The Influence of Radial Area Variation on Wind Turbines to the. Axial Induction Factor

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2 The Influence of Radial Area Variation on Wind Turbines to the Axial Induction Factor A Thesis submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of Master of Science in the School of Aerospace Engineering and Engineering Mechanics of the College of Engineering and Applied Sciences by KEDHARNATH SAIRAM B.E., Anna University MAY, 2009 Committee Chair: Dr. Mark. G. Turner Sc.D

3 Abstract Many countries around the world are realizing the importance of renewable energy for a sustainable future and are investing in various Green Technologies. Improvements in the aerodynamic design will lead to more efficient wind turbines with higher power production. In the present study, a 3-D parametric gas turbine blade geometry building code, 3DBGB, has been modified in order to include wind turbine design capabilities. This approach enables greater flexibility of the design along with the ability to design more complex geometries with relative ease. A wind turbine design code was developed using the Blade-Element-Momentum theory in order to aid the process of boot-strapping the inputs to 3DBGB. The NREL NASA Phase VI wind turbine was considered as a test case for validation and as a baseline by which modified designs could be compared. The design parameters were translated into 3DBGB input to create a 3D model of the wind turbine which can also be imported into any CAD program. Design modifications included replacing the airfoil section, modifying the thickness to chord ratio as a function of span, running constant chord and adding winglets. These models were imported into a high-fidelity CFD package, Fine/TURBO by NUMECA. Fine/TURBO is a specialized CFD platform for turbo-machinery analysis. A code - geomturbo - was used to convert the 3D model of the wind turbine into the native format used to define geometries in the Fine/TURBO meshing tool, AutoGrid. The CFD results were post processed using a newly developed 3D force analysis code. The radial forces were found to play a significant role in the performance of wind turbine blades. The radial component of the blade surface area as it varies in span is the dominant contributor of the radial forces. Through the radial momentum equation, these radial forces are responsible for creating the streamline curvature that leads to the expansion of the streamtube (slipstream) that is responsible for slowing the wind velocity ahead of the wind turbine leading edge, which is quantified as the axial induction factor. These same radial forces also play a role in changing the slipstream for propellors. Through the design modifications, simulated with CFD and post-processed appropriately, this connection with the radial component of area to the radial forces to the axial induction factor, and finally the wind turbine power is demonstrated. The results from the CFD analysis and 3D force analysis are presented in this thesis. i

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5 Acknowledgments I would like to thank my advisor Dr.Mark Turner for his tremendous support, invaluable guidance and for imparting a great wealth of knowledge. I would also like to thank Dr. Paul Orkwis and Dr.Shabaan Abdallah for agreeing to be members of my defense committee and taking time off their busy schedules to review my research work. I would like to thank LATEXfor reducing document formatting time to a bare minimum. A special thanks to Kiran Siddapaji and Soumitr Dey for their help and brainstorming sessions for my research. Thanks to Rob Ogden for helping me with many license and Linux issues. I would like to thank Robert Knapke, Marshall Galbraith and Andy Schroder for their support and help. I would also like to thank the NUMECA support team ( Roque Lopez and Autumn Fjeld ) for their timely help with Fine Turbo troubleshooting. Sincere thanks to my wife, my brother and last but not the least, my MOM and DAD for their unwavering support. iii

6 Contents Abstract i Acknowledgments iii Contents vi List of Figures xi Nomenclature xii 1 Introduction 1 2 Literature Review Historical Overview Evolution In The 20th Century Recent Developments Current Wind Turbine Design Approaches Momentum Theory Blade Element Theory Blade Element-Momentum Theory Blade Geometry Importance of the Axial Induction Factor Velocity Triangles QPROP and QMIL Wind Turbine Geometry Definition using 3DBGB Blade Design Process iv

7 5 3D-CFD Case Set-Up and Analysis using Fine Turbo Grid Setup Flow Setup and Solution Winglets - Design and Effects Winglet Design using 3DBGB Effect of Winglets on Downwash D Force Analysis Code Formulation Results and Comparisons NREL Original Blade vs. NREL Constant-Chord Blade NACA 24XX Series Airfoils NREL Original Blade vs. NACA 2420 Blade NACA 2420 vs. NACA NACA 2420 vs. NACA vs. NACA Pressure Side and Suction Side Stacking Power Effect of Radial Area Variation Radial Momentum Equation Conclusion Overview Key Findings Future Work References 85 Appendix 87 A BEM Blade Design Code 88 B 3DBGB Input Files 90 B.1 NREL Original Blade v

8 B.2 NREL - Downstream Winglet B.3 NREL - Constant Chord B.4 NACA B.5 NACA B.6 NACA B.7 NACA PS B.8 NACA SS C NUMECA Fine/Turbo Tutorial for Wind Turbine 139 C.1 Grid Generation C.2 CFD Analysis using Fine/Turbo C.3 Running Fine/Turbo in batch mode on Linux D CALC PdA - 3D Force Analysis Code 156 E Polygeom 162 vi

9 List of Figures 1.1 Wind Turbine Aerodynamics in 2D [1] Winglet on a Sub-Sonic Boeing Aircraft [2] Wind Turbine Rotor with Winglet [2] Actuator disc model of a wind turbine from reference [3]. The actuator disc is not actually rotating Airfoil Geometry and Nomenclature [3] Common Wind Turbine Nomenclature [1] Common Axial Turbine Nomenclature [1] Decomposition of Blade Relative Velocity [1] DBGB Process Flow Chart [4] Nomenclature[4] Meridional View[4] DBGB generated airfoils[4] Lofted blade using Unigraphics[4] Swept Blades using 3DBGB[4] Bladerow with bent-tips using 3DBGB[4] Wind Turbine Blade using 3DBGB[4] Wind Turbine Assembly - Blade generated using 3DBGB[4] Geometry initialization in Autogrid B2B mesh at 20 percent span Grid Quality Report D Grid viewed in IGG Convergence History vii

10 5.6 3D static pressure contour - pressure side and suction side - NREL original blade Sectional static pressure contours at multiple radial locations Azimuthal area averaged static pressure - NREL original blade Effect of downwash on the local flow over a section of the wing [5] Design parameters of winglets [6] Lift Coefficient vs. Angle of Attack - NREL S809 Airfoil [7] Geometric, Induced and Effective Alpha vs. Span - NREL original blade Geometric, Induced and Effective Alpha vs. Span - NREL downstream winglet case Downwash vs. Span Comparison Effective Alpha vs. Span Comparison Lift Coeffcient vs. Span Comparison NREL tip streamtubes NREL-Winglet tip streamtubes D Slabs created using CFD data Diagonal vectors and force vectors on slabs Resultant force vectors on slabs Cross sectional area vs. span da/dr vs. span Average Static Pressure vs. span Radial Force vs. span Tangential Force vs. span Axial Force vs. span Torque vs. span Area averaged Vz in front of blade vs. span Axial Induction Factor vs. span Effective angle of attack vs. span NACA 2420 Airfoil Lift Coefficient vs. Angle of Attack - S809 and NACA Lift Coefficient vs. Angle of Attack - NACA Series Cross sectional area vs. span da/dr and F r vs. span - NREL Original Blade viii

11 8.16 da/dr and F r vs. span - NACA Average static pressure vs. span Radial Force vs. span Tangential Force vs. span Axial Force vs. span Torque vs. span Area averaged Vz in front of blade vs. span Axial induction factor vs. span Effective angle of attack vs. span Lift coefficient vs. span Cross sectional area vs. span da/dr and F r vs. span - NACA da/dr and F r vs. span - NACA Average Static Pressure vs. span Radial Force vs. span Radial Force using gauge pressure vs. span Tangential Force vs. span Axial Force vs. span Torque vs. span Area averaged Vz in front of blade vs. span Axial induction factor vs. span Effective angle of attack vs. span Lift coefficient vs. span Cross sectional area vs. span da/dr and F r vs. span - NACA da/dr and F r vs. span - NACA da/dr and F r vs. span - NACA Average Static Pressure vs. span Radial Force vs. span Tangential Force vs. span Axial Force vs. span Torque vs. span ix

12 8.48 Area averaged Vz in front of blade vs. span Axial induction factor vs. span Effective angle of attack vs. span Lift coefficient vs. span Pressure side, meanline and suction side stacking da/dr and F r vs. span - NACA da/dr and F r vs. span - NACA PS da/dr and F r vs. span - NACA SS Average Static Pressure vs. span Radial Force vs. span Tangential Force vs. span Axial Force vs. span Torque vs. span Area averaged Vz in front of blade vs. span Axial induction factor vs. span Effective angle of attack vs. span Lift coefficient vs. span NREL power curve [8] Power Output Comparison Power Output Comparison-NACA Blades Percentage power Output Comparison-NACA Blades Streamtube expansion isometric view Streamtube expansion side view Streamtube expansion viewed from upstream Meridional streamline velocity triangle First term in Eq.(9.14) p r vs. span comparison - NACA 2420 and NACA ( ) 9.6 Third term in Eq.(9.14) p pp+ps 1 Λ 2 Λ r vs. span comparison - NACA 2420 and NACA Azimuthal area averaged static pressure - NACA Azimuthal area averaged static pressure - NACA Average streamline radius vs. z at transition zone - NACA 2420 and NACA x

13 9.10 Average streamline radius vs. z at mid-span - NACA 2420 and NACA Average streamline radius vs. z at tip - NACA 2420 and NACA Average streamtube radius vs. z at tip - NACA Average streamtube radius vs. z at tip - NACA Streamtube Radius vs. z at tip - NACA 2420 and NACA Streamlines Average streamtube area vs. z at tip - NACA 2420 and NACA Average streamtube area ratio vs. z at tip - NACA 2420 and NACA xi

14 Nomenclature a Axial induction factor a Angular induction factor c ṁ p r u v w z A B C C d C l C P F F D F L F N F T M P Q R Chord Mass flow rate Pressure Radius Externally induced velocity Blade induced velocity Downwash Axial direction Cross-sectional area Number of blades Streamline curvature Coefficient of drag Coefficient of lift Coefficient of Power Prandtl s tip loss factor Drag force Lift force Normal force Thrust force Mach number Rated Power Torque Blade radius xii

15 T U U 1 4 V z W Thrust Rotor wheel speed Wind velocity at stations in actuator disc model Velocity in axial direction Relative velocity Greek α β ζ ɛ θ Θ λ r λ Λ ρ σ τ φ Φ ψ ω Ω Angle of attack Blade angle Stagger angle Lean angle Tangential direction Pitch angle Local tip-speed ratio Tip-speed ratio Ratio of open circumference to total circumference Density Solidity Circulation Streamline angle Relative flow angle Twist angle Angular velocity imparted to flow stream Angular velocity of rotor Subscripts 1-4 Stations in actuator disc model a in m max out Axial Inlet Meridional direction Maximum Outlet xiii

16 r rel t x/z θ Radial direction in cylindrical coordinate system Relative tangential Axial direction in cylindrical coordinate system Tangential direction in cylindrical coordinate system Abbreviations 2D 3D BEM CAD CFD 3DBGB NACA NREL 2-Dimensional 3-Dimensional Blade-Element-Momentum Computer Aided Design Computational Fluid Dynamics 3D Blade Geometry Builder National Advisory Committee for Aeronautics National Renewable Energy Laboratory xiv

17 Chapter 1 Introduction Wind energy is one of the fastest growing energy sectors today. Apart from being a very promising source of energy, it also has other advantages. It is a source of green power and hence is a very critical part of the solution to the global climate change crisis. It is affordable and cost effective. The cost of manufacturing and monitoring wind turbines has reduced drastically over the last few decades owing to advancements in manufacturing technology. It improves economic development by providing a range of job opportunities in the communities where the wind farms are located. It is a sustainable source of energy and widely available [9]. In the United States, the National Renewable Energy Laboratory was established in 1974 in order to tackle the growing energy crisis and to decrease dependency on non-renewable sources of energy. The NREL has been a major contributor in the field of small scale wind turbines and in other areas of research and development [10]. The power output of a wind turbine is directly related to the swept area of the rotors [3] P wind = 0.5ρAV 3 z (1.1) P mech = 0.5ρAV 3 z C p (1.2) Where P wind is the power available in the kinetic energy of the wind. The power coefficient depends on the overall aerodynamic and mechanical efficiency of the wind turbine design. Therefore, the power output of a wind turbine at a prescribed wind velocity can be improved by increasing the swept area of the rotor. However, not all wind turbine installation sites are suitable for large rotors and a large part of the capital cost is related to the rotor size. One of the key aspects of wind turbine design is the ability to extract as much energy from the wind as possible and 1

