2011fall-t2-wingletsforwindturbinerotorblades

EML 4905 SENIOR DESIGN PROJECT

A B.S. THESIS PREPARED IN PARTIAL FULFILLMENT OF THE

REQUIREMENTS FOR THE DEGREE OF BACHELOR OF SCIENCE

IN MECHANICAL ENGINEERING

Winglet Design and Analysis for Wind Turbine Rotor Blades 100% Report

Rinaldo Gonzalez Galdamez Diego Moreno Ferguson

Juancarlo Rodriguez Gutierrez

Advisor: Professor George Dulikravich Professor Igor Tsukanov

November 30, 2011

This B.S. thesis is written in partial fulfillment of the requirements in EML 4905. The contents represent the opinion of the authors and not the Department of

Mechanical and Materials Engineering.

Design Optimization of Winglets for Wind Turbine Rotor Blades R.G. Galdamez, D. Moreno, J. Rodriguez

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Ethics Statement and Signatures

The work submitted in this B.S. thesis is solely prepared by a team consisting of RINALDO GONZALEZ GALDAMEZ, DIEGO MORENO FERGUSON, and JUANCARLO RODRIGUEZ GUTIERREZ and it is original. Excerpts from others’ work have been clearly identified, their work acknowledged within the text and listed in the list of references. All of the engineering drawings, computer programs, formulations, design work, prototype development and testing reported in this document are also original and prepared by the same team of students.

Rinaldo Gonzalez Galdamez Diego Moreno Ferguson Juancarlo Rodriguez Gutierrez

Team Member Team Member Team Member

Dr. George Dulikravich

Dr. Igor Tsukanov

Faculty Advisor

Faculty Advisor


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Table of Contents

1 Introduction ........................................................................................................................... 11 1.1 Problem Statement ......................................................................................................... 11 1.2 Motivation ...................................................................................................................... 12 1.3 Literature Survey ............................................................................................................ 12

1.3.1 Introduction to Wind Turbines................................................................................ 12 1.3.2 Modern Wind Turbine Design ................................................................................ 17 1.3.3 Wind turbine aerodynamics .................................................................................... 20 1.3.4 Wind turbine loads and structure ............................................................................ 37

2 Conceptual design ................................................................................................................. 45 2.1 Winglet design................................................................................................................ 45 2.2 Airfoils and blade geometry ........................................................................................... 47

3 Design components ............................................................................................................... 50 3.1 Theoretical Design ......................................................................................................... 51

3.1.1 Blade pitch angle..................................................................................................... 51 3.1.2 Blade twist angle ..................................................................................................... 51 3.1.3 Chord distribution ................................................................................................... 51

3.2 Proposed Initial Design .................................................................................................. 51 4 Final Design .......................................................................................................................... 63

4.1 Blade Design with Winglet ............................................................................................ 63 4.1.1 Sizing and parameters ............................................................................................. 63

4.2 Parameterization of Design ............................................................................................ 63 4.2.1 Cant angle ............................................................................................................... 63 4.2.2 Radius (Percentage of Height) ................................................................................ 64 4.2.3 Height ...................................................................................................................... 64 4.2.4 Randomization of Geometries ................................................................................ 64

4.3 Final CAD design ........................................................................................................... 65 4.4 Winglet Implementation ................................................................................................. 69

5 CFD simulations ................................................................................................................... 72 5.1 CFD modeling and setup in ANSYS Fluent .................................................................. 72

5.1.1 Pre-processing ......................................................................................................... 72 5.1.2 Domain decomposition ........................................................................................... 74 5.1.3 Boundary conditions ............................................................................................... 76 5.1.4 Turbulence modeling .............................................................................................. 77 5.1.5 Results of CFD simulations .................................................................................... 79

6 Timeline and Team Responsibilities ..................................................................................... 92 7 Prototype, Testing and Cost Analysis ................................................................................... 94

7.1 Wind tunnel testing ........................................................................................................ 94 7.1.1 Calculation of parameters and scaling for wind tunnel testing ............................... 96


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7.2 Materials ......................................................................................................................... 97 7.3 Prototype Design ............................................................................................................ 99 7.4 Prototype Assembly Costs ........................................................................................... 103 7.5 FEA study for prototype prior to wind tunnel testing .................................................. 104

7.5.1 FEA Results .......................................................................................................... 110 7.6 Test Results .................................................................................................................. 116

8 Conclusions and Recommendations ................................................................................... 118 9 Acknowledgements ............................................................................................................. 119 References ................................................................................................................................... 120 Appendix A: Technical Drawings for Wind Turbine ................................................................. 122 Appendix B: Vestas V39 Technical specifications ..................................................................... 123 Appendix C: Material and Supplies Quotes................................................................................ 124 Appendix D: Technical Drawings for Prototype ........................................................................ 125 Appendix E: Data from Testing .................................................................................................. 126

Results for test with winglets .................................................................................................. 126 Results for test without winglets ............................................................................................. 127


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Table of Figures

Figure 1: Vortices created for airplane wings with and without winglets[3] ............................... 11Figure 2: Smith-Putnam Wind Turbine[12] .................................................................................. 13Figure 3: Gedser Wind Turbine (Johannes Juul and the Vester Egesborg Turbines)[13] ............ 13Figure 4: (a) NASA MOD-0 Turbine, (b) Boeing MOD-5B Turbine[14] ................................... 14Figure 5: Budget history for the DOE Wind Power Program. Source: DOE-EERE.[16] ............ 14Figure 6: Budget breakdown for DOE Wind Power Program udget FY2010.[16] ...................... 15Figure 7: Current installed power capacity (MW). Source: DOE-EERE[17] .............................. 15Figure 8: System integration for wind power plan 2030. Source: DOE-EERE [1]. ..................... 16Figure 9: Projected installed capacity by state for 2030. Source: DOE-EERE [1]. ...................... 16Figure 10: Offshore wind turbines (REpower M5 turbines)[18] .................................................. 17Figure

11: (a) Components of a horizontal axis wind turbine, (b) Detailed view of components.

Source: DOE-EERE.[19],[20]. ..................................................................................................... 18Figure

12: Gearbox, rotor shaft and brake assembly being installed in a horizontal axis wind

turbine[18]..................................................................................................................................... 18Figure 13: Actuator Disc Concept[11] .......................................................................................... 20Figure 14: Stream tube defined by actuator disc[11] .................................................................... 21Figure 15: Coefficients of Power and Thrust vs. Axial Induction Factor ..................................... 23Figure

16: Path of a particle of air traveling through the rotor disc, subject to tangential

moment[11] ................................................................................................................................... 24Figure 17: Development of tangential velocity in rotor disc (Thickness)[11].............................. 24Figure 18: Blade Element Velocities and Forces [11] .................................................................. 26Figure 19: Power Coefficient vs. Tip Speed Ratio[11] ................................................................. 29Figure 20: Span-wise Variation of the Blade Geometry Parameter with and without Drag[11] .. 31Figure 21: Variation of Inflow Angle with Local Speed Ratio with and without Drag[11] ......... 31Figure 22: The Variation of Coefficient of Power with Design Tip Speed Ratios[11] ................ 32Figure 23: Helical Trailing Tip Vortices[11] ................................................................................ 33Figure 24: A helicoidal Vortex Sheet[11] ..................................................................................... 34Figure

25: Variation of Coefficient of Power with Design Tip Speed Ratios for Various L/D

ratios[11] ....................................................................................................................................... 36Figure 26: Separated Flow Pressure Distribution Around a Cylinder[11] ................................... 36Figure 27: Components of a blade[10] ......................................................................................... 38Figure 28: Structural parameters for a cross section of the blade. Reproduced from [10]. .......... 38Figure 29: Blade section and reference axes. Reproduced from [10]. .......................................... 39Figure 30: Cantilever beam analysis. Reproduced from [10]. ...................................................... 40Figure 31: Loading caused by the Earth's Gravitational Field[10] ............................................... 42Figure 32: Loading caused by Braking the Rotor[10] .................................................................. 43Figure 33: Effect of coning the rotor[10] ...................................................................................... 44Figure 34: Parameters describing winglet geometry [6]. .............................................................. 45


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Figure 35: Winglets with different curvature radius [7] ............................................................... 46Figure 36: Winglets with different sweep angles [7] .................................................................... 47Figure 37: Winglets with different height [7] ............................................................................... 47Figure 38: Blade profiles from NACA 63-430 and FFA-W3-301[9]. .......................................... 48Figure 39: NREL airfoils for small sized blades[22] .................................................................... 49Figure 40: NREL airfoils for medium sized blades[22] ............................................................... 49Figure 41: NREL airfoil family for large blades[22] .................................................................... 52Figure 42: Airfoil configuration plotted in Qblade ....................................................................... 52Figure 43: Design of the blade in Qblade ..................................................................................... 55Figure 44: Plot of Coefficient of Lift (Cl) vs. Angle of Attack (alpha) ........................................ 55Figure 45: Plot of Coefficient of Lift (Cl) vs. Coefficient of Drag (Cd) ...................................... 56Figure 46: Plot of Cl/Cd vs. Angle of Attack (alpha) ................................................................... 56Figure 47: Plot of Twist angle vs. Blade length............................................................................ 57Figure 48:Front view of blade without winglet ............................................................................ 57Figure 49: Isometric view of blade without winglet ..................................................................... 58Figure 50: Side view of blade without winglet ............................................................................. 58Figure 51: Winglet, view 1 ........................................................................................................... 59Figure 52: Winglet, view 2 ........................................................................................................... 59Figure 53: Blade with winglet....................................................................................................... 60Figure 54: Blade with winglet, isometric view ............................................................................. 60Figure 55: Isometric view of nacelle ............................................................................................ 61Figure 56: Nacelle ......................................................................................................................... 61Figure 57: Isometric view of blade-nacelle assembly................................................................... 62Figure 58: Nacelle with three blades assembly............................................................................. 62Figure 59: Parameterization of winglet design ............................................................................. 64Figure 60: Final Blade with Stations ............................................................................................ 66Figure 61: Inserting Curves in SolidWorks .................................................................................. 66Figure 62: Curves in SolidWorks Front View .............................................................................. 67Figure 63: Curves in SolidWorks Isometric View ........................................................................ 67Figure 64: Loft of curves in SolidWorks ...................................................................................... 68Figure 65: Finalized Blade ............................................................................................................ 68Figure 66: Parameterization in SolidWorks .................................................................................. 69Figure 67: Equations set for parameterization of winglet ............................................................. 69Figure 68: Final Winglet Design................................................................................................... 70Figure 69: Winglet geometry parameterized in SolidWorks ........................................................ 70Figure 70: Blade final design with winglet isometric view .......................................................... 71Figure 71: Blade with winglet mounted on one third hub ............................................................ 71Figure 72: Airfoil twist for blade geometry .................................................................................. 72Figure 73: ANSYS Workbench project outline ............................................................................ 72Figure 74: ANSYS DesignModeler .............................................................................................. 73


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Figure 75: Named selections for left and right sides of the domain ............................................. 74Figure 76: Inlet and Outlet named selections ............................................................................... 75Figure 77: Wall blade named selections ....................................................................................... 75Figure 78: Boundary conditions implemented in ANSYS Meshing as named selections ............ 76Figure 79: Use of Periodic Boundaries to Define Swirling Flow in a Cylindrical Vessel ........... 77Figure 80: Plot for residuals .......................................................................................................... 79Figure 81: Statistics on parallel computations .............................................................................. 80Figure 82: Pressure contour plot on back of blade ....................................................................... 81Figure 83: Pressure contour plot in front of blade ........................................................................ 82Figure 84: Flow field for entire wind turbine ............................................................................... 82Figure 85: Vector plot around tip of blade without winglet showing vortices ............................. 83Figure 86: Symmetric flow conditions for all three blades ........................................................... 84Figure 87: Pressure contour in front of blade ............................................................................ 85Figure 88: Pressure contour for the back of the blade .................................................................. 85Figure 89: Pressure contour on leading edge of blade .................................................................. 86Figure 90: Pressure contour on proximity to winglet ................................................................... 86Figure 91: Pressure contour .......................................................................................................... 87Figure 92: Velocity contour plot behind blade ............................................................................. 87Figure 93: Velocity contour plot behind blades using symmetry planes ...................................... 88Figure 94: Velocity contour plot around blade airfoil close to root ............................................. 88Figure 95: Vector plot for velocity close to blade winglet ........................................................... 89Figure 96: Vector plot for velocity in the entire domain using symmetry.................................... 90Figure 97: Symmetric flow conditions for all three blades with winglet ..................................... 90Figure 98: Close up on vortices moving away from tip of blade by using winglets .................... 91Figure 99: Senior Design Project Gantt chart ............................................................................... 93Figure 100: Open Circuit Wind Tunnel ........................................................................................ 94Figure 101: Closed Circuit Wind Tunnel...................................................................................... 95Figure 102: Testing equipment circuit schematic[8]. ................................................................... 95Figure 103: Testing setup for scaled wind turbine[8] ................................................................... 96Figure 104: Prototype Wind Turbine .......................................................................................... 100Figure 105: T-Mount................................................................................................................... 100Figure 106: T-Mount and Blade Assembly ................................................................................ 101Figure 107: Parallax Stepper Motor ............................................................................................ 101Figure 108: Single Set Screw ...................................................................................................... 102Figure 109: Blade ........................................................................................................................ 102Figure 110: Hub .......................................................................................................................... 103Figure 111: Computational Domain for the Wind Turbine Prototype ........................................ 104Figure 112: SolidWorks CFD Study Settings ............................................................................. 105Figure 113: SolidWorks CFD Study Settings ............................................................................. 106Figure 114: CFD Study for the Prototype ................................................................................... 107


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Figure 115: CFD Study for the Prototype, Pressure Profile ....................................................... 108Figure 116: Fixed Components in Blade Prototype .................................................................... 109Figure 117: Mesh for Structural Analysis ................................................................................... 109Figure 118: Von Mises Stresses without Winglet Implementation ............................................ 110Figure 119: Deflection without Winglet Implementation ........................................................... 111Figure 120: Strain without Winglet Implementation .................................................................. 112Figure 121: Von Mises Stress with Winglet Implementation ..................................................... 113Figure 122: Displacement with Winglet Implementation ........................................................... 114Figure 123: Strain with Winglet Implementation ....................................................................... 115Figure 124: Average improvement ............................................................................................. 116Figure 125: Load vs. % Improvement ........................................................................................ 117


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List of Tables

Table 1: Winglet Design Parameter Ranges ................................................................................. 46 Table 2: Airfoils for blade design[22] .......................................................................................... 53 Table 3: Position of airfoils along length of the blade .................................................................. 53 Table 4: Parameters for blade design[23] ..................................................................................... 54 Table 5: Airfoil Station Distribution for Final Blade Design ....................................................... 65 Table 6: Airfoil Configuration ...................................................................................................... 65 Table 7: Final Winglet Parameters ............................................................................................... 70 Table 8: Breakdown of tasks for Senior Design Project ............................................................... 92 Table 9: Comparison of materials ................................................................................................. 98 Table 10: Technical specifications ................................................................................................ 99 Table 11: Cost of parts and supplies ........................................................................................... 103 Table 12: Max and Min Stresses, Displacement and Strains for No Winglet Configuration ..... 112 Table 13: Max and Min Stresses, Displacement and Strains for Winglet Configuration ........... 115 Table 14: Load vs. % Improvement ............................................................................................ 117


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Abstract

One of the major challenges in this new century is the efficient use of energy resources as well as the production of energy from renewable sources. Undoubtedly, researchers from around the world have shown that global warming has been caused in part by the greenhouse effect which is largely due to the use of fossil fuels for transportation and electricity. There are several alternative forms of energy that have already been explored and developed such as geothermal, solar, wind and hydroelectric power. Moreover, the advancement in renewable energy technologies has been possible thanks to the vast amount of research performed by scientists and engineers in order to make them more efficient and most importantly, more affordable. The affordability and performance of renewable energy technologies is the key to ensure the availability to the mass market.

