Small Wind Turbines for Electricity and Irrigation: Design and Construction

351 Pages·2019·12.53 MB·English

by  Mario Alejandro Rosato

Small Wind Turbines for
Electricity and Irrigation

Small Wind Turbines for
Electricity and Irrigation
Design and Construction
Mario Alejandro Rosato
CRC Press
Taylor & Francis Group
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Contents
Foreword ................................................................................................................xv
Preface ..................................................................................................................xvii
Author ...................................................................................................................xxi
1. Small Wind Turbines: A Technology for Energy Independence
and Sustainable Agriculture ........................................................................1
1.1 Introduction: Why “Small” Wind Turbines? .....................................1
1.2 Why Not “Big” Wind Turbines? ........................................................10
1.3 How Small Are Hence, “Small” Wind Turbines? ...........................13
1.4 Why Small Wind Turbines for Pumping Water? ............................13
1.5 General Plan of This Book and Acknowledgments .......................14
Bibliography ...................................................................................................16
2. General Theory of Wind-Driven Machines ............................................19
2.1 Betz’s Theorem ....................................................................................19
2.2 The Extension of Betz’s Theorem to Vertical Axis Wind
Turbines ................................................................................................22
2.2.1 Discussion of the Extension of Betz’s Theorem to
Vertical Axis Turbines ...........................................................24
2.3 Notions on the Theory of Wing Sections .......................................25
2.4 Action of the Air on a Wing in Motion ............................................30
2.4.1 Lift, Drag, and Moment Coefficients ..................................30
2.4.2 Graphical Representation of the Aerodynamic
Coefficients C and C ............................................................32
x z
2.4.2.1 Cartesian Representation of C , C , and C
x m z
as a Function of the Pitch Angle ..........................32
2.4.2.2 Eiffel’s Polar .............................................................32
2.4.2.3 Lilienthal’s Polar .....................................................33
2.4.2.4 Mixed Representations ..........................................33
2.4.3 Definitions and Terminology ...............................................34
2.4.3.1 Solidity Coefficient, σ .............................................34
2.4.3.2 Specific Speed, λ......................................................34
2.4.3.3 Coefficient of Motor Torque, C ...........................35
M
2.4.3.4 Coefficient of Axial Force, C ................................35
F
2.4.3.5 Coefficient of Power, C .........................................35
P
2.4.3.6 Relationships between Dimensionless
Coefficients .............................................................36
2.4.3.7 Reynolds’ Number .................................................37
v
vi Contents
2.5 Classification of Wind Turbines ........................................................37
2.5.1 Vertical Axis Wind Turbines ...............................................38
2.5.1.1 Reaction-Driven Turbines .....................................38
2.5.1.2 Aerodynamic Action Turbines .............................38
2.5.1.3 Hybrid Turbines .....................................................38
2.5.2 H orizontal Axis Wind Turbines ..........................................38
2.5.2.1 Fast Turbines ...........................................................38
2.5.2.2 Slow Wind Turbines ...............................................41
2.5.3 “ Undefinable” Wind-Driven Machines .............................43
2.5.4 C omparison between Different Types of Wind
Turbines .................................................................................44
2.6 Accessory Devices of Wind Turbines ...............................................46
2.7 Exercises ...............................................................................................47
2.7.1 Application of Betz’s Theorem .............................................47
2.7.2 Application of Dimensionless Coefficients ........................47
Bibliography ...................................................................................................49
3. Simplified Aerodynamic Theory for the Design of the Rotor’s
Blades ..............................................................................................................51
3.1 Definition of the Problem ...................................................................51
3.1.1 Speed Loss Coefficient, a .......................................................53
3.1.2 Coefficient of Specific Local Speed, λ .................................54
r
3.1.3 C oefficient of Angular Speed, a′ ..........................................54
3.2 The Theory of the Annular Flow Tube with Vortical Trail ...........55
3.3 The Theory of the Aerodynamic Forces on the Element
of Blade ...............................................................................................63
3.3.1 O ptimum Variation of the Angle θ .....................................69
3.3.2 O ptimum Variation of the Product σ·C .............................71
l z