18 reducing aerodynamic and mechanical losses to a minimum. A general illustration of 2D wind turbine aerodynamics is given in Figure 1.1. When the on-coming wind hits the wind turbine blade, a low pressure field is created on the suction side of the airfoil and a high pressure field is created on the pressure side of the airfoil. This creates a resultant force to act on the blade which can be represented as components of the force that are normal to each other i.e the lift and drag on the airfoil. The drag force is small compared to the lift force. This lift causes the blade to rotate. Figure 1.1: Wind Turbine Aerodynamics in 2D [1]. 2D force analysis is a great way to understand the fundamentals of aerodynamics. However, in reality, complex 3D effects occur which need to be analyzed in order to optimize the blade design. A post-processing code was developed using MatLab for 3D force analysis on the blade. This postprocessing capability allows the interpretation of forces relevant to a wind turbine. The effect of radial forces on the performance of the blade was discovered to be significant. The radial forces have been found to act as a main driver for the stream tube area expansion. New blades were designed to further explore the effect of radial forces in detail by manipulating the geometry. Access to the 3D parametric blade geometry builder - 3DBGB [4], a gas turbine blade geometry developing tool, proved to be an exciting way to approach the design of wind turbines with complex geometries. Using the built-in airfoil definition, tip-offset, sweep and rake options, it was possible to manipulate the rotor geometry and create winglets on the wind turbine blade. CAD models of the blade 2

19 were created using the output from 3DBGB. The design was then analyzed using a high fidelity CFD package - Fine/Turbo. Post-processing was carried out by the 3D force analysis code - Calc-PdA. The NREL Phase VI wind turbine was used as a starting point because of the availability of detailed design and analysis data [8]. Winglets are wing tip devices which enable reduction in losses due to vortices created at the wing tip that results from a pressure imbalance between the suction and pressure sides of the blade. They have been successfully employed in sub-sonic aircraft to reduce the tip vortices. At a time where a lot of effort in the wind industry is going into improving manufacturing processes for the purpose of cost reduction, fabricating complex blade geometries has become far less complicated. The freedom to pursue innovations in the blade geometry design has ushered in a new era in wind turbine aerodynamics. An interesting area being probed into in this field is the aerodynamic advantage of adding winglets. One of the test cases presented in this thesis explores the effects of adding a winglet to the blade. Figures 1.2 and 1.3 show examples of winglets on an aircraft wing and a wind turbine blade respectively. Very little investigation has been done on manipulating the geometry to modify the radial forces on the blades. This research aims to kick off an in-depth exploration of radial-force manipulation to improve the performance of not only wind turbines, but also propellers and other turbo-machinery applications as well. The incorporation of winglets into wind turbine rotor blades is an area that is being explored by current researchers in the industry. They significantly reduce the losses and complex 3D effects created by the vortices and hence, improve the power coefficient of the blade. Chapter 2 reviews the literature that the current design concepts are based on. In Chapter 3 the fundamental wind turbine design approaches are described in detail. Wind turbine geometry definition using 3DBGB and 3D CFD analysis using Fine/Turbo are explained in Chapters 4 and Chapter 5. The design and effects of winglets is explored in Chapter 6. A detailed explanation of the 3D force analysis code is given in Chapter 7. The results and comparison for all the wind turbine test cases are presented in Chapter 8. Chapter 9 attempts to explain the effect of radial area variation on wind turbine rotor blades and finally the thesis is concluded in Chapter 10. 3

20 Figure 1.2: Winglet on a Sub-Sonic Boeing Aircraft [2]. Figure 1.3: Wind Turbine Rotor with Winglet [2]. 4

21 Chapter 2 Literature Review 2.1 Historical Overview Human beings have been harnessing wind energy for thousands of years. With the invention of sails we realized the marvelous potential of the kinetic energy available in the wind. With time, wind energy was also utilized for other purposes such as grinding and pumping. One of the biggest advantages of wind energy over other forms of energy is that it is ubiquitous. As a side effect of this, people harnessed wind energy in different ways based on geographic location. The beginnings of modern day wind turbines can be traced back to 9th century Iran. They were horizontal axis wind turbines which were used to pump water and for milling. The technology slowly spread to other parts of Asia such as India and China. Europe witnessed the use of wind turbines during the middle ages. The first turbines to come out of Europe were vertical axis wind turbines. With the advent of electricity in the 19th century, one more use was added to wind turbines - driving generators in order to produce electric power. The first such wind turbines was built in 1887 in Scotland by Prof. James Blyth. Since then there have been numerous design changes in wind turbines in order to improve their performance and efficiency. Over the past century, wind power has slowly grown to become one of the major renewable energy sources available to human kind [2]. 2.2 Evolution In The 20th Century The technological strides made in the field of turbo-machinery during the first half of the 20th century aided in improving the design of wind turbine rotor blades in order to increase the efficiency and performance. This period saw a lot of the theoretical ground work upon which modern day wind turbines are developed. The most notable among these theoretical developments is the Betz limit [11]. Prof. Albert 5

22 Betz came up with a theoretical limit, aptly named the Betz limit, which defines the maximum amount of power that could be extracted from a wind turbine. The Blade-Element-Momentum theory, which today serves as the industry standard for designing wind turbines, was also developed during this period. The principles of linear and angular momentum are applied to the rotor blades using a control volume analysis in order to derive equations for the thrust and torque produced [3]. Blade aerodynamic analysis is used to give the equations for the normal force and tangential force. These are equated with the thrust and torque equations to arrive at parametric design equations. This is explained in detail in chapter 3. The World Wind Energy Report of 2010 [12] informs that the total wind power installed in the world has reached 196,630 Mega Watts with a growth rate of 23.6 percent in the year 2010 alone. Today China is the leading country when it comes to wind power generation in the world. Experts estimate that the world s total wind power installation will reach 1,500,000 Mega Watts by the years After the emergence of computers, codes were developed to design wind turbines using the bladeelement-momentum theory. Pioneering work in this field has been done by Wilson and Lissaman [13], [14]., Wilson et al. [15]. and De Vries [16]. Another useful method for designing wind turbine rotors is the Vortex Wake Method, successfully implemented by Hansen and Butterfield [17]. The National Renewable Energy Laboratory has developed various codes for the successful aerodynamic and structural design of wind turbines such as AERODYN, YAWDYN, WTPERF and FAST-ADAMS [15], [18], [19]. These codes use the Blade Element Momentum theory to design and predict performance characteristics. 2.3 Recent Developments The biggest priority in rotor design is to improve the overall efficiency by reducing losses and optimizing the twist distribution in order to extract the maximum energy from the wind. Due to the pressure differences on the suction and pressure side of the wind turbine blade, an inward spanwise flow and outward spanwise flow are produced respectively. This leads to the creation of vortices at the blade tip, thereby creating a downwash and an induced drag associated with it. Winglets are load carrying devices that move these tip vortices away from the rotor plane and reduce the induced drag [20]. Winglets were first introduced in sub-sonic aircraft wings to improve efficiency by Whitcomb [21]. The wind turbine industry is reaching its maturity. At this point in time, a wide range of research is being carried out on the aerodynamics of design modifications such as winglets, swept or raked blades and whale blades. Out of these, winglets have been proven to improve the coefficient of power and the 6

23 coefficient of thrust [22]. The tip effects are governed by complex three dimensional physics. Computational fluid dynamics has been utilized to model these effects as close to physical reality as possible and a lot more work needs to be done to understand the physical reality in its entirety [23]. It has already been shown that the power augmentation due to the addition of winglets is not because of the downwind velocity and wake vorticity shift, but rather due to the reduction of these complex three dimensional tip effects [24]. For axial turbomachinery with high hub-radius to tip-radius ratio, the assumption that the flow is two dimensional works well because the radial flow is very negligible. If the hub-tip ratio is low, as in the case of high aspect ratio geometries such as wind turbines, then the radial flow is no longer negligible and needs to be taken into account [25]. 7

24 Chapter 3 Current Wind Turbine Design Approaches Wind turbine rotor blades are made up of airfoils that produce a lift force due to pressure differences on the suction and pressure sides. The wind turbine system can be considered as an actuator disc; thereby, the flow field can be represented using the equations of linear and angular momentum. Using the knowledge of the performance characteristics of the airfoils, the geometry of the rotor can be calculated. The momentum theory is a control volume approach to calculating the forces using the equation of linear and angular momentum. Blade Element theory is an analysis of the forces at any given section of the blade. Combining these two theories, we get the Blade Element- Momentum Theory. 3.1 Momentum Theory Developed by Betz [11], this theory is used to determine the power and thrust of an ideal turbine rotor. It is based on a control volume approach. The boundaries of the control volume define the stream tube. The turbine is represented as an actuator disc. The actuator disc creates a discontinuity in the pressure field. The Momentum theory assumes the following: Homogenous, incompressible, steady state flow No frictional drag An infinite number of blades Uniform thrust over the disc A non rotating wake The static pressure far upstream and downstream is equal to the ambient static pressure 8

25 Figure 4.1 shows the actuator disk model of a turbine. From the balance of linear momentum and forces defined from Newton s second law, the net force on the actuator disc can be established. The thrust is equal and opposite to the change in momentum of the air stream. T = U 1 (ρau) 1 U 4 (ρau) 4 (3.1) (ρau) 1 = (ρau) 2 = (ρau) 3 = (ρau) 4 = ṁ (3.2) T = ṁ(u 1 U 4 ) (3.3) Using Bernoulli s equation, p ρU 2 1 = p ρU 2 2 (3.4) p ρU 2 3 = p ρU 2 4 (3.5) The thrust is also the net sum of forces on each side of the actuator disc, T = A 2 (p 2 p 3 ) (3.6) T = 0.5ρA 2 (U 2 1 U 2 4 ) = 0.5ρA 2 (U 1 + U 4 )(U 1 U 4 ) (3.7) From Equations (3.2), (3.3) and (3.7), we obtain U 2 = U 1 + U 4 2 (3.8) If an axial induction factor is considered as the decrease in wind velocity between the free stream and rotor plane, we have it defined as a = U 1 U 2 U 1 (3.9) U 2 = U 1 (1 a) (3.10) U 4 = U 1 (1 2a) (3.11) As the axial induction factor increases, the wind velocity behind the rotor decreases. Once it reaches 0.5, the velocity behind the rotor becomes zero and this theory is no longer valid. The power output is the product of the thrust and the velocity at the rotor because the power is force it takes to move something through a distance over a period of time. From the above equations we arrive 9

26 at P = 0.5ρAU 3 4a(1 a) 2 (3.12) where U = U 1. The power coefficient of the wind turbine which is the ratio of the rotor power to the total power in the wind, can be expressed as C P = P 0.5ρU 3 A (3.13) C P = 4a(1 a) 2 (3.14) The power coefficient is maximum when the axial induction factor, a = 1/3. This yields, C P max = 16/27 = (3.15) This limit imposed on the power output of a wind turbine is known as the Betz limit. It is the maximum theoretically possible power output. It is often stated as the wind turbine efficiency, but should not be confused with an adiabatic efficiency. Figure 3.1: Actuator disc model of a wind turbine from reference [3]. The actuator disc is not actually rotating. If the control volume is assumed to move with the angular velocity of the blades (Ω), the pressure difference before and after the blade can be determined using the energy equation [26]. The angular velocity of the air, in relation to the blade, increases from Ω to Ω + ω, where ω is the angular velocity imparted to the flow stream. 10

