Wind Turbines Under Atmospheric Icing Conditions

181 Pages·2013·3.46 MB·English

The Pennsylvania State University
The Graduate School
Department of Aerospace Engineering
Wind Turbines Under Atmospheric Icing Conditions
- Ice Accretion Modeling, Aerodynamics, and
Control Strategies for Mitigating Performance
Degradation
A Thesis in
Aerospace Engineering
by
Dwight Brillembourg
(cid:13)c 2013 Dwight Brillembourg
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Master of Science
August 2013
The thesis of Dwight D. Brillembourg was reviewed and approved* by the following:
Sven Schmitz
Assistant Professor of Aerospace Engineering
Thesis Advisor
Dennis K. McLaughlin
Professor of Aerospace Engineering
George A. Lesieutre
Professor of Aerospace Engineering
Head of the Department of Aerospace Engineering
*Signatures are on file in the Graduate School
ii
Abstract
This thesis presents a combined engineering methodology of ice accretion, airfoil data, and rotor
performance analysis of wind turbines subject to moderate atmospheric icing conditions. The
Turbine Icing Operation Control System (TIOCS) is based on strip theory for both ice accretion
and aerodynamic modeling. The tool is valid for small amounts of accreted ice in the order of a
few percent of the sectional airfoil chord. The TIOCS methodology is a fast engineering analysis
tool for the wind industry and wind turbine operators that allows for finding guidelines for wind
turbine operation during and post moderate icing events. In this thesis, the icing event was
relatively short (less than an hour) and three control strategies were explored to determine wind
turbine performance degradation. Preliminary results obtained for the NREL Phase VI rotor, the
NREL 5MW rotor, and the in-house designed PSU-2.5 MW wind turbines subject to a
representative icing condition indicate that performance degradation with respect to power loss
can be mitigated with appropriate control strategies during and post an icing event.
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Contents
Page
List of Figures vii
List of Tables xii
List of Symbols xiv
Acknowledgments xvi
Chapter 1 Introduction 1
Chapter 2 Ice Accretion Modelling - TIOCS 3
2.1 TIOCS Objectives and Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 TIOCS Software: XTURB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.1 Blade Element Momentum Theory . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.2 Momentum Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.3 Blade Element Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.4 Blade Element Momentum Theory Equations . . . . . . . . . . . . . . . . . . 9
2.2.5 Prandtl’s Root and Tip Loss Factor . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.6 BEMT Solution Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Ice Accretion Software: LEWICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Icing Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.5 Types of Ice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.6 Method of Updating Airfoil Aerodynamic Properties Subject to Ice Accretion . . . . 17
2.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.6.2 Ice Shape Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.6.3 Three Dimensional Lift and Drag Interpolation . . . . . . . . . . . . . . . . . 19
2.7 TIOCS Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.7.1 Main TIOCS Routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.7.2 XTURB Routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.7.3 LEWICE Routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.7.4 Iced Airfoil Performance Routine . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.8 TIOCS: Software Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
iv