3.3.3 Optimum Blade for Maximum Aerodynamic
Efficiency .............................................................................71
3.4 Conclusions ..........................................................................................72
3.4.1 V ariation of the Chord ...........................................................72
3.4.2 R elationship between Solidity, Specific Speed, and
Efficiency of the Turbine .......................................................72
3.4.2.1 Solidity and Specific Speed ...................................73
3.4.2.2 Solidity and Aerodynamic Efficiency .................74
3.4.3 I nfluence of the Fineness Coefficient of the Airfoil ..........74
3.5 Practical Exercises ...............................................................................75
3.5.1 I nfluence of the Induced Drag .............................................75
3.5.1.1 Classical Windmill for Water Pumping ..............75
3.5.1.2 Multi-Blade Turbine ...............................................76
3.5.1.3 A Three-Blade Fast Turbine ..................................76
3.5.1.4 Practical Conclusions .............................................77
Bibliography ...................................................................................................77
Contents vii
4. Practical Design of Horizontal Axis Wind Turbines ............................79
4.1 Generalities ..........................................................................................79
4.2 The Method to Design the Rotor ......................................................80
4.2.1 P re-Dimensioning of the Diameter and Number of
Blades .......................................................................................80
4.2.1.1 Pre-Dimensioning Fast Turbines .........................80
4.2.1.2 Pre-Dimensioning of Slow Turbines ...................81
4.2.2 Dimensioning of the Yaw System: Vane or Rotor
Conicity ...................................................................................81
4.2.2.1 Orientation by Means of a Vane ...........................82
4.2.2.2 Orientation by Conicity .........................................82
4.2.2.3 Orientation by Means of a Servomotor ...............83
4.2.3 Selection of the Most Suitable Airfoil for the Blades ........84
4.2.4 Division of the Blade in N Discrete “Differential
Elements” ................................................................................88
4.2.5 Calculation of the Chord and Pitch Angle for Each
Discrete Element ....................................................................88
4.2.5.1 Calculation of the Optimum Chord and
Pitch Angle for Each Discrete Element ...............88
4.2.5.2 Calculation of Sub-optimum Blades
in Order to Facilitate the Handcrafted
Construction ...........................................................89
4.2.6 Discrete Integration of the Tangential and Axial
Forces along the Blade ...........................................................90
4.3 Analysis of the Aerodynamic Features and Construction
Choices of the Rotor ............................................................................90
4.3.1 Fixed Pitch Rotor ....................................................................91
4.3.1.1 Fixed Speed Rotor and Unlimited (or Very
High Limit) Speed of Rotation .............................92
4.3.1.2 Fixed Pitch Rotor with Passive Stall and
Constant Speed .......................................................92
4.3.1.3 Fixed Pitch Rotor Controlled by Active Stall
and Variable Speed ...............................................95
4.3.1.4 Fixed Pitch Rotor Controlled by
Aerodynamic Brakes .............................................95
4.3.2 Variable Pitch Rotor ...............................................................97
4.3.2.1 Variation of the Pitch by Means of
Servomechanisms ..................................................97
4.3.2.2 Variation of the Pitch by Means of
Centrifugal Force ....................................................97
4.3.2.3 Pitch Control by Aerodynamic Moment ...........100
4.3.3 Yaw Systems and Variation of the Exposed Surface .......101
4.4 Selecting the Materials and Techniques for the Blades’
Manufacture ......................................................................................103
viii Contents
4.4.1 Wood ......................................................................................103
4.4.2 Fiber Reinforced Plastic Resin (FRPR) ..............................103
4.4.3 Aluminum Alloys ................................................................103
4.4.4 Sail Rotor ...............................................................................104
4.4.5 Wooden Frame Covered with Tarpaulin, or Plastic
Foil, or Thin Metal Sheet .....................................................106
4.5 Practical Examples ............................................................................106
4.5.1 Low-Cost Rotor with Profiled Sail ....................................106
4.5.1.1 Definition of the Problem ...................................106
4.5.1.2 Pre-dimensioning .................................................107
4.5.1.3 Yaw System............................................................107
4.5.1.4 Selection of the Airfoil .........................................108
4.5.1.5 Dimensioning of the Blade .................................108
4.5.2 Design of an Optimum 3-Bladed Rotor for Electrical
Generation .............................................................................109
4.5.2.1 Definition of the Problem ....................................109
4.5.2.2 First Step: General Size of the Turbine and
