Wind Energy

More documents

Recommendations

Info

250 V.L. Okulov and J.N. Sørensen Γ 0 Ω 0 x Z r hub a V 0 h = 2πl Γ Γ 2r core Fig. 46.1. Sketch of N tip helical vortices embedded in assigned flow (Ω0,V0) and relative velocity plots about vortex axis for (a) unstable and (b) stable far wakes 4πa2 � 2 1+τ B = s (N − s) Γ �3/2 τ 3 N − 2 − 2N +2 τ 2 1 + τ (1 + τ 2 ) 3/2 �� τ 2 − 1 �� E + ψ − 4 s � − N N � s + 3 4 − 2τ 2 � � 2 1+τ − ln Nε � �� 3/2 + τ 1+2τ2 τ (1 + τ 2 ) 1/2 τ + 3 � 2τ 4 − 6τ 2 + 3 � 1.20206 4 N 2 4πa2 + Γ BA (1 + τ 2 ) 9/2 y a b (46.1) where s = [0; N − 1] is the subharmonic wave number; E = 0.5772. . . is the Euler constant and the psi-function ψ(·) takes values such as ψ(−1/2) = 0.0395..., ψ(−1/3) = 1.6818..., ψ(−2/3) = −1.6320... (see, e.g. [1]). The last term of BA in (46.1) describes the influence of the assigned velocity field due to root vorticity and the hub of the rotor. Three important examples of the central axisymmetrical helical vortices have been considered with R- (step-shape), L- (Gaussian) and S- (hat-type) axial vorticity distribution corresponding to Rankine, Lamb and Scully vortices at τ →∞[4]. For those types of assigned flow field the BA-term takes form: � −1, r < δ, BA =4Nγ 1 � τ 2δ2 (2-R) ,r≥ δ, 1 BA =4Nγ 1+δ2 � 2 1+τ τ 2 δ2 � − 1 , (2-L) 1+δ2
46 Stability of the Tip Vortices in the Far Wake behind a <strong>Wind</strong> Turbine 251 �� 2 1+τ BA =4Nγ δ2 � � +1 exp − τ 2 1 δ2 � � − 1 . (2-S) where γ = Γ0/NΓ is the circulation ratio i.e. the central (hub) vortex strength normalized by the total multiple circulation of the tip vortices. The dimensionless hub vortex pitch τ keeps the same value as that of the multiples and the hub vortex radius δ = rhub/a is normalized by a, the radius of cylinder supporting helical vortex axis of the multiple. Note that BA does not contain any term with wind speed implying that translatory motion from wind does not influence the stability. The stability condition of the tip vortex configuration only depends on the sign of B. The vortex system is unstable if B ≥ 0, where the relative velocity field in the vortex position has an unstable critical point (Fig. 46.1a) and for B
Page 1 and 2:
Wind Energy Proceedings of the Euro
Page 3 and 4:
Prof. Dr. Joachim Peinke Dr. Stepha
Page 5 and 6:
VI Preface been presented, spanning
Page 7 and 8:
VIII Contents 3.3 Stochastic Wind F
Page 9 and 10:
X Contents 12.6 Subgrid Scale Turbu
Page 11 and 12:
XII Contents 22 Stochastic Small-Sc
Page 13 and 14:
XIV Contents 32 Handling Systems Dr
Page 15 and 16:
XVI Contents 41 3D Numerical Simula
Page 17 and 18:
XVIII Contents 51 Comparing WAsP an
Page 19 and 20:
XX Contents 58.3 Ultra-High Perform
Page 21 and 22:
XXII List of Contributors Lars Berg
Page 23 and 24:
XXIV List of Contributors Renata Gn
Page 25 and 26:
XXVI List of Contributors A. Kiss D
Page 27 and 28:
XXVIII List of Contributors El˙zbi
Page 29 and 30:
XXX List of Contributors Ivo Sláde
Page 31 and 32:
1 Offshore Wind Power Meteorology B
Page 33 and 34:
1 Offshore Wind Power Meteorology 3
Page 35 and 36:
1 Offshore Wind Power Meteorology 5
Page 37 and 38:
2 Wave Loads on Wind-Power Plants i
Page 39 and 40:
Trubaduren 2 Wave Loads on Wind-Pow
Page 41 and 42:
Base moment (10 6 Nm) 0.4 0.2 −0.
Page 43 and 44:
2 Wave Loads on Wind-Power Plants i
Page 45 and 46:
3 Time Domain Comparison of Simulat
Page 47 and 48:
3 Time Domain Comparison Using Cons
Page 49 and 50:
7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 3 T
