An Experimental Study on Global Turbine Array Effects in Large Wind Turbine Clusters Patrik ...

115 Pages·2013·22.11 MB·English

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