Within the scope of this subject, the Mechanical Engineering Senior Design Project Team composed of Juancarlo Rodriguez, Rinaldo Gonzalez and Diego Moreno has decided to develop a project based on the design and analysis of winglets for wind turbine rotor blades. Winglets are wing tip devices commonly used in the aeronautical industry to reduce drag on airplanes. However, some investigations have shown that these winglets can be used in wind turbine blades in order to maximize the power produced using wind resources. This type of application in rotating machinery is a fairly recent subject and some research has been performed by scientists at the RISO National Laboratory in Denmark, a country for which wind power provides almost 20% of the electricity production.

The research project will involve the modeling of wind turbine winglets using computational fluid dynamics (CFD) with turbulent models integrated in the simulation in order to better account for the fluid forces and aerodynamic analysis of the winglet at the tip of the rotor blade. Some of the tasks developed for this project include:

• Design of blades with attached winglets in CAD software • CFD simulation of wind turbine winglet structures with turbulence model • Winglet design structural study using Finite Element Analysis (FEA) software • Prototype experimental wind tunnel testing (Embry Riddle Aeronautical University)

Once all the computational modeling and design is finished, the rotor blade and winglet will be printed in a rapid 3D prototype for testing procedures to be completed in a wind tunnel testing facility. It is expected that this project will give the students an excellent background capability on the use of high level computational modeling and design, comparable to the ones that research engineers perform in the aerospace industry. The project will serve as a stepping stone for other Senior Design Projects that involved CFD and FEM analysis as well as provide prestige to the FIU College of Engineering in such a new field of research.


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1 Introduction

1.1 Problem Statement

One of the major challenges in this century is the efficient use of energy resources as well as the growing production of energy from renewable sources. There are several alternative forms of energy that have been explored and developed such as geothermal, solar, wind and hydroelectric power. The affordability and performance of renewable energy technologies is the key to ensure the availability to the mass market.

The U.S. Department of Energy is aiming to expand the wind energy share in the U.S. energy mix. Currently 11.6 GW of power are installed and operational; with an expected growth the U.S. wind capacity will be at 305 GW, representing 20% of the nation’s power needs [1]. Hence, the development of enhanced and cost-effective components and technologies for this energy sector is critical for DOE to fulfill this mission.

Furthermore, there is an increasing concern about the environmental impact of wind turbines on wildlife, specifically bats. Biologists have shown that one major cause of bat death is due to barotraumas- tissue damage to air-containing structures caused by rapid or excessive pressure change [2]. Although bats have the ability of echolocation, hence they are able to detect and avoid the blades; they may be killed or incapacitated by pressure drops around the blades. This pressure differential is greater at the tip of the blade, just like for airplanes, vortices are formed. This phenomenon can be observed in Figure 1.

Figure 1: Vortices created for airplane wings with and without winglets[3]

Consequently, there is a need to explore the use of winglets for wind turbine rotor blades, which will help address an increase in performance and lower the environmental impact of wind power.


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1.2 Motivation

Wind energy presents several challenges in order to generate electricity. The uncertainty on the constant availability of wind resource, the dynamic loads on the rotor and other components of the wind turbine due to the variable wind speed, the aerodynamic efficiency of the turbine blades, and other constraints that have been shown in the use of this renewable technology. Some of these challenges have been addressed since the 1970’s and recently wind power has seen a growing investment in several countries [4].

Within this context, this B.S. thesis seeks to develop the design optimization of winglets for wind turbine rotor blades. Winglets are wing tip devices commonly used in the aeronautical industry to reduce drag on airplanes. However, some investigations have shown that these winglets can be used on wind turbine blades in order to maximize the power produced by the turbine by minimizing the vortex created at the tip of the blade, which in turn decreases drag [5],[6],[7][8],[9]. However, the previous referenced studies have not been comprehensive. The focuses of these published projects have been specific to numerical methods, computational fluid dynamics (CFD), experimental testing or structural analysis of winglets for wind turbines.

With the use of optimization algorithms, CFD, finite element analysis (FEA), and experimental testing; this thesis will provide an extensive and encompassing analysis in support of these recent research efforts.

1.3 Literature Survey

1.3.1 Introduction to Wind Turbines

Historically, the force of the wind has been harnessed in various different applications, most importantly for the propulsion of ships by the use of sails. This resource has also been used by windmills to grind grains or for agricultural irrigation. The use of wind turbines to generate electricity began by the late nineteenth century, when a 12 kW windmill generator was constructed by Brush in the United States and LaCour, in Denmark, started doing research in this field. However, with the invention of the steam engine and the growing use of fossil fuels, these technologies took a larger part in electricity generation [10].

However after the Second World War, the research and development of larger and more efficient wind turbines was pursued in countries such as Germany, France, United Kingdom, Denmark and the United States. One good example of this period is the 1250 kW Smith-Putnam wind turbine constructed in the United States in 1941. This turbine had a 53 m diameter, full-span pitch control and flapping blades designed to reduce loads on the structure. The blade spar failed in 1945, however it remained the largest wind turbine constructed for around 40 years [11].


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Figure 2: Smith-Putnam Wind Turbine[12]

There were several development efforts across the world, notably the Andrea Enfield 100 kW (U.K.) in the 1950s, the 200 kW Gedser turbine (Denmark) built in 1956 and the 1.1 MW turbine from EDF (France) that was tested in 1963. Also, there were several prototypes developed by Hutter in Germany for lightweight designs in the 1960s [11]. Despite of these numerous projects, there was little interest and investment in wind power until the 1973 oil crisis.

Figure 3: Gedser Wind Turbine (Johannes Juul and the Vester Egesborg Turbines)[13]

In the mid- 1970s, the U.S. Department of Energy (DOE) sponsored projects in an effort to develop alternative sources of energy. This led to the development of large machines, notably the 38 m diameter 100 kW NASA MOD-0 in 1975 up to the 3.2 MW 98 m diameter Boeing MOD-5B turbine. DOE also supported smaller projects such as a test facility in Rocky Flats, Colorado. It is important to state that notable progress did not start until the late 1970s. The U.S. Federal government passed the Public Utility Act of 1978 which required utilities to: (1) allow wind turbines to be connected to the electrical grid and (2) to pay the "avoided" cost for each kWh generated by the turbines and fed back to the grid


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Figure 4: (a) NASA MOD-0 Turbine, (b) Boeing MOD-5B Turbine[14]

Currently, the investment in wind power from DOE has increased from $54.37 million to $79.0 million between 2009 and 2010 [15]. Figure 4 shows the budget history for the wind power program, it can be observed that this increasing trend also corresponds for the period between 1990 to 2010. As it was also explained before, it can be observed that there was a budget increase in the late 1970s. It is important to state that the budget that the wind power program had for FY2010 is the largest amount that this project has ever achieved since 1975.

Figure 5: Budget history for the DOE Wind Power Program. Source: DOE-EERE.[16]


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Figure 6: Budget breakdown for DOE Wind Power Program udget FY2010.[16]

Figure 6 shows the pie chart for the breakdown of the wind power program budget, where it can be observed that 31% of the program's budget- the largest portion, is directed towards research and testing for new wind technologies[15]. There is also a significant amount of funding (25%) being directed towards systems integration. This increase in funding is in accordance with DOE's plan to increase the share of electricity production coming from wind power to 20% by the year 2030 [1]. Figure 7 shows the current installed wind power capacity across the United States. The states that have the largest number of installations are California, Oregon, Washington and Texas. There is also a significant capacity installed in Iowa with 3670 MW. The largest installations are in Texas with 9727 MW of wind power capacity.

Figure 7: Current installed power capacity (MW). Source: DOE-EERE[17]

Figure 8 shows the map of the necessary system integration and transmission lines that need to be implemented in order to achieve the wind power expansion plan by 2030.


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Figure 8: System integration for wind power plan 2030. Source: DOE-EERE [1].

Figure 9 shows the projected installed capacity by state for the 2030 plan. If Figure 7 and Figure 9 are compared, it can be seen that there are planned wind energy projects in the states of Florida, Georgia, South Carolina, and North Carolina amongst other states where there are currently no wind turbines installed. More in detail, it can be observed that some of these wind turbines will be installed in offshore locations, all along the East coast, from the central Florida to the New York and Connecticut. The state of Nevada is also projected to have new installations for wind power projects. In terms of total capacity, in 2006 there were only 11.6 GW installed in the U.S., the aim for 2030 will require an increase to 305 GW [1].

Figure 9: Projected installed capacity by state for 2030. Source: DOE-EERE [1].

It is also interesting to comment on the position of the U.S. in the international development of wind power. According to the 2010 Global Wind Statistics published by the Global Wind


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Energy Council, China leads with 21.8% of the worldwide wind capacity, the United States comes in a close second with 20.7 % whereas the nearest competitor is Germany with 14%. Moreover, for the year 2010, China can be attributed 46.1% of the new installed capacity, whereas the U.S. is behind with only 14.3%. It is clear that China is leading the way in the development of this renewable energy technology. Hence, these facts stress the importance of DOE's 2030 wind power plan [4].

This section provided a quick overview on the history of wind turbines, from its early development in Europe and the United States, as well as a review of the current status of the investments in wind power programs by the Department of Energy. It is interesting to also show the global perspective of this technology, where China is leading in this field with the largest capacity of installed wind power in the world. It is important for the United States to invest and continue the research and development (R&D) of technologies, methods or processes that will improve the efficiency and lower the cost of wind turbines.

1.3.2 Modern Wind Turbine Design

A wind turbine uses the aerodynamic force of the lift to rotate a shaft which in turn helps in the conversion of mechanical power to electricity by means of a generator. This differs from a simple windmill, which only considers the converts the wind's power to mechanical power. This mechanical work can be used for agricultural purposes such as grinding grains or irrigation procedures.

For large networks, modern wind turbines are connected to the grid and serve the purpose of reducing the total electrical load. It must be noted that the electrical output of a wind turbine is fluctuating since the wind resource is not found at constant input, the speed varies significantly.

The most common design of a wind turbine is the horizontal axis wind turbine (HAWT). The rotation axis is parallel to the ground as it can be observed in Figure 10.

Figure 10: Offshore wind turbines (REpower M5 turbines)[18]


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The major components of a HAWT are shown in Figure 11, for which the most important include:

The rotor: blades and hub Drive train: including shafts, gearbox, brake system and generator Nacelle: housing and yaw system Tower and foundation Electrical and control system

Figure 11: (a) Components of a horizontal axis wind turbine, (b) Detailed view of components. Source: DOE-EERE.[19],[20].

Figure 12: Gearbox, rotor shaft and brake assembly being installed in a horizontal axis wind turbine[18]

1.3.2.1 Rotor

The rotor consists of the hub and the blades for the wind turbine. These components are often considered the most important in terms of performance improvement and cost efficiency. Nowadays, most designs have three blades and some manufacturers have included pitch control for the angle of pitch (rotated blade) as it can be observed in Figure 11(b). Some intermediate


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sized turbines have fixed pitch, especially in Denmark [19]. The turbine blades are manufactured from composite materials including fiberglass reinforced plastic, epoxy and wood laminates.

1.3.2.2 Drive train

The drive train is composed of the rotating components of the wind turbine. As it can be observed in Figure 11, these include the low-speed and high-speed shaft, gearbox and the generator. Some smaller components are also included such as bearings and couplings. A gearbox is used in order to transfer the mechanical power from the low-speed shaft, which is connected to the rotor to a high-speed shaft which will have a suitable angular velocity (rpm) to drive a generator. It must be noted that due to the fluctuating nature of the wind, the structural loads are dynamic and loads vary on the components of the drive train.

1.3.2.3 Generator

The vast majority of wind turbines use induction generators. This type of generator operates at a slightly higher range of speeds than synchronous speed, such as a four-phase generator has a 1800 rpm in a 60 Hz grid. Induction generators are solid, inexpensive and easy to adapt to the electrical grid [19].

1.3.2.4 Nacelle

The nacelle includes the housing for the wind turbine interior components, as well as the yaw system. The housing cover helps protect the components from weather conditions. As it can be observed in Figure 11(b), the yaw system consists of a gear drive along with a motor. The purpose of this system is to rotate or control the orientation of the wind turbine with respect to the wind direction. The wind direction is specified by a sensor mounted outside, as the wind vane that can be seen in Figure 11(b). Figure 11 also shows the brake assembly which is used to keep the nacelle in the desired position.