Page 51 and 52:
4 Mean Wind and Turbulence in the A
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
5 Wind Speed Profiles above the Nor
Page 59 and 60:
5 Wind Speed Profiles above the Nor
Page 61 and 62:
Height [m] 100 90 80 70 60 50 40 30
Page 63 and 64:
6 Fundamental Aspects of Fluid Flow
Page 65 and 66:
f Suu(f, z) / σ 2 u(z) 10 0 10 −
Page 67 and 68:
a) c) −0,375 6 Fluid Flow over Co
Page 69 and 70:
7 Models for Computer Simulation of
Page 71 and 72:
y/h 2.5 2 1.5 1 0.5 0 7 Models for
Page 73 and 74:
8 Power Performance via Nacelle Ane
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
9 Pollutant Dispersion in Flow Arou
Page 81 and 82:
x1/B 0.3 0.5 0.8 1.0 9 Pollutant Di
Page 83 and 84:
9 Pollutant Dispersion in Flow Arou
Page 85 and 86:
10 On the Atmospheric Flow Modellin
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
11 Comparison of Logarithmic Wind P
Page 93 and 94:
Height above ground in m 100 90 80
Page 95 and 96:
12 Turbulence Modelling and Numeric
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
13 Gusts in Intermittent Wind Turbu
Page 105 and 106:
Page 107 and 108:
Durations (s) 25 20 15 10 5 13 Gust
Page 109 and 110:
Page 111 and 112:
14 Report on the Research Project O
Page 113 and 114:
height z (m) 100 80 60 40 20 0 14 R
Page 115 and 116:
14.6 Outlook 14 Report on the Resea
Page 117 and 118:
15 Simulation of Turbulence, Gusts
Page 119 and 120:
S(ƒ)(m/s) 2 /Hz 15 Simulation of T
Page 121 and 122:
15 Simulation of Turbulence, Gusts
Page 123 and 124:
16 Short Time Prediction of Wind Sp
Page 125 and 126:
ms prediction error [m/s] 16 Short
Page 127 and 128:
16 Short Time Prediction of Wind Sp
Page 129 and 130:
17 Wind Extremes and Scales: Multif
Page 131 and 132:
Log10 E(k)*k**(5/3) 6 4 2 0 5/3 cor
Page 133 and 134:
17.3 Discussion and Conclusion 17 W
Page 135 and 136:
18 Boundary-Layer Influence on Extr
Page 137 and 138:
z/H (a) (b) 4 2 18 Boundary-Layer I
Page 139 and 140:
18.6 Concluding Remarks 18 Boundary
Page 141 and 142:
19 The Statistical Distribution of
Page 143 and 144:
19 The Statistical Distribution of
Page 145 and 146:
20 Superposition Model for Atmosphe
Page 147 and 148:
h(u) 0.5 0.3 0.1 20 Superposition M
Page 149 and 150:
21 Extreme Events Under Low-Frequen
Page 151 and 152:
21 Extreme Events Under Low-Frequen
Page 153 and 154:
22 Stochastic Small-Scale Modelling
Page 155 and 156:
p(σ⏐u) 1 0.8 0.6 0.4 0.2 22 Stoc
Page 157 and 158:
22 Stochastic Small-Scale Modelling
Page 159 and 160:
23 Quantitative Estimation of Drift
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
24 Scaling Turbulent Atmospheric St
Page 167 and 168:
24 Scaling Turbulent Atmospheric St
Page 169 and 170:
25 Wind Farm Power Fluctuations P.
Page 171 and 172:
25 Wind Farm Power Fluctuations 141
Page 173 and 174:
d rc q rc V 0 q V 25 Wind Farm Powe
Page 175 and 176:
References 25 Wind Farm Power Fluct
Page 177 and 178:
26 Network Perspective of Wind-Powe
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
27 Phenomenological Response Theory
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
28 Turbulence Correction for Power
Page 191 and 192:
28 Turbulence Correction for Power
Page 193 and 194:
29 Online Modeling of Wind Farm Pow
Page 195 and 196:
29 Online Modeling of Wind Farm Pow
Page 197 and 198:
30 Uncertainty of Wind Energy Estim
Page 199 and 200:
Page 201 and 202:
Page 203 and 204:
31 Characterisation of the Power Cu
Page 205 and 206:
Page 207 and 208:
Page 209 and 210:
32 Handling Systems Driven by Diffe
