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262 S. Ivanell et al. Assuming that all wake vorticity is included in the tip and the root vortex, the circulation at tip and root should approximately correspond to the maximum bound circulation of the blade. This is of course an idealization, since the roll-up of the vortex sheets is expected to form a concentrated vorticity distribution in the far wake [7]. The computed circulation at the blades is given in Fig. 48.3. Figure 48.3 shows some wiggles that start at about 500 ◦ behind the blades for the root vortex and about 800 ◦ behind the blade for the tip vortex. These are most likely due to integration errors when integrating the circulation. At these positions the vortex core starts to be smeared out and it therefore becomes difficult to identify a good integration path. The results, however, correspond fairly well to classical theories from Helmholtz. The tip vortex leaves the blade with a circulation value close to the maximum bound circulation at the blades. The root vortex leaves the blade with a much lower value of the circulation, but it increases rapidly and reaches values at the same order as the bound circulation. The reason why the root vortex is smeared out earlier than the tip vortex is partly because the vortex cores are closer at the root and partly because of the radial gradient of the circulation. The result is in good agreement with classical theorems from Helmholtz, from which it follows that the wake tip vortex has the same circulation as the maximum value of the bound circulation on the blade. A likely explanation for this good agreement is that the symmetry of the flow domain prohibits the roll-up of the vortex sheet from the blades. Circulation 0.14 0.13 0.12 0.11 0.1 0.09 0.08 0.07 0.06 0.05 96 Tip,eps =1 Re1 96 Tip,eps =1 Re2 96 Tip,eps =1 Re3 96 Rot,eps =1 Re1 96 Rot,eps =1 Re2 96 Rot,eps =1 Re3 Maximum circulation at blade 0 200 400 600 800 1000 1200 Deg. behind blade Fig. 48.3. The figure shows the circulation distribution in the wake at three different Reynolds number compared with the maximum circulation at the blade [8]
References 48 Numerical Computations of Wind Turbine Wakes 263 1. Sørensen J N, Shen W Z, Numerical Modeling of Wind Turbine Wakes, Journal of Fluid Engineering, vol. 124, June 2002 2. R. Mikkelsen (2003) Actuator Disc Methods Applied to Wind Turbines. PhD Thesis, DTU, Lyngby, MEK-FM-PHD 2003-02 3. Sørensen N N, General perpose flow solver applied to flow over hills, PhD Thesis, Risø National Laboratory, Roskilde, Denamark, 1995 4. Michelsen J A, Basis3D – a platform for development of multiblock PDE solvers, Report AFM 92-06, Dept. of Fluid Mechanics, DTU, 1992 5. Michelsen J A, Block structured multigrid solution of 2D and 3D elliptic PDE’s, Report AFM 94-06, Dept. of Fluid Mechanics, DTU, 1994 6. Tjaereborg Data, http://www.afm.dtu.dk/wind/tjar.html 7. Sørensen J N, Okulev V L, Modelling of Far Wake Behind Wind Turbine, Proceeding of the Euromech Colloquium 464b – Wind Energy, Springer, 2006 8. S. Ivanell (2005) Numerical Computations of Wind Turbine Wakes, Lic. Thesis, Royal Institute of Technology, Stockholm, ISRN/KTH/MEK/TR/–05/10–SE
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Wind Energy Proceedings of the Euro
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Prof. Dr. Joachim Peinke Dr. Stepha
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VI Preface been presented, spanning
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VIII Contents 3.3 Stochastic Wind F
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X Contents 12.6 Subgrid Scale Turbu
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XII Contents 22 Stochastic Small-Sc
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XIV Contents 32 Handling Systems Dr
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XVI Contents 41 3D Numerical Simula
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XVIII Contents 51 Comparing WAsP an
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XX Contents 58.3 Ultra-High Perform
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XXII List of Contributors Lars Berg
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XXIV List of Contributors Renata Gn
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XXVI List of Contributors A. Kiss D
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XXVIII List of Contributors El˙zbi
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XXX List of Contributors Ivo Sláde
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1 Offshore Wind Power Meteorology B
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1 Offshore Wind Power Meteorology 3
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1 Offshore Wind Power Meteorology 5
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2 Wave Loads on Wind-Power Plants i
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Trubaduren 2 Wave Loads on Wind-Pow
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Base moment (10 6 Nm) 0.4 0.2 −0.