1.3.2.5 Tower and foundation

Wind turbine towers are manufactured with steel tubes, truss or concrete towers. The ratio between rotor diameter and tower height is typically 1 to 1.5. It is to be noted that the tower height is also dependent on the geography and weather conditions of the site where it is installed. Moreover, the structural stiffness of the tower is of great importance due to induced vibrations from the rotor due to unsteady wind loads.


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1.3.2.6 Electrical and control system

The components related to this system are typically the following [19]:

Sensors for temperature, flow, current, voltage and wind speed.

Controllers for mechanical devices and computerized electrical components.

Power amplifiers: switches, pumps, valves, amplifiers.

Mechanical actuators: motors, pistons, and solenoids.

1.3.3 Wind turbine aerodynamics

1.3.3.1 Actuator disc concept

During the operation of a horizontal axis wind turbine, the properties of the wind flowing through are constantly changing in relation with the distance upstream or downstream the flow field. Far upstream from the turbine, a circular boundary region starts forming, giving a cylindrical shape to the flow field. Such boundary is marked by the rotor blades sweeping around the turbine axis, and it defines the so called actuator disc. This definition is graphically demonstrated in Figure 13.

Figure 13: Actuator Disc Concept[11]

The actuator disc is functionally defined as a device that extracts the kinetic energy from the wind and ideally transmits this power to a generator by means of a rotating shaft. Certain assumptions are made in the actuator disc concept, which are:

Incompressible flow

Irrotational flow

Steady uniform flow upstream of the disc

Steady uniform velocity at the disc


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The air flowing through the disc is contained within a stream duct

According to the continuity equation, mass flow rate along the stream-tube must remain constant. Moreover, velocity of air through a turbine gradually decreases; and pressure increases in order to maintain the same mass flow rate; thus the augmenting the cross sectional area of the stream-tube. According to Figure 14, in order to have balance between the upstream and downstream regions, the pressure in the wake region (downstream) is lower than atmospheric pressure and increases back again to atmospheric pressure far down in the free stream. The resultant of this is a change of kinetic energy, but no change in overall pressure [11].

Figure 14: Stream tube defined by actuator disc[11]

The mass of air passing through the cross section of the stream tube per unit time is ρAU, for which ρ is the density of air, A is the cross sectional area and U is the flow velocity.

𝜌𝐴∞𝑈∞ = 𝜌𝐴𝑑𝑈𝑑 = 𝜌𝐴𝑤𝑈𝑤 (1)

Where the subscripts ∞ denotes flow far upstream the actuator disc, d denotes flow properties at the actuator disc, and w denotes far wake.

Since air is considered incompressible, it should be understood that the cross sectional area of the disc varies as a function of flow velocity. This factor of variation is defined as the axial flow induction factor a, and the stream-wise component of this induced flow is given by -aU∞.

The net stream-wise velocity at the disk is given by

𝑈𝑑 = 𝑈∞(1 − 𝑎) (2)

The overall change in velocity U∞-UW multiplied by the mass flow rate represents the rate of change in momentum

𝑅𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 = (𝑈∞ − 𝑈𝑤)𝜌𝐴𝑑𝑈𝑑 (3)


Page | 22

The rate of change in momentum comes from the force caused by the change in pressure. This is the only force present in the flow field.

(𝑝𝑑+ − 𝑝𝑑−)𝐴𝑑 = (𝑈𝑑 − 𝑈𝑤) 𝜌𝐴𝑑𝑈∞(1 − 𝑎) (4)

The pressure difference between the front and the back of the disc if attained by implementing an appropriate form of Bernoulli’s equation, for upstream and downstream flow conditions, resulting in

(𝑝𝑑+ − 𝑝𝑑−) =

12𝜌(𝑈∞2 − 𝑈𝑤2 ) (5)

It is then deducted from combining equations 4 and 5 that

𝑈𝑤 = (1 − 2𝑎)𝑈∞ (6)

It can be observed from Equation (6) that half of the speed loss takes place in the upstream and the other half occurs downstream of the disc. By combining Equation (6) and Equation (4), the force becomes

𝐹 = (𝑝𝑑+ − 𝑝𝑑−)𝐴𝑑 = 2𝜌𝐴𝑑𝑈∞2 𝑎(1 − 𝑎) (7)

Power extracted from the wind is calculated using force and the air speed at the actuator disc, thus

𝑃𝑜𝑤𝑒𝑟 = 𝐹𝑈𝑑 = (𝑝𝑑+ − 𝑝𝑑−)𝐴𝑑 = 2𝜌𝐴𝑑𝑈∞3 𝑎(1 − 𝑎)2 (8)

Now, the coefficient of power is acquired by dividing the power extracted from the wind by the calculated available power in the air when the actuator disc is not present

𝐶𝑃 =𝑃𝑜𝑤𝑒𝑟

12𝜌𝑈∞

3 𝐴𝑑 (9)

𝐶𝑃 = 4𝑎(1 − 𝑎)2 (10)

Theoretically, the maximum value for the power coefficient is achieved for a = 1/3.

𝑑𝐶𝑃𝑑𝑎

= 4(1 − 𝑎)(1 − 3𝑎) = 0 (11)

Giving a power coefficient of

𝐶𝑃𝑚𝑎𝑥 =1627

= 0.593 (12)

This is known as the Betz limit, for which no wind turbine has achieved this value.. The reason being is not related to the performance of the turbine design, but to the approach used to obtain the coefficient. Perhaps, a fairer but not recognized definition of the coefficient of power would be


Page | 23

𝐶𝑃 =𝑃𝑜𝑤𝑒𝑟 𝑒𝑥𝑡𝑟𝑎𝑐𝑡𝑒𝑑𝑃𝑜𝑤𝑒𝑟 𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒

=𝑃𝑜𝑤𝑒𝑟

1627 (1

2𝜌𝑈∞3 𝐴𝑑)

(13)

A non-dimensionalized form of the force equation can be used to calculate the Coefficient of Thrust

𝐶𝑇 =𝑃𝑜𝑤𝑒𝑟

12𝜌𝑈∞

2 𝐴𝑑 (14)

𝐶𝑇 = 4𝑎(1 − 𝑎) (15)

When the axial induction factor a ≥ ½, the description given of the rate of change of momentum is no longer valid under the given conditions; thus, an empirical approach such as the rotor blade theory must be implemented. Figure 15 graphically demonstrates the behavior of CP and CT related to the axial induction factor a[11].

Figure 15: Coefficients of Power and Thrust vs. Axial Induction Factor

1.3.3.2 Rotor disc theory

Different ways of converting the energy extracted from the wind into usable energy are implemented in wind turbines. In horizontal axis wind turbines, the method used to convert wind energy to electrical power is referred to as the Rotor Disc Theory, which consists of a system of blades rotating about an axis parallel to the wind direction. The rotor disc produces torque which is then transferred to a generator through a shaft, where such torque is converted to electrical power. Such rotation incurs changes in the flow pressure and velocity as mentioned before, which make the rotor disc maintain a rotational speed Ω.

The induction of torque by the air in the rotor disc produces an equal and opposite torque in the air downstream, called wake rotation. Symmetrically within the thickness of the rotor disc, air being pushed by the blades in the rotation direction gain rotational momentum in the direction opposite to the rotation, generating a rotational motion in the air particles about the rotor axis. Such motion is responsible for the pressure drop downstream of the actuator disc, mentioned in the previous section.


Page | 24

The magnitude of the rotational momentum and of the tangential velocity of rotation is proportional to a radial distance r of the air particle from the axis of rotation, and to the rotational speed Ω. The term Tangential Flow Induction Factor (a’) is used to express the relation of rotational momentum and tangential velocity with the radial distance r.

Tangential velocity immediately downstream of the disc, at a distance r from the axis of rotation is equal to 2Ωra’, and in the middle of the disc is Ωra’. As particles travel radially downstream, axial force works against them and reduces their radial speed. Figure 16 explains the trajectory of particle of air traveling through the rotor disc, and Figure 17 shows in detail the development of the tangential velocity as blades cut through the air[11].

Figure 16: Path of a particle of air traveling through the rotor disc, subject to tangential moment[11]

Figure 17: Development of tangential velocity in rotor disc (Thickness)[11]

The torque at a radial distance r is calculated in the following manner

Torque = rate of change of angular momentum


Page | 25

= mass flow rate ×change of tangential velocity × radius

𝛿𝑄 = 𝜌𝛿𝐴𝑑𝑈∞(1 − 𝑎)2Ω𝑎′𝑟2 (16)

δAd represents the area of the circle or radius r, distance from the axis of rotation. The power on the shaft varies according to the tangential velocity Ω as follows

𝛿𝑃 = 𝛿𝑄Ω (17)

The power used in Equation (17) is the same power deduced by using Equation (8) in the previous section. Therefore

2𝜌𝛿𝐴𝑑𝑈∞3 𝑎(1 − 𝑎)2 = 𝜌𝛿𝐴𝑑𝑈∞(1− 𝑎)2Ω2𝑎′𝑟2 (18)

Resulting in

𝑈∞2 𝑎(1 − 𝑎) = Ω2𝑎′𝑟2 (19)

The local speed ratio 𝜆 = Ω𝑟/𝑈∞ is substituted into Equation (19), and when r = R (Edge radius), λ is known as the tip speed ratio

𝑎(1 − 𝑎) = 𝜆𝑟2𝑎′ (20)

Since the area of the circle with radius r distance from the axis of rotation is𝛿𝐴𝐷 = 2𝜋𝑟𝛿𝑟, the incremental shaft power on that area is

𝛿𝑃 = 𝛿𝑄Ω = (12𝜌𝑈∞3 2𝜋𝑟𝛿𝑟)4𝑎′(1− 𝑎)𝜆𝑟2 (21)

The term inside the parenthesis in Equation (21) refers to the power flux through the annulus; and the elements outside represent the efficiency of the blade in capturing the power from the air. Hence, recalling the definition of the power coefficient:

𝑑𝑑𝑟𝐶𝑃 = 8(1 − 𝑎)𝑎′𝜆2𝜇3 (22)

Where 𝜇 = 𝑟𝑅. If a and a’ are known, the power coefficient of the disc can be found given a speed

ratio λ.

The maximum coefficient of power in the rotational wake case is the same as for the non-rotational, which is

𝐶𝑃𝑚𝑎𝑥 =1627

= 0.593 (23)


Page | 26

1.3.3.3 BEM theory

An annular ring is created when a blade element is swept in the axial direction of the blade while the blade rotates. If two dimensional airfoil characteristics along with an angle of attack calculation are utilized, then the forces present on this blade element can be calculated. In the case of the axial flow induction factor a and the tangential flow induction factor a’, values can be calculated with information about the aerofoil characteristic coefficient of drag Cd and coefficients of lift Cl[11].

For the following equations, consider a wind turbine with N blades of tip radius R each with chord c. Let the blades be rotating at angular velocity Ω and let wind speed be U∞, angle φ is the angle between the drag vector and the lift vector and angle α is the angle of attack.

Figure 18: Blade Element Velocities and Forces [11]

As shown in Figure 18, we can conclude that the resultant relative velocity W at the blade is

𝑊 = �𝑈∞2 (1 − 𝑎)2 + 𝛺2𝑟2(1 + 𝑎′)2 (24)

The lift force can be expressed as

𝛿𝐿 =12𝜌𝑊2𝑐𝐶𝑙𝛿𝑟 (25)

and the drag force will be

𝛿𝐷 =12𝜌𝑊2𝑐𝐶𝑑𝛿𝑟 (26)

According to BEM theory, the force of a blade element is exclusively responsible for the change of momentum of the air which passes through the annulus swept by the element. This is an assumption that only holds if there is no interaction between the flows through contiguous annuli. The only way to comply with this assumption is having the axial flow induction factor a


Page | 27

not varying radially. In real life situations this is not achieved due to different factors in the blade which cause losses.

The component of aerodynamic force on N blade elements resolved in the axial direction is

𝛿𝐿 cos𝜑 + 𝛿𝐷 sin𝜑 =12𝜌𝑊2𝑁𝑐(𝐶𝑙 cos𝜑 + 𝐶𝑑 sin𝜑)𝛿𝑟 (27)

The rate of change of axial momentum of the air passing through the swept annulus is

𝜌𝑈∞(1 − 𝑎)2𝜋𝑟𝛿𝑟2𝑎𝑈∞ = 4𝜋𝜌𝑈∞2 𝑎(1 − 𝑎)𝑟𝛿𝑟 (28)

Taking also into consideration the dynamic head and knowing that the drop in wake pressure caused by wake rotation is equal to the increase of this dynamic head we can conclude that the axial force elements equation can be simplified into

𝑊2

𝑈∞2𝑁𝑐𝑅

(𝐶𝑙 cos𝜑 + 𝐶𝑑 sin𝜑) = 8𝜋(𝑎(1 − 𝑎) + (𝑎′𝜆𝜇)2)𝜇 (29)

Also in the axial direction, we can conclude that the torque caused by aerodynamics forces on the blade is

(𝛿𝐿 sin𝜑 − 𝛿𝐷 cos𝜑)𝑟 =12𝜌𝑊2𝑁𝑐(𝐶𝑙 sin𝜑 − 𝐶𝑑 cos𝜑)𝑟𝛿𝑟 (30)

Besides axial direction components, we have also a rate of change of angular momentum present of the air passing through the annulus, this can be expressed as

𝜌𝑈∞(1 − 𝑎)𝛺𝑟2𝑎′𝑟2𝜋𝑟𝛿𝑟 = 4𝜋𝜌𝑈∞(𝛺𝑟)𝑎′(1 − 𝑎)𝑟2𝛿𝑟 (31)

If we equate together the rotor axial torque and the rate of change of the angular momentum, and simplify we will obtain

𝑊2

𝑈∞2𝑁𝑐𝑅

(𝐶𝑙 sin𝜑 − 𝐶𝑑 cos𝜑) = 8𝜋𝜆𝜇2𝑎′(1 − 𝑎) (32)

where μ = r/R.