27 p 2 p 3 = ρ(ω + 0.5ω)ωr 2 (3.16) Hence the thrust on an element dt is, dt = (p 2 p 3 )da = [ρ(ω + 0.5ω)ωr 2 ]2πrdr (3.17) The angular induction factor is defined as, a = ω/2ω (3.18) dt = 4a (1 + a )0.5ρΩ 2 r 2 2πrdr (3.19) The thrust can also be expressed using the axial induction factor, dt = 4a(1 a)0.5ρu 2 2πrdr (3.20) dt = 4a(1 a)ρu 2 πrdr (3.21) An expression for the torque can be arrived at by using the equation of angular momentum. The change in the angular momentum of the wake must equal the torque. dq = dṁ(ωr)r = (ρu 2 2πrdr)(ωr)r (3.22) This can be reduced to dq = 4a (1 a)ρuωr 3 πdr (3.23) The power produced at each element is given by dp = ΩdQ (3.24) 3.2 Blade Element Theory With the Blade Element Theory the forces on an airfoil section depend on the angle of attack, lift coefficient and drag coefficient. The blade can be divided into indivudual sections and the forces can be analyzed for each section. This can then be integrated over the span to provide the overall thrust and 11

28 torque. The assumption made in the Blade Element theory are: There are no aerodynamic interactions between elements. The forces are dependent only on the lift and drag chracteristics of the airfoil. Figure 3.2: Airfoil Geometry and Nomenclature [3]. From Figure 3.2 we can deduce the following relations, θ T = θ P θ P,0 (3.25) Where tanφ = Φ = θ P + α (3.26) U(1 a) Ωr(1 + a ) = 1 a (1 + a )λ r (3.27) λ r = Ωr/U (3.28) U rel = U(1 a)/sinφ (3.29) df L = C l 0.5ρUrel 2 cdr (3.30) 12

29 df D = C d 0.5ρUrel 2 cdr (3.31) df N = df L cosφ + df D sinφ (3.32) df T = df L sinφ df D cosφ (3.33) The total forces on any given section are, Thrust contribution: df N = B0.5ρU 2 rel (C lcosφ + C d sinφ)cdr (3.34) Torque contribution: dq = B0.5ρU 2 rel (C lsinφ C d cosφ)crdr (3.35) Where B is the total number of blades. By using Equation 3.29 the relative velocity can be expressed in terms of the free stream wind velocity. Where σ is the local solidity, df N = σπρ U 2 (1 a) 2 sin 2 Φ (C lcosφ + C d sinφ)rdr (3.36) dq = σπρ U 2 (1 a) 2 sin 2 Φ (C lsinφ C d cosφ)r 2 dr (3.37) σ = Bc/2πr (3.38) 3.3 Blade Element-Momentum Theory To calculate the induction factors a and a, C d is set to zero as the drag is negligible in airfoils with a low drag coefficient [14]. The thrust from momentum theory, dt is the same as the normal force from the blade-element theory, df N. Equating 3.21 and 3.36 with C d = 0 we get, a (1 a) = σc cosφ l 4sin 2 Φ (3.39) By equating the torque eqauations 3.23 and 3.37 and setting C d = 0 we get, a (1 a) = σc l 4λ r sinφ (3.40) 13

30 Through further algebraic and trignometric manipulation we arrive at, a a = λ r tanφ (3.41) a = 1/[1 + 4sin 2 Φ/(σC l cosφ)] (3.42) a = 1/[4cosΦ/(σC l )) 1] (3.43) 3.4 Blade Geometry A combination of the Momentum theory and Blade Element theory yeilds the Blade Element Momentum theory [3], which can be used to calculate the rotor blade geometry parameters. For any given tip-speed ratio λ = ΩR/U, the optimum blade shape for maximum power output can be calculated. From the calculation of the Betz limit [11], the axial induction factor a = 1/3 for maximum power output. The following assumptions are made: Wake rotation is neglected, a = 0. Drag is considered to be negligible, C d = 0. There are no losses from a finite number of blades. There are no tip effect. For a given airfoil, the angle of attack is chosen such that the C l is high but has a comfortable range in order to avoid stalling. Knowledge of the angle of attack is also used to derive the twist distribution of the blade. The number of blades is chosen based on the tip-speed ratio. Using these inputs in the momentum theory we get, From the Blade Element theory we have, dt = ρu 2 8 πrdr (3.44) 9 tanφ = 2 3λ r (3.45) df N = B 1 2 U 2 rel (C lcosφ)cdr (3.46) U rel = U(1 a)/sinφ = 2U 3sinΦ (3.47) 14

31 By combining these equations we get, C l Bc 4πr = tanφsinφ (3.48) C l Bc 4πr = 2 3λ r sinφ (3.49) Φ = tan 1 2 [ ] (3.50) 3λ r c = 8πrsinφ 2BC l λ r (3.51) The overall power coefficient of the rotor can be calculated from the following equation [16], C P = 8 λ λ 2 sin 2 Φ(cosΦ λ r sinφ)(sinφ + λ r cosφ)[1 (C d /C l )cotφ]λ 2 rdλ r (3.52) λ h The effects of wake rotation can be incorporated by taking a partial derivative of the integral of C P, which is a function of Φ, and setting it to zero. Φ [sin2 Φ(cosΦ λ r sinφ)(sinφ + λ r cosφ)] = 0 (3.53) λ r = Ωr U (3.54) Φ = 2 3 tan 1 (1/λ r ) (3.55) c = 8πr BC l (1 cosφ) (3.56) 3.5 Importance of the Axial Induction Factor The axial induction factor is a vital performance parameter of a wind turbine. It clearly shows what percentage of the free stream wind s kinetic energy is being converted into useful work. Even though there is a theoretical limit imposed on the axial induction factor, current wind turbine designs are still short of achieving axial induction factors close to the limit. The axial induction factor (a) and the angular induction factor (a ) are found through an iterative solution. The initial values of a and a are guessed. The relative flow angle is calculated from Equation The angle of attack is calculated from the relative flow angle and blade twist angle. 15

32 Using Equations 3.42 and 3.43 the values of a and a are calculated again and these values are used as input for the next iteration. This process is carried on till the new induction factors are within an acceptable tolerance of the previous iteration. At the very best, this is still only an approximation and does not account for complex 3D effects. A matlab code was written to calculate the blade geometry in order to obtain the inputs for the 3D parametric blade geometry builder code 3DBGB. This code can be found in Appendix A. 3.6 Velocity Triangles A simple way to decompose the flow field at the blade is by utilizing velocity triangles. By knowing the velocity of the incoming wind and the angular velocity of the blade we can calculate the relative velocity of the wind and the flow angle. The blade stagger angle and twist angle can then be calculated at each radial station to obtain any desired angle of attack. There are many variations in conventional turbine nomenclature and wind turbine nomenclature. Figures 3.3 and 3.4 help to compare the common nomenclatures and eliminate any confusion. Using the velocity triangles, the following relations can be deduced: V = W + U (3.57) U = rω (3.58) W 2 = U 2 + V 2 z (3.59) Φ = tan 1 V z U (3.60) β = tan 1 U V z = π 2 Φ (3.61) ζ = cos 1 c axial c actual (3.62) For airfoils with low camber, β = ζ (3.63) ψ = π 2 ζ (3.64) α = Φ ψ (3.65) 16

33 Figure 3.3: Common Wind Turbine Nomenclature [1]. Figure 3.4: Common Axial Turbine Nomenclature [1]. 17

34 3.7 QPROP and QMIL QPROP [27] is a program for performance analysis of propeller-motor combinations. It has a companion code, QMIL, for the design of propellers and wind turbines with the Minimum Induced Loss condition (MIL) [28] and to acheive maximum total power. The code extends the work of [29], [30] and [28] to include : Radially varying induced velocities. Perfect consistency of the formulations. Solution by a global Newton method. Inclusion of maximum total power condition The induced velocities are decomposed into their axial and tangential components as shown in figure Figure 3.5: Decomposition of Blade Relative Velocity [1]. v a and v t are the blade induced velocities in the axial and tangential directions respectively. They are positive for a propeller and negative for a wind turbine. u a and u t are the externally induced velocities in the axial and tangential directions respectively. They are zero in the case of a wind turbine. Using Helmholtz theorm, the circumferentially averaged v t can be related to the circulation, v t = Bτ 4πr (3.66) 4R v t = v t F 1 + ( λ r πbr )2 (3.67) 18

35 v t = Bτ 4πr F is the Prandtl s factor for tip loss, given by, 1 (3.68) F 1 + ( 4R λ rπbr )2 v a = v t W t W a (3.69) F = 2 π cos 1 (e f ) (3.70) f = B 2 (1 r R )λ r (3.71) This formulation is true only for a helical wake that is non-contracting and if the pitch remains constant throughout the radius. Also, the Prandtl s factor for tip loss is only a rough approximation which cannot account for complex 3D effects at the tip. Thus, it is difficult to accurately predict the induced velocites by this method. 19

36 Chapter 4 Wind Turbine Geometry Definition using 3DBGB 3DBGB[4] is a blade geometry generation tool that uses a parametric approach to design blades for turbomachinery applications. Due to its parametric nature, a wide range of blades can be designed with relative ease. 2D airfoil sections are created using geometric and aerodynamic input quantities. The sections are stacked in a 3D cylindrical space and are transformed to cartesian space. This can be imported into any CAD package to create 3D solid models. Conventional wind turbines are stacked radially, but other input can be used to define a stacking axis and location on the blade for stacking. The geometry builder is also capable of creating complex geomtries such as bent tips and split tips with minimum change to the inputs. Figure 4.1: 3DBGB Process Flow Chart [4]. 20

37 4.1 Blade Design Process 3DBGB uses the input file 3dbgbinput.dat to extract the input parameters and create 3D sections. The number of blades, scaling factor and number of streamlines are specified in the first few lines of the input file. A switch to use non-dimensional actual chord values is available to enable reverse engineering of known blades. At each streamline (actually a construction curve shown in figure 4.3) the blade inlet and outlet angles, relative mach number at inlet, non-dimensional actual chord, thickness to chord ratio, incidence, deviation and secondary flow angle are specified. The blade stagger angle can be input through the inlet and outlet leading edge and trailing edge angles. Figure 4.2: Nomenclature[4]. The streamlines or construction lines are defined in the x s, r s plane. 3DBGB has the capability to Figure 4.3: Meridional View[4]. generate a variety of airfoils. Due to its parametric nature it is easy to define different airfoils at different sections which makes the design process highly flexible. Presently, the code has the capability to create 21

38 circular sections, NACA 4-digit airfoils, NREL S809 airfoils and the default mixed camber airfoil. New airfoils can also be included in the code. Figure 4.4: 3DBGB generated airfoils[4]. Using the stacking information and control points, the blade definition can be further altered to produce design features such lean, sweep, bent tips,split tips, etc. Figure 4.5: Lofted blade using Unigraphics[4]. Figure 4.6: Swept Blades using 3DBGB[4]. 22

39 Figure 4.7: Bladerow with bent-tips using 3DBGB[4]. Figure 4.8: Wind Turbine Blade using 3DBGB[4]. Figure 4.9: Wind Turbine Assembly - Blade generated using 3DBGB[4]. All the 3DBGB input files used for the various cases in this current research can be found in Appendix B. 23

40 Chapter 5 3D-CFD Case Set-Up and Analysis using Fine Turbo F INE/T urbo T M is a Computational Fluid Dynamics (CFD) analysis tool from NUMECA International [31]. It stands for Flow Integrated Environment and it is a complete CFD package which includes grid generation, flow solver and post-processing capabilities. FINE/Turbo is specialized to simulate internal, rotating and turbomachinery flows for all types of fluids. The package has a fully hexahedral and highly automated grid generation module AutoGrid T M. The package uses a 3D Reynolds Averaged Euler and Navier Stoles flow solver EURANUS. CF V iew T M is an advanced post-processing module which is also part of the package. This chapter provides an overview of the CFD analysis using FINE/- Turbo. A detailed tutorial on how to run a wind turbine case can be found in Appendix C. 5.1 Grid Setup The grid generation module, AutoGrid, provides the option of either importing and linking a CAD file or importing a.geomturbo file, which is the native file format. The blade generation code 3DBGB has the capability to output the blade geometry in the.geomturbo file format, which makes importing the blade geometry simple as it initializes the grid parameters and geometry definition. The built-in wind turbine wizard mode in AutoGrid makes the grid generation process effortless. Figure 5.1 shows a wind turbine blade imported and initialized using a.geomturbo file. Once the grid parameters are specified using the wizard mode, a blade to blade mesh can be generated and previewed. After making the required changes to the parameters and making sure the blade to blade mesh is accurate, the 3D mesh can be generated. A complete description of all the parameters and 24