2.8.1 TIOCS: Input Directory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.8.2 TIOCS: Output Directory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.8.3 TIOCS: Miscellaneous Directories . . . . . . . . . . . . . . . . . . . . . . . . 29
Chapter 3 NREL Phase VI Results 30
3.1 NREL Phase 6 Wind Turbine Parameters . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2 Atmospheric Icing Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.3 Case 1: Baseline Operating Conditions during Icing Event . . . . . . . . . . . . . . . 34
3.4 Case 2: Wind Turbine Operation at a Higher Tip Pitch Angle and Decreased RPM . 37
3.5 Case 3: Parking the Wind Turbine with High Tip Pitch Angle . . . . . . . . . . . . 40
3.6 Comparison Between Cases 1-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.7 Validation of TIOCS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Chapter 4 NREL 5 MW Results 50
4.1 Atmospheric Icing Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.1.1 NREL 5MW Wind Turbine Parameters . . . . . . . . . . . . . . . . . . . . . 50
4.2 Case 1: Baseline Operating Conditions during Icing Event . . . . . . . . . . . . . . . 52
4.3 Case 2: Wind Turbine Operation at a Higher Tip Pitch Angle and Decreased RPM . 55
4.4 Case 3: Parking the Wind Turbine with High Tip Pitch Angle . . . . . . . . . . . . 58
4.5 Comparison Between Cases 1-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.6 Validation of TIOCS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Chapter 5 PSU 2.5MW Results 66
5.1 Atmospheric Icing Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.1.1 PSU 2.5MW Wind Turbine Parameters . . . . . . . . . . . . . . . . . . . . . 66
5.2 Case 1: Baseline Operating Conditions during Icing Event . . . . . . . . . . . . . . . 68
5.3 Case 2: Wind Turbine Operation at a Higher Tip Pitch Angle and Decreased RPM . 71
5.4 Case 3: Parking the Wind Turbine with High Tip Pitch Angle . . . . . . . . . . . . 74
5.5 Comparison Between Cases 1-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Chapter 6 Summary and Conclusions 81
References 83
Appendix A Wind Turbine Configurations 86
A.1 NREL Phase VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
A.2 NREL 5 MW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
A.3 PSU 2.5 MW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Appendix B TIOCS Input Files 95
B.1 TIOCS Input File: User Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
B.1.1 TIOCS User Sub-Input File: Directory Sub-Input . . . . . . . . . . . . . . . 96
v
B.1.2 TIOCS User Sub-Input File: Blade Properties Sub-Input . . . . . . . . . . . 97
B.1.3 TIOCS User Sub-Input File: Output Files . . . . . . . . . . . . . . . . . . . . 98
B.1.4 TIOCS User Sub-Input File: File Extensions . . . . . . . . . . . . . . . . . . 99
B.2 TIOCS Input Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
B.2.1 LEWICE Input Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
B.2.2 XTURB Input Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
B.2.3 Iced Airfoil Aerodynamics Input Files . . . . . . . . . . . . . . . . . . . . . . 105
Appendix C TIOCS Output Files 117
C.1 TIOCS Output File: LEWICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
C.2 TIOCS Output File: XTURB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
C.3 TIOCS Output File: TIOCS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
Appendix D TIOCS MATLAB Scripts 123
D.1 Start TIOCS Script . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
D.2 TIOCS MAIN Script . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
D.3 TIOCS Subroutines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
D.4 TIOCS Plotting Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
D.5 TIOCS Output File Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
vi
List of Figures
Page
2.1 TIOCS Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Streamlines past the actuator disk as well as velocity and pressure upstream and