The main purpose of this equation is to obtain the values for both flow induction factors, a and a’. To successfully obtain them, an iterative process using Equations (33) and (34) must be done, where the right hand sides are evaluated using existing values of the flow induction factors yielding in this way, simple equations for the next iteration. For our convenience, before presenting the equations we can let Cx and Cy be

𝐶𝑋 = 𝐶𝑙 cos𝜑 + 𝐶𝑑 sin𝜑

𝐶𝑌 = 𝐶𝑙 sin𝜑 − 𝐶𝑑 cos𝜑


Page | 28

The equations for finding the induction factors are

𝑎

1 − 𝑎=

𝜎𝑟4 sin𝜑2 �

(𝐶𝑋) −𝜎𝑟

4 sin2 𝜑𝐶𝑌2� (33)

𝑎

1 + 𝑎′=

𝜎𝑟𝐶𝑌4 sin𝜑 cos𝜑

(34)

where σr is the chord solidity. The chord solidity is defined as the total blade chord length at a given radius divided by the circumferential length at that radius. It can be expressed as

𝜎𝑟 =𝑁𝑐

2𝜋𝑟=

𝑁𝑐2𝜋𝜇𝑅

(35)

We have to remember that BEM theory is strictly only applicable if the blades have uniform circulation. This means that a must be uniform throughout the whole blade. When this is not the case, a radial interaction and an exchange of moment will be present between flows through adjacent element in the annulus ring. BEM theory takes only into consideration the pressure drop as the only force that acts on the flow that goes through a given annular ring. If a is not uniform, more forces will be needed to take into account[11].

1.3.3.4 Torque and Power

In order to calculate the torque and power developed by the rotor the value of the flow induction factor must be determined first. After having these values from Equations (33) and (34), it is logical to assume that the right hand side of Equation (31) can be used to determine the torque, but we have to remember that this set of previous equation do not include the influence of drag in the system. Therefore, adding drag only for the torque calculation we can conclude that the rotor develops a total torque Q that can be expressed as

𝑄 =12𝜌𝑈∞2 𝜋𝑅3𝜆 �� 𝜇2 �8𝑎′(1− 𝑎)𝜇 −

𝑊𝑁 𝑐𝑅

𝑈∞𝜋𝐶𝑑(1 + 𝑎′)� 𝑑𝜇

𝑅

0� (36)

The power developed by the rotor is P=QΩ and the power coefficient can be calculated with

𝐶𝑃 =𝑃

12𝜌𝑈∞

3 𝜋𝑅2 (37)

As we can notice, torque and power are functions of the tip speed ratio. If we plot different coefficient of power values against tip speed ratios values we will be able to find the most efficient induction flow factor for which the power is maximized. A modern high-speed wind turbine curve is shown in Figure 19.


Page | 29

Figure 19: Power Coefficient vs. Tip Speed Ratio[11]

As the flow induction factor a approximates to the Betz limit of 1/3, the maximum CP occurs at a tip speed ratio that corresponds to this value for a as shown in Figure 19.

1.3.3.5 Blade geometry

In order to extract as much energy as it is possible from a wind turbine all of its components should be optimized. In order to optimize the blade geometry, we should take into consideration its mode of operation; this can be variable rotational speed or constant rotational speed.

1.3.3.5.1 Optimal Design for Variable-Speed Operation

The biggest advantage that a variable-speed wind turbine has is that it can maintain a constant tip speed ratio that will produce the maximum power coefficient regardless of wind speed. For this constant tip speed ratio, the torque will be maximized if

𝑑𝑑𝑎′

𝑎 =1 − 𝑎𝑎′

(38)

If we divide Equations (29) and (32) this relationship between the flow induction factors can be obtained.

𝐶𝑙𝐶𝑑

tan𝜑 − 1

𝐶𝑙𝐶𝑑

tan𝜑 + 1=

𝜆𝜇𝑎′(1 − 𝑎)𝑎(1 − 𝑎) + (𝑎′𝜆𝜇)2

(39)

The flow angle φ is given by

tan𝜑 =1 − 𝑎

𝜆𝜇(1 − 𝑎′) (40)

If we substitute Equation (40) into Equation (39) and simplify we will obtain

�𝐶𝑙𝐶𝑑

(1 − 𝑎) − 𝜆𝜇(1 − 𝑎′)� [𝑎(1 − 𝑎) + (𝑎′𝜆𝜇)2]

= �𝜆𝜇(1 − 𝑎′)𝐶𝑙𝐶𝑑

+ (1 − 𝑎)� [𝜆𝜇(1 − 𝑎′)]

(41)


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If drag is ignored, Equation (41) can be reduced to

𝑎(1 − 𝑎) − 𝜆2𝜇2𝑎′ = 0 (42)

Differentiating with respect to a’ gives

(1 − 2𝑎)𝑑𝑑𝑎′

𝑎 − 𝜆2𝜇2 = 0 (43)

and if we substitute Equation (38) into (40)

(1 − 2𝑎)(1 − 𝑎) − 𝜆2𝜇2𝑎′ = 0 (44)

Using Equations (42) and (44) together we can obtain the optimized for operation induction factors

𝑎 ≔13

𝑎𝑛𝑑 𝑎′ =𝑎(1 − 𝑎)𝜆2𝜇2

(45)

In the other hand, circulation must be uniform along the blade span in order to maintain an optimized operation. Circulation can be expressed as

𝛤 = 4𝜋𝑈∞2

𝛺𝑎(1 − 𝑎) (46)

After taking into consideration the above parameters, the blade geometry can be determined. For blade geometry we can understand, how the chord size vary along the blade and what pitch angle distribution is necessary. From Equation (32) we can obtain the following expression

𝑁𝑐

2𝜋𝑅=

4𝜆𝜇2𝑎′𝑊𝑈∞

𝐶𝑙 (47)

The only unknown in Equation (47) is the coefficient of lift so it can be included on the left hand side of the equation. Also, taking into consideration Equation (35) and the tip speed ratio we can develop a blade geometry parameter expression.

𝜎𝑟𝜆𝐶𝑙 =𝑁𝑐

2𝜋𝑅𝜆𝐶𝑙 =

4𝜆2𝜇2𝑎′

�(1 − 𝑎)2 + (𝜆𝜇(1 + 𝑎′))2 (48)

After introducing the optimum conditions from Equation (45)

𝜎𝑟𝜆𝐶𝑙 =

89

�(1 − 13)2 + 𝜆2𝜇2 �1 + 2

9(𝜆2𝜇2)�2

(49)


Page | 31

1.3.3.5.2 Effects of Drag on Optimal Blade Design

The problem with including drag is that it largely increases the complexity of the numerical analysis. Polynomials equations have to be solved for both flow induction factors. In the presence of drag, the induction factor cannot be considered anymore as constant thru ought the disc as the hypothetical drag free situation.

Nevertheless, including Equation (32) into the blade geometry parameter and comparing blade geometry parameter against local speed ratio from both situations, zero drag and with a lift-drag ratio of 40, we find that drag has very little effect on blade optimal design. The same happens with inflow angle.

𝑁𝑐

2𝜋𝑅𝜆𝐶𝑙 =

4𝜆2𝜇2𝑎′(1− 𝑎)𝑊𝑈∞

�(1 − 𝑎) − 𝜆𝜇(1 + 𝑎′)𝐶𝑑𝐶𝑙� (50)

Figure 20: Span-wise Variation of the Blade Geometry Parameter with and without Drag[11]

Figure 21: Variation of Inflow Angle with Local Speed Ratio with and without Drag[11]


Page | 32

As far as blade design is concerned drag can be ignored, but in the other hand, this situation is opposite to what happens with the Coefficient of Power. Figure 22 shows how Cp decreases when the tip speed ratio increases. Without drag, Cp is always constant.

Figure 22: The Variation of Coefficient of Power with Design Tip Speed Ratios[11]

1.3.3.5.3 Optimal Blade Design for Constant-Speed Operation

If the rotor will maintain a constant speed, λ will vary and the most optimal condition will be present just in specific times. There is no simple technique for the optimization of this type of operation but non-linear programming methods could be applied in order to maximize wind energy capture on a site with a specific wind distribution pattern.

In this case it will also be possible to design the wind turbine for the most common tip speed ratio of the site, in this way obtaining the largest amount of energy from the wind. Also, a more practical method could be adjusting the pitch angle to maximize energy capture.

1.3.3.6 Discrete Number of Blades

All the previous analysis assumes that in the turbine a large number of blades is present, enough to consider it a disk when it is rotating. This will make every particle of air to interact with a blade so all the fluid particles will undergo the same loss of momentum. When only three blades are present, the majority of the fluid particles will pass through the space between the blades, so the loss of momentum of the fluid particles will not be equal throughout the rotating disk, it will vary depending on the proximity of this fluid particle to a blade.


Page | 33

1.3.3.6.1 Tip Losses

One of the most important problems with a small number of blades is tip losses. At the tip of blade occurs a peculiar phenomenon, the induction factor suddenly increases, which makes the inflow angle small and consequently the component of the lift force will be small which will produce a reduced torque. With a low torque, power will be immediately decreased.

This phenomenon produces a vortex at the outermost part of the blade, just as the vortexes that form at the tip of an aircraft wing. The only difference is that in the case of a wind turbine blade, since the blade follows a circular path, a trailing vortex of helical structure is formed as shown in Figure 23.

Figure 23: Helical Trailing Tip Vortices[11]

Also, the discrete number of blades leaves another problem, with a small quantity of blades rather with a continuous disk, the axial flow induction factor is not uniform anymore. The average value of a, azimuthally, is radially uniform which means that in the vicinity of the blade a has high values while low values occurs on the blade. When the tip of the blade is analyzed the value of a substantially increases. The ratio between the average value of a and that at a blade position is called tip-loss factor. This factor is constant throughout the majority of the surface of the blade until the tip approximates where the factor rapidly falls to zero[11].

This changing value of the flow induction factor has repercussions in the coefficient of power of the blade. Taking into consideration the presence of tip-loss the increment of Cp from a blade element is

𝛿𝐶𝑃 = 8𝜇𝑎(1 − 𝑎)(1 − 𝑎𝑟)𝛿𝜇 (51)

where a = 1/3 is the average axial flow induction factor and ar is the value local to the blade.


Page | 34

Since a falls to zero towards the blade tips, then circulation must also fall to zero in the same manner. The circulation falling to zero causes that each blade shed a helicoidal sheet of vorticity rather than a single helical vortex as shown in Figure 23, this is shown in Figure 24.

Figure 24: A helicoidal Vortex Sheet[11]

All this phenomenon happens at the blade tip because of the pressure difference between the blade surfaces.

It can be concluded that the induction factor variation is a function of r and θ so the azimuthally averaged value of a(r) = ab(r)𝑓(r) , where 𝑓(r) is known as the tip loss factor. It has a value of the unity inboard and falls to zero as it is approaching the tip of the blade. The value of ab(r) is the level of axial flow induction factor that occurs locally at a blade element. Using this new notation we can say:

The mass flow rate through an annulus = 𝜌𝑈∞�1 − 𝑎𝑏(𝑟)𝑓(𝑟)�2𝜋𝑟𝛿𝑟

The azimuthally averaged overall change of axial velocity = 2𝑎𝑏(𝑟)𝑓(𝑟)𝑈∞

The rate of change of axial momentum = 4𝜋𝑟𝜌𝑈∞�1 − 𝑎𝑏(𝑟)𝑓(𝑟)�𝑎𝑏(𝑟)𝑓(𝑟)𝛿𝑟

The blade element forces = 12𝜌𝑊2𝑁𝑐𝐶𝑙 𝑎𝑛𝑑 1

2𝑒𝑊2𝑁𝑐𝐶𝑑

1.3.3.6.2 Prandtl’s Approximation for the Tip-Loss Factor

Until now, no expression for the tip-loss factor has been presented. This is because there is no analytical mean to find its exact value. Nevertheless, Ludwig Prandtl developed an approximate solution. The tip-loss factor is given by

𝑓(𝜇) =2𝜋

cos �𝑒((𝑁2)(1−𝜇)/𝜇)�1+(𝜆𝜇)2/(1−𝑎)2� (52)


Page | 35

Circulation is also affected by tip-losses, now that is known that circulation is not uniform we can express it as a function of r also. Therefore

𝛤(𝑟) =4𝜋

1 − 𝑎𝑈∞2

𝛺𝑎𝑓(𝑟)(1 − 𝑎𝑓(𝑟))2 (53)

1.3.3.6.3 Optimum Blade Design and Tip-Loss

The objective of blade design is to find the most optimal value for a, in order to calculate blade parameters that will lead to the most efficient shape. Since a is not uniform in this case, a new expression must be found.

This new value for a and a’ which takes into account tip-losses can be expressed as

𝑎 =13

+13𝑓 −

13�1 − 𝑓 + 𝑓2 (54)

𝑎′ = 𝑎(1 − 𝑎

𝑓)

𝜆2𝜇2

(55)

Knowing the induction factor, makes possible the calculation of the blade geometry parameter which will give the most optimum blade design.

𝜎𝑟𝜆𝐶𝑙 =4𝑎(1 − 𝑎)

��1 − 𝑎𝑓�

2+ �𝜆𝜇 �1 +

𝑎(1 − 𝑎𝑓)

𝜆2𝜇2𝑓 ��

2

(56)

In the same way, the inflow angle distribution must be determined with a different expression.

tan𝜑 =

1 − 𝑎𝑓

𝜆𝜇 �1 +𝑎(1 − 𝑎

𝑓)

𝜆2𝜇2𝑓 �

(57)

For the calculation of the power coefficient the new values from both induction factors must be used.

𝐶𝑃 =𝑃

12 𝜌𝑈∞

3 𝜋𝑅2= 8𝜆2 � 𝑎′(1− 𝑎)𝜇3𝑑𝜇

1

0 (58)


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Coefficient of power is largely reduced when tip-losses are taken into account, especially at low tip speed ratios as shown in Figure 25.

