Michael Graham - Wind Energy Handbook

5 Chapter 4 Figure 4.1 A wind turbine yawed to the wind direction. Figure 4.2 Deflected wake of a yawed turbine and induced velocities. Figure 4.3 Power coefficient variation with yaw angle and axial flow factor.... Figure 4.4 Velocities and lift and induced drag forces on an autogyro in fas... Figure 4.5 Velocities normal to the yawed rotor. Figure 4.6 The deflected vortex wake of a yawed rotor showing the shed vorti... Figure 4.7 A yawed rotor wake without wake expansion. Figure 4.8 Plan view of yawed actuator disc and the skewed vortex cylinder w... Figure 4.9 Average induced velocities caused by a yawed actuator disc. Figure 4.10 Maximum power coefficient variation with yaw angle, comparison o... Figure 4.11 Axis system for a yawed rotor. Figure 4.12 Flow expansion function variation with radial position and skew ... Figure 4.13 Azimuthal and radial variation of horizontal ( v ) and vertical ( w Figure 4.14 Flow expansion functions for one, two and three blade rotors by ... Figure 4.15 Approximate flow expansion functions for two and three blade rot... Figure 4.16 Øye's curve fit to Coleman's flow expansion function. Figure 4.17 Flow expansion causes a differential angle of attack. Figure 4.18 The velocity components in the plane of a blade cross‐section. Figure 4.19 Azimuthally averaged induced velocity factors for the Delft turb... Figure 4.20 Component velocities, normalised with wind speed, at 30° of yaw.... Figure 4.21 Angle of attack variation at 30° of yaw. Figure 4.22 Measured yaw moments on the Delft turbine. Figure 4.23 Calculated yaw moments on the Delft turbine. Figure 4.24 Measured tilt moments on the Delft turbine. Figure 4.25 Calculated tilt moments on the Delft turbine.Figure 4.26 Radial loading distributions of the first two solutions and thei...Figure 4.27 The form of the loading distribution that yields a yawing moment...Figure 4.28 Yawing moment on the Tjæreborg turbine at 32° yaw and 8.5 m/s.Figure 4.29 Measured and calculated blade root bending moment responses to b...Figure 4.30 Unsteady flow and structural velocities adjacent to a rotor blad...Figure 4.31 Wake development after an impulsive change of angle of attack.Figure 4.32 Lift development after an impulsive change of angle of attack.Figure 4.33 The (a) real and (b) imaginary parts of Theodorsen's function.Figure 4.34 Typical dynamic stall behaviour.Figure 4.35 Growing leading edge vortex and idealised feeding sheet.Figure 4.36 Normal force coefficients for a NACA0012 aerofoil in cyclic pitc...Figure 4.37 Sketch of vortex lattice panels on a blade surface and wake.Figure 4.38 Vorticity downstream of a rotor–blade–tower interaction.Figure 4.39 Volume rendering of computed turbulent wakes of a 4 × 4 array of...