downstream. [16] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Streamlines past the rotating rotor disk. [17] . . . . . . . . . . . . . . . . . . . . . . 6
2.4 Forces and moments on an airfoil section; α, angle of attack; c, airfoil chord [17] . . 7
2.5 Schematic of blade elements; c, airfoil chord length; dr, radial length of element; r,
radius; R, rotor radius; Ω, angular velocity of rotor [17] . . . . . . . . . . . . . . . . 8
2.6 Blade Element Airfoil Forces; L lift force; D, drag force; φ blade flow angle; V free
0
stream velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.7 Local velocity triangle of a rotating blade section . . . . . . . . . . . . . . . . . . . . 9
2.8 Helical wake pattern of single tip vortex [19] . . . . . . . . . . . . . . . . . . . . . . . 11
2.9 Total Loss Factor, F = F ∗F vs. r/R [20] . . . . . . . . . . . . . . . . . . . . . 12
root tip
2.10 BEMT iterative solution method [21] . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.11 Sample Input File for LEWICE [13] . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.12 Icing Severity [23]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.13 Glaze ice forming on a wind turbine blade . . . . . . . . . . . . . . . . . . . . . . . . 16
2.14 Rime ice forming on a wind turbine blade . . . . . . . . . . . . . . . . . . . . . . . . 16
2.15 Simulated Glaze Ice Shapes on the NLF-0414 as used by Kim and Bragg [25] . . . . 18
2.16 Normal vector calculations on a clean S809 airfoil with an arbitrary ice shape. . . . . 19
2.17 Lift loss due to surface roughness (k/c = 0.0014) and simulated ridge ice (k/c =
0.0139): NACA 23012m and Re = 1.8E6 taken from Lee and Bragg [14]. . . . . . . . 20
2.18 Drag gain due to surface roughness (k/c = 0.0014) and simulated ridge ice (k/c =
0.0139): NACA 23012m and Re = 1.8E6 taken from Lee and Bragg [14]. . . . . . . . 20
2.19 Change in lift vs. angle of attack and ice location at k/c = 0.0014 for the ice shape
shown in Figure 2.16.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.20 Change in drag vs. angle of attack and ice location at k/c = 0.0014 for the ice shape
shown in Figure 2.16.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.21 Effect of simulated ridge ice of various heights at x/c = 0.10 location on the NACA
23012m: Re = 1.8E6 taken from Lee and Bragg [14]. . . . . . . . . . . . . . . . . . . 22
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2.22 Digitized plot of the effect of simulated ridge ice of various heights at x/c = 0.10
location on the NACA 23012m: Re = 1.8E6 taken from Lee and Bragg [14]. . . . . . 22
2.23 Main TIOCS Routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.24 XTURB Routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.25 LEWICE Routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.26 Iced Airfoil Performance Routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.27 TIOCS Input Directory Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.28 TIOCS Output Directory Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1 Chord Distribution of the NREL Phase VI Wind Turbine Blade . . . . . . . . . . . . 31
3.2 Twist Distribution of the NREL Phase VI Wind Turbine Blade . . . . . . . . . . . . 31
3.3 Lift Coefficient vs. Angle of Attack for the S809 @ Re = 1.5E6 . . . . . . . . . . . . 32
3.4 Drag Coefficient vs. Angle of Attack for the S809 @ Re = 1.5E6 . . . . . . . . . . . 32
3.5 Nominal Power vs r/R for the NREL Phase VI at a wind speed of 7 m/s . . . . . . . 33
3.6 Nominal Thrust vs r/R for the NREL Phase VI at a wind speed of 7 m/s . . . . . . 33
3.7 Case 1: Angle of Attack vs. Radial Location of the Clean and Iced NREL Phase VI
at a wind speed of 7 m/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.8 Case 1: Lift Coefficient vs. Radial Location of the Clean and Iced NREL Phase VI