Figure 25: Variation of Coefficient of Power with Design Tip Speed Ratios for Various L/D ratios[11]

1.3.3.7 Definitions of drag and lift

1.3.3.7.1 Drag

The force on an immersed body that is parallel to the flow direction is called drag. This force in very slow-moving fluids is caused by the viscous, frictional stresses between the wall of the body and the fluid. In relatively high fluid velocities and within a low viscosity fluid the drag force is mainly caused by an asymmetric pressure distribution as shown in Figure 26.

Figure 26: Separated Flow Pressure Distribution Around a Cylinder[11]


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Drag can be expressed as

𝐷𝑟𝑎𝑔 = 3𝜋𝜇𝑈𝑑 (59)

where U is the flow velocity and d is the diameter of the cylinder.

The definition of the drag coefficient for an aircraft wing or a wind turbine blade will be

𝐶𝑑 =𝐷𝑟𝑎𝑔/𝑢𝑛𝑖𝑡 𝑠𝑝𝑎𝑛

12𝜌𝑈

2𝑐 (60)

where c is the chord length of the airfoil.

1.3.3.7.2 Lift

When a body is immersed on a fluid, it will experience a force that is normal to the flow direction, this force is called Lift. This force will not occur if there is no circulatory flow around the body. In the case of the wind turbines, the blade is considered a non-rotating body, so in order to achieve lift in this situation the body must have a sharp trailing edge like an airfoil cross-sectional shape or a thin plate.

Lift force can be expressed as

𝐿 = 𝜌(𝛤 × 𝑈) (61)

where Γ is the circulation. In the case of a wind turbine blade circulation can be expressed as

𝛤 = 𝜋𝑈𝑐 sin𝛼 (62)

where c is the chord length of the airfoil and α is the angle of attack.

For aircraft wings and wind turbine blades, the lift coefficient is defined as

𝐶𝑙 = 𝑎0 sin𝛼 (63)

where a0 is called the lift-curve slope and is about 5.73. This term, a0, should not be confused with the flow induction factor.

1.3.4 Wind turbine loads and structure

1.3.4.1 Beam theory for wind turbine blades

The majority of wind turbines are manufactured using carbon fiber reinforced plastics. The manufacturing process consists first of laying a thin-film of gelcoat in moulds. This gelcoat gives the smooth white finish to the blade. In order to increase the strength and stiffness of the blade, webs are glued between the two shells before these are glued together. This construction can be observed in more detail in Figure 27.


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Figure 27: Components of a blade[10]

This box-like structure can be modeled as a beam for structural purposes[10]. The blade will then have a value for E, G and I which are the modulus of elasticity, shear modulus and the moment of inertia respectively. The analysis begins by defining the parameters found in Figure 28.

Figure 28: Structural parameters for a cross section of the blade. Reproduced from [10].

For which the parameters are given as:

EI1 - bending stiffness about the first principal axis

EI2- bending stiffness about the second principal axis

GIv- torsional stiffness

XE- distance from the reference point to the point of elasticity

Xm- distance from the reference point to the center of mass

XS- distance from the reference point to the shear center

β- twist of the airfoil section with respects to the tip chord line

v- angle between chord line and the first principal axis

β+v- angle between tip chord line and the first principal axis


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The point of elasticity is defined as the point where a normal force does not give rise to a bending of the beam. The shear center is the point where a force on the plane does not rotate the airfoil[10].

Figure 29: Blade section and reference axes. Reproduced from [10].

Furthermore, other quantities are defined in regards to the XR and YR axes:

Longitudinal stiffness: 𝐸𝐴 = ∫ 𝐸𝑑𝐴𝐴

Moment of stiffness about XR: 𝐸𝑆𝑋𝑅 = ∫ 𝐸𝑌𝑅𝑑𝐴𝐴

Moment of stiffness about YR: 𝐸𝑆𝑌𝑅 = ∫ 𝐸𝑋𝑅𝑑𝐴𝐴

Moment of inertia about XR : 𝐸𝐼𝑋𝑅 = ∫ 𝐸𝑌𝑅2𝑑𝐴𝐴

Moment of inertia about YR : 𝐸𝐼𝑌𝑅 = ∫ 𝐸𝑋𝑅2𝑑𝐴𝐴

Moment of centrifugal stiffness : 𝐸𝐷𝑋𝑌𝑅 = ∫ 𝐸𝑋𝑅𝑌𝑅𝑑𝐴𝐴

Hence the point of elasticity can be calculated as:

𝑋𝐸 =𝐸𝑆𝑌𝑅𝐸𝐴

(64)

𝑌𝐸 =𝐸𝑆𝑋𝑅𝐸𝐴

(65)

Assuming that E and the density ρ are constant, the point of elasticity corresponds to the center of mass. The moments of inertia and centrifugal stiffness are moved to the coordinate system X'Y' which is parallel to the system XRYR by the following calculations:


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𝐸𝐼𝑋′ = � 𝐸(𝑌′)2𝑑𝐴 = 𝐸𝐼𝑋𝑅 − 𝑌𝐸2𝐴

𝐸𝐴 (66)

𝐸𝐼𝑌′ = � 𝐸(𝑋′)2𝑑𝐴 = 𝐸𝐼𝑌𝑅 − 𝑋𝐸2𝐴

𝐸𝐴 (67)

𝐸𝐷𝑋′𝑌′ = � 𝐸𝑋′𝑌′𝑑𝐴 = 𝐸𝐷𝑋𝑌𝑅 − 𝑋𝐸𝑌𝐸𝐴

𝐸𝐴 (68)

Given this transformation, the angle α can now be calculated [10] :

𝛼 =12𝑡𝑎𝑛−1 �

2𝐸𝐷𝑋′𝑌′𝐸𝐼𝑌′ − 𝐸𝐼𝑋′

� (69)

𝐸𝐼1 = 𝐸𝐼𝑋′ − 𝐸𝐷𝑋′𝑌′ tan𝛼 (70)

𝐸𝐼2 = 𝐸𝐼𝑌′ − 𝐸𝐷𝑋′𝑌′ tan𝛼 (71)

Finally, the stress 𝜎(𝑥, 𝑦) in the cross-section with bending moments Mx and My and normal force N is found by:

𝜎(𝑥,𝑦) = 𝐸(𝑥,𝑦)𝜀(𝑥,𝑦) (72)

The strain is calculated by:

𝜀(𝑥,𝑦) =𝑀1

𝐸𝐼1𝑦 −

𝑀2

𝐸𝐼2𝑥 +

𝑁𝐸𝐴

(73)

Positive values of σ, ε and N are for tension and negative values are for compression. The values of M1 and M2 can be calculated by the following analysis of a beam:

Figure 30: Cantilever beam analysis. Reproduced from [10].

Given the external loads Py and Pz, the shear forces Vz and Vy as well as the bending moments My and Mz are calculated as follows:

𝑑𝑉𝑧𝑑𝑥

= −𝑝𝑧(𝑥) + 𝑚(𝑥)𝑢�̈�(𝑥) (74)

𝑑𝑉𝑦𝑑𝑥

= −𝑝𝑦(𝑥) + 𝑚(𝑥)𝑢�̈�(𝑥) (75)

𝑑𝑀𝑦

𝑑𝑥= 𝑉𝑧 (76)


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𝑑𝑀𝑧

𝑑𝑥= −𝑉𝑦 (77)

If the blade is in equilibrium then 𝑢�̈�(𝑥) = 0. Hence, M1 and M2 are given by:

𝑀1 = 𝑀𝑦 cos(𝛽 + 𝑣) −𝑀𝑧 sin(𝛽 + 𝑣) (78)

𝑀2 = 𝑀𝑦 sin(𝛽 + 𝑣) −𝑀𝑧 cos(𝛽 + 𝑣) (79)

1.3.4.2 Dynamic structural model

Since wind loads are not constant and vary with time, it is important to consider a dynamic structural model in order to study the unsteady loads on the different components of the wind turbine. The deflection and velocities of thee components can be calculated as time dependent values by using a time dependent load from the BEM method.

Although the structural modeling for this project is developed using FEA, a short description will be given on the use of a model using the principle of virtual work [10].

The system is setup following Newton's second law, for M, the mass matrix, K, the stiffness matrix and C the damping matrix in the following manner:

𝐌�̈� + 𝐂�̇� + 𝐊𝐱 = 𝐅𝐠 (80)

Where Fg is the general force vector coming from the external loads p. Given the loads and conditions for the velocities and deformations, this equation can be solved for the accelerations hence the velocity and deformation of the next time step can be determined as well. The number of elements in x is called the number of degrees of freedom (DOF). In some studies, modal shape functions are used to reduce the number of DOF. In aeroelastic codes such as FLEX, 17 to 20 DOFs are used for a three-blade wind turbine[10].

The values in the vector x are known as the general coordinate. To each of thee, a deflection shape ui is associated, which serves to describe the deformation of the structure.

If the deflections x and velocities �̇� are known, the following formulation can be written:

𝐌�̈� = 𝐅𝐠 − 𝐂�̇� − 𝐊𝐱 = 𝐟(�̇�, 𝐱, 𝐭) (81)

Where function f is generally non linear. If the behavior of this function is known for time 𝑡𝑛 = 𝑛∆𝑡, the acceleration at time 𝑡𝑛 can be found by:

𝐱�̈� = 𝐌−𝟏𝐟(𝐱�̇�,𝐱𝐧, 𝐭𝐧) (82)


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Given the accelerations, velocities and positions at time 𝑡𝑛 , then the velocities and positions at 𝑡𝑛+1 can be calculated by a Runge-Kutta-Nyström integration scheme. The new loads at 𝑡𝑛+1 can also be calculated by an unsteady BEM method [10].

1.3.4.3 Sources of loads in wind turbines

1.3.4.3.1 Gravitational loading

The earth’s gravitational field causes a sinusoidal loading on each blade. The load is sinusoidal because as shown in Figure 31, when the blade goes from position 1 to position 2, the stresses on its surfaces change from tensile to compressive and vice versa.

Figure 31: Loading caused by the Earth's Gravitational Field[10]

This cyclic loading causes fatigue in the wind turbine, especially when it is taken into consideration that a wind turbine blade might weight several tons and be more than 30 meters long.

1.3.4.3.2 Inertial loading

Inertial loading can occur in various situations. When the turbine is accelerated or decelerated is one of those situations. Braking of the rotor will cause that a small section of the blade will feel a force dF in the direction of the rotation as shown in Figure 32.


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Figure 32: Loading caused by Braking the Rotor[10]

This force can be found with the expression

𝑑𝐹 = �̇�𝑟𝑚𝑑𝑟 (83)

where m is the mass per length of the blade, r the radius from the rotational axis to the section and dr the size of the small section; �̇� = 𝑑𝜔/𝑑𝑡 can be found from

𝐼𝑑𝜔𝑑𝑡

= 𝑇 (84)

where I is the moment of inertia of the rotor and T is the torque.

Another common type of inertial loading is due to the centrifugal force acting on the blades. This type of loading causes a flapwise bending moment which can be reduced by coning the rotor backwards with a cone angle of θcone as shown in Figure 33.


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Figure 33: Effect of coning the rotor[10]

1.3.4.3.3 Aerodynamic loading

This is the most important type of loading on a wind turbine. Aerodynamic loading is caused by the air flow past the whole stricter, blades and tower. The wind speeds of this airflow increases as the height is larger and causes shear forces on the blades.

Wind shear causes a sinusoidal variation of wind speeds seen by the blade. Also, the turbulent fluctuations superimposed on the mean wind speed also produces a variation in the wind speed and thus in the angle of attack. This constant change of the angle of attack causes fatigue on the blades and should be carefully studied using the most realistic wind field as possible.

The turbine tower also has an influence in how the wind affects the structure. The tower is changing the flow pattern thus the velocity and the pressure of the wind is altered.

Since wind fields in reality, are hard to predict, wind turbines commonly operate in yaw conditions, this means that the direction of the wind is not in the right angle for the blade design. This condition increment the loads on the blade due to increased drag, therefore it will contribute to the fatigue loads that will reduce the expected lifetime of the rotor.

It can be concluded that the change of the angle of attack on the blades can highly increase the loading in the structure. These changes can be mainly produced by turbulence, wind shear, turbine tower and yaw/tilt[10].


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2 Conceptual design

2.1 Winglet design

The geometry of a winglet is defined by six parameters:

Height

Sweep angle

Cant angle

Curvature radius

Toe angle

Twist angle

The geometry of winglets has been extensively investigated for the aeronautical industry and specifically for high performance sailplanes [21]. Since it has been shown that winglets decrease drag and improve aerodynamic performance of wind turbine rotor blades, it is important to understand and analyze the design and performance improvement process that these researchers used for this application. This gives a good overview and provides with ideas on how to manage the design process for the wind turbine application.

Figure 34: Parameters describing winglet geometry [6].

These geometric parameters can serve as the variables for input to the optimization algorithm in order to find the optimal shape given the aerodynamic constraints and goals.


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Following the investigations studied in the provided literature survey; the winglet height, curvature radius, sweep and twist angles will be taken into account in order to study different design alternatives.

When proposing preliminary designs to optimize the winglet, a certain numerical range is assigned to each parameter. The initial design proposed consists of the following ranges shown in Table 1.

Table 1: Winglet Design Parameter Ranges

Parameter Range Winglet Height (h) (%R) 1%-5% (Δh=1%) Curvature Radius (%h) 10%-100% (Δcurvature=10%)

Sweep Angle (-30°) - 30° (Δsweep=10°) Cant Angle 40°-90° (Δcant=10%)

Graphical definitions of each parameter are given below.

Figure 35: Winglets with different curvature radius [7]


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Figure 36: Winglets with different sweep angles [7]

Figure 37: Winglets with different height [7]

2.2 Airfoils and blade geometry

In order to select a main blade to conduct the most extensive part of the optimization, 12 random winglet configurations are taken from the design parameters range table. A blade is selected to perform more extensive optimization experiments after implementing a winglet. Selecting a


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single blade avoids having to implement the winglet in three different blades, reducing the experiment time outrageously.

There are many different types of airfoils used for wind turbine rotor blades. Just to name a few that have been used to design blades for wind turbines and also studied in the available winglet research literature are:

NACA 64-518

NACA 64-018

NACA 64-430

FFA-W3-301

Some researchers have used blended wings using two different types of airfoils in order to achieve the desired design. Such a design is shown in Figure 38.