41 Figure 5.1: Geometry initialization in Autogrid. definitions can be found in the NUMECA User Manuals [32]. After the 3D mesh is generated, a quality report is generated which provides information about negative cells, orthogonality, aspect ratio, skewness and angular deviation of the cells. Saving the project creates a.igg file which contains the complete grid definition. This file can be opened in the IGG module to view and edit the boundary conditions. A.CGNS file is also created which stores the solution and is used by the post-processing module. Figure 5.2: B2B mesh at 20 percent span. 25

42 Figure 5.3: Grid Quality Report. Figure 5.4: 3D Grid viewed in IGG. 5.2 Flow Setup and Solution The Fine/Turbo flow solver module is an intuitive platform to set up the flow properties and to run a simulation. Once the boundary conditions are appropriately assigned using the IGG module, the path to the IGG file is specified in the flow solver module and the flow parameters are specified. The parameters used for the wind turbine case are given below. 26

43 Configuration Fluid Model - The fluid properties to be used by the computation. Current case uses Air- (perfect gas) as the fluid model. Flow Model - Characteristics of the flow : * Time configuration - Steady * Mathematical Model Mathematical Model - Turbulent Navier-Stokes Turbulence Model - Spalart-Allmaras * Low speed flow - M < 0.3 Rotating Machinery - Defines the rotational speed of the grid blocks generated in rpm. Optional Models - Additional models can be used. Transition Model with AGS modeling is available here. Boundary Conditions - The boundary condition already generated in Autogrid are available for additional input definition. Numerical Model - Allows the definition of CFL number, grid level -(coarse or fine) and preconditioning parameters. Initial Solution - Provides the option to start a computation from the values specified or from a previous run file. Outputs - Required outputs can be checked and viewed in the post processor. Computation Steering - This option sets the control variables; i.e. maximum number of iterations to be performed along with the convergence criteria. Once the flow properties are set, the flow solver EURANUS can be started and the convergence can be monitored. Fine/Turbo also provides the option of running the solution in batch processing mode. The commands to run Fine/Turbo in batch mode can be found in Appendix C. After the flow converges, the flow solver ends and writes a.run file which contains all the solution data. The convergence history can be viewed graphically for the global residuals, torque, efficiency and axial thrust. Using the CFView module, the solution can be post-processed to visualize the flow feild properties. 27

44 Figure 5.5: Convergence History. Figure 5.6: 3D static pressure contour - pressure side and suction side - NREL original blade. 28

45 Figure 5.7: Sectional static pressure contours at multiple radial locations. 29

46 Figure 5.8: Azimuthal area averaged static pressure - NREL original blade. Figures 5.6, 5.7 and 5.8 show some of the results for the NREL original blade obtained from the Fine/turbo simulation. Using the built-in post processing module, CFView, a wide range of plotting options can be exploited. Further post-processing was done using Asgard. Asgard is a collection of visualization/post-processing tools. The asgard library serves as the backbone for file manipulations, calculations, and feature extractions. 30

47 Chapter 6 Winglets - Design and Effects The characteristics of a finite wing differ considerably from that of a theoretical infinite wing because complex 3D effects come into play. The pressure imbalance between the pressure side and suction side of the wing causes the flow to curl near the tip causing a downstream trailing vortex flow. This vortex causes a small downward velocity component at the wing called the downwash (w). The effect of this downwash is to create a local induced drag on the airfoil section. This can also be understood as a reduction in the geometric angle of attack of the airfoil as shown in figure 6.1. The effective angle of attack that the section actually sees is lesser than the design geometric angle of attack due to a negative induced angle of attack [5]. Figure 6.1: Effect of downwash on the local flow over a section of the wing [5]. 31

48 α effective = α geometric α induced (6.1) At any given radial station on a wind turbine rotor, the induced angle of attack can be defined as 1 w(r) α induced (r) = tan (6.2) V z Winglets are wing tip devices that reduce losses at the tip by weakening the vortex shedding. By weakening the vortex shedding it effectively reduces the downwash at the blade and thereby increases the effective angle of attack. This enables the blade to operate closer to the design geometric angle of attack and increases the power extraction. 6.1 Winglet Design using 3DBGB 3DBGB provides the capability to create complex geomtries including winglets. It enables the user to define a set of spanwise control points, which allows the blade sections to be leaned or swept. In conventional turbomachinery, sweep is defined as a translation of the blade section in the m direction in the m -θ plane and lean is defined as a translation of the blade section in the θ direction in the m - θ plane. This definition is based on Smith [33] whereas an alternate definition by Denton [34] is that sweep is tangent to the chord and lean is normal to it. Since windturbines are usually highly staggered, a translation of the blade section in the m direction corresponds to a lean and a translation of the blade section in the θ direction corresponds to a sweep. Figure 6.2: Design parameters of winglets [6]. 32

49 The important parameters for winglet design are shown in figure 6.2. The height of the winglet can be assigned in 3DBGB using the control points. The translation of the tip blade section in the m direction is specified as a percentage of span. Starting from the last control point with a zero lean, the sections are leaned up to the tip blade section. The required cant angle can be set by varying the amount of lean. Only a pure lean in the downstream direction is explored in this thesis to probe into the effect of winglets on downwash. 6.2 Effect of Winglets on Downwash The NREL Phase VI wind turbine was chosen as a test case due to the ready availability of design and analysis data for validation [8]. The NREL Phase VI wind turbine has two blades with a diameter of meters. From the design data, the blade was modelled using 3DBGB. The 3DBGB input files can be found in Appendix B. An upstream and downstream winglet were added to this wind turbine and CFD analysis was carried out using Fine/Turbo. The static pressure at each grid point on the blade was extracted using ASGARD - an in-house post processing tool. This data was used to calculate the pressure coefficient, lift coefficient and drag coefficient at each section using a 2D analysis matlab code - Calc-L-D-M which has been integrated into Calc-PdA (refer Chapter 7). The wind turbine uses the S809 airfoil which was created by NREL to have a high restrained maximum lift coeffcient [35]. By comparing the C l vs. α curve obtained from XFOIL [7] (figure 6.3) for the S809 airfoil and the C l for each section calculated from the code, the downwash and the induced angle of attack were calculated. Figure 6.3: Lift Coefficient vs. Angle of Attack - NREL S809 Airfoil [7]. 33

50 Figure 6.4: Geometric, Induced and Effective Alpha vs. Span - NREL original blade. Figure 6.5: Geometric, Induced and Effective Alpha vs. Span - NREL downstream winglet case. Comparing figures 6.4 and 6.5 reveals a noticeable reduction in the induced angle of attack above 80% span due to the addition of a winglet. From figure 6.6 we can see that the downwash is considerably reduced above 80% span in the downstream winglet case. Reduction in downwash is a result of the successful weakening of the tip vortices due to the production of additional thrust in the circulation field 34

51 by the winglet. Figure 6.6: Downwash vs. Span Comparison. Figure 6.7: Effective Alpha vs. Span Comparison. 35

52 Figure 6.8: Lift Coeffcient vs. Span Comparison. Figure 6.9: NREL tip streamtubes. 36

53 Figure 6.10: NREL-Winglet tip streamtubes. The increase in the effective angle of attack above 80% span as seen in figure 6.7 results in an improved lift coefficient (figure 6.8) for the downstream winglet case. This means that the torque, and hence, the power output, will increase due to the addition of a downstream winglet. Figures 6.9 and 6.10 show the streamtubes at the tip of the NREL original blade and the NREL blade with a winglet. Vortices can be seen to start developing in the NREl blade due to the pressure imbalances whereas the same effects are less pronounced in the streamtubes on the blade with the winglet. The original NREL blade has a power output of KW. This increases to a power ouput of KW due to the addition of a downstream winglet amounting to a 2.63% increase in the power purely by improving the aerodynamics of the blade by reducing complex 3D tip effects. 37

54 Chapter 7 3D Force Analysis The flow field around a wind turbine is complex and no matter how close a 2D approximation is, it will still be innacurate and fail to account for all the details. This was the reason a code was developed using MatLab for 3D force analysis which can be found in Appendix D. From the CFD results, the data from each grid point on the blade was extracted using ASGARD. This data was processed to arrive at the aerodynamic forces acting on elemental slabs of the wind turbine blade and these forces were integrated over the span to arrive at the global force, torque and power output of the blade. 7.1 Code Formulation Using the data extracted from ASGARD, the blade was divided into the individual sections. Each section and the section above it in the radial direction were treated as a 3D slab. Figure 7.1: 3D Slabs created using CFD data. 38

55 Figure 7.1 shows two consecutive 3D slabs. Each slab is divided into elemental areas. Points A,B,C and D enclose one such area. The static pressure at each point is known. The average static pressure acting on the elemental area is found. p = (p A + p B + p C + p D )/4 (7.1) The area vector of the elemental area is found by using the diagonal vectors which is then multiplied with the average pressure to obtain the force ( f) acting on the elemental area. The resultant force ( F ) acting on the slab is the summation of the forces acting on all the n elemental areas on the slab. da = 1 2 ( ACX BD) (7.2) f = p da (7.3) F = n 1 p da = n f (7.4) 1 Figure 7.2: Diagonal vectors and force vectors on slabs. Figure 7.2 shows two slabs with diagonal vectors and force vectors on each elemental area. The cartesian force vectors are transformed into cylindrical force vectors. The position vector for the transformation is taken as the centroid of the slab. The centroid is found using a MatLab function - Polygeom - which can be found in Appendix E. 39

56 θ = tan 1 y centroid x centroid (7.5) F r F θ F z = cosθ sinθ 0 sinθ cosθ F x F y F z (7.6) The product of the tangential force and the local radius gives the torque of the slab. Summing all the torques yeilds the global torque of the blade. The product of the global torque and the rotational speed of the blade gives the power output output of the blade which can be multiplied with the total number of blades to give the total power output of the wind turbine. tip Q = F θ r (7.7) hub P = BQΩ (7.8) It should be noted that shear forces are not taken into account in this analysis as they were found to be very negligible owing to the high Reynold s number. Figure 7.3 shows the resultant force vectors on two 3D slabs. Figure 7.3: Resultant force vectors on slabs. 40

57 Chapter 8 Results and Comparisons The 3D force analysis discussed in chapter 7 was carried out on the NREL Phase VI blade and used as a baseline. The same blade was modified to have a constant chord throughout the span and analyzed to see how the lack of radial forces affects the performance of the blade. In order to analyze the effect of the radial forces in great detail, the NREL blade s S809 airfoil was substituted with a NACA 2420 airfoil since this was a close approximation to the S809 airfoil. Further, blades were designed to have varying airfoil sections with span using the NACA 24XX family of aifoils. This was done to vary the thickness to chord ratio of the airfoil at various span locations to change the radial component of the surface area. The results from these analyses are compared in this chapter. 8.1 NREL Original Blade vs. NREL Constant-Chord Blade The NREL blade uses the S809 airfoil which has a thickness to chord ratio of 20.95% [8]. The change in chord over the span creates a change in the surface area of the blade. The radial component of this surface area variation is directly related to the radial forces acting on the blade. To investigate the impact of no radial forces acting on the blade, the NREL blade was redesigned to have a constant chord throughout the span, thereby eliminating any radial component of the surface area. Figure 8.1 shows the variation of cross sectional area over span. The constant-chord case has no change in cross-sectional area except in the hub transition zone. 41

58 Figure 8.1: Cross sectional area vs. span. Figure 8.2: da/dr vs. span. Figure 8.3: Average Static Pressure vs. span. 42

59 Figure 8.4: Radial Force vs. span. Figure 8.5: Tangential Force vs. span. Figure 8.6: Axial Force vs. span. 43

60 Figure 8.7: Torque vs. span. Figure 8.8: Area averaged Vz in front of blade vs. span. Figure 8.9: Axial Induction Factor vs. span. 44