6 Chapter 5Figure 5.1 Variation of turbulence intensity with wind speed for the normal ...Figure 5.2 IEC 61400‐1 extreme rising and falling gust with 50 year return p...Figure 5.3 Simulated wind speed time series constrained to give a 44.5 m/s p...Figure 5.4 (a) Blade SC40 chord and thickness distributions. (b) Blade SC40 ...Figure 5.5 (a) Spanwise variation of resonant and quasi‐static moments – bla...Figure 5.6 Distribution of blade in‐plane and out‐of‐plane aerodynamic loads...Figure 5.7 Distribution of blade in‐plane and out‐of‐plane aerodynamic bendi...Figure 5.8 Blade out‐of‐plane root bending moment during operation in steady...Figure 5.9 Aerofoil data for LM 19.0 blade for various thickness/chord ratio...Figure 5.10 (a) Variation of blade root bending moment with azimuth, for an ...Figure 5.11 (a) Variation of blade root bending moments with azimuth due to ...Figure 5.12 Tower shadow parameters.Figure 5.13 Profiles of velocity deficit due to tower shadow at different di...Figure 5.14 Variation of blade root out‐of‐plane bending moment with azimuth...Figure 5.15 Blade SC40 gravity bending moment distribution.Figure 5.16 Gyroscopic acceleration of a point on a yawing blade.Figure 5.17 (a) Geometry for the derivation of the velocity auto‐correlation...Figure 5.18 Normalised auto‐correlation and cross‐correlation functions for ...Figure 5.19 (a) Rotationally sampled power spectra of longitudinal wind spee...Figure 5.20 Comparison of rotationally sampled power spectra at 40 m radius ...Figure 5.21 Rotationally sampled cross‐spectrum of longitudinal wind speed f...Figure 5.22 Simulated time series of wind speed fluctuations at two points 1...Figure 5.23 Deflection of tip due to flapwise bending of twisted blade (view...Figure 5.24 Restoring moments due to centrifugal force for in‐plane and out‐...Figure 5.25 Blade out‐of‐plane root bending moment dynamic response to tower...Figure 5.26 Blade out‐of‐plane root bending moment dynamic response to tower...Figure 5.27 Campbell diagram for blade SC40.Figure 5.28 Power spectrum of blade SC40 first out‐of‐plane mode tip deflect...Figure 5.29 Teeter geometry.Figure 5.30 Teeter angle power spectrum for two bladed rotor with SC40 blade...Figure 5.31 Fundamental mode shapes of blade and tower.Figure 5.32 Tower top and blade tip deflections resulting from tower shadow,...Figure 5.33 Derivation of blade bending stresses at radius r * due to aerodyn...Figure 5.34 Effect of variation of phase angle between harmonics on combined...Figure 5.35 Low‐speed shaft and front bearing before assembly. The hub mount...Figure 5.36 Shaft bending moments with rotating axis system referred to blad...Figure 5.37 Shaft bending moment fluctuations due to wind shear.Figure 5.38 Components of blade 1 out‐of‐plane root bending moment about fix...Figure 5.39 Rotor thrust during operation in steady, uniform wind: variation...Figure 5.40 Power spectra of rotor thrust and resultant tower base fore–aft ...Figure 5.41 Power spectra of rotor thrust and resultant tower base fore–aft ...Figure 5.42 Blade root bending moment in steady wind.Figure 5.43 Blade root bending moment in turbulent wind for a fixed rotation...Figure 5.44 Spectra of out‐of‐plane loads in turbulent wind.Figure 5.45 Spectra of in‐plane loads in turbulent wind.Figure 5.46 Comparison of techniques for fitting a straight line to empirica...Figure 5.47 Comparison of GEV distributions fitted to empirical data on a Gu...Figure 5.48 Gumbel plot comparison of three extreme value distributions fitt...Figure 5.49 Gumbel plot comparison of four extreme value distributions fitte...Figure 5.50 Local extremes derived from blocks of 12 seconds' duration.Figure 5.51 Probability of j or fewer occurrences of the non‐exceedance of t...Figure A5.1 Power spectrum of wind turbulence and frequency response functio...Figure A5.2 Size reduction factors for the first mode resonant response due ...

7 Chapter 6Figure 6.1 Variation of optimum turbine size with wind shear based on simpli...Figure 6.2 (a) Variation of specific blade mass with diameter for LM blades ...Figure 6.3 Variation of cost of energy with turbine diameter for NREL baseli...Figure 6.4 Variation in cost of energy with rated power for a 70 m diameter,...Figure 6.5 Rated power vs swept area for turbines in production in 2008Figure 6.6 Rated power vs swept area for turbines in or close to production ...Figure 6.7 Variation of coefficient of performance, root bending moment coef...Figure 6.8 Variation of maximum C Pand corresponding tip speed ratio with li...Figure 6.9 Comparison of C P– λ curves for three bladed baseline machin...Figure 6.10 Pitch‐teeter couplingFigure 6.11 Comparison of power curves for (i) stall‐regulated, fixed‐speed;...Figure 6.12 Power curves for different positive pitch angles: 70 m diameter ...Figure 6.13 Schedule of pitch angles vs wind speed for limiting the power ou...Figure 6.14 Pitch linkage system used in conjunction with a single hydraulic...Figure 6.15 Blade pitching system using separate hydraulic actuators for eac...Figure 6.16 Blade pitching system using a separate electric motor for each b...Figure 6.17 Passive control of tip blade, using screw on tip shaft and sprin...Figure 6.18 Schedule of pitch angles required to limit 70 m diameter turbine...Figure 6.19 Power curves for different negative pitch angles: 70 m diameter ...Figure 6.20 Locus of operation of a two‐speed wind turbineFigure 6.21 Control objective of a variable‐speed wind turbine (see also Cha...Figure 6.22 Wind turbine architectures. (a) Fixed‐speed induction generator,...Figure 6.23 Evolution of commercially available wind turbine generator syste...Figure 6.24 Mechanical analogues of directly connected generatorsFigure 6.25 Superconducting rotor synchronous generatorFigure 6.26 Radial flux magnetic gearboxFigure 6.27 Principle of a cascaded brushless doubly fed induction generator...Figure 6.28 Parallel connection of direct current wind turbine generatorsFigure 6.29 View of nacelle showing traditional drive shaft arrangementFigure 6.30 Nacelle arrangement for the Nordex N60 turbine.Figure 6.31 Drive train side view. From left to right the components visible...Figure 6.32 Turbine assembly in the air (1): View of nacelle of 1.5 MW NEG M...Figure 6.33 Turbine assembly in the air (2): View of low‐speed shaft and fro...Figure 6.34 Direct drive generator arrangementFigure 6.35 Integrated gearbox on the Zond Z‐750 turbine. (The gearbox is mo...Figure 6.36 Nineteen rotors spaced at 30 m mounted on a space frame structur...Figure 6.37 Nineteen rotors spaced at 30 m mounted on a tubular ‘tree’ struc...