Orientation Vane, Generating the Optimum
Blade Shape ...........................................................111
4.5.2.3 Second Step: Performance of the Optimum
Blade .......................................................................111
4.5.2.4 Third Step: Evaluating Alternatives ..................111
Bibliography .................................................................................................111
5. Practical Design of Aerodynamic Action Vertical Axis Wind
Turbines ........................................................................................................113
5.1 General Considerations about Vertical Axis Turbines ................113
5.2 Simplified Theory of the Darrieus Turbines .................................115
5.3 Design of H-Type Darrieus Turbines .............................................123
5.3.1 Pre-dimensioning of H-Type Darrieus Turbines .............123
5.3.2 Choosing the Airfoil for the Rotor ....................................124
5.3.3 Calculating the Coefficient a for Different Arbitrary
Values of λ′ and Determination of the Forces, Torque,
C , and λ .................................................................................124
P
5.4 Analysis of the Aerodynamic Features and Constructive
Choices of the Rotor ..........................................................................127
5.4.1 Speed Control .......................................................................127
5.4.2 Production of the Blades .....................................................127
5.5 Practical Example: Making a Low-Cost Darrieus Rotor .............128
5.5.1 Definition of the Problem ...................................................128
5.5.2 Pre-dimensioning ................................................................128
5.5.3 S election of the Airfoil ........................................................129
5.5.4 D imensioning of the Blade .................................................129
5.6 Exercise ...............................................................................................130
Bibliography .................................................................................................131
Contents ix
6. Practical Design of Savonius Turbines and Derived Models ...........133
6.1 Generalities ........................................................................................133
6.2 Practical Calculation of Savonius Rotors .......................................141
6.2.1 D etermine the Power Obtainable from a Given
Speed of Wind ......................................................................141
6.2.2 D etermine the Torque .........................................................142
6.2.3 D etermine the Necessary Torque for Driving the
Pump......................................................................................142
6.2.4 C alculation of the Mass Flow .............................................143
6.2.5 C urve of Mass Flow as a Function of the Wind
Speed, V .................................................................................143
Bibliography .................................................................................................143
7. Engineering of the Support Structures for Wind Turbines ...............145
7.1 Generalities ........................................................................................145
7.2 Calculation Procedure of a Wind Turbine’s Support
Structure .......................................................................................146
7.2.1 Determination of the Loads ...............................................146
7.2.1.1 Maximum Load on the Hub under Limited
Operational Conditions .......................................147
7.2.1.2 Maximum Load on the Hub with Blocked
Rotor .......................................................................147
7.2.1.3 Load Acting on the Support Structure..............148
7.2.2 Choice of the Pole .................................................................148
7.2.2.1 Standard Steel Poles .............................................148
7.2.2.2 Wooden Poles ........................................................151
7.2.2.3 Prefabricated Concrete Poles ..............................153
7.2.3 Sizing of the Foundations ...................................................153
7.2.4 Guyed Masts and Towers ...................................................154
7.2.4.1 Generalities ...........................................................154
7.2.4.2 A Simplified Calculation Method: Range of
Validity and Description .....................................155
7.2.4.3 Wind-Induced Vibrations and Fatigue Stress .....158
7.2.5 Foldable or Hinged Poles ....................................................160
7.3 Practical Exercises .............................................................................160
7.3.1 Design of the Support Pole and Foundation Block of
a Wind Turbine .....................................................................160
7.3.2 Wooden and Concrete Poles ...............................................163
7.3.3 Guyed Mast ...........................................................................163
7.3.4 von Karman Vortexes and Resonance Phenomena ........164
Bibliography .................................................................................................165
8. Probability Distribution of the Wind Speed and Preliminary
Design of Wind Power Installations ......................................................167
8.1 Generalities ........................................................................................167