61 Figure 8.10: Effective angle of attack vs. span. Figure 8.2 shows the radial component of the cross-sectional area over the span. Comparing this with figure 8.4, which shows the radial force over the span, it unequivocally demonstrates the dependence of the radial forces on the radial component of the surface area. This can be seen mathematically through the integral form of the radial momentum equation. t p ρv r rdθdrdz + v r dṁ + prdθdz = r rdθdrdz + ρv 2 θ rdθdrdz (8.1) r The third term on the left hand side is the radial force term and rdθdz is the radial component of the surface area. Clearly, the constant-chord blade is an inferior design compared to the original NREL blade. This can be attributed mostly to a redistribution of lift forces acting on thrust and torque, but also to to the lack of radial forces acting on the constant-chord blade. The relation between the radial forces and the axial induction factor will be discussed in detail in chapter 9. Figures 8.8 and 8.9 show the Vz just upstream of the blade and the axial induction factor respectively. The constant-chord blade has a lower axial induction factor than the original NREL blade over most of the span. This impacts the performance of the constant-chord case, as reflected in figure 8.7. The NREL original blade has a better torque output over the span because a higher effective angle of attack is maintained over most of the span than the constant-chord blade, as seen in figure

62 8.2 NACA 24XX Series Airfoils The NACA 4-digit series of airfoils was chosen to mimic the shape and characteristics of the NREL S809 airfoil in order to have better design flexibility in the analysis of the impact of radial forces on the blade. The 4-digits are defined as [36]: First digit describing maximum camber as percentage of the chord. Second digit describing the distance of maximum camber from the airfoil leading edge in tens of percents of the chord. Last two digits describing maximum thickness of the airfoil as percent of the chord. Figure 8.11: NACA 2420 Airfoil. Figure 8.12: Lift Coefficient vs. Angle of Attack - S809 and NACA

63 The NACA 2420 airfoil was found to be a very close approximation to the S809 airfoil in both thickness and lift coefficient characteristics. Figure 8.12 shows the lift coefficient comparison between S809 and NACA 2420 airfoils. It can be seen that the difference in the lift coefficient is within a tolerable margin in the angle of attack range from 0 to 7 degrees, which is the region where the effective angle of attack lies for the blade. The maximum difference in C l is 0.04 at 0 degrees and 7 degrees. It is for these reasons that the NACA 2420 airfoil was chosen to be the baseline for further investigation into the effect of radial forces on the blade. The addition of the NACA 4-digit airfoil generation capability in the 3DBGB code provided a tremendous range of airfoil sections that could be included in the design. The thickness to chord ratio of the airfoils is the key parameter that is used to manipulate the radial component of the surface area. Two blades were created with gradually varying airfoil sections - NACA 2420 at the hub to NACA 2404 at the tip. NACA 2430 at the hub to NACA 2404 at the tip. Figure 8.13 shows the lift coeffienct characteristics of a few NACA airfoils that have been used in the blade design. It can be seen that they all have very similar C l vs. α curves. NACA 2404 does not follow the same characteristcs beyond an angle of attack of 6 degrees, but the tip region, where the NACA 2420 airfoil is used, lies in the effective angle of attack range of 0 to 2 degrees. The NACA 2430 airfoil seems to be the odd one out, but the airfoil has been chosen to demonstrate some key aspects of the radial force manipulation which will be discussed in detail in section 8.4. Figure 8.13: Lift Coefficient vs. Angle of Attack - NACA Series. 47

64 8.3 NREL Original Blade vs. NACA 2420 Blade The NACA 2420 airfoil has a slightly larger cross-sectional area than the NREL S809 airfoil. Figure 8.14 shows the area comparison. Since the chord profile for the NACA 2420 blade is the same as the NREL original blade, the curves are identical and the NACA 2420 curve is slightly offset from the NREL S809 curve. Figure 8.14: Cross sectional area vs. span. Figure 8.15: da/dr and F r vs. span - NREL Original Blade. 48

65 Figure 8.16: da/dr and F r vs. span - NACA Figure 8.17: Average static pressure vs. span. Figure 8.18: Radial Force vs. span. 49

66 Figure 8.19: Tangential Force vs. span. Figure 8.20: Axial Force vs. span. Figure 8.21: Torque vs. span. 50

67 Figure 8.22: Area averaged Vz in front of blade vs. span. Figure 8.23: Axial induction factor vs. span. Figure 8.24: Effective angle of attack vs. span. 51

68 Figure 8.25: Lift coefficient vs. span. The NACA 2420 blade has better effective angles of attack than the NREL S809 blade (figure 8.24) because it has a slightly better C l characteristic, which reduces the induced angles of attack. The higher effective angles of attack also imply higher sectional lift coefficients (figure 8.25). The NACA 2420 blade also has higher radial forces (figure 8.18) than the NREL S809 blade; therefore, it is able to bend the streamlines more effectively and further reduce Vz upstream of the blade (figures 8.22 and 8.23). These effects improve the tangential forces; therefore, the torque (figures 8.19 and 8.21), thereby extracting more power from the wind. 8.4 NACA 2420 vs. NACA The NACA blade consists of the NACA 2420 airfoil till 50% span and then gradually decreases to NACA 2404 at the tip as shown in figure Due to the greater change in the radial component of the area, the NACA blade has higher radial forces acting on the blade than the NACA 2420 blade. The jump in the radial force and da/dr at 50% span for the NACA blade can be clearly seen in figure The tangential forces, axial forces and torque are also greater for the NACA blade than the NACA 2420 blade as seen in figures 8.32, 8.33 and

69 Figure 8.26: Cross sectional area vs. span. Figure 8.27: da/dr and F r vs. span - NACA Figure 8.28: da/dr and F r vs. span - NACA

70 Figure 8.29: Average Static Pressure vs. span. Figure 8.30: Radial Force vs. span. Figure 8.31: Radial Force using gauge pressure vs. span. 54

71 Figure 8.32: Tangential Force vs. span. Figure 8.33: Axial Force vs. span. Figure 8.34: Torque vs. span. 55

72 Figure 8.35: Area averaged Vz in front of blade vs. span. Figure 8.36: Axial induction factor vs. span. Figure 8.37: Effective angle of attack vs. span. 56

73 Figure 8.38: Lift coefficient vs. span. Figure 8.31 shows the radial force comparison between the NACA 2420 and NACA blades using gauge pressure instead of static pressure. This is done by substituting the pressure term in the force equation with [p-p ref ] where p ref is the reference static pressure in the far-field pascals. The NACA blade performs better than the NACA 2420 blade because it bends the streamlines more than the NACA 2420 blade. This causes the Vz to go down in front of the blade (figure 8.35), improving the effective angles of attack (figure 8.37); thereby improving the lift coefficient (figure 8.38). Figure 8.36 shows the axial induction factor. The area averaged axial induction factor for the blades are: a2420 (r)rdr rdr = (8.2) a (r)rdr rdr = (8.3) The mass flow rate is constant through a streamtube for each design. From the actuator disc theory figure 4.1, subscript 1 corresponds to the station far upstream and subscript 2 corresponds to the station just in front of the leading edge. ṁ 2420 = ρa V = ρa V = ρa 2420 V 2420 (8.4) ṁ = ρa V = ρa V = ρa V (8.5) 57

74 A A 2420 = V 2420 V = (1 a 2420)U 1 (1 a )U 1 (8.6) A = V 2420 ( ) = = (8.7) A 2420 V ( ) The subtle and gradual radial area variation between the NACA 2420 and NACA blades has resulted in a 1.96% decrease in the streamtube area far upstream of the blade. This area change results in a lower Vz in front of the blade, increasing the effective angles of attack over the span of the blade and directly contributes to the increase in the tangential forces acting on the blade. The increase in tangential forces ultimately improves the power output of the blade. C P = 4a(1 a) 2 (8.8) C P 2420 = ( ) 2 = (8.9) C P = ( ) 2 = (8.10) C P C P 2420 = (8.11) The power output of the NACA blade is 5.661% more than the NACA 2420 blade. 8.5 NACA 2420 vs. NACA vs. NACA The NACA starts with the NACA 2430 airfoil at the hub, gradually decreases to NACA 2420 at 50% span and then continues to gradually decrease to NACA 2404 at the tip as seen in figure Even though the NACA airfoils from 2425 to 2430 have undesirable C l vs. α characteristics, the NACA case was explored purely to see how gradually varying the thickness all the way from the hub to the tip affects the performance of the blade instead of abruptly starting to vary the thickness at mid-span, as in the NACA blade. Although there is greater area variation in the hub region for the NACA blade, the poor C l values of the airfoils in that region result in lower tangential forces; hence, lower torque values. For this reason, the NACA blade performs better than the NACA blade. This will become more evident through the following figures. 58

75 Figure 8.39: Cross sectional area vs. span. Figure 8.40: da/dr and F r vs. span - NACA Figure 8.41: da/dr and F r vs. span - NACA

76 Figure 8.42: da/dr and F r vs. span - NACA Figure 8.43: Average Static Pressure vs. span. Figure 8.44: Radial Force vs. span. 60

77 Figure 8.45: Tangential Force vs. span. Figure 8.46: Axial Force vs. span. Figure 8.47: Torque vs. span. 61

78 Figure 8.48: Area averaged Vz in front of blade vs. span. Figure 8.49: Axial induction factor vs. span. Figure 8.50: Effective angle of attack vs. span. 62

79 Figure 8.51: Lift coefficient vs. span. Figure 8.44 shows the radial force comparison. The jump in the NACA curve at midspan is due to the change in the area variation as the airfoil sections begin to decrease in thickness. The increased radial forces bend the streamlines more than the NACA 2420 blade does; therefore, increasing the streamtube area. This increase in area decreases the Vz (figure 8.48) in front of the blade more for the NACA and NACA blades, thereby increasing the effective angles of attack, tangential forces and eventually the torque (figures 8.45, 8.47 and 8.50). The NACA blade has low lift coefficients in the hub and lower span region due to the high thickness of the airfoils (figure 8.51); hence, the effective angles of attack, tangential force and torque are lower than the NACA 2420 and NACA blades in this region. 8.6 Pressure Side and Suction Side Stacking The 3DBGB code was modified to include the ability to stack airfoil sections either on the pressure side or the suction side in addition to the default meanline stacking. Stacking the airfoils on the suction side increases the radial forces and stacking on the pressure side decreases the radial forces. The degree to which the radial forces increase or decrease depends upon the airfoils used. The NACA blade was used to explore the effect of these stacking options. Figure 8.52 compares the three types of stacking. This can also be thought of as a type of leaning of the blade over the span. 63

80 Figure 8.52: Pressure side, meanline and suction side stacking. Figure 8.53: da/dr and F r vs. span - NACA Figure 8.54: da/dr and F r vs. span - NACA PS. 64

81 Figure 8.55: da/dr and F r vs. span - NACA SS. Figure 8.56: Average Static Pressure vs. span. Figure 8.57: Radial Force vs. span. 65

82 Figure 8.58: Tangential Force vs. span. Figure 8.59: Axial Force vs. span. Figure 8.60: Torque vs. span. 66

83 Figure 8.61: Area averaged Vz in front of blade vs. span. Figure 8.62: Axial induction factor vs. span. Figure 8.63: Effective angle of attack vs. span. 67

84 Figure 8.64: Lift coefficient vs. span. The difference in radial forces between the three blades is evident in the lower span region and it becomes smaller as we move up the span as seen in figure This is because the difference in the radial component of the surface area due to pressure and suction side stacking is more prominent when the airfoils are thick and with high chord values. The higher radial forces in the lower span for the suction side stacked blade bends the streamlines more than the meanline stacked blade. The lower radial forces in the lower span for the pressure side stacked blade bends the streamlines lesser than the meanline stacked blade. This can be seen in figure 8.61 and 8.62 where the Vz of the meanline stacked blade lies between the Vz of the pressure side stacked blade and the suction side stacked blade. Hence, the effective angles of attack, lift coefficient, tangential force and torque of the suction side stacked blade is more than the meanline stacked blade and pressure side stacked blade in this region (figures 8.58, 8.60, 8.63 and 8.64). As we move up the span and the airfoils get thinner, possibly a separate lean effect comes into play. This could be the reason why the performance of the suction side stacked blade is lower than the meanline stacked blade in this region. The pressure side stacked blade, as expected, is lower than the meanline stacked blade. This effect of stacking is not explored further in this thesis. 8.7 Power The power output of all the blades was calculated from the torque. Q Blade = Q slab (8.12) P = BQ Blade Ω (8.13) 68