at a wind speed of 7 m/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.9 Case 1: Drag Coefficient vs. Radial Location of the Clean and Iced NREL Phase VI
at a wind speed of 7 m/s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.10 Case 1: Power vs. Radial Location of the Clean and Iced NREL Phase VI . . . . . . 36
3.11 Case 1: Thrust vs. Radial Location of the Clean and Iced NREL Phase VI . . . . . 37
3.12 Case 2: Angle of Attack vs. Radial Location of the Clean and Iced NREL Phase VI 38
3.13 Case 2: Lift Coefficient vs. Radial Location of the Clean and Iced NREL Phase VI . 39
3.14 Case 2: Drag Coefficient vs. Radial Location of the Clean and Iced NREL Phase VI 39
3.15 Case 2: Power vs. Radial Location of the Clean and Iced NREL Phase VI . . . . . . 40
3.16 Case 2: Thrust vs. Radial Location of the Clean and Iced NREL Phase VI . . . . . 40
3.17 Case 3: Bending Moment vs. Blade Tip Pitch Angle for the NREL Phase VI . . . . 41
3.18 Case 3: Angle of Attack vs. Radial Location at various Tip Pitch Angles for the
NREL Phase VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.19 Case 3: Angle of Attack vs. Radial Location of the Clean and Iced NREL Phase VI 43
3.20 Case 3: Lift Coefficient vs. Radial Location of the Clean and Iced NREL Phase VI . 43
3.21 Case 3: Drag Coefficient vs. Radial Location of the Clean and Iced NREL Phase VI 44
3.22 Case 3: Power vs. Radial Location of the Clean and Iced NREL Phase VI . . . . . . 44
3.23 Case 3: Thrust vs. Radial Location of the Clean and Iced NREL Phase VI . . . . . 45
3.24 Clean and Iced Airfoil Shapes for All Three Radial Locations . . . . . . . . . . . . . 46
3.25 Clean and Iced Airfoil Shapes for All Three Radial Locations . . . . . . . . . . . . . 46
3.26 Clean and Iced Airfoil Shapes for All Three Radial Locations . . . . . . . . . . . . . 47
viii
3.27 Clean: Torque [Nm] versus Approach Wind Speed [m/s] for the simulated NREL
Phase VI rotor [28] [31]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.28 Iced: Torque [Nm] versus Approach Wind Speed [m/s] for the simulated NREL
Phase VI rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.29 Iced: Torque Percent Power Loss versus Approach Wind Speed [m/s] for the simu-
lated NREL Phase VI rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.1 Chord Distribution of the NREL 5MW Wind Turbine Blade . . . . . . . . . . . . . . 51
4.2 Twist Distribution of the NREL 5MW Wind Turbine Blade . . . . . . . . . . . . . . 51
4.3 Nominal Power vs r/R for the NREL 5MW . . . . . . . . . . . . . . . . . . . . . . . 52
4.4 Nominal Thrust vs r/R for the NREL 5MW . . . . . . . . . . . . . . . . . . . . . . . 52
4.5 Case 1: Angle of Attack vs. Radial Location of the Clean and Iced NREL 5MW . . 53
4.6 Case 1: Lift Coefficient vs. Radial Location of the Clean and Iced NREL 5MW . . . 54
4.7 Case 1: Drag Coefficient vs. Radial Location of the Clean and Iced NREL 5MW . . 54
4.8 Case 1: Power per unit span vs. Radial Location of the Clean and Iced NREL 5MW 55
4.9 Case 1: Thrust per unit span vs. Radial Location of the Clean and Iced NREL 5MW 55
4.10 Case 2: Angle of Attack vs. Radial Location of the Clean and Iced NREL 5MW . . 56
4.11 Case 2: Lift Coefficient vs. Radial Location of the Clean and Iced NREL 5MW . . . 57
4.12 Case 2: Drag Coefficient vs. Radial Location of the Clean and Iced NREL 5MW . . 57
4.13 Case 2: Power vs. Radial Location of the Clean and Iced NREL 5MW . . . . . . . . 58
4.14 Case 2: Thrust vs. Radial Location of the Clean and Iced NREL 5MW . . . . . . . 58
4.15 Case 3: Bending Moment vs. Blade Tip Pitch Angle for the NREL 5MW . . . . . . 59
4.16 Case 3: Angle of Attack vs. Radial Location at various Tip Pitch Angles for the
NREL 5MW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.17 Case 3: Angle of Attack vs. Radial Location of the Clean and Iced NREL 5MW . . 60
