Optimization of Wind Turbine Airfoils/Blades and Wind Farm Layouts

184 Pages·2016·7.82 MB·English

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All Theses and Dissertations (ETDs)
Spring 1-20-2014
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Xiaomin Chen
Washington University in St. Louis
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Chen, Xiaomin, "Optimization of Wind Turbine Airfoils/Blades and Wind Farm Layouts" (2014). All Theses
and Dissertations (ETDs). 1228.
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WASHINGTON UNIVERSITY IN ST. LOUIS

School of Engineering and Applied Science
Department of Mechanical Engineering & Materials Science

Dissertation Examination Committee:
Ramesh Agarwal, Chair
Ken Jerina
Norman Katz
Mori Mani
David Peters
Palghat Ramanchandran

Optimization of Wind Turbine Airfoils/Blades and Wind Farm Layouts

by
Xiaomin Chen

A dissertation presented to the
Graduate School of Arts and Sciences
of Washington University in
partial fulfillment of the
requirements for the degree
of Doctor of Philosophy

May 2014
Saint Louis, Missouri
© 2014, Xiaomin Chen
Table of Contents
List of Figures ................................................................................................................................ vi
List of Tables ................................................................................................................................. xi
Nomenclature ................................................................................................................................ xii
Acknowledgments........................................................................................................................ xiv
Abstract of the Dissertation ......................................................................................................... xvi
Chapter 1 Introduction .................................................................................................................... 1
1.1 Overview ............................................................................................................................... 1
1.2 Wind Turbines ....................................................................................................................... 3
1.3 Wind Farms ........................................................................................................................... 6
1.4 CFD, BEM and Genetic Algorithms ..................................................................................... 7
1.4.1 Introduction to CFD ..................................................................................................... 7
1.4.2 Introduction to BEM .................................................................................................... 8
1.4.3 Genetic Algorithms ...................................................................................................... 9
1.5 Dissertation Outline ............................................................................................................. 10
Chapter 2 Motivation .................................................................................................................... 12
2.1 Overview ............................................................................................................................. 12
2.2 Optimization of Wind-Turbine Airfoils and Blades............................................................ 14
2.3 Blade Element Momentum (BEM) Theory for 3D Wind Turbine Applications ................ 15
2.4 Wind Farm Layout Optimization ........................................................................................ 17
2.5 Genetic Algorithms ............................................................................................................. 18
Chapter 3 Literature Review ......................................................................................................... 19
3.1 Airfoil and Wind Turbine Optimization .............................................................................. 19
3.2 Optimization Methods ......................................................................................................... 22
3.3 Wind Farm Optimization .................................................................................................... 23
3.4 Brief Literature Review of Flatback, DU, FX, NACA 64 Series, RAE 2822 and NACA
0012 Airfoils ............................................................................................................................. 26
3.4.1 Flatback Airfoils ........................................................................................................ 26
3.4.2 FX, DU and NACA 64 Series of Airfoils .................................................................. 27
Chapter 4 Methodology ................................................................................................................ 29
4.1 Overview ............................................................................................................................. 29
4.2 Genetic Algorithm ............................................................................................................... 31
4.2.1 Single-Objective Genetic Algorithm (SOGA) ........................................................... 31
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4.2.2 Multi-Objective Genetic Algorithm (MOGA) ........................................................... 34
4.3 Computational Fluid Dynamics .......................................................................................... 35
4.3.1 Overview .................................................................................................................... 35
4.3.2 Governing Equations .................................................................................................. 36
4.3.3 Turbulence ................................................................................................................. 37
4.3.4 Turbulence Modeling for RANS Equations ............................................................... 38
4.3.5 Turbulence Models .................................................................................................... 39
(a) Spalart-Allmaras Model ........................................................................................ 39
(b) Shear-stress Transport (SST) k-ω Model .............................................................. 41
(c) The k-kl-ω Transition Model ................................................................................ 43
4.3.6 Boundary Conditions and Initial Conditions ............................................................. 44
(a) Boundary Conditions: ........................................................................................... 45
(b) Initial Conditions: ................................................................................................. 46
4.3.7 Discretization Methods .............................................................................................. 46
4.3.8 Type of Flow Solvers ................................................................................................. 47
4.3.9 Description of CFD solver FLUENT ......................................................................... 50
4.4 Shape Parameterization ....................................................................................................... 50
Chapter 5 Validation of Optimization Methodology .................................................................... 52