Page 211 and 212:
32 Handling Systems Driven by Diffe
Page 213 and 214:
33 Experimental Researches of Chara
Page 215 and 216:
33 Experimental Researches of Chara
Page 217 and 218:
34 Methodical Failure Detection in
Page 219 and 220:
34 Methodical Failure Detection in
Page 221 and 222:
35 Modelling of the Transition Loca
Page 223 and 224:
35 Modelling an Airfoil with Surfac
Page 225 and 226:
(Cl/Cd)max 120 110 100 90 80 70 60
Page 227 and 228:
35 Modelling an Airfoil with Surfac
Page 229 and 230: 36 Helicopter Aerodynamics with Emp
Page 235 and 236: 37 Determination of Angle of Attack
Page 237 and 238: 37 Determination of Angle of Attack
Page 239 and 240: 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
Page 247 and 248: 39 Multi-Criteria Shape Optimizatio
Page 249 and 250: 39 Multi-Criteria Shape Optimizatio
Page 251 and 252: 40 Rotation and Turbulence Effects
Page 253 and 254: Cp Xsep/c 1 0.6 0.2 −0.2 −0.6
Page 255 and 256: Standard deviation of Cp 0.7 0.6 0.
Page 257 and 258: 41 3D Numerical Simulation and Eval
Page 259 and 260: 41 3D-CFD-Simulation of a Wind Turb
Page 261 and 262: 42 Performance of the Risø-B1 Airf
Page 263 and 264: 42 Performance of the Risø-B1 Airf
Page 265 and 266: 43 Aerodynamic Behaviour of a New T
Page 271 and 272: 44 Numerical Simulation of Dynamic
Page 273 and 274: 44 Numerical Simulation of Dynamic
Page 275 and 276: 45 Modeling of the Far Wake behind
Page 277 and 278: 8 6 uz 4 2 45 Modeling of the Far W
Page 279: 46 Stability of the Tip Vortices in
Page 283 and 284: 47 Modelling Turbulence Intensities
Page 289 and 290: 48 Numerical Computations of Wind T
Page 291 and 292: Z X Y 48 Numerical Computations of
Page 293 and 294: References 48 Numerical Computation
Page 295 and 296: 49 Modelling Wind Turbine Wakes wit
Page 297 and 298: U mean / U ref 1 0.9 0.8 0.7 49 Mod
Page 299 and 300: 49.5 Conclusion 49 Modelling Wind T
Page 301 and 302: 50 Prediction of Wind Turbine Noise
Page 303 and 304: 0.8 0.6 0.4 0.2 −0.2 −0.4 −0.
Page 305 and 306: 51 Comparing WAsP and Fluent for Hi
Page 307 and 308: Table 51.1. Measurements and simula
Page 309 and 310: 51 Comparing WAsP and Fluent for Hi
Page 311 and 312: 52 Fatigue Assessment of Truss Join
Page 317 and 318: 53 Advances in Offshore Wind Techno
Page 319 and 320: Simulation Measurement pitch angle
Page 321 and 322: 53 Advances in Offshore Wind Techno
Page 323 and 324: 54 Benefits of Fatigue Assessment w
Page 325 and 326: ∆σN [N/mm²] 100 10 54 Benefits
Page 327 and 328: 55 Extension of Life Time of Welded
Page 329 and 330: Transverse residual stresses [N/mm
Page 331 and 332:
56 Damage Detection on Structures o
Page 333 and 334:
56 Damage Detection on Structures o
Page 335 and 336:
57 Influence of the Type and Size o
Page 337 and 338:
[W/m 2 ] q t [W/m 5000 4000 3000 20
Page 339 and 340:
58 High-cycle Fatigue of “Ultra-H
Page 341 and 342:
(a) (b) 450 Load [kN] 400 350 300 2
Page 343 and 344:
59 A Modular Concept for Integrated
Page 345 and 346:
Page 347 and 348:
Page 349 and 350:
60 Solutions of Details Regarding F
Page 351 and 352:
SR 1000 800 600 400 200 100 80 60 4
Page 353 and 354:
60 Solutions of Details Regarding F
Page 355 and 356:
61 On the Influence of Low-Level Je
Page 357 and 358:
Relative Power and Loading [%] 61 O
Page 359 and 360:
62 Reliability of Wind Turbines Exp
Page 361 and 362:
62 Reliability of Wind Turbines 331
Page 363:
This page intentionally left blank
show all

Wind Energy

Create successful ePaper yourself

Delete template?

Save as template?