85 The NREL design report provides a power vs. wind speed curve for the blade as shown in figure The CFD simulations were run at a wind speed of 7 m/s and the power output from the simulation for the original NREL blade is close to the data obtained from the report. Figure 8.65: NREL power curve [8]. Figure 8.66: Power Output Comparison. 69

86 Figure 8.67: Power Output Comparison-NACA Blades. Figure 8.68 shows a performance summary of all the NACA blades. The NREL original blade has a power output of Kilo watts at 7 m/s wind speed. This corresponds to the power curve data obtained from the NREL report [8]. The NACA 2420 blade has a power output of Kilo Watts which is 25.8% more than the NREL original blade. This increase in the power output is due to the slightly better C l characteristics of the NACA 2420 airfoil than the S809 airfoil. The NACA blade gives the best performance with a power output that is 6.8% higher than the NACA 2420 blade while the NACA blade s power output is 1.5% lower than the NACA blade because of reasons discussed in chapter 8.4. The pressure-side-stacked NACA blade s power output is 3.5% lower than the meanline-stacked NACA blade and the suction-side-stacked NACA blade has a power output that is 0.04% higher than the meanline-stacked NACA blade. 70

87 Figure 8.68: Percentage power Output Comparison-NACA Blades. 71

88 Chapter 9 Effect of Radial Area Variation In the actuator disc model discussed in chapter 3, the wind velocity in stations 2 and 3, U 2 and U 3, are assumed to be the same and that the area expansion occurring in the streamtube is solely because of U 4 being lesser than U 1. This is not a complete description; hence, the twist distribution of the wind turbine blade calculated using the BEM theory will not be optimal. Analyzing the results from the 3D force analysis code described in chapter 7 revealed that the expansion of the streamtube is in fact driven in part by the radial forces acting on the blade. It also revealed that the manipulation of these radial forces will lead to further expansion of the streamtube; therefore, reducing the wind velocity just upstream of the blade. This velocity just upstream of the blade is U 2, as shown in the actuator disc model, which is related to the axial induction factor. U 2 = U 1 (1 a) (9.1) Figures 9.1, 9.2 and 9.3 show the isometric, side vide and upstream view of the relative velocity streamtubes for a wind turbine generated using Asgard. Figure 9.1: Streamtube expansion isometric view. 72

89 Figure 9.2: Streamtube expansion side view. Figure 9.3: Streamtube expansion viewed from upstream. 9.1 Radial Momentum Equation The inviscid momentum equation expressed in cylindrical coordinates (r,θ,z) is as follows: Radial momentum - [ vr ρ t + v v r r r + v ] θ v r r θ + v v r z z v2 θ = p r r (9.2) The continuity equation in cylindrical coordinates is ρ t + 1 (rρv r ) + 1 (ρv θ ) + (ρv z) = 0 (9.3) r r r θ z Multiplying equation (9.3) by v r, we get ρ v r t + v r (rρv r ) + v r (ρv θ ) (ρv z ) + v r = 0 (9.4) r r r θ z 73

90 Adding equations (9.2) and (9.4) and using chain rule yeilds (ρv r ) t + 1 r (v r rρv r ) r + 1 r (v r ρv θ ) θ + 1 r (v r ρv z r) z + 1 r (rp) r p r (ρv2 θ ) r = 0 (9.5) Equation (9.5) can be represented in integral form as t p ρv r rdθdrdz + v r dṁ + prdθdz = r rdθdrdz + ρv 2 θ rdθdrdz (9.6) r For a steady, axisymmetric case, the time and angular derivatives are zero. Therefore, the radial momentum equation becomes [ ] v r ρ v r r + v v r z z v2 θ = p r r (9.7) Figure 9.4: Meridional streamline velocity triangle. Figure 9.4 shows the meridional streamline velocity triangle, where v m is the meridionally projected streamline velocity, v r is the radial velocity component and v z is the axial velocity component. φ is the angle made by the meridional projection of the streamline with the axial velocity component. The streamline curvature is defined as C = dφ dm = 1 r m (9.8) where r m is the radius of curvature of the meridional projection of the streamline. The radial momentum equation can be expressed in terms of the streamline curvature, using the streamline curvature 74

91 approach as outlined in [37], as follows. v r v m m = v v r r r + v v r z z = v2 θ r 1 p ρ r (9.9) Using equation (9.8) and assuming φ 0, v r = v m sinφ (9.10) v 2 mcosφ φ m + v msinφ v m v m (9.11) 1 p ρ r = v2 mc + v2 θ r (9.12) L.H.Smith, Jr. derived an equation to describe the radial variation of circumferentially averaged flow properties inside a turbomachinery blade row [38]. Circumeferential averaging of a flow property x is defined as ( x) = 1 θ s θ p θs θ p (x)dθ (9.13) where θ is the circumferential angle in radians and subscript p stands for the pressure side of a blade and subscript s stands for the suction side of the next blade. Smith derived an equation for the circumferentially averaged radial pressure distribution in [38]. p r = p r + ( ) ps p p tanɛm θ s θ p r ( + p p ) p + p s 1 Λ 2 Λ r (9.14) Λ is the ratio of the open circumference to the total circumference and ɛ m is the blade lean angle in the meridional direction. Λ = B θ 2π tanɛ m = r θ m r (9.15) (9.16) The first term on the right hand side of equation (9.14) is the desired radial gradient of the average pressure. The second term is related to the radial component of the blade force on the fluid and the last term is attributed to a blockage effect. Smith [38] goes on to state that the last term vanishes when the pressure varies linearly in the θ direction and drops it from the equation. This is a good approximation for 75

92 many turbomachinery flows where high velocities are involved such as jet engines. Since wind turbines operate at a mere fraction of the velocities involved with conventional axial turbomachinery, the pressure does not vary linearly in the θ direction so this term cannot be neglected. Substituting equation 9.14 in a circumferentially averaged equation (9.12) we obtain ) ( 1 p ρ r = ) [ ( 1 p ρ r + ( ) ps p p tanɛm θ s θ p r ( + p p ) p + p s 1 2 Λ ] Λ = v m r 2 C + v 2 θ r (9.17) When the lean angle ɛ m 0 then the above equation becomes ) ( 1 p ρ r = ) [ ( ( 1 p ρ r + p p ) p + p s 1 2 Λ ] Λ = v m r 2 C + v 2 θ r (9.18) Figure 9.5 shows the comparison of the first term in equation (9.14), the radial gradient of the circumferentially averaged pressure, between the NACA 2420 and NACA blades. The p r term for the NACA blade is lower than the NACA 2420 blade over most of the span, especially from 40%-60% of the span and from 82%-100% span. Figure 9.5: First term in Eq.(9.14) p r vs. span comparison - NACA 2420 and NACA The third term in equation (9.14), the blockage effect term, is compared between the NACA 2420 and the NACA blades in figure 9.6. It is slightly higher for the NACA blade than the NACA 2420 blade at mid-span. From 62%-100% span, it is lower for the NACA blade than the NACA 2420 blade. 76

93 ( ) Figure 9.6: Third term in Eq.(9.14) p pp+ps 1 Λ 2 Λ r vs. span comparison - NACA 2420 and NACA The difference between the two cases is the cause for the difference in the circumferencial averaged radial pressure gradient. The streamline curvature is directly related to the circumferentially averaged radial pressure gradient through equation 9.18; hence, the NACA 2420 and NACA blades have different streamline curvatures. The NACA blade is able to bend the streamlines more than the NACA 2420 blade, thereby increasing the streamtube area expansion and reducing the wind speed ahead of the blade more effectively. This enables the NACA blade to extract more energy from the wind and perform better than the NACA 2420 blade. Figures 9.7 and 9.8 show the azimuthal area averaged static pressure contours for the NACA 2420 and NACA blades respectively. It can be seen how the static pressure is slightly different upstream and downstream of the blade for the NACA blade than the NACA 2420 blade. It is this pressure difference that drives the streamlines to bend. 77

94 Figure 9.7: Azimuthal area averaged static pressure - NACA Figure 9.8: Azimuthal area averaged static pressure - NACA Figures 9.9, 9.10 and 9.11 shows the comparison of a set of streamlines for the NACA 2420 and NACA blades. 78

95 Figure 9.9: Average streamline radius vs. z at transition zone - NACA 2420 and NACA Figure 9.10: Average streamline radius vs. z at mid-span - NACA 2420 and NACA Figure 9.11: Average streamline radius vs. z at tip - NACA 2420 and NACA

96 Figure 9.12: Average streamtube radius vs. z at tip - NACA Figure 9.13: Average streamtube radius vs. z at tip - NACA In order to get the circumferential average streamtube radius, thirty streamlines were spawned, equi- 80

97 distant from each other, on a line between the leading edge and trailing edge of the two blades for the NACA 2420 and NACA cases using ASGARD. A comparison of the thirty streamtubes between the NACA 2420 and NACA blades can be seen in figure The average streamtube radius for the NACA 2420 blade and NACA blade are shown in figures 9.12 and They are embedded on their respective azimuthal averaged static pressure contours. It can be seen how the streamlines are bent more for the NACA blade at the tip than the NACA 2420 blade. The area ratio is the streamtube area of the NACA blade over the streamtube area of the NACA 2420 blade. Figures 9.15 and 9.16 show the streamtube area and area ratio respectively. Figure 9.14: Streamtube Radius vs. z at tip - NACA 2420 and NACA Streamlines. Figure 9.15: Average streamtube area vs. z at tip - NACA 2420 and NACA The blade lies between Z = 47.7 meters and Z = 48 meters. The upstream streamtube area of the tip streamlines for the NACA blade is slightly higher than the NACA 2420 blade. When the streamlines reach the blade tip, the difference in area grows large. The NACA blade is able to reduce the wind velocity and increase the streamtube area at the blade more than the NACA

98 blade; thereby, extracting more kinetic energy from the wind. Figure 9.16: Average streamtube area ratio vs. z at tip - NACA 2420 and NACA The average axial induction factor just upstream of the NACA 2420 blade is and the average axial induction factor just upstream of the NACA blade is Theoretically, the maximum possible axial induction factor is according to Betz [11]. From figure 9.16, it can be seen that the area ratio just upstream of the blade is This area ratio can be related to the average axial induction factor through equation 8.7. The axial induction factor depends on the streamtube area which, in turn, depends on how much the streamlines are bent in front of the blade. Higher radial area variation on the blade facilitates this bending of the streamlines by creating a higher radial pressure gradient. The lowering of Vz in front of the blade improves the effective angles of attack over the span; thereby increasing the lift coefficients over the span. As a result, the tangential forces acting on the blade are improved; hence, the power output is higher. As shown in equations 8.6 and 8.10, a 1.96% increase in the streamtube area in front of the blade causes the power to increase by 5.661%. The power output results from CFD analysis show that the NACA blade has an output that is % higher than that of the NACA 2420 blade. 82

99 Chapter 10 Conclusion 10.1 Overview In the present research work methods to improve the performance of wind turbines have been explored. 3D CFD analysis was carried out on an NREL phase VI wind turbine. This was compared to the performance of the same wind turbine with a winglet added to the tip. This reduced the strength of the tip vortices and improved the aerodynamic performance by 2.63%. 3D analysis of the forces acting on the blade established the magnitude of the radial force acting on the blade to be much larger than the tangential and axial forces. The impact of radial area variation on the performance of the blade was explored using the NACA four digit airfoil series. The thickness to chord ratio was manipulated over the span of the blade to explore its effect. The results from these findings have been documented and analyzed Key Findings The dependence of the performance of a wind turbine blade on the cross-sectional area variation has been established in this thesis. The NACA blade has been found to have the best performance amongst the various cases that have been analyzed. The key findings of this research work are as follows: The radial component of the surface area of the blade is a key contributor to the magnitude of the radial forces acting on the blade. The radial pressure gradient is responsible for bending the streamlines. For wind turbines which operate at low wind speeds, this circumferentially averaged radial pressure gradient term depends on the blockage effect. 83