5.1 Overview ............................................................................................................................. 52
5.2 Airfoil Parameterization ...................................................................................................... 54
5.3 Algorithm Implementation .................................................................................................. 56
5.3.1 Implementation of MOGA ......................................................................................... 56
5.3.2 Mesh Generation ........................................................................................................ 58
5.3.3 Flow Field Computation ............................................................................................ 59
5.4 Results and Discussion ........................................................................................................ 60
5.4.1 Optimization Results .................................................................................................. 60
5.4.2 Discussion .................................................................................................................. 65
Chapter 6 Optimization of Wind Turbine Airfoils ....................................................................... 68
6.1 Overview ............................................................................................................................. 68
6.2 Airfoil Parameterization ...................................................................................................... 72
6.3 Algorithm Implementation .................................................................................................. 76
6.3.1 Implementation of SOGA .......................................................................................... 76
6.3.2 Implementation of MOGA ......................................................................................... 77
6.3.3 Mesh Generation ........................................................................................................ 79
6.3.4 Flow Field Computation ............................................................................................ 81
6.4 Results and Discussion ........................................................................................................ 82
iii
6.4.1 Optimization of Flatback Airfoils .............................................................................. 82
(a) SOGA Results ....................................................................................................... 82
(b) MOGA Results ...................................................................................................... 88
6.4.2 Optimization of DU, FX and NACA 64 Airfoils ....................................................... 91
Chapter 7 Blade Element Momentum Theory (BEM) for Wind Turbine Applications ............... 97
7.1 Overview ............................................................................................................................. 97
7.2 Blade Element Momentum Theory ..................................................................................... 98
7.2.1 Momentum Theory .................................................................................................... 99
7.2.2 Blade Element Theory ............................................................................................. 100
7.2.3 Tip Loss Correction and Modified BEM Theory ..................................................... 102
7.3 Simplified Dynamic Inflow Aerodynamic Model ............................................................ 104
7.4 Airfoil Data Preparation .................................................................................................... 106
7.5 Results and Discussion ...................................................................................................... 107
7.5.1 Validation of BEM Analysis Tool ........................................................................... 107
7.5.2 Results of the Performance of Thick Airfoils .......................................................... 112
7.5.3 Results of Simplified Dynamic Inflow Model ......................................................... 119
Chapter 8 Optimization of Wind Farm Layouts ......................................................................... 124
8.1 Overview ........................................................................................................................... 124
8.2 Wake, Power and Cost Modeling of a HAWT .................................................................. 124
8.2.1 Jensen's Wake Modeling of a HAWT ...................................................................... 124
8.2.2 Werle's Wake Modeling of a HAWT ....................................................................... 126
8.2.3 Multiple Wake and Cost Modeling for HAWT ....................................................... 127
8.3 Wake, Power and Cost Modeling of a VAWT .................................................................. 128
8.3.1 Single Stream Model of a VAWT ............................................................................ 128
8.3.2 Wake Model for a VAWT ....................................................................................... 129
8.4 Results and Discussion ...................................................................................................... 130
8.4.1 Layout Optimization of HAWT Wind Farm ............................................................ 130
8.4.2 Layout Optimization of VAWT Wind Farm ............................................................ 135
Chapter 9 Optimization of a 3-D Wind-Turbine Blade .............................................................. 138
9.1 Overview ........................................................................................................................... 138
9.2 Wind Tunnel Modeling and Mesh Generation .................................................................. 139
9.3 Implementation of MOGA ................................................................................................ 142
9.3.1 Flow Field Computation .......................................................................................... 142
9.3.2 Blade Section Parameterization ............................................................................... 142
9.3.3 Algorithm Implementation ....................................................................................... 144
9.4 Results and Discussion ...................................................................................................... 144
9.4.1 Optimization Results ................................................................................................ 144
iv
9.4.2 Discussions ............................................................................................................... 148
Chapter 10 Conclusions .............................................................................................................. 151
Chapter 11 Future Work ............................................................................................................. 154
References ................................................................................................................................... 155
Vita .............................................................................................................................................. 163