Figure 38: Blade profiles from NACA 63-430 and FFA-W3-301[9].

As it can be observed, the NACA series airfoils are quite popular in this type of application. However, it has been shown that these airfoils have noticeable performance degradation from roughness effects resulting from leading-edge contamination. This leads to energy losses which can be of great importance for stall-regulated rotors.

The National Renewable Energy Laboratory (NREL) began its development of new airfoils specific for wind turbine application. The annual energy improvements from the NREL airfoil families are projected to be 23%to 35% for stall-regulated turbines, 8% to 20% for variable-pitch turbines and 8% to 10% for variable-rpm turbines.


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Figure 39: NREL airfoils for small sized blades[22]

Figure 40: NREL airfoils for medium sized blades[22]

Figure 39 and Figure 40 show two examples of NREL airfoils for small and medium size blades. It can be observed that the design of the airfoil is not constant throughout the length of the blade. In the case of the airfoil family of small blades, it can be seen that NREL S822 and S823 airfoils are used, from the tip region to the root region respectively. The blade is thicker at the root close to the rotor and gets thinner through the length of the blade. There is another factor that must be taken into account and it is the fact that the angle of attack is not constant for a wind turbine blade. Unlike airplanes, wind turbine blades need to pick up air and create lift for a rotational motion, hence there is a certain degree of twist (correlated to the difference in angle of attack) that is designed for the blade. Moreover, as it can be observed in Figure 38, the airfoil size is not


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constant either, as it can be seen that there is a certain scale down ratio for each cross section of the blade.

These are the type of considerations that will be taken into account for the design of the blade.

3 Design components In order to completely test any winglet design and notice and prove any improvements delivered from winglet design alternatives, the design must be tested on an existing wind turbine configuration for which power output, aerodynamic and operational data are known or can be found.

The proposed wind turbine to conduct all aerodynamics and structural studies consists of an upwind tri-blade horizontal axis turbine, with a rotor diameter D=32m, rotor height h=30 m, power output of approximately 400 kW, tip speed ratio of 4-10, at a wind speed of 0-15 m/s. The design parameters for the wind turbine are referenced from the Vestas V39 Wind Turbine (Vestas Tech Specs in Appendix B). Based on this design, the blades are changed and tested, and winglets are implemented and tested.

To attain maximum power generation from a wind turbine, the correct and optimized design of the blades is necessary. An optimal blade features a maximum lift coefficient for which roughness has no effect[22]. It is also a goal of the airfoil family to reach the minimum Cd/Cl possible. Through the length of an optimal blade, different airfoil shapes are present. Usually, 3 to 5 different airfoil shapes are distributed along a blade, and the distance between them depends on the behavior of the flow around each individual airfoil at a radial position from the rotor center.

In the extent of this project, three different families of airfoils are tested for best performance, with and without a winglet. From a specified rotor diameter, wind speed and range of tip speed ratio, and a random selection of twelve winglet configurations, the three blade configurations are tested for maximum Cl. The best performing blade featuring a winglet is to be used for further winglet design optimization; however, final optimized designs are to be tested in all three blades.

The airfoil families to be used in this project have been extracted from various sources, including a paper from the National Renewable Energy Laboratory (NREL) and Airfoils Inc., and the RISO DTU National Laboratory for Sustainable Energy.


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3.1 Theoretical Design

3.1.1 Blade pitch angle

A critical part of the rotor design includes the selection of either a variable speed ratio or a fixed speed ratio, and this is determined by either implementing a variable blade pitch system or selecting a fixed blade pitch angle. For the purpose of this project, a fixed blade pitch angle is chosen.

Recalling previous definitions, the tip speed ratio is defined as the ratio between the blade tip speed and the wind speed. Since the wind speed in a regular environment is a variable phenomenon, it is physically right to say that having a fixed blade pitch angle produces a variable tip speed ratio. An optimal blade pitch angle is attained by means of BEM and later optimized through CFD.

3.1.2 Blade twist angle

A variable angle of attack through the length of the blade is given by a specified twist angle. The distribution of the twist angle is based on the aerodynamic behavior (Cd/Cl and other parameters) of each individual airfoil at a certain angle of attack. This angle of attack is then translated to the angle of relative wind by adding the initial twist angle of the blade. Equation (84) yields to the angle of relative wind φ.

𝜑 = �23� tan−1(

1𝜆𝑟

) (85)

where λr is the local speed ratio [19]. The distribution of the twist angle is given in the proposed design, and it is equal to φ minus the angle of attack α.

3.1.3 Chord distribution

The chord length of each airfoil in a blade is also variable, and it is obtained with Equation (85).

𝑐 = �8𝜋𝑟𝐵𝐶𝑙

� (1 − 𝑐𝑜𝑠𝜑) (86)

where B is the number of blades [19] The distribution of the chord length is given in the proposed design.

3.2 Proposed Initial Design

The design of the blade has been preliminarily performed using Qblade, an available wind turbine blade design software which works together with Xfoil in order to design and analyze a blade with different airfoils for each cross section as well as twist angle along the length of the blade.


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For the purpose of this project, the following airfoil family has been chosen, which is composed of NREL airfoils S813, S812, S814. Airfoil NREL S815 was added to the configuration. An example of an NREL thick airfoil family is shown in Figure 41.

Figure 41: NREL airfoil family for large blades[22]

Figure 42: Airfoil configuration plotted in Qblade

The parameters for the design of the blade were taken from a student design optimization in which a wind turbine blade was optimized using several methodologies including design of experiments (DOE), gradient-based sequential quadratic programming optimization and a multi-objective genetic algorithm [23]. The objective functions of this optimization project are to maximize the power output while minimizing the blade volume and structural stress.

The chosen blade radius is 16 m, and in the case of the project presented by the MIT students, the blade design consists of NREL airfoils S814 and S813 only.


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Given that the purpose of this B.S. thesis is the design, analysis and optimization of winglets, the blade design will be based upon the findings of this optimization project. In order to have an original blade design for this project, the following NREL airfoil family was used for the blade geometry. Table 2 shows the configuration for a medium to large blade length recommended by NREL [22]. It can be observed that this configuration is similar to the one used by the MIT students, except the fact that the shape of the blade is more defined along its cross sections by including transition airfoils before airfoil S814 and S813.

Unlike typical airfoils used in aeronautics, these airfoils have been specifically designed for wind turbines. The camber in these airfoils is higher than others and from the configuration shown in Figure 42, it can be observed that the thickness of the blade is higher at its root, and decreases along its length, until the thinnest airfoil is used at the tip.

Table 2: Airfoils for blade design[22]

Blade Length

(m)

Generator (kW)

Thickness category Airfoil family (root to tip)

10-15 150-400 thick S815 S814 S812 S813

The location of the airfoil family along the length of the blade is described in Table 2, where x is the position from the root to the tip of the blade and R is the radius of the blade (16 m).

Table 3: Position of airfoils along length of the blade

Airfoil x/R x(m) S815 0.3 4.8 S814 0.4 6.4 S812 0.75 12 S813 0.95 15.2

The twist angle, defined as the angle between the airfoil chord line and the plane of the blade rotation, is shown in Table 4. Also, another parameter that is detailed in this table is the chord length of the airfoil. It can be observed that the chore length decreases along the length of the blade. This design technique is called tapering.


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Table 4: Parameters for blade design[23]

X (m) x/R Twist angle (deg)

Chord length (m)

3.2 0.200 0 1.900 4.0 0.250 8.23 1.734 4.8 0.299 16.47 1.567 5.6 0.351 24.20 1.409 6.4 0.403 30.69 1.268 7.2 0.450 36.67 1.118 8.0 0.500 40.91 1.001 8.8 0.552 43.89 0.884 9.6 0.601 44.87 0.784

10.4 0.651 45.11 0.692 11.2 0.700 45.09 0.601 12.0 0.750 45.08 0.525 12.8 0.802 45.06 0.442 13.6 0.851 45.05 0.383 14.4 0.901 45.03 0.316 15.2 0.950 45.02 0.266 16.0 1.000 45.00 0.232

As previously stated, the design of the blade was accomplished using Qblade, for which a screenshot is given in Figure 43. In this software, each cross section of the blade is defined with a specific airfoil, for which the coordinates are loaded as .dat files, avaible from online sources. Once the specific airfoil for the cross section is set, then the chord length and twist angle are specified, as well as the location x/R of this blade section. This process is repeated for n cross section of the blade. It can be observed that the blade is constructed with a surface lofted throughout the blade geometry. The output of this design is given as a list of X, Y and Z coordinates of the section airfoil at each x/R. This enables the user to import each cross section as a curve in a CAD program, a spline is used to connect the point cloud and the part can be created by means of a loft technique, such as in SolidWorks. The output for the blade built for this project is given in Appendix C.


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Figure 43: Design of the blade in Qblade

Another capability of the Qblade program is the analysis of each airfoil aerodynamic performancce measurements. This analysis is made possible by its ability to use XFoil to analyze the aerodynamic properties of the foil.

An example of output is given in Figure 44 is the coefficient of lift vs. the angle of attack of the airfoil. It can be observed that for a higher angle of attack, the lift coefficient increases up to a point where the airfoil experiences stall, hence the sudden drop in the graph. It can be seen that a higher lift is achieved by airfoil S815, which is thicker and its camber is greater.

Figure 44: Plot of Coefficient of Lift (Cl) vs. Angle of Attack (alpha)


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Figure 45: Plot of Coefficient of Lift (Cl) vs. Coefficient of Drag (Cd)

Other plots shown as well are the coefficient of lift vs. coefficient of drag in Figure 45 and the Cl/Cd ratio vs. angle of attack in Figure 46. It is interesting to observer that the Cl/Cd ratio is higher for the S813 airfoil which is located at the edge of the blade. Although the other airfoils have higher lift, this created more drag as well given the high camber. It can be stated that the Cl/Cd ratio is increased from the root to the tip region of the blade. This is quite logical given that performance of a wind turbine is to be completed by increasing the rotation speed, hence torque, of the rotating blades. If the Cl/Cd ratio is higher in the tip region, hence a higher torque is generated for the wind turbine.

Figure 46: Plot of Cl/Cd vs. Angle of Attack (alpha)


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Figure 47: Plot of Twist angle vs. Blade length

Figure 48:Front view of blade without winglet


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Figure 49: Isometric view of blade without winglet

Figure 50: Side view of blade without winglet


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Figure 51: Winglet, view 1

Figure 52: Winglet, view 2


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Figure 53: Blade with winglet

Figure 54: Blade with winglet, isometric view


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Figure 55: Isometric view of nacelle

Figure 56: Nacelle


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Figure 57: Isometric view of blade-nacelle assembly

Figure 58: Nacelle with three blades assembly


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4 Final Design

4.1 Blade Design with Winglet

4.1.1 Sizing and parameters

There are several sizing aspects involved in the design of a wind turbine, specifically a wind turbine blade. Based on previous designs and research, an optimal blade design has been implemented for this project, involving airfoils, twisting, setup, and scaling factors from the National Renewable Energy Laboratory.

The rotor diameter for the wind turbine is 30 meters, and the winglet configuration selected will add approximately one meter to this dimension, depending on the configuration used. This dimension could be altered by changes in one or more characteristics of the winglet.

The design parameters of the winglet that this project involves are height, radius and cant angle.

4.2 Parameterization of Design

Parameterization consists in converting each of the geometric characteristics of the winglet into a variable, which can easily be identified and whose value can be effectively modified. Error! Reference source not found. shows the setup of the parameters in the blade geometry.

4.2.1 Cant angle

The cant angle of a winglet has been previously defined in this report. The range of variation for the cant angle for the purpose of this project is from 10° to 90°. Changing this parameter automatically by using a randomizer is only possible by parameterizing the dimension. Parameterization is done through SolidWorks in this case, although any CAD software should facilitate this task.


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Figure 59: Parameterization of winglet design

4.2.2 Radius (Percentage of Height)

The radius between the turbine blade and the winglet varies as a function of the winglet height; therefore the parameter setup for this case is a multiple of the height. The radius varies from 10% to 100% of the height of the winglet, and it will be defined by a parameterized multiple of the height. In this design, the parameter that changes the radius has been given the name “PRad”.

4.2.3 Height

The height of the winglet fluctuates in relation with the turbine rotor radius, varying from 1% to 2% of the rotor radius. This parameter is setup to change in the range of 0.16 to 0.32 meters.

4.2.4 Randomization of Geometries

After setting up the parameters, the complete geometry is inserted into the optimization software, ModeFRONTIER. This software organizes the complete study, from the creation of geometric variations of the winglet to the evaluation and optimization of results. A function of the program called SOBOL Randomizer creates a series of random values within the selected ranges for each parameter, given a certain delta value.


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4.3 Final CAD design

The blade final design is based on the NREL airfoil family as the preliminary design. The length of the blade changed due to prototyping and testing issues. The new airfoil configuration is shown in Table 5 and Table 6.

Table 5: Airfoil Station Distribution for Final Blade Design

X (m) x/R Twist angle (deg)

Chord length (m)

3.2 0.200 0 1.900 4.0 0.250 8.23 1.734 4.8 0.299 16.47 1.567 5.6 0.351 24.20 1.409 6.4 0.403 30.69 1.268 7.2 0.450 36.67 1.118 8.0 0.500 40.91 1.001 8.8 0.552 43.89 0.884 9.6 0.601 44.87 0.784

10.4 0.651 45.11 0.692 11.2 0.700 45.09 0.601 12.0 0.750 45.08 0.525 12.8 0.802 45.06 0.442

Table 6: Airfoil Configuration

Airfoil x/R x(m) S815 0.3 4.8 S814 0.4 6.4 S812 0.75 12 S813 0.95 15.2

The length of the blade decreases by 3.2 meters from the preliminary design due to a prototype scaling problem. The prototype scale will be discussed later on.


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Figure 60: Final Blade with Stations

Figure 60 shows the final blade design and the respective airfoil stations that shaped the geometry of the blade. These changes in chord length of the airfoil and the specific twist angle at each station will produce the lift and the rotation needed.