100 The axial induction factor depends on the streamtube area which, in turn, depends on how much the streamlines are bent by the blade. The axial induction factor influences the effective angle of attack seen by the blade sections. An increase in the streamtube area by 1.96% results in an increase in power output by 5.661%. The NACA blade has a power output that is % higher than the NACA 2420 blade Future Work An exact mathematical relation needs to be developed between the radial variation of the cross-sectional area and the axial induction factor. This will aid in desigining wind turbine blade geometries with high axial induction factors to extract the maximum possible power from the wind. The 3D force analysis code developed for this thesis can be used for a wide range of applications. The findings in this thesis are not only restricted to wind turbines but can also be applied to propellers, transonic fans, open rotors and other turbomachinery applications. 84

101 References [1] Dey, S., Wind turbine blade design system - aerodynamic and structural analysis. Master s thesis, University of Cincinnati, Cincinnati, OH, May. [2] Wikipedia [3] Manwell, J. F., McGowan, J. G., and Rogers, A. L., Wind energy explained : Theory, design and application. Wind Energy. John Wiley and Sons, Inc., 1st edition, 111 River Street,Hoboken, NJ [4] Siddappaji, K., Turner, M. G., Dey, S., Park, K., and Merchant, A., Optimization of a 3-stage booster- part 2: The parametric 3d blade geometry modeling tool. In ASME GT2011, no [5] John D Anderson, J., Fundamentals of Aerodynamics. McGraw-Hill. [6] Maughmer, M. D., The design of winglets for high-performance sailplanes. Tech. Rep. 2406, AIAA. [7] Drela, M., and Youngren, H. XFOIL- Subsonic Airfoil Development System - [8] Giguere, P., and Selig, M. S., Design of a tapered and twisted blade for the nrel combined experiment rotor. Tech. Rep. SR , NREL. [9] Appalachian State University - North Carolina Wind Energy [10] National Renewable Energy Laboratory [11] Betz, A., Windenergie und ihre ausnutzung durch wind-muhlen:vandenhoeckund ruprecht. [12] World wind energy association world wind energy report Website 85

102 [13] Wilson, R. E., and Lissaman, P. B. S., Applied aerodynamics of wind power machine. Oregon State University. [14] Wilson, R. E., Lissaman, P. B. S., and Walker, S. N., Aerodynamics performance of wind. Tech. Rep. ERDA/NSF/ /1, Energy Research and Development Administration. [15] Wilson, R. E., Walker, S. N., and Heh, S. N., Technical and user manual for the fast-ad advanced dynamics code. Tech. Rep , Oregon State University, OSU/NREL. [16] Vries, O. D., Fluid dynamic aspects of wind energy conversion. advisory group for aerospace research and development. Tech. Rep. AGARD-AG-243, North Atlantic Treaty Organization. [17] Hansen, A. C., and Butterfield, C. P., Aerodynamics of horizontal-axis wind turbines. Tech. Rep. 1993:25:115-49, Annual Rev.Fluid Mech. [18] Hansen, A. C., Yaw dynamics of horizontal axis wind turbines. Tech. Rep. Final Report Sub-Contract No.XL , SERI Report. [19] M L Buhl, J., Wt-Pref users guide. NREL,Boulder CO. [20] Johansen, J., and Sorensen, N. N., Numerical analysis of winglets on wind turbine blades using cfd. Tech. Rep. Riso-R-1543-EN, Riso National Laboratory, Technical University of Denmark. [21] Whitcomb, R., Jul, A design approach and selected wind-tunnel results at high subsonic speeds for wing-tip mounted winglets. Tech. Rep. TN D-8260, NASA. [22] Braaten, M. E., and Gopinath, A., Aero-structural analysis of wind turbine blades with sweep and winglets: Coupling a vortex line method to adams/aerodyn. Tech. Rep. GT pp , ASME 2011 Turbo Expo: Turbine Technical Conference and Exposition - GT2011. [23] Shimooka, M., Iida, M., and Arakawa, C., Basic study of winglet effects on aerodynamics and aeroacoustics using large-eddy simulation. In European Wind Energy Conference, no. Session Code: BT4. [24] Gaunaa, M., and Johansen, J., Determination of the maximum aerodynamic efficiency of wind turbine rotors with winglets. In Journal of Physics, no [25] Dixon, S. L., Fluid mechanics and thermodynamics of turbomachinery. Elsevier Butterworth Heinman. 86

103 [26] Glauert, H., The Elements of Aerofoil and Airscrew Theory. Cambridge University Press. [27] Drela, M., QPROP Formulation. MIT, Cambridge, MA. [28] Larrabee, E. E., and French, S. E., Minimum induced loss windmills and propellers. In Journal of Wind Engineering and Industrial Aerodynamics. [29] Goldstein, S., On the vortex theory of screw propellers. In Royal Society. [30] Theodorsen, T., Theory of Propellers. McGraw-Hill. [31] Numeca. [32] Numeca User Manuals. [33] Smith, L. H., and Yeh, H., Sweep and dihedral effects in axial turbomachinery. Tech. Rep. Basic Engineering 85, pp , ASME. [34] Denton, J. D., The effect of lean and sweep on transonic fan performance: A computational study. Tech. Rep. Task Quarterly 6 No 1 (2001), Whittle Laboratory Cambridge University, July. [35] Somers, D. M., Design and experimental results for the s809 airfoil. Tech. Rep. SR , National Renewable Energy Laboratory. [36] Jacobs, E. N., Ward, K. E., and Pinkerton, R. M., The characteristics of 78 related airfoil sections from tests in the variable-density wind tunnel. Tech. Rep. 460, NACA. [37] Novak, R. A., Streamline curvature computing procedures for fluid-flow problems. In Journal of Engineering for Power, ASME. [38] L H Smith, J., The radial-equilibrium equation of turbomachinery. In Journal of Engineering for Power, ASME. 87

104 Appendix A BEM Blade Design Code %%%%%%%%%%%%%%%%% BEM Design Code %%%%%%%%%%%%%%%%% load DESARRAYS.mat R = 5; %meters - Blade radius ns = 30; %Number of sections Xle = [Leading edge x points in r-x plane]; alpha = 8 %Design angle of attack - degrees i = 1:ns; Vz = 7; %m/s Wind velocity r = linspace(0,r,ns); Lambda = 8; %Tip-speed ratio Lambdar(i) = Lambda*[(r(i))/R]; %Local tip-speed ratio U(i) = Lambdar(i)*Vz; %Local wheel speed x(i) = Vz.^2; y(i) = U(i).^2; z(i) = x(i)+y(i); w(i) = z(i).^0.5; %Local relative wind velocity Mrel(i) = w(i)./340; beet(i) = U(i)./Vz; Beta(i) = atan(beet(i)); BETA(i) = rad2deg(beta(i)); %Blade inlet angle L = 1./Lambdar; T(i) = atan(l(i)); 88

105 Phi(i) = (2/3)*T(i); PHI(i) = rad2deg(phi(i)); %Relative flow angle a(i) = [(8*pi*r(i))/(B*0.92)]; b(i) = (1-cos(Phi(i))); c = a.*b; %meters - Chord TWIST(i) = PHI(i)-alpha; Twist(i) = deg2rad(twist(i)); STAGGER(i) = 90-TWIST(i); Stagger(i) = deg2rad(stagger(i)); caxial(i) = cos(stagger(i)).*c(i); caxialnd(i) = caxial(i)./r; cactualnd(i) = c(i)./r; cactualnd_3dbgb(i) = c(i)./r(i); %Non-dimensionalizing using local radius Xte = Xle + caxialnd; %Trailing edge x points in r-x plane grid on plot (r/r,phi); title('relative Flow Angle vs. Radius'); ylabel('phi (deg)'); xlabel('r/r'); figure plot (r/r,twist); title('twist vs. Radius'); ylabel('twist (deg)'); xlabel('r/r'); figure plot (r/r,c); title('chord vs. Radius'); ylabel('chord (m)'); xlabel('r/r'); figure plot (r/r,caxial); title('axial Chord vs. Radius'); ylabel('axial Chord (m)'); xlabel('r/r'); figure plot (Xle,r/R,Xte,r/R); title('xleading edge & Xtrailing edge'); ylabel('r/r'); xlabel('x'); 89

106 Appendix B 3DBGB Input Files 90

107 B.1 NREL Original Blade Input parameters ( version 1.0 ) nrel Blade row # : 1 Number of blades in this row : 2 Blade Scaling factor (mm ) : Number of streamlines : 30 Non dimensional Actual chord (0=no,1=yes ) : 1 91 J in_beta out_beta mrel_in chord t / c_max Incidence Deviation Sec. Flow Angle

108 LE / TE curve (x, r ) definition : Number of Curve points : 30 xle rle xte rte

109 Airfoil type{bf1 (sect1 ) + bf2 (sect2 ) +... } : J type 1 s809m 2 s809m 3 s809m 4 s809m 5 s809m 6 s809m 7 s809m 8 s809m 9 s809m 10 s809m 11 s809m 12 s809m 13 s809m 14 s809m 15 s809m 16 s809m 17 s809m 18 s809m 19 s809m 20 s809m 21 s809m 22 s809m 23 s809m 24 s809m 25 s809m 26 s809m 27 s809m 28 s809m 29 s809m 30 s809m Control table for blending section variable :

110 5 0 0 span bf1 bf E Stacking axis as a fraction of chord(2.=centroid ) : Control points for delta_m : 6 span delta_m E E E E E Control points for delta_theta : 5 span delta_theta E E E E E E+000 Control points for in_beta * : 5 span in_beta* E E E E E E+000 Control points for out_beta * :

111 5 span out_beta* E E E E E E+000 Control points for chord : 5 span chord E E E E E E Control points for tm / c : 5 span tm / c E E E E E E+000 Hub offset E+000 Tip offset E+000 Streamline Data x_s r_s

112

113

114

115

116

117

118

119

120 B.2 NREL - Downstream Winglet Input parameters ( version 1.0 ) nrel Blade row # : 1 Number of blades in this row : 2 Blade Scaling factor (mm ) : Number of streamlines : 31 Non dimensional Actual chord (0=no,1=yes ) : J in_beta out_beta mrel_in chord t / c_max Incidence Deviation Sec. Flow Angle

121 LE / TE curve (x, r ) definition : Number of Curve points : 31 xle rle xte rte

122 Airfoil type{bf1 (sect1 ) + bf2 (sect2 ) +... } : J type 1 s809m 2 s809m 3 s809m 4 s809m 5 s809m 6 s809m 7 s809m 8 s809m 9 s809m 10 s809m 11 s809m 12 s809m 13 s809m 14 s809m 15 s809m 16 s809m 17 s809m 18 s809m 19 s809m 20 s809m 21 s809m 22 s809m 23 s809m 24 s809m 25 s809m 26 s809m 27 s809m 28 s809m 29 s809m 30 s809m

123 31 s809m Control table for blending section variable : span bf1 bf E Stacking axis as a fraction of chord(2.=centroid ) : Control points for delta_m : 6 span delta_m E E E E E Control points for delta_theta : 6 span delta_theta E E E E E Control points for in_beta * : 5 span in_beta* E E E E+000

124 E E+000 Control points for out_beta * : 5 span out_beta* E E E E E E Control points for chord : 5 span chord E E E E E E+000 Control points for tm / c : 5 span tm / c E E E E E E+000 Hub offset E+000 Tip offset E+000 Streamline Data same as NREL case.