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List of Figures
Figure 1-1 Global wind power cumulative capacity ...................................................................... 1
Figure 1-2 (a) Megawatts of installed wind power generating capacity since 2001 (b) Thousand
megawatthours generated since 1997 ............................................................................................. 2
Figure 1-3 Map illustrating installed wind power generating capacity for U.S. states at the end of
2012................................................................................................................................................. 3
Figure 1-4 An example of off-shore HAWT wind farm ................................................................ 4
Figure 1-5 An example of Darius type VAWT wind farm ............................................................ 4
Figure 1-6 An example of Horizontal-Axis Wind Turbine (HAWT) ............................................ 5
Figure 1-7 An example of wind turbine airfoil .............................................................................. 6
Figure 1-8 Example of onshore wind farm: the Shepherds Wind Farm ........................................ 7
Figure 1-9 Example of offshore wind farm near Copenhagen, Denmark ...................................... 7
Figure 1-10 An illustration of the general iteration process using GA for achieving the optimized
solution .......................................................................................................................................... 10
Figure 2-1 Wind turbine design process ...................................................................................... 13
Figure 3-1 Time-averaged pressure distributions of the TR-35 and TR-35-10 airfoils at
Re=4.5x106, α=8 deg, free transition ............................................................................................ 27
Figure 4-1 Illustration of information flow in optimization process ........................................... 29
Figure 4-2 Illustration of information flow in optimization process ........................................... 30
Figure 4-3 Illustration of information flow in optimization process ........................................... 30
Figure 4-4 Illustration of k individuals in the initial generation .................................................. 31
Figure 4-5 Biological individual from a biological generation ................................................... 32
Figure 4-6 An example of natural selection in the biological world ........................................... 32
Figure 4-7 Illustration of the General Crossover Function in GA ............................................... 33
Figure 4-8 Bezier curves of various degrees ................................................................................ 51
Figure 5-1 RAE 2822 airfoil: Pressure contours and streamlines at M = 0.75, Re = 6.2*106, α =
2.8º ................................................................................................................................................ 52
Figure 5-2 RAE 2822 airfoil: Pressure distribution at M = 0.75, Re = 6.2*106, α = 2.8º............ 53
Figure 5-3 Geometry of the blade section of NACA 0012 airfoil ............................................... 53
Figure 5-4 Example of Bezier curves and Bezier control points ................................................. 54
Figure 5-5 Illustration of information flow in MOGA process ................................................... 56
Figure 5-6 Pareto solutions for RAE 2822 airfoil ........................................................................ 58
Figure 5-7 C-Grid around the RAE 2822 airfoil .......................................................................... 59
Figure 5-8 O-Grid around the NACA 0012 airfoil ...................................................................... 59
Figure 5-9 Convergence history of shape optimization of NACA 0012 II airfoil using the GA
algorithm ....................................................................................................................................... 61
Figure 5-10 Results for optimized RAE 2822 airfoil, M = 0.73, α = 2 degree ............................ 63
Figure 5-11 Results for optimized RAE 2822 airfoil, M = 0.75, α = 2.8 degree ......................... 63
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Figure 5-12 Results for optimized NACA 0012 airfoil, M = 0.75, α = 2 degree ........................ 64
Figure 5-13 Results for optimized NACA 0012 airfoil, M = 0.85, α = 1.5 degree ..................... 65
Figure 5-14 Comparison of original and optimized RAE 2822 airfoil shapes and pressure
distributions; M = 0.73, α = 2 degree ............................................................................................ 66
Figure 5-15 Comparison of original and optimized RAE 2822 airfoil shapes and pressure
distributions; M = 0.75, α = 2.8 degree ......................................................................................... 66
Figure 5-16 Comparison of original and optimized NACA 0012 airfoil shapes and pressure
distribution; M = 0.75, α = 2 degree ............................................................................................. 67
Figure 5-17 Comparison of original and optimized NACA 0012 airfoil shapes and pressure
distributions; M = 0.8, α = 1.5 degree ........................................................................................... 67
Figure 6-1 Geometries of blade sections of three flatback FB series of airfoils given in Baker et
al. ................................................................................................................................................... 68
Figure 6-2 Geometry of the blade section of FX 66-S196-V1 airfoil.......................................... 70
Figure 6-3 Geometry of the blade section of DU 91-W2-250 airfoil .......................................... 70
Figure 6-4 Geometries of blade sections of (a) NACA 64418 and (b) 64421 airfoils ................. 71
Figure 6-5 Example of Bezier curves and Bezier control points ................................................. 72
Figure 6-6 Example of Bezier curves and Bezier control points ................................................. 75
Figure 6-7 Illustration of information flow in GA process .......................................................... 76
