tim fletcher post-doctoral research assistant richard brown mechan chair of engineering simulating...
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Tim FletcherPost-doctoral Research Assistant
Richard BrownMechan Chair of Engineering
Simulating Wind Turbine Interactions using theVorticity Transport Model
28th ASME Wind Energy Symposium
Orlando, USA, 5-8th January 2009
Why are Aerodynamic Interactions of Interest?
• Aerodynamic interactions are known to lead to power losses within wind farms
• The percentage of power lost as a result of interaction varies with wind conditions and the configuration of the turbines
• Turbines are aligned to minimise interaction in prevailing wind conditions, however, turbines often operate off-design
• Local topography can significantly influence the distribution of wind turbines in a farm
• Typical separation between rotors:– 10R for West Kilbride, Scotland– 14R for Horns Rev, Denmark
• Increasing constraints are being applied to the location and size of wind farms
Source: Olivier Tetard
Source: Philip Hertzog
28th ASME Wind Energy Symposium
Orlando, USA, 5-8th January 2009
Computational Aerodynamics
• Aerodynamic model solving the vorticity-velocity form of time-dependent incompressible Navier-Stokes equation
• Lifting-line blade aerodynamic model, trailed and shed vorticity is transferred into the computational domain using the source term, S
• Numerical diffusion of vorticity is limited by using a Riemann problem technique based on Toro’s Weighted Average Flux method – wake structure is preserved
• Solved in finite-volume form on a structured Cartesian mesh
ωνSuωωuωt
2
• Ground plane and atmospheric boundary layer not modelled
• Validated against experimental data for co-axial helicopter rotors
• Wake assumed inviscid
28th ASME Wind Energy Symposium
Orlando, USA, 5-8th January 2009
Wind Turbine Model
Main Rotor4 blades-8° linear twistRotational speed ΩNACA 23012
Type of rotor Rigid
No. of blades 3
Rotor radius R
Airfoil NREL S809
Rotational speed Constant
Blade tip pitch 3 deg
• Tip speed ratios of 6 and 8
• Rotor separations of 4R, 8R and 12R
• Yaw angles of 15 deg, 30 deg and 45 deg
• Downwind rotors with opposing sense of rotation also simulated
28th ASME Wind Energy Symposium
Orlando, USA, 5-8th January 2009
Verification of Aerodynamic Predictions
• NREL Unsteady Aerodynamics Experiment – Phase VI• Wind speed = 7 m/s (axial)• Blade tip pitch = 3 deg• Upwind rotor configuration
• Error bars represent maximum and minimum values during entire experiment
28th ASME Wind Energy Symposium
Orlando, USA, 5-8th January 2009
Power Loss in Axial Wind Conditions
• Expressed as a percentage of the reference rotor Cp
• Power coefficient reduces by a large proportion at low inter-rotor separations
• Performance recovers as the separation is increased
• Greater percentage of power is lost at higher tip speed ratio
28th ASME Wind Energy Symposium
Orlando, USA, 5-8th January 2009
Power Coefficient in Axial Wind Conditions
Tip speed ratio = 6
Tip speed ratio = 8
28th ASME Wind Energy Symposium
Orlando, USA, 5-8th January 2009
Blade Aerodynamic Performance in Axial Wind Conditions
Tip speed ratio = 6 Tip speed ratio = 8
28th ASME Wind Energy Symposium
Orlando, USA, 5-8th January 2009
Wake Structure and Flow Speed Distribution
• Tip speed ratio = 8
• At left: instantaneous iso-surfaces of vorticity representing the wake
• At right: contours of flow speed normalized using the rotor tip speed
28th ASME Wind Energy Symposium
Orlando, USA, 5-8th January 2009
High Resolution Simulation of the Flow Field
Tip speed ratio = 7, Rotor separation =4R
28th ASME Wind Energy Symposium
Orlando, USA, 5-8th January 2009
Variation in Power Coefficient during Yawed Operation
28th ASME Wind Energy Symposium
Orlando, USA, 5-8th January 2009
Wake Structure during Yawed Operation
• Ψ=15 deg – subtle aerodynamic coupling between the reference and downwind rotors» Positive effect on the performance of the downwind rotor
• Ψ=30 deg – partial immersion of the downwind rotor in the wake of the reference rotor» Unsteadiness in aerodynamic loading is very large
• Ψ=45 deg – complete immersion» Deficit in mean power coefficient is largest
28th ASME Wind Energy Symposium
Orlando, USA, 5-8th January 2009
Blade Loading during Yawed Operation
Normal force
coefficient
Tangential force
coefficient
28th ASME Wind Energy Symposium
Orlando, USA, 5-8th January 2009
The Effect of the Sense of Rotor Rotation
Tip speed ratio = 6
28th ASME Wind Energy Symposium
Orlando, USA, 5-8th January 2009
Conclusions
• A turbine rotor develops a substantially lower power coefficient when operating within the wake of a second turbine. Performance recovers as the separation is increased.
• Power coefficient of the downwind rotor as a fraction of the upwind rotor’s CP reduces with increasing tip speed ratio
• In yawed wind conditions, the largest reduction in the mean power coefficient of the downwind rotor occurs when upwind rotor wake impinges on the entire disk
• Considerable unsteadiness can arise in the performance of the downwind rotor when partially immersed within the wake of the upwind rotor – caused by asymmetric loading
• Some evidence of a sensitivity in the performance of the downwind rotor to its direction of rotation with respect to the upwind rotor
• Wake of the upwind rotor reduces the local wind speed at the downwind rotor, thus causing a power deficit. However, natural instabilities within the wake moderate the deficit by reducing the aerodynamic coupling at larger rotor separations
• The numerical techniques and results presented will hopefully be helpful in reducing the inefficiencies that arise from the aerodynamic interactions between wind turbines