125 B.3 NREL - Constant Chord Input parameters ( version 1.0 ) nrel Blade row # : 1 Number of blades in this row : 2 Blade Scaling factor (mm ) : Number of streamlines : 31 Non dimensional Actual chord (0=no,1=yes ) : J in_beta out_beta mrel_in chord t / c_max Incidence Deviation Sec. Flow Angle

126 LE / TE curve (x, r ) definition : Number of Curve points : 31 xle rle xte rte

127 Airfoil type{bf1 (sect1 ) + bf2 (sect2 ) +... } : J type 1 s809m 2 s809m 3 s809m 4 s809m 5 s809m 6 s809m 7 s809m 8 s809m 9 s809m 10 s809m 11 s809m 12 s809m 13 s809m 14 s809m 15 s809m 16 s809m 17 s809m 18 s809m 19 s809m 20 s809m 21 s809m 22 s809m 23 s809m 24 s809m 25 s809m 26 s809m 27 s809m 28 s809m 29 s809m 30 s809m

128 31 s809m Control table for blending section variable : span bf1 bf E Stacking axis as a fraction of chord(2.=centroid ) : Control points for delta_m : 6 span delta_m E E E E E Control points for delta_theta : 6 span delta_theta E E E E E Control points for in_beta * : 5 span in_beta* E E E E+000

129 E E+000 Control points for out_beta * : 5 span out_beta* E E E E E E Control points for chord : 5 span chord E E E E E E+000 Control points for tm / c : 5 span tm / c E E E E E E+000 Hub offset E+000 Tip offset E+000 Streamline Data same as NREL case.

130 B.4 NACA Input parameters ( version 1.0 ) nrel Blade row # : 1 Number of blades in this row : 2 Blade Scaling factor (mm ) : Number of streamlines : 30 Non dimensional Actual chord (0=no,1=yes ) : J in_beta out_beta mrel_in chord t / c_max Incidence Deviation Sec. Flow Angle

131 LE / TE curve (x, r ) definition : Number of Curve points : 30 xle rle xte rte

132 Airfoil type{bf1 (sect1 ) + bf2 (sect2 ) +... } : J type

133 Control table for blending section variable : span bf1 bf E Stacking axis as a fraction of chord(2.=centroid ) : Control points for delta_m : 6 span delta_m E E E E E Control points for delta_theta : 6 span delta_theta E E E E E Control points for in_beta * : 5 span in_beta* E E E E E E+000

134 Control points for out_beta * : 5 span out_beta* E E E E E E+000 Control points for chord : 5 span chord E E E E E E Control points for tm / c : 5 span tm / c E E E E E E+000 Hub offset E+000 Tip offset E+000 Streamline Data same as NREL case.

135 B.5 NACA Input parameters ( version 1.0 ) nrel Blade row # : 1 Number of blades in this row : 2 Blade Scaling factor (mm ) : Number of streamlines : 30 Non dimensional Actual chord (0=no,1=yes ) : J in_beta out_beta mrel_in chord t / c_max Incidence Deviation Sec. Flow Angle

136 LE / TE curve (x, r ) definition : Number of Curve points : 30 xle rle xte rte

137 Airfoil type{bf1 (sect1 ) + bf2 (sect2 ) +... } : J type

138 Control table for blending section variable : span bf1 bf E Stacking axis as a fraction of chord(2.=centroid ) : Control points for delta_m : 6 span delta_m E E E E E Control points for delta_theta : 6 span delta_theta E E E E E Control points for in_beta * : 5 span in_beta* E E E E E E+000

139 Control points for out_beta * : 5 span out_beta* E E E E E E+000 Control points for chord : 5 span chord E E E E E E Control points for tm / c : 5 span tm / c E E E E E E+000 Hub offset E+000 Tip offset E+000 Streamline Data same as NREL case.

140 B.6 NACA Input parameters ( version 1.0 ) nrel Blade row # : 1 Number of blades in this row : 2 Blade Scaling factor (mm ) : Number of streamlines : 30 Non dimensional Actual chord (0=no,1=yes ) : J in_beta out_beta mrel_in chord t / c_max Incidence Deviation Sec. Flow Angle

141 LE / TE curve (x, r ) definition : Number of Curve points : 30 xle rle xte rte

142 Airfoil type{bf1 (sect1 ) + bf2 (sect2 ) +... } : J type

143 Control table for blending section variable : span bf1 bf E Stacking axis as a fraction of chord(2.=centroid ) : Control points for delta_m : 6 span delta_m E E E E E Control points for delta_theta : 6 span delta_theta E E E E E Control points for in_beta * : 5 span in_beta* E E E E E E+000

144 Control points for out_beta * : 5 span out_beta* E E E E E E+000 Control points for chord : 5 span chord E E E E E E Control points for tm / c : 5 span tm / c E E E E E E+000 Hub offset E+000 Tip offset E+000 Streamline Data same as NREL case.

145 B.7 NACA PS Input parameters ( version 1.0 ) nrel Blade row # : 1 Number of blades in this row : 2 Blade Scaling factor (mm ) : Number of streamlines : 30 Non dimensional Actual chord (0=no,1=yes ) : J in_beta out_beta mrel_in chord t / c_max Incidence Deviation Sec. Flow Angle

146 LE / TE curve (x, r ) definition : Number of Curve points : 30 xle rle xte rte

147 Airfoil type{bf1 (sect1 ) + bf2 (sect2 ) +... } : J type

148 Control table for blending section variable : span bf1 bf E Stacking axis as a fraction of chord(2.=centroid ) : Control points for delta_m : 6 span delta_m E E E E E Control points for delta_theta : 6 span delta_theta E E E E E Control points for in_beta * : 5 span in_beta* E E E E E E+000

149 Control points for out_beta * : 5 span out_beta* E E E E E E+000 Control points for chord : 5 span chord E E E E E E Control points for tm / c : 5 span tm / c E E E E E E+000 Hub offset E+000 Tip offset E+000 Streamline Data same as NREL case.

150 B.8 NACA SS Input parameters ( version 1.0 ) nrel Blade row # : 1 Number of blades in this row : 2 Blade Scaling factor (mm ) : Number of streamlines : 30 Non dimensional Actual chord (0=no,1=yes ) : J in_beta out_beta mrel_in chord t / c_max Incidence Deviation Sec. Flow Angle

151 LE / TE curve (x, r ) definition : Number of Curve points : 30 xle rle xte rte

152 Airfoil type{bf1 (sect1 ) + bf2 (sect2 ) +... } : J type

153 Control table for blending section variable : span bf1 bf E Stacking axis as a fraction of chord(2.=centroid ) : Control points for delta_m : 6 span delta_m E E E E E Control points for delta_theta : 6 span delta_theta E E E E E Control points for in_beta * : 5 span in_beta* E E E E E E+000

154 Control points for out_beta * : 5 span out_beta* E E E E E E+000 Control points for chord : 5 span chord E E E E E E Control points for tm / c : 5 span tm / c E E E E E E+000 Hub offset E+000 Tip offset E+000 Streamline Data same as NREL case.

155 Appendix C NUMECA Fine/Turbo Tutorial for Wind Turbine C.1 Grid Generation Numeca s F ine/t urbo T M package includes a gridding module called AutoGrid. This is a very useful tool for quick grid generation. A step by step guide to meshing wind turbine blades using AutoGrid is presented here. 1. Open F ine/t urbo T M and in the Module menu select AutoGrid5. 139

156 2. In the AutoGrid window, import the required blade geomturbo file, which is the native format of AutoGrid, using the Impory Geometry File option in the Geometry Definition menu. Geometries can also be imported from CAD using the Import and Link CAD option. 3. Select the geomturbo file and click OK 140

157 4. In the Row Definition menu click on the + sign before row 1 to get the drop down list. Right click on Main Blade and select Check Geometry. Click on Check to make sure the geometry definition is Ok. Select Data Reduction if prompted to do so. 5. Click on Wizard Mode from the drop down menu on the top-right corner and then click on Row Mesh Wizard. Check the row definition in the prompt box and make sure that the geometry is Ok. Click Next. 141

158 6. Select the Wind Turbine option. Enter the number of blades, the RPM, select Rotor and click Next. 7. Enter the Blade Tip R Value, Farfield Zmin and Farfield Zmax Values and click Next. 8. Enter the Spanwise Grid Point Number, Percentage Constant Cell value, Cell Width at Hub, 142

159 Cell Width at Shroud and click Next. 9. Enter the farfield Spanwise Grid Point Number, Percentage Constant Cell value, Farfield R value and click Next. wizard. 10. Click on Preview B2b to see the Blade to Blade mesh. Click Finish to complete the row mesh 11. In order to avoid any negative cells certain changes have to be done in the expert mode. Select Expert Mode from the drop down menu on the top-right corner. In the Mesh Control menu open the Row Mesh Control sub-menu. Change the Flow Paths Number to 125 or a higher value depending on the desired grid quality. Change Spanwise Interpolation to

160 12. Click on Flow Paths Control. Change the Percentage of Mid-Flow Cells to 70 and click Generate. 13. Click on the B2B Mesh Topology Control. Click on Topology, select Wind Turbine (W T ) and click Ok. 14. In the Row Definition menu, right click on Main Blade and select Expand Geometry. Select Stick Leading and Trailing Edge and click Apply. 144

161 15. In the Row Definition menu, right click on row 1 far field and click on Edit. Unselect the Radial Expansion and Periodic Full Non Matching options. Then click Clost Edition Mode on the top-right corner. 16. Click on Generate B2B to create the Blade to Blade mesh. Once the mesh is generated the mesh at desired span locations can be viewed by changing the Active Layer value in the Active B2B Layer menu. 145

162 17. If the Spanwise Expansion Ratio is high, an error will appear in the bottom of the screen. In the Row Mesh Control menu click on B2B Mesh Topology Control and click on Mesh. Reduce the Expanstion Ratio and generate B2B mesh again. 146

163 18. Once the B2B mesh is generated without any errors, the 3D mesh can be generated. Click on Select All in the Rows Definitions menu and then click on Generate 3D button on the top-right corner. Once the 3D mesh is generated a quality report will be generated. Make sure there are no negative cells and save the project. 147

164 C.2 CFD Analysis using Fine/Turbo 1. Open a saved project or create a new project from the Project Selection dialog box. 148

165 2. Select the IGG file created using AutoGrid from the file selection box near the Play button. Select the units and coordinate system and click Ok. 3. Select the fluid from the Fluid Model sub-menu in the Configuration drop down menu. 4. Set up the model for the flow simulation using the Flow Model sub-menu. 149

166 5. Group the rotating blade blocks together and the rotating far field blocks together and specify the RPM for both the groups in the Rotating Machinery sub-menu. 6. The optional Transition Model for the blade can be setup from the Optional Models menu. The Abu-Ghanam-Shaw model (AGS) is selected for the wind turbine cases. 150

167 7. The boundary conditions are specified from the Boundary Conditions menu. By clicking on the IGG button from the menu bar the boundary conditions for each block can be accessed and edited. The rotating periodic boundary conditions are specified in the Periodic tab. The solid boundary conditions for the blade and hub are specified in the Solid tab. Euler condition can be imposed on the hub using the Expert mode. External boundary conditions are specified in the External tab. The external Vz and corresponding static pressure and temperature are specified. 151

168 8. The CFL number and grid level are specified in the Numerical Model menu. The grid level can be coarse grid, medium grid or fine grid. Pre-conditioning parameter options are Hakimi and Merkle. The Merkle option is selected for wind turbine case. 9. The initial conditions are specified in the Initial Solution menu. The initial conditions can either 152

169 be manually entered using the Constant Values button or by specifying a previous.run file using the From File button. 10. The required output variables are specified in the Outputs menu. Area or mass averaged variables can be specified in the Azimuthal Averaged Variables sub-menu. 11. The computation parameters such as number of iterations and precision are entered in the Con- 153

170 trol Variables sub-menu under the Computational Steering menu. By changing to Expert Mode the expert parameters can be changed. For the wind turbine case the expert parameter - IVELSY is set to 0 - Equations are solved for Absolute Velocities in Relative System. The parameter IFRCTO is set to 2 to get partial force and torque outputs in the.wall file. The parameter CFFNMB is set to 0 - Old implementation for FNMB connection. 12. The EURANUS flow solver can be started by clicking on the Play button in the menu bar. Once the solution is done the convergence history can be viewed from the Convergence History sub-menu. 154