4.18 Case 3: Lift Coefficient vs. Radial Location of the Clean and Iced NREL 5MW . . . 61
4.19 Case 3: Drag Coefficient vs. Radial Location of the Clean and Iced NREL 5MW . . 61
4.20 Case 3: Power vs. Radial Location of the Clean and Iced NREL 5MW . . . . . . . . 62
4.21 Case 3: Thrust vs. Radial Location of the Clean and Iced NREL 5MW . . . . . . . 62
4.22 Clean and Iced Airfoil Shapes for All Three Radial Locations . . . . . . . . . . . . . 63
4.23 Clean and Iced Airfoil Shapes for All Three Radial Locations . . . . . . . . . . . . . 64
4.24 Clean and Iced Airfoil Shapes for All Three Radial Locations . . . . . . . . . . . . . 64
4.25 A Comparison of Power Coefficient versus Tip Speed Ratio between Homola et al.
[4] and TIOCS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.1 Chord Distribution of the PSU 2.5MW Wind Turbine Blade . . . . . . . . . . . . . . 67
5.2 Twist Distribution of the PSU 2.5MW Wind Turbine Blade . . . . . . . . . . . . . . 67
5.3 Nominal Power vs r/R for the PSU 2.5MW . . . . . . . . . . . . . . . . . . . . . . . 68
5.4 Nominal Thrust vs r/R for the PSU 2.5MW . . . . . . . . . . . . . . . . . . . . . . . 68
5.5 Case 1: Angle of Attack vs. Radial Location of the Clean and Iced PSU 2.5MW . . 69
ix
5.6 Case 1: Lift Coefficient vs. Radial Location of the Clean and Iced PSU 2.5MW . . . 70
5.7 Case 1: Drag Coefficient vs. Radial Location of the Clean and Iced PSU 2.5MW . . 70
5.8 Case 1: Power per unit span vs. Radial Location of the Clean and Iced PSU 2.5MW 71
5.9 Case 1: Thrust per unit span vs. Radial Location of the Clean and Iced PSU 2.5MW 71
5.10 Case 2: Angle of Attack vs. Radial Location of the Clean and Iced PSU 2.5MW . . 72
5.11 Case 2: Lift Coefficient vs. Radial Location of the Clean and Iced PSU 2.5MW . . . 73
5.12 Case 2: Drag Coefficient vs. Radial Location of the Clean and Iced PSU 2.5MW . . 73
5.13 Case 2: Power vs. Radial Location of the Clean and Iced PSU 2.5MW . . . . . . . . 74
5.14 Case 2: Thrust vs. Radial Location of the Clean and Iced PSU 2.5MW . . . . . . . 74
5.15 Case 3: Bending Moment vs. Blade Tip Pitch Angle for the PSU 2.5MW . . . . . . 75
5.16 Case 3: Angle of Attack vs. Radial Location at various Tip Pitch Angles for the
PSU 2.5MW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.17 Case 3: Angle of Attack vs. Radial Location of the Clean and Iced PSU 2.5MW . . 76
5.18 Case 3: Lift Coefficient vs. Radial Location of the Clean and Iced PSU 2.5MW . . . 77
5.19 Case 3: Drag Coefficient vs. Radial Location of the Clean and Iced PSU 2.5MW . . 77
5.20 Case 3: Power vs. Radial Location of the Clean and Iced PSU 2.5MW . . . . . . . . 78
5.21 Case 3: Thrust vs. Radial Location of the Clean and Iced PSU 2.5MW . . . . . . . 78
5.22 Clean and Iced Airfoil Shapes for All Three Radial Locations . . . . . . . . . . . . . 79
5.23 Clean and Iced Airfoil Shapes for All Three Radial Locations . . . . . . . . . . . . . 80
5.24 Clean and Iced Airfoil Shapes for All Three Radial Locations . . . . . . . . . . . . . 80
A.1 Chord and Twist Distribution for the NREL Phase VI Wind Turbine. . . . . . . . . 86
A.2 Lift and Drag Coefficient vs Angle of Attack for the S809 Airfoil . . . . . . . . . . . 87
A.3 Chord and Twist Distribution for the NREL 5 MW Wind Turbine . . . . . . . . . . 88
A.4 Lift and Drag Coefficient vs Angle of Attack for the Cylinder01 Airfoil . . . . . . . . 89
A.5 Lift and Drag Coefficient vs Angle of Attack for the Cylinder02 Airfoil . . . . . . . . 89
A.6 Lift and Drag Coefficient vs Angle of Attack for the DU40 Airfoil . . . . . . . . . . . 89
A.7 Lift and Drag Coefficient vs Angle of Attack for the DU35 Airfoil . . . . . . . . . . . 89
A.8 Lift and Drag Coefficient vs Angle of Attack for the DU30 Airfoil . . . . . . . . . . . 90
A.9 Lift and Drag Coefficient vs Angle of Attack for the DU25 Airfoil . . . . . . . . . . . 90
A.10Lift and Drag Coefficient vs Angle of Attack for the DU21 Airfoil . . . . . . . . . . . 90
A.11Lift and Drag Coefficient vs Angle of Attack for the NACA64 Airfoil . . . . . . . . . 90
A.12Chord and Twist Distribution for the PSU 2.5 MW Wind Turbine . . . . . . . . . . 91
A.13Lift and Drag Coefficient vs Angle of Attack for the Cylinder05 Airfoil . . . . . . . . 92
A.14Lift and Drag Coefficient vs Angle of Attack for the Cylinder04 Airfoil . . . . . . . . 92
A.15Lift and Drag Coefficient vs Angle of Attack for the Cylinder03 Airfoil . . . . . . . . 92
A.16Lift and Drag Coefficient vs Angle of Attack for the 00W2401DUT Airfoil . . . . . . 93
A.17Lift and Drag Coefficient vs Angle of Attack for the 00W2350DUT Airfoil . . . . . . 93
A.18Lift and Drag Coefficient vs Angle of Attack for the 97W300DUT Airfoil. . . . . . . 93
A.19Lift and Drag Coefficient vs Angle of Attack for the 91W2250DUT Airfoil . . . . . . 94
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