An Experimental Study on Global Turbine Array Effects in Large Wind Turbine Clusters by Patrik Berkesten H¨agglund September 2013 Master of Science Thesis Royal Institute of Technology KTH Mechanics SE-100 44 Stockholm, Sweden PatrikBerkestenH¨agglund2013,An Experimental Study on Global Tur- bine Array Effects in Large Wind Turbine Clusters KTH Mechanics SE–100 44 Stockholm, Sweden Abstract Itiswellknownthatthelayoutofalargewindturbineclusteraffectstheenergy output of the wind farm. The individual placement and distances between turbines will influence the wake spreading and the wind velocity deficit. Many analyticalmodelsandsimulationshavebeenmadetryingtocalculatethis,but still there is a lack of experimental data to confirm the models. This thesis is describing the preparations and the execution of an experiment that has been conductedusingabout250smallrotatingturbinemodelsinawindtunnel. The turbine models were developed before the experiment and the characteristics wereinvestigated. Themainfocuswaslaidonspecialeffectsoccurringinlarge wind turbine clusters, which were named Global Turbine Array Effects. It was shown that the upstream wind was little affected by a large wind farm downstream, even though there existed a small difference in wind speed between the undisturbed free stream and the wind that arrived to the first turbines in the wind farm. The difference in wind speed was shown to be under 1% of the undisturbed free stream. It was also shown that the density of the wind farm was related to the reduced wind velocity, with a more dense farm the reduction could get up to 2.5% of the undisturbed free stream at the upstream center turbine. Less velocity deficit was observed at the upstream corner turbines in the wind farm. When using small rotating turbine models some scaling requirements had tobeconsideredtomaketheexperimentadaptabletoreality. Itwasconcluded thatthethrustcoefficientoftheturbinemodelswasthemostimportantparam- eter when analysing the effects. One problem discussed was the low Reynolds number, an effect always present in wind tunnel studies on small wind turbine models. A preliminary investigation of a photo measuring technique was also per- formed, but the technique was not fully developed. The idea was to take one or a few photos instantaneously and then calculate the individual rotational speed of all the turbine models. It was difficult to apply the technique be- cause of fluctuations in rotational speed during the experiment, therefore the calculatedvaluescouldnotrepresentthemeanvalueoveralongertimeperiod. Descriptors: GTAE, Global Turbine Array Effects, Wind tunnel, Reynolds number, Tip speed ratio, Thrust coefficient, Induction factor, Turbine model, Wake effects, Wind farm, Aerodynamic scaling, Thrust measurement, Bound- ary corrections, Velocity profile i Patrik Berkesten H¨agglund 2013, En experimentell unders¨okning av glo- bala str¨omningseffekter i stora vindkraftsparker KTH Mekanik SE–100 44 Stockholm, Sverige Sammanfattning Det ¨ar v¨al k¨ant att utseendet av en vindkraftspark p˚averkar parkens tota- la energiproduktion. Avst˚anden mellan de individuella turbinerna har inver- kan p˚a vakutbredningen och uppbromsningen av vinden. Det finns en hel del analytiska modeller och simuleringar f¨or att ber¨akna dessa f¨orluster men de beh¨over st¨arkas med mer experimentell data. Detta examensarbete beskriver f¨orberedelserna och utf¨orandet av ett vindtunnelexperiment som har utf¨orts med 250 fritt roterande turbinmodeller. Modellerna utvecklades med specifi- ka egenskaper som utv¨arderades innan utf¨orandet. Under experimentet lades st¨orst vikt p˚a globala effekter som uppst˚ar i stora vindkraftsparker, effekterna namngavs Global Turbine Array Effects. Detvisadesigattenstorvindkraftsparkp˚averkadeinfl¨odettillparkenoch detuppkomenskillnadmellanvindensomn˚addedenf¨orstaradeniparkenoch denost¨ordafristr¨ommen.Skillnadenvarenreduktionavvindhastighetenistor- leksordningen1%avdenost¨ordafristr¨ommen.Detframkom¨avenattenh¨ogre uppbromsning av vindhastighet uppkom f¨or en t¨atare park, en reduktion upp till 2.5 % av den ost¨orda fristr¨ommen observerades f¨or centrumturbinen i den f¨orstaraden.Enl¨agreuppbromsningavvindenobserveradesf¨orh¨ornturbinerna ¨an f¨or centrumturbinen i den f¨orsta raden av