The design process of the blade can be described in three different steps. These are: Airfoil Selection, Airfoil Distribution and Twist Angle design, and finally CAD implementation.

The first two steps are explained in Sections 2.2 and 3.2 respectively. The third step, CAD implementation, was done using SolidWorks and the process is explained below.

From the airfoil distribution and twist angle design using QBlade, a file with the exported airfoil stations in a coordinate system form was obtained. This file includes the points that describe each airfoil and its location in a Cartesian plane. These points were imported into SolidWorks as curves as shown in Figure 61, Figure 62 and Figure 63.

Figure 61: Inserting Curves in SolidWorks


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Figure 62: Curves in SolidWorks Front View

Figure 63: Curves in SolidWorks Isometric View


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The next step is to use the Loft feature in SW to create the geometry of blade, the selection of the right points in the different airfoils is critical for the loft to be successful.

Figure 64: Loft of curves in SolidWorks

The Loft feature will produce the geometry needed for the blade with an accurate resolution. As a recommendation, the selection of the guide points should always be in the trailing edge of the airfoil to produce the most accurate solution for the geometry.

Figure 65: Finalized Blade


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4.4 Winglet Implementation

The winglet to be implemented has the same airfoil as the tip of the blade, in this case NREL S813. The winglet has several parameters that define its geometry. Between these parameters we can find the height, the radius and the cant angle. These parameters were taken into consideration in the design of the winglet as shown in Figure 66.

These values were parameterized for convenient modifications and to reduce the design time.

Figure 66: Parameterization in SolidWorks

Figure 67: Equations set for parameterization of winglet

The winglets final design consists on a tapered airfoil which decreases its size from the root of the same to the tip. The parameters used in the final design are as follows:


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Table 7: Final Winglet Parameters

Height 0.4 meters Radius 0.28 meters

Cant Angle 70 degrees

Figure 68: Final Winglet Design

Figure 69: Winglet geometry parameterized in SolidWorks


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Figure 70: Blade final design with winglet isometric view

Figure 71: Blade with winglet mounted on one third hub


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Figure 72: Airfoil twist for blade geometry

Further detail on the final CAD design is included in the technical drawings in Appendix A.

5 CFD simulations

5.1 CFD modeling and setup in ANSYS Fluent

5.1.1 Pre-processing

The computational fluid dynamics solver chosen for the project is ANSYS Fluent version 12.1. ANSYS is launched from the Workbench utility which allows the user to set up a case step-by-step in an ordered procedure.

Figure 73: ANSYS Workbench project outline


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Figure 73 shows the project outline as it is seen in ANSYS Workbench. It can be observed that geometry is first imported in the project. This geometry can be loaded in several different formats, in our case the geometry was created in SolidWorks with parts and then put together as an assembly to be imported into ANSYS. After the geometry is loaded, then this is opened in ANSYS DesignModeler, where some changes are made to the geometry in order for the solver to recognize which domains are solid and which are fluid domains.

Figure 74: ANSYS DesignModeler

In order to simplify the CFD analysis and to save computational resources, the domain was designed as a 120° wedge model, assuming symmetry boundary conditions on the left and right sides of the domain.

Moreover, since this an external flow problem, the geometry that is part of the wind turbine (as a solid) is suppressed from the model, and then the rest of the geometry domains is specified as an enclosure. This allows for the meshing utility to recognize that there is a body inside the enclosure and it is suppressed because only a surface mesh is needed for it. A volume mesh is not necessary in this case because we are only interested in obtaining results for flow conditions around the blade. If this was a structural mechanics problem or a fluid-structure interaction model, then a volume mesh would need to be created for the interior of the blade and its material properties would need to be specified.


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5.1.2 Domain decomposition

As it was previously stated, the domain was simplified to a 120° wedge. This assumes that flow conditions and effects on the blades are symmetrical to each other. The wind turbine considered for this project has three blades; hence the domain is one third of a full 360° domain that could be modeled for the entire turbine.

Moreover, the mesh is composed of different named selections in ANSYS Meshing which correspond to the boundary conditions that will be implemented in ANSYS Fluent. These named selections allow for the naming of the faces of the mesh to be recognized with a specific name and be automatically assigned to the specified condition in ANSYS Fluent.

Figure 75: Named selections for left and right sides of the domain

The figure below shows the named selections for the inlet and outlet boundary conditions in ANSYS Fluent.


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Figure 76: Inlet and Outlet named selections

The following image also shows the boundary conditions for the wall blades. As it can be observed, only the surface mesh of the blade is considered in the model given the fact that the geometry of the blade was suppressed from the rest of the domain and the neighboring parts designed in SolidWorks were specified as enclosures.

Figure 77: Wall blade named selections


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5.1.3 Boundary conditions

The boundary conditions for the CFD model are set up following the literature research that was conducted for simulations that have been carried out for this type of simulation. Qunfeng et al. [24] published a paper with specific details on how a wind turbine simulation was set up in ANSYS Fluent. This proved to be an excellent resource in order to set up the model in Fluent given that this type of simulation can be exceptionally challenging. The model does not only involve the air flow conditions, but also periodicity and rotational machinery capabilities in order to correctly replicate the real-world situation for wind turbines.

Figure 78: Boundary conditions implemented in ANSYS Meshing as named selections

ANSYS Fluent has the ability to model fluid flow in complex geometries. Unlike other software used for wind turbine analysis (such as BEM based software), it does not need to use predetermined airfoil data for the prediction of the fluid flow, but instead solves the governing fluid equations at thousands or millions of positions, depending on the mesh density, on and around the blade in an iterative process.

All the velocities, including the span wise velocity are taken into account. Hence the results by CFD methods such as Fluent are more realistic and precise than codes based on BEM theory.

The inlet boundary conditions for the wind speed were set as a fixed uniform entrance velocity of 7 m/s. This reference velocity was taken from Qunfeng et al. [24] and it is higher than the cut-in speed specified on the Vestas V39 wind turbine specification data sheet. This means that if the


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wind inlet speed is higher than the cut-in speed, the wind turbine is withstanding a higher speed than the minimum necessary for the blades to rotate.

As it was specified before, the whole domain was a third of a horizontally placed cylinder with only one blade inside, as shown in Figure 78. Each side of the domain was given periodic boundary conditions. This is also in accordance to the boundary conditions that were used by Digraskar in a comprehensive CFD study of wind turbines using OpenFOAM [25]. When periodic boundary conditions are used, it implied that the velocities going out of a shadow boundary (left symmetry boundary) can enter the boundary on the other side in an infinite loop. This setting is made under the assumption that the flow conditions on either side of the 120° wedge are fully symmetric.

Figure 78 illustrates a typical application of periodic boundary conditions. In this example the flow entering the computational model through one periodic plane is identical to the flow exiting the domain through the opposite periodic plane.

Figure 79: Use of Periodic Boundaries to Define Swirling Flow in a Cylindrical Vessel

5.1.4 Turbulence modeling

As it was explained before, the computational fluid dynamics simulations will be completed by solving the full Navier-Stokes equations for fluid flow. In order to correctly capture the turbulent flow structures as well as the vortices created at the tip of the blade close to the winglet. Given the literature research conducted on turbulence models and the available reference papers, the chosen turbulence model is the shear-stress transfer (SST) k-ω turbulence model. This model effectively uses the robust and accurate formulation of the k-ω model in the near wall region with the free-stream capabilities of the k-ε model in the far field. The transport equations for the SST k-ω model are shown as[24]:


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𝜕𝜕𝑡

(𝜌𝑘) +𝜕𝜕𝑡

(𝜌𝑘𝑢𝑖) =𝜕𝜕𝑥𝑗

�Γ𝑘𝜕𝑘𝜕𝑥𝑗

� + 𝐺𝑘� − 𝑌𝑘 + 𝑆𝑘 (87)

𝜕𝜕𝑡

(𝜌𝜔) +𝜕𝜕𝑥𝑗

(𝜌𝜔𝑢𝑖) =𝜕𝜕𝑥𝑗

�Γ𝜔𝜕𝜔𝜕𝑥𝑗

� + 𝐺𝜔 − 𝑌𝜔 + 𝐷𝜔 + 𝑆𝜔 (88)

In these equations, 𝐺𝑘� represents the generation of turbulence kinetic energy due to the mean velocity gradients. 𝐺𝜔 represents the generation of ω. Γ𝑘 and Γ𝜔 represent the effective diffusivity of k and ω. 𝑌𝑘 and 𝑌𝜔 represent dissipation of k and ω due to turbulence. 𝐷𝜔 represents the cross-diffusion term. 𝑆𝑘 and 𝑆𝜔 are user-defined source terms.

When defining the boundary conditions for the inlet turbulence parameters, the turbulence intensity was set to 1% and the length scale was set to 0.01, in order to better represent the incoming wind flow. This in agreement with what it can also be experimentally tested in a wind tunnel, since most of these will replicate flow at low turbulence only.

The rotational model for the wind turbine was set to steady state, multiple rotating frames (MRF) model. Given the extensive literature review that was done for this type of rotational flow, MRF has the advantage of being able to run a simulation at steady state and without a moving mesh as other methods. A moving grid application is transient and is much more computationally expensive given the fact that the mesh needs to be updated or rebuilt for each time step of the rotational motion. The prescribed rotational speed is at 120 rpm for the wind turbine, this in accordance to the velocity of the incoming flow and the tip speed ratio of the turbine [24].

Moreover, in the solution controls page for the ANSYS Fluent, the explicit under-relaxation factors were changed from the default values of 0.75 to 0.4 in order to help with convergence. The Courant number was set to 20. Also, the under-relaxation factors were taken to half of the default values in order to bring down the fluctuation of the residuals. The under-relaxation factors for turbulence were all set to 0.95. The pressure and velocity coupling was changed from the SIMPLE algorithm to the Coupled setting. This solver reduces the time to reach overall convergence, by solving momentum and pressure-based continuity equations in a coupled manner. Although there is a slight increase in memory requirements, the advantages outweigh the drawbacks of using this solver. The Coupled solver is increasingly becoming the solver of choice for subsonic applications.


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5.1.5 Results of CFD simulations

The results for the CFD simulations carried out using ANSYS Fluent are provided in this section. Figure 80 shows a plot for the residuals of the calculations for the continuity equation, velocity components as well as the turbulence parameters k and ω.

The convergence of the results is directly related to this plot of the residuals for the items detailed above. The criteria or tolerance for convergence of residuals was set to 10-3 in order to achieve a fast result of the simulation. This is the default setting for ANSYS Fluent, however for most engineering applications, the convergence criteria for the residuals is set to 10-4. It was decided that 10-3 would provide enough accuracy given the objectives of this project. For a master's thesis or a doctoral dissertation, further accuracy needs to be obtained. However, from what is seen on the plot, the convergence of the residuals is done almost with no fluctuations and is achieved quite fast considering the complexity of the flow in this simulation. This means that the mesh that was constructed for this geometry is a good quality grid and the turbulence parameters chosen for the velocity inlet as well as the under-relaxation factors set in the solution controls in ANSYS Fluent were definitely chosen correctly.

Figure 80: Plot for residuals


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Figure 81: Statistics on parallel computations

Figure 81 shows the statistics of the computational time that was needed to complete the simulation. Total wall-clock time was less than 1 hours at 2488 seconds to complete the run.

The purpose of showing this data is to emphasize the usefulness of running this type of simulations on a parallel computer such as the one available at the MAIDROC Laboratory at FIU. The simulations was run on 15 nodes, therefore the computations are parallelized to obtain results much more efficiently and exponentially faster.

A simulation like this, if it was run on a serial computer would have taken many more hours to complete, most likely more than 1 day to achieve convergence at the specified criteria.


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5.1.5.1 Results without Winglet

Once the simulation was completed in ANSYS Fluent, the case and data file were saved and output to the corresponding folder. Later, these files were downloaded via secure ftp from the MAIDROC Tesla front end machine a local computer for post-processing of the data.

The post-processing is done by using CFD-Post, which is the results visualization engine integrated in ANSYS Workbench. This comprehensive program allows to obtain contour plots, vector plots, streamlines and many other plots for computational fluid dynamics simulations. Other similar software in this category include Tecplot and ParaView.

Figure 82: Pressure contour plot on back of blade

Figure 82 and Figure 83 show the contour plots for the back and the front of the blade respectively. As expected, it can be observed that the pressure in the front of the blade is higher than on the back given the incoming air flow.

Figure 84 shows the flow field for the entire three-bladed wind turbine. This image was achieved by using symmetry planes and by plotting vector for the velocity in the stationary frame. There are two frames in this simulation, the stationary and the rotational frame. The latter corresponds to the shroud of the blade and the blade itself which are rotating at the prescribed rotational speed.


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Figure 83: Pressure contour plot in front of blade

Figure 84: Flow field for entire wind turbine


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Figure 85: Vector plot around tip of blade without winglet showing vortices

Figure 85 shows the presence of a large vortex around the tip of the blade without a winglet. It can be observed that the structure of the vortex is situated on this location and is well structured within the flow of air. This is precisely the expected result from the CFD simulation. It can be seen that the velocity around the vortex shedding is 56.68 m/s . This gives an idea of how vortices are formed at the tip of the wind turbine blade at a real scale.

For the simulation with the winglet, it was expected to see a slightly smaller vortex around the tip of the blade, and perhaps see it moved down and away from the blade in order to provide higher velocity of rotation for the blade by decreasing the drag created by these vortices.


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Figure 86: Symmetric flow conditions for all three blades

5.1.5.2 Results with winglet

Similarly for the results without winglet, Figure 87and Figure 88 provide the contour plots for the front and back of the blade with winglet.

For further detail, Figure 89 and Figure 90 show the pressure contour on the leading edge of the blade as well as the pressure difference on the winglet. This is an expected result since the winglet reduced vortices around the tip of the blade, hence there will be a higher pressure difference resulting from this alteration in the flow conditions, not only on the surface of the blade but also downstream of the flow.

Figures 92 through 94 shows the velocity contour plots behind the blades and across the airfoil. It can be observed the high velocity on the leading edge of the airfoil and also on the lower end of the airfoil where most of the lift is produced.


