Tim Fletcher Post-doctoral Research Assistant Richard Brown Mechan Chair of Engineering Simulating Wind Turbine Interactions using the Vorticity Transport Model

28 th ASME Wind Energy Symposium Orlando, USA, 5-8 th 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

28 th ASME Wind Energy Symposium Orlando, USA, 5-8 th 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 Ground plane and atmospheric boundary layer not modelled Validated against experimental data for co-axial helicopter rotors Wake assumed inviscid

28 th ASME Wind Energy Symposium Orlando, USA, 5-8 th January 2009 Wind Turbine Model Main Rotor 4 blades -8° linear twist Rotational speed Ω NACA Type of rotorRigid No. of blades3 Rotor radiusR AirfoilNREL S809 Rotational speedConstant Blade tip pitch3 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

28 th ASME Wind Energy Symposium Orlando, USA, 5-8 th 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

28 th ASME Wind Energy Symposium Orlando, USA, 5-8 th January 2009 Power Loss in Axial Wind Conditions Expressed as a percentage of the reference rotor C p 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

28 th ASME Wind Energy Symposium Orlando, USA, 5-8 th January 2009 Power Coefficient in Axial Wind Conditions Tip speed ratio = 6 Tip speed ratio = 8

28 th ASME Wind Energy Symposium Orlando, USA, 5-8 th January 2009 Blade Aerodynamic Performance in Axial Wind Conditions Tip speed ratio = 6Tip speed ratio = 8

28 th ASME Wind Energy Symposium Orlando, USA, 5-8 th 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

28 th ASME Wind Energy Symposium Orlando, USA, 5-8 th January 2009 High Resolution Simulation of the Flow Field Tip speed ratio = 7, Rotor separation =4R

28 th ASME Wind Energy Symposium Orlando, USA, 5-8 th January 2009 Variation in Power Coefficient during Yawed Operation

28 th ASME Wind Energy Symposium Orlando, USA, 5-8 th 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

28 th ASME Wind Energy Symposium Orlando, USA, 5-8 th January 2009 Blade Loading during Yawed Operation Normal force coefficient Tangential force coefficient

28 th ASME Wind Energy Symposium Orlando, USA, 5-8 th January 2009 The Effect of the Sense of Rotor Rotation Tip speed ratio = 6

28 th ASME Wind Energy Symposium Orlando, USA, 5-8 th 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 C P 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