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2 Wave Loads on Wind-Power Plants i
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3 Time Domain Comparison of Simulat
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3 Time Domain Comparison Using Cons
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7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 3 T
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4 Mean Wind and Turbulence in the A
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5 Wind Speed Profiles above the Nor
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5 Wind Speed Profiles above the Nor
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Height [m] 100 90 80 70 60 50 40 30
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6 Fundamental Aspects of Fluid Flow
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f Suu(f, z) / σ 2 u(z) 10 0 10 −
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a) c) −0,375 6 Fluid Flow over Co
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7 Models for Computer Simulation of
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y/h 2.5 2 1.5 1 0.5 0 7 Models for
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8 Power Performance via Nacelle Ane
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9 Pollutant Dispersion in Flow Arou
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x1/B 0.3 0.5 0.8 1.0 9 Pollutant Di
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9 Pollutant Dispersion in Flow Arou
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10 On the Atmospheric Flow Modellin
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11 Comparison of Logarithmic Wind P
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Height above ground in m 100 90 80
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12 Turbulence Modelling and Numeric
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13 Gusts in Intermittent Wind Turbu
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Durations (s) 25 20 15 10 5 13 Gust
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14 Report on the Research Project O
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height z (m) 100 80 60 40 20 0 14 R
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14.6 Outlook 14 Report on the Resea
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15 Simulation of Turbulence, Gusts
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S(ƒ)(m/s) 2 /Hz 15 Simulation of T
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15 Simulation of Turbulence, Gusts
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16 Short Time Prediction of Wind Sp
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ms prediction error [m/s] 16 Short
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16 Short Time Prediction of Wind Sp
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17 Wind Extremes and Scales: Multif
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Log10 E(k)*k**(5/3) 6 4 2 0 5/3 cor
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17.3 Discussion and Conclusion 17 W
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18 Boundary-Layer Influence on Extr
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z/H (a) (b) 4 2 18 Boundary-Layer I
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18.6 Concluding Remarks 18 Boundary
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19 The Statistical Distribution of
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19 The Statistical Distribution of
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20 Superposition Model for Atmosphe
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h(u) 0.5 0.3 0.1 20 Superposition M
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21 Extreme Events Under Low-Frequen
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21 Extreme Events Under Low-Frequen
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22 Stochastic Small-Scale Modelling
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p(σ⏐u) 1 0.8 0.6 0.4 0.2 22 Stoc
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22 Stochastic Small-Scale Modelling
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23 Quantitative Estimation of Drift
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24 Scaling Turbulent Atmospheric St
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24 Scaling Turbulent Atmospheric St
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25 Wind Farm Power Fluctuations P.
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25 Wind Farm Power Fluctuations 141
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d rc q rc V 0 q V 25 Wind Farm Powe
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References 25 Wind Farm Power Fluct
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26 Network Perspective of Wind-Powe
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27 Phenomenological Response Theory
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28 Turbulence Correction for Power
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28 Turbulence Correction for Power
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29 Online Modeling of Wind Farm Pow
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29 Online Modeling of Wind Farm Pow
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30 Uncertainty of Wind Energy Estim
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31 Characterisation of the Power Cu
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32 Handling Systems Driven by Diffe
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32 Handling Systems Driven by Diffe
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33 Experimental Researches of Chara
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33 Experimental Researches of Chara
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34 Methodical Failure Detection in
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34 Methodical Failure Detection in
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35 Modelling of the Transition Loca
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35 Modelling an Airfoil with Surfac
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(Cl/Cd)max 120 110 100 90 80 70 60
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35 Modelling an Airfoil with Surfac
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36 Helicopter Aerodynamics with Emp
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37 Determination of Angle of Attack
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37 Determination of Angle of Attack
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Drag coefficient 0.5 0.4 0.3 0.2 0.
Page 241 and 242: 38 Unsteady Characteristics of Flow
Page 243 and 244: PSD PSD 38 Unsteady Characteristics
Page 245 and 246: 39 Aerodynamic Multi-Criteria Shape
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Page 275 and 276: 45 Modeling of the Far Wake behind
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Page 279 and 280: 46 Stability of the Tip Vortices in
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Page 283 and 284: 47 Modelling Turbulence Intensities
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Page 297 and 298: U mean / U ref 1 0.9 0.8 0.7 49 Mod
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Page 305 and 306: 51 Comparing WAsP and Fluent for Hi
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Page 311 and 312: 52 Fatigue Assessment of Truss Join
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59 A Modular Concept for Integrated
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60 Solutions of Details Regarding F
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SR 1000 800 600 400 200 100 80 60 4
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60 Solutions of Details Regarding F
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61 On the Influence of Low-Level Je
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Relative Power and Loading [%] 61 O
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62 Reliability of Wind Turbines Exp
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62 Reliability of Wind Turbines 331
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