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ROTOR THEORY blade for optimum performance under certain assumptions, which is elaborated in the next section. Notable assumptions when using the described BEM theory is that the prevailing wind is uniform and aligned with the rotor axis, and that the blades rotate in the rotor plane, per- pendicular to the rotor axis. Due to factors such as wind shear, yaw error and turbulence, real performance may differ from the modelled performance. The force and power output that is calculated using the BEM theory is referred to as nominal output in the present project thesis. B.2 Optimum blade shape Using the BEM theory described in the previous section it is possible to approximate the blade shape that would provide the maximum power given the following parameters: � Tip-speed ratio (�) � Number of blades (B) � Radius (R) � Lift (Cl) and drag (Cd) characteristics of the airfoil (at optimum angles of attack) The approximation of the ideal blade shape can be carried out using different theories such as Betz or Schmitz [12, p. 121-132]. Betz encloses several assumptions: � No wake rotation (a’ = 0) � No drag (Cd = 0) � No tip loss (F = 1) � Axial interference factor (a) of 1/3 in each annular element Schmitz’ theory does not presume a value of zero for the tangential interference factor and hence takes into account wake rotation, which originates from a rotating flow behind the rotor. This theory can therefore be seen as an augmented and a more accurate version than the Betz’ theory, and it is hence used in the determination of the blade shape for an ideal rotor. One can determine the angle of relative wind � and the chord of the blade c for each element of the ideal rotor [12, p. 132]: 2 � 1 � � = atan� � 3 � � � 8� r c = ( 1 � cos( �) ) B Cl (B.18) (B.19) 135
LIST OF ATTACHMENTSROTOR THEORY Choosing the optimum angle of attack � where glide ratio (Cl/Cd) is maximum, makes it further possible to calculate the blade pitch �, see (B.1). Figure B.3 and figure B.4 show the optimum non-dimensional chord and blade pitch according to both Betz and Schmitz. The graphs are based on the following assumptions: Tip- speed ratio � = 5, the airfoil lift coefficient Cl = 0.99, number of blade B = 3 and optimal angle of attach � = 7�. Figure B.3: Chord length according to Betz and Schmitz theory. Shown for tip-speed ratio � = 5, the airfoil lift coefficient Cl = 0.99, number of blade B = 3 and optimal angle of attach � = 7� 136
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WIND TURBINE DESIGN
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ABSTRACT At the request of the Engi
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CONTENTS 1 Introduction ...........
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E Structural analysis of blades ...
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INTRODUCTION members. Today EWB-DK
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INTRODUCTION Figure 1.2: Left pictu
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INTRODUCTION 6
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PROBLEM STATEMENT reconfigured with
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PROBLEM STATEMENT 10
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METHODOLOGY Figure 3.1: Flow chart
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METHODOLOGY 14 3.1 Calculation meth
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CONCEPTUALISATION the kinetic wind
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CONCEPTUALISATION Figure 4.3: (a) D
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CONCEPTUALISATION issues due to tur
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CONCEPTUALISATION 22 Figure 4.8: Ty
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CONCEPTUALISATION � Darrieus 24 F
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CONCEPTUALISATION 26 Figure 4.13: G
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CONCEPTUALISATION Figure 4.14: Powe
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CONCEPTUALISATION 30 ID Requirement
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CONCEPTUALISATION most suitable sol
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CONCEPTUALISATION The embodiment de
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DESIGN PRESENTATION The main dimens
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DESIGN PRESENTATION The design prop
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DESIGN PRESENTATION The background
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ROTOR 42 6.1 Number of blades Moder
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ROTOR 44 Figure 6.4: Blade design s
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ROTOR Table 6.3 provides a material
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ROTOR Figure 6.7 displays the lift
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ROTOR Figure 6.9: Rotor power outpu
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ROTOR 6.2.3 Manufacturing During th
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ROTOR 54 The three sides of the tem
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ROTOR When the carving process is f
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ROTOR 58 Figure 6.17: Blade attachm
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ROTOR 60 Figure 6.19: Rotor power o
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ROTOR 62 Figure 6.22: Efficiency
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ROTOR sidering the output from the
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ROTOR 66
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GENERATOR AND ELECTRICAL SYSTEM 68
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GENERATOR AND ELECTRICAL SYSTEM The
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GENERATOR AND ELECTRICAL SYSTEM Fig
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GENERATOR AND ELECTRICAL SYSTEM 74
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YAW AND FURLING For an upwind wind
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YAW AND FURLING (16), which are bol
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YAW AND FURLING 80 8.2 Furling syst
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YAW AND FURLING 82 8.3 Summary The
Page 91 and 92: TOWER Concrete tower 84 Figure 9.1:
Page 93 and 94: TOWER 86 Figure 9.4: Turbulent air
Page 95 and 96: TOWER Figure 9.7 shows the tower ba
Page 97 and 98: TOWER models [41, p. 111]. Under ce
Page 99 and 100: ALTERNATIVE BLADE DESIGN 92 10.1 Ai
Page 101 and 102: ALTERNATIVE BLADE DESIGN 94 10.3 Su
Page 103 and 104: DESIGN EVALUATION 96 6 W Low-cost m
Page 105 and 106: DESIGN EVALUATION Weaknesses 1) The
Page 107 and 108: FURTHER DEVELOPMENT � Foundation
Page 109 and 110: FURTHER DEVELOPMENT 102
Page 111 and 112: CONCLUSION proposal is highly flexi
Page 113 and 114: NOMENCLATURE Abbreviation Descripti
Page 115 and 116: NOMENCLATURE Lgs Distance between u
Page 117 and 118: NOMENCLATURE 110
Page 119 and 120: BIBLIOGRAPHY [14] Magenn Power Inc.
Page 121 and 122: BIBLIOGRAPHY [53] H. J. Larsen, H.
Page 123 and 124: LIST OF ATTACHMENTSBASIS FOR CALCUL
Page 139 and 140: LIST OF ATTACHMENTSROTOR THEORY Thi
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Page 145 and 146: LIST OF ATTACHMENTSROTOR THEORY 138
Page 147 and 148: LIST OF ATTACHMENTSROTOR DESIGN TOO
Page 149 and 150: LIST OF ATTACHMENTSROTOR DESIGN TOO
Page 151 and 152: LIST OF ATTACHMENTSAIRFOIL With the
Page 153 and 154: LIST OF ATTACHMENTSAIRFOIL Complete
Page 155 and 156: LIST OF ATTACHMENTSSTRUCTURAL ANALY
Page 191 and 192: LIST OF ATTACHMENTSBLADE ATTACHMENT
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LIST OF ATTACHMENTSBLADE ATTACHMENT
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LIST OF ATTACHMENTSBLADE ATTACHMENT
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LIST OF ATTACHMENTSSTRUCTURAL VERIF
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LIST OF ATTACHMENTSTOWER ANALYSIS T
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LIST OF ATTACHMENTSFURLING AND YAW
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LIST OF ATTACHMENTSALTERNATIVE AIRF
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LIST OF ATTACHMENTSCOMPLIANCE WITH
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