Figure 6-8 Pareto solutions for FX 66-S-196 V1 airfoil .............................................................. 79
Figure 6-9 O-Grid around the FB-3500-0875 airfoil ................................................................... 80
Figure 6-10 C-Grid around the FX 66-S-196 V1 airfoil .............................................................. 80
Figure 6-11 O-Grid around the DU 91-W2-250 airfoil ............................................................... 80
Figure 6-12 Convergence history of optimization for a typical airfoil using the SOGA algorithm
....................................................................................................................................................... 82
Figure 6-13 Results for optimized FB 3500-0050 airfoil, Re = 666,000, α = 10 (free transition)
(a) Airfoil shape (b) Pressure distribution (c) Velocity contours ................................................. 85
Figure 6-14 Results for Optimized FB 3500-0875 Airfoil, Re = 666,000, α = 10 (free transition)
(a) Airfoil shape (b) Pressure distribution (c) Velocity contours ................................................. 85
Figure 6-15 Results for Optimized FB 3500-1750 Airfoil, Re = 666,000, α = 10 (free transition)
(a) Airfoil shape (b) Pressure distribution (c) Velocity contours ................................................. 86
Figure 6-16 Comparison of computed C and C (shown by arrows)for original FB-3500-0050
l d
airfoil (with free transition) and SOGA-optimized airfoil (with fixed transition) at Re = 666,000
and α = 10 with experimental data reported by Baker et al. for both fixed and free transition for
(a) Lift curves and (b) Drag polars ............................................................................................... 87
Figure 6-17 Comparison of computed C and C (shown by arrows)for original FB-3500-0875
l d
airfoil (with free transition) and SOGA-optimized airfoil (with fixed transition) at Re = 666,000
and α = 10 with experimental data reported by Baker et al. for both fixed and free transition for
(a) Lift curves and (b) Drag polars ............................................................................................... 87
Figure 6-18 Comparison of computed C and C (shown by arrows)for original FB-3500-1750
l d
airfoil (with free transition) and SOGA-optimized airfoil (with fixed transition) at Re = 666,000
vii
and α = 10 with experimental data reported by Baker et al. for both fixed and free transition for
(a) Lift curves and (b) Drag polars ............................................................................................... 88
Figure 6-19 Comparison of original and optimized FB-0050 (a) Airfoil shapes and (b) Pressure
distributions obtained using MOGA algorithm ............................................................................ 89
Figure 6-20 Comparison of original and optimized FB-0875 (a) Airfoil shapes and (b) Pressure
distributions obtained using MOGA algorithm ............................................................................ 89
Figure 6-21 Comparison of original and optimized FB-1750 (a) Airfoil shapes and (b) Pressure
distributions obtained using MOGA algorithm ............................................................................ 89
Figure 6-22 Convergence history of MOGA for two separate objectives for FB 1750 airfoil .... 90
Figure 6-23 Convergence history of a typical optimized airfoil using GA algorithm ................. 91
Figure 6-24 Results for Optimized FX 66-S-196 V1 Airfoil, Re = 1.5e6, α = 7.5 degree .......... 93
Figure 6-25 Results for Optimized DU 91-W2-250 Airfoil, Re = 3e6, α = 7.5 degree ............... 93
Figure 6-26 Results for Optimized NACA 64418 Airfoil, Re = 3e6, α = 7.5 degree .................. 94
Figure 6-27 Results for Optimized NACA 64421 Airfoil, Re = 3e6, α = 7.5 degree .................. 94
Figure 6-28 Comparison of original and optimized FX 66-S-196 V1 airfoil shapes and pressure
distributions obtained using MOGA algorithm ............................................................................ 95
Figure 6-29 Comparison of original and optimized DU 91-W2-250 airfoil shapes and pressure
distributions obtained using MOGA algorithm ............................................................................ 95
Figure 6-30 Comparison of original and optimized NACA 64418 airfoil shapes and pressure
distributions obtained using MOGA algorithm ............................................................................ 95
Figure 6-31 Comparison of original and optimized NACA 64421 airfoil shapes and pressure
distributions obtained using MOGA algorithm ............................................................................ 96
Figure 7-1 Actuator disk model of a wind turbine ....................................................................... 99
Figure 7-2 Rotating annular stream tube ................................................................................... 100
Figure 7-3 Iterative procedure for induction factors calculation ............................................... 103
Figure 7-4 Evaluation procedure for dynamic inflow model calculation .................................. 106
Figure 7-5 Airfoil data extrapolation compared with the available experimental data ............. 107
Figure 7-6 Geometric properties of NREL Phase II wind turbine ............................................. 108
Figure 7-7 Geometric properties of NREL Phase III wind turbine ........................................... 109
Figure 7-8 Geometric properties of Risoe wind turbine ............................................................ 110
Figure 7-9 Comparison of BEM calculations with test data for NREL Phase II wind turbine . 111
Figure 7-10 Comparison of BEM calculations with test data for NREL Phase III wind turbine
..................................................................................................................................................... 111
Figure 7-11 Comparison of BEM calculations with test data for Risoe wind turbine ............... 112
Figure 7-12 Geometric properties of wind turbine using thick airfoil sections ......................... 113
Figure 7-13 Comparison of power output of a wind turbine of Table 7-4 with different airfoil
sections with the original NREL Phase II wind turbine with S809 airfoil section ..................... 113
Figure 7-14 Geometric properties of wind turbine using thick airfoil sections ......................... 115
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