parken. F¨orattexperimentetskulleblianpassningsbarttillfullskaligaf¨orh˚allanden kr¨avdes krav p˚a nedskalningen. Det konstaterades att dragkraftskoefficienten var den viktigaste parametern f¨or att unders¨oka de globala effekterna. Ytterli- gare en parameter som diskuterades var Reynolds nummer, vilket ¨ar l¨agre ¨an f¨or fullskaliga f¨orh˚allanden n¨ar sm˚a vindturbinsmodeller anv¨ands. Ett f¨orarbete till en bildigenk¨anningsteknik gjordes ¨aven. Tanken var att kunna ber¨akna rotationshastigheten p˚a samtliga turbiner i experimentet med ett enskilt foto. Det var sv˚art att applicera denna teknik d˚a variationer i rota- tionshastigheterna observerades och ett enskilt foto kunde s˚aledes inte repre- sentera medelhastigheten under en l¨angre tidsperiod. iii Contents Abstract i Summary in Swedish iii Nomenclature ix Chapter 1. Introduction 1 Chapter 2. Theoretical Presentations 7 2.1. Atmospheric Conditions 7 2.2. Aerodynamics of Wind Turbines 9 2.3. One-Dimensional Momentum Theory for an Ideal Wind Turbine 10 2.4. Momentum Theory with Rotational Wake 13 2.5. Blade Element Momentum Theory (BEM) 14 2.6. Wake Aerodynamics 15 Chapter 3. Experimental Requirements 19 3.1. Aerodynamic scaling 19 3.2. Velocity Profile 20 3.3. Turbulence level 23 3.4. Lillgrund and Thanet 23 3.5. Boundary Corrections in Wind Tunnels 24 Chapter 4. Measuring Techniques 27 4.1. Particle Image Velocimetry (PIV) 27 4.2. Pressure Rake 27 4.3. Traversed Turbine 28 4.4. Photo Sensor Technique 28 Chapter 5. Experimental Apparatus and Procedure 29 5.1. Development of Turbine Models 29 v 5.2. Development of Photo Measuring Technique 42 5.3. Preparation and Execution of the Extensive Test in G¨avle Wind Tunnel 45 Chapter 6. Results and Discussion 53 6.1. Test 1 53 6.2. Test 2 58 6.3. Test 3 63 6.4. Test 4 65 6.5. General Discussion 68 Chapter 7. Conclusion 69 Chapter 8. Future Work 71 Acknowledgements 73 Bibliography 75 Appendix A. G¨avle Wind Tunnel Characteristics 77 Appendix B. Results from Wind Tunnel Tests with Different Turbine Models 79 Appendix C. Drawings 84 Appendix D. Park Efficiency Calculations in WindPRO 87 Nomenclature α Surface roughness factor [−] λ Tip speed ratio [−] ν Kinematic viscosity of air [m2/s] Ω Rotational speed [rad/s] Ω Rotational speed of the turbine model [rad/s] M ∆p Mean pressure difference [Pa] v Mean free stream velocity [m/s] 1 φ Inflow angle of the relative velocity component [rad] Π Error [m2/s2] ρ Air density [kg/m3] ε Blockage ratio [−] A Cross-sectional area perpendicular to the flow [m2] a Axial induction factor [−] a(cid:48) Tangential induction factor [−] A Streamtubecross-sectionalareafarupstreamofanactuatorrotordisc 1 [m2] A Stream tube cross-sectional area far downstream of an actuator rotor 4 disc [m2] A Swept area [m2] s C Wind tunnel sectional cross section [m2] c Chord length of a turbine blade [m] C Power coefficient [−] p C(cid:48) Corrected power coefficient [−] p C Tangential velocity component [m/s] θ C Drag coefficient [−] d C Lift coefficient [−] l C Thrust coefficient [−] t C(cid:48) Corrected thrust coefficient [−] t D Drag force [N] d Turbine diameter [m] d Diameter of the test disc in G¨avle wind tunnel [m] D F Total thrust [N] tot F Thrust force on tower [N] tow vii F Axial thrust force [N] t h Model turbine hub height [m] M h Reference height [m] ref h Reference height [m] ref h Height z meters above ground [m] z k Wake decay constant [−] k Constant [[V/N] 1 L Lift force [N] M Turbine generator torque [Nm] P Absorbed power [W] p Pressure just in front of an actuator rotor disc [Pa] 2 p Pressure just behind an actuator rotor disc [Pa] 3 P Fluid dynamic power [W] 1 r Turbine radius [m] r Radius of the turbine model [m] M V Voltage [V] v Undisturbed free stream velocity [m/s] 1 v Wind speed just in front of an actuator rotor disc [m/s] 2 v Wind speed far downstream of an actuator rotor disc [m/s] 4 v Velocity deficit after n upstream turbines [m/s] n v Wind speed at the distance x meters from a turbine [m/s] x v Wind speed at the rotor top [m/s] (+) v Wind speed at the rotor bottom [m/s] (−) v Wind speed correction [m/s] corr V Reference voltage [V] ref v Reference wind speed [m/s] ref v Relative wind speed [m/s] r v Wind speed z meters above flat ground [m/s] z0 v Wind speed z meters above ground [m/s] z