. Total cell number: 42 200 (500 nodes on hydrofoil).

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Figure 4

Domain size and boundary conditions for the 3D numerical simulations about the AR = 7 hydrofoil equipped with the same endplates as on the experimental prototype

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Figure 5

The mesh is divided in 5 distinct mesh zones, four of which are moving in rigid body motion (each hydrofoil is encapsulated in a rigidly rotating mesh zone which is itself part of a large heaving mesh zone). A buffer mesh zone is present near the domain boundaries in order to allow the heaving deformation of the heaving mesh zones. Total cell number: 181 200 (700 nodes on each hydrofoil). Domain is 70c high and 75c long.

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Figure 6

Two levels of grid refinement for the 3D single foil. (a) Coarser mesh (mesh 3D-1) and (b) refined mesh (mesh 3D-2).

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Figure 7

Comparison of instantaneous force, moment and power coefficients between 2D URANS simulations using different turbulence models. Re = 500 000, f* = 0.14, θ0  = 75°, H0  = c, xp /c = 1/3.

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Figure 8

Comparison of time sequences (t/T = 0, 0.125, 0.25) of vorticity fields (red: counterclockwise vorticity, blue: clockwise vorticity) for simulations using different turbulence models. Re = 500 000, f* = 0.14, θ0  = 75°, H0  = c, xp /c = 1/3.

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Figure 9

Comparison of time sequences (t/T = 0, 0.25) of vorticity fields (red: counterclockwise vorticity, blue: clockwise vorticity) and velocity vectors colored by dynamic pressure (see colormap in Fig. 1) for tandem simulations using different turbulence models. NACA 0015, Re = 500,000, f* = 0.14, H0 /c = 1, θ0  = 75°, xp /c = 1/3, Lx  = 5.4c, φ1-2  = 180°.

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Figure 10

Instantaneous total power coefficient for (a) the upstream foil, (b) the downstream foil and (c) the total contributions for simulations of 3D tandem hydrofoils using two different turbulence models, namely, the one-equation Spalart-Allmaras model with curvature correction and the two-equations shear-stress-transport model (SST) model with low-Reynolds damping. Results are shown for the fourth oscillation cycle after the impulsive start. (f* = 0.14, θ0  = 75°, H0  = c, AR = 7, Lx  = 5.4c, φ1-2  = 180°, Re = 500,000).

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Figure 11

Comparison between 2D and 3D URANS numerical results and experimental data. Hydrodynamic power extraction efficiency versus reduced frequency for the single-hydrofoil turbine configuration.

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Figure 12

Isosurfaces of vorticity (blue for negative vorticity and red for positive) at two instants in the hydrofoil oscillation cycle. At f* = 0.08 (left), massive dynamic stall and leading-edge vortex shedding occurs. At f* = 0.16 (right), boundary layers remain close to the hydrofoil and no vortex shedding occurs.

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Figure 13

Estimated hydrodynamic power extraction efficiency versus reduced frequency for dual-hydrofoil turbine testing

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Figure 14

Example of advantageous vortex-hydrofoil instantaneous positioning in the case f* = 0.14 and Lx  = 5.4c. Velocity vectors colored by dynamic pressure ratio (|V|/U∞)2 and isolines of vorticity (dashed for negative vorticity). The downstream foil benefits from the instant vortex-induced dynamic pressure.

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Figure 15

Comparison between 3D vortices from the 3D simulation (b) with their 2D equivalent from the 2D simulations (a). The vortices are shown using an isosurface at λ2  = −0.15. f* = 0.14, t = 0.2T.

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Figure 16

Comparison between 3D vortices from the 3D simulation (b) with their 2D equivalent from the 2D simulations (a). The vortices are shown using an isosurface at λ2  = −0.15. f* = 0.08, t = 0.2T.

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Figure 17

2D mesh details and boundary conditions for the actual dual-hydrofoil prototype in tandem configuration. Total cell number: 178 000 (700 nodes on each hydrofoil).

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Figure 18

Total power coefficient evolution over one periodic cycle for an arc-circle-trajectory simulation (solid) compared to a simulation with idealized vertical heaving motion (dashed). Case E1.

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Figure 19

Upstream hydrofoil power coefficient evolution over one periodic cycle for an arc-circle-trajectory simulation (solid) compared to a simulation with idealized vertical heaving motion (dashed). Case E1.

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Figure 20

Downstream hydrofoil power coefficient evolution over one periodic cycle for an arc-circle-trajectory simulation (solid) compared to a simulation with idealized vertical heaving motion (dashed). Case E1.

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Figure 21

Effective angle-of-attack evolutions over one periodic cycle for an arc-circle-trajectory simulation compared to a simulation with idealized vertical heaving motion (case E1). Asymmetries between downstroke and upstroke motions are clearly visible for each hydrofoil and discrepancies with the idealized case are further marked for the downstream hydrofoil.

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Figure 22

Instantaneous phase-averaged angular velocity of the low-speed side of the rotating shaft for experimental case E1

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Figure 23

Comparison of total power coefficient evolution for two URANS simulations incorporating respectively the phase-averaged instantaneous shaft rotational speed (experimentally recorded, dashed) and a constant shaft angular speed (assuming perfect speed control, solid)

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Figure 24

Instantaneous phase-averaged upstream velocity for experimental case E1

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Figure 25

Comparison of the total power coefficient evolution for two URANS simulations incorporating the experimentally recorded kinematics and constant (dashed) or fluctuating (solid) upstream velocity

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