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Figure 87: Pressure contour in front of blade

Figure 88: Pressure contour for the back of the blade


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Figure 89: Pressure contour on leading edge of blade

Figure 90: Pressure contour on proximity to winglet


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Figure 91: Pressure contour

Figure 92: Velocity contour plot behind blade


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Figure 93: Velocity contour plot behind blades using symmetry planes

Figure 94: Velocity contour plot around blade airfoil close to root


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Figure 95: Vector plot for velocity close to blade winglet

Figure 95 shows one of the most important plots for this project. This is a vector velocity plot for the flow directly downstream from the tip of the blade with winglet. It can be observed that the vortex is no longer well structured as when the blade is implemented without winglet. The vortex is split into two smaller vortices and one of them is moved away from the tip of the blade. There is a slightly higher velocity on this area at approximately 56.83 m/s.

This is definitely a result that was expected to happen given the objectives of this project. The winglet design that has been implemented can effectively reduce the size of the vortices around the tip the blade and even move away these turbulent structures away or further downstream of the flow in order to decrease the drag on the blades produced by these structures.

Figure 98 provides a zoomed in image of the velocity vector plot close to the winglet in order to see how the winglet alters the flow conditions at the tip of the blade.


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Figure 96: Vector plot for velocity in the entire domain using symmetry

Figure 97: Symmetric flow conditions for all three blades with winglet


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Figure 98: Close up on vortices moving away from tip of blade by using winglets


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6 Timeline and Team Responsibilities The responsibilities for each team member are described in Table 8, as well as the start and end date for each task.

The project tasks have been equally divided among the members of the team in order to have better project management and for the purpose of learning throughout this thesis, some of the major tasks will be developed jointly in order for all the members to acquire knowledge on any specifics such as the CFD and optimization processes. This can be of great use in other project throughout the engineer’s career.

Figure 99 presents the Gantt chart for a graphical overview of the project tasks and time management.

Table 8: Breakdown of tasks for Senior Design Project

Task Description Task Lead Start Date End Date Duration (days)

1 Literature review All 1/10/2011 3/23/2011 72 2 Blade conceptual designs Juancarlo Rodriguez 3/23/2011 4/6/2011 14 3 Winglet conceptual designs All 3/23/2011 4/6/2011 14 4 Blade preliminary design Juancarlo Rodriguez 4/6/2011 4/13/2011 7 5 Proposed design Juancarlo Rodriguez 4/13/2011 4/20/2011 7 6 Initial CFD and FEA analysis Rinaldo Galdamez 4/13/2011 4/20/2011 7 7 Training on analytical methods All 4/20/2011 5/6/2011 16 8 CFD model setup and boundary conditions Rinaldo Galdamez 5/6/2011 5/20/2011 14 9 CFD simulations Rinaldo Galdamez 5/20/2011 7/20/2011 61 10 CFD post-processing and analysis All 7/20/2011 8/20/2011 31 11 Optimization of designs Diego Moreno 8/20/2011 9/3/2011 14 12 FEA of final optimal design Diego Moreno 9/3/2011 9/17/2011 14 13 Rapid prototyping and manufacturing All 9/17/2011 10/1/2011 14 14 Construction of testing setup All 9/17/2011 10/1/2011 14 15 Wind tunnel testing All 10/3/2011 10/7/2011 4 16 Test results analysis Diego Moreno 10/10/2011 10/21/2011 11 17 Report completion All 10/21/2011 11/11/2011 21


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Figure 99: Senior Design Project Gantt chart


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7 Prototype, Testing and Cost Analysis

7.1 Wind tunnel testing

The need of testing a scale model of the wing turbine with the winglets implemented on a wind tunnel arises when Computational Fluid Dynamics software leave an uncertainty level in the results obtained. The only feasible way to corroborate the results obtained from the simulations is to test it in real-life conditions. Wind tunnels take advantage of an aerodynamic phenomenon that simplifies and reduce the cost of the test. In the case of the body immersed on a fluid, the pressure on the surface of the body and the forces that result from those pressures are the same regardless of whether the body is stationary and the air is moving or the air is stationary and the body is moving through it. As long as the relative motion is identical, the aerodynamic forces will be the same. Under this theory, the Reynolds Number Re of the fluid inside the wind tunnel and the Reynolds Number of the full scale condition must remain equal. The prototype and the full scale model must be immersed in the same fluid for it to work. We can recall that Re depends on the velocity of the fluid and the length of the object. So if the fluid remains constant, the relationship between the prototype and the full scale model must remain constant if the velocity and length are well selected.

Wind tunnels are classified into two main categories; they can be open circuit or closed circuit. Open circuit refers to a tunnel in which the air passes through a basically straight duct and does not recirculate.

Figure 100: Open Circuit Wind Tunnel

This type of tunnel is cheaper and is commonly used in experiments where clean and fresh air is needed to test the prototype.

In the other hand, closed circuit wind tunnels employ a duct which guides the air around a closed path, resulting in air continually recirculating through the test section.


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Figure 101: Closed Circuit Wind Tunnel

The experimental testing of a small scaled wind turbine was achieved by Merchant et al. [8]. The researchers tested three different blade configurations, one without winglets and two with winglets as part of the blade design. The setup for this experiment is similar to what will be used for this project. The wind turbine blades were manufactured using a rapid 3D prototyping machine. The testing equipment consisted of:

Four pole stepper motor (used as generator)

Four Schottky diodes

1 capacitor

Instruments

Figure 102: Testing equipment circuit schematic[8].

The circuit schematic is shown in Figure 102, and it can be observed that this setup is fairly simple to replicate. The voltage and current are measured and the power is calculated. The researchers have found that for two different winglet configurations, there was an increase in the power generated by the turbine. One increase was of 2.76% and the other was 6.23%.


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Figure 103: Testing setup for scaled wind turbine[8]

Although the CFD results presented in the available literature are not higher than 3% increase in mechanical power output, it is expected that similar results can be obtained[7]. It must be taken into account that the CFD simulation was performed on a full-sized wind turbine, whereas the 6.23% increase was at a small scale. Also, there is a certain loss for the conversion of mechanical power to electrical power.

7.1.1 Calculation of parameters and scaling for wind tunnel testing

Building a scale sized prototype becomes a challenge depending on the selected scale. Since the prototype has to fit inside a fixed dimension wind tunnel, the size of the prototype is limited by such dimensions. Embry Riddle Aeronautical University’s wind tunnel is to be used for this experiment, and its test section dimensions are 30x40 inches (76x102 cm). Another constraint given by the wind tunnel test is that the Reynolds number has to be maintained constant in the transition from the real size to the scaled model. To calculate the necessary test parameters, recall Reynolds number equation:

𝑅𝑒 =𝜌𝑉𝐷𝜇

(89)

Before conducting calculations, consider 𝑅𝑒𝑎 as the actual size Reynolds number, and 𝑅𝑒𝑡 as the test size Reynolds number. For the test to be realistic in numerical terms, 𝑅𝑒𝑎must be equal to 𝑅𝑒𝑡. Therefore the following expression is derived:

𝑅𝑒𝑎 = 𝑅𝑒𝑡 (90)

𝜌𝑎𝑉𝑎𝐷𝑎𝜇𝑎

=𝜌𝑡𝑉𝑡𝐷𝑡𝜇𝑡

(91)


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The wind conditions for the computation of both 𝑅𝑒𝑡 and 𝑅𝑒𝑎are Standard Day Conditions, so the difference between them becomes the D term of the equation stating the characteristic length, meaning the airfoil cord length in the scope of this project. The chord length used is the largest in the whole blade, which is 𝐷𝑎 = 1.90𝑚. The wind speed at the airfoil is calculated using the previously given equation:

𝑊 = �𝑈∞2 (1 − 𝑎)2 + 𝛺2𝑟2(1 + 𝑎′)2 (92)

𝑎 =13

𝑎𝑛𝑑 𝑎′ =𝑎(1 − 𝑎)𝜆2𝜇2

(93)

where μ = r/R, r is the local length of the blade along the span and R is the total length of the blade. The velocity given by this calculation is then used to calculate the Reynolds number for the real scale which allows us to calculate the wind speed necessary in the scaled model testing in order to maintain realistic results, given that a scale for the prototype has been chosen, and a scaled model maximum chord length 𝐷𝑡 is available. The maximum wind speed attained by the ERAU tunnel is 160 ft/s, which is taken in consideration when calculating the wind aerodynamic effect on the scaled model.

7.2 Materials

In the construction of the prototype, the materials taken in consideration are directly related with the testing environment and the manufacturing process.

Nowadays the most common material use in the construction of wind turbine blades is fiberglass, due to its combination of high strength and light weight. In a scaled prototype, fiberglass does not help in weight reduction neither in price reduction, due to the small size of the prototype. A lighter type of plastic resin is chosen, and it is called Somos NanoTool. This resin is selected after a comparison process between resistant plastics taking into consideration price range and the detail that could be achieved in the finished prototype.


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Table 9: Comparison of materials

MATERIAL CHARACTERISTICS Polyjet instead of FDM

Much higher resolution, fantastic for extremely small intricate parts such as gears, text and features with details smaller than 0.020"

Polyjet instead of SLA

Parts are smooth without any sanding or vapor honing, thus more accurate when immediately used for fit. Small Polyjet parts are often a fraction of the price of the same SLA parts, have much faster leadtimes, finer details & smoother features.

Polyjet instead of Urethane Casted Parts

Polyjet offers very fast multiples on smaller parts with intricate features, yet cost a fraction of the price per part. Elastomer/Rubber parts (although not as strong) can be delivered within one to two days and eliminate the costly mold.

Somos NanoTool NanoTool produces strong, stiff, high temperature resistant composite parts on conventional stereolithography machines. This material is heavily filled with non-crystalline nanoparticles allowing for faster processing. It provides superior sidewall quality, along with excellent detail resolution as compared to other composite stereolithography materials. The prototype using this material is built in .004” layers.

NanoTool is able to provide a smooth surface quality and high initial modulus, making it an excellent resin for metal plating, or to be used alone. It is also ideal for creating strong, stiff parts that need to resist high temperatures, including wind tunnel models for aerospace and automotive applications. A third major application area is rapid tooling for injection molding.


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The mechanical properties for the NanoTool material can be found in the following table.

Table 10: Technical specifications

Somos NanoTool UV Poscure Mechanical Properties (Metric)

ASTM Method Description D638M Tensile Strength 61.7 - 78.0 MPa

Tensile Modulus 11,000 - 11,400 MPA Elongation at Break 0.7 - 1.0 % Poisson’s Ratio 0.34 - 0.38

D790M Flexural Strength 79 - 121 MPa Flexural Modulus 10,200 - 10,800 MPa

D256A Izod Impact-Notched 0.12 - 0.15 J/cm D2240 Hardness (Shore D) 94

D570-98 Water Absorption 0.23%

Further details on the materials and the quotes from different vendors are included in Appendix C.

7.3 Prototype Design

The design of the original wind turbine had to be modified and adapted for the wind tunnel testing. In the components modified we can find the hub and the blade, and in the components created we can find a T-mount coupler that will adapt the electric motor with the blades and the hub.

The prototype designed maintains only the aerodynamic functionality of the real size model, meaning that the inner structure of the wind turbine is not built or considered in building a scaled size model, due to the high complexity this involves. In reality, a wind turbine includes many mechanical controlling components that directly affect the conditions of operation of a real wind turbine as it was previously shown in Figure 11(b), but for the scope of this project, these conditions are fixed to the most effective conditions as directed by previous research. The conditions kept constant in the scaled model are blade pitch and yaw, the shaft is directly connected to the generator since there is not a gearbox, and the speed of the system is given by the wind speed, since no brakes are implemented in the scaled model.

The designed prototype is a modification of the real size wind turbine, not changing aerodynamic functionality but only structural composition, in order to obtain a prototype suitable for wind tunnel testing. The components modified include the hub and the blade, and also a T-mount coupler was created. The T-mount is used to engage the electric motor with the blades and the hub.


Page | 100

Figure 104: Prototype Wind Turbine

The T-Mount is the part that will join the blades with the hub. The design is shown in Figure 105.

Figure 105: T-Mount

The T-Mount will be mounted to a hexagonal nut that will work as a mechanical transmission between the rotational motion of the blades and the electric generator. The assembly of the T-Mount and the blades is shown in Figure 106.


Page | 101

Figure 106: T-Mount and Blade Assembly

The electric generator that will be used for transformation of rotational energy into electric energy will be a Parallax™ 4-Phase / 12 Volt Unipolar Stepper Motor. It is shown in Figure 106.

Figure 107: Parallax Stepper Motor

The electric motor shaft is connected through an aluminum single set screw, which at the same time includes the ¼ inch diameter bolt where the blade assembly will be mounted. Figure 108 shows the one set screw with the bolt in place.


Page | 102

Figure 108: Single Set Screw

The blade has also been modified, it includes a portion that will couple with the T-Mount, and it is shown in Figure 109.

Figure 109: Blade


Page | 103

The hub is also different in only one small feature; it now includes a threaded hole that will attach it to the T-Mount, the single set screw and the generator.

Figure 110: Hub

The technical drawings for the prototype are included in Appendix D.

7.4 Prototype Assembly Costs

The actual cost for the manufacturing of the prototype is included in Table 11.

Table 11: Cost of parts and supplies

Part No. Description Quantity Unit Price Total Price 1 Set of blades with winglets 1 $ 250.00 $ 250.00 2 Set of blades without winglets 1 $ 250.00 $ 250.00 3 Set of T-mount, nose cone 1 $ 160.00 $ 160.00 4 Mounting tower 1 $ 100.00 $ 100.00 5 Wind turbine support 1 $ 6.00 $ 6.00 6 Wiring and other misc. 1 $ 60.00 $ 60.00 7 Parallax 4-phase stepper motor 1 $ 12.99 $ 12.99 8 Schottky diode 4 $ 1.00 $ 4.00 9 5000 μF capacitor 1 $ 1.00 $ 1.00

10 Decade Power Resistor Box 1 $ 350.00 $ 350.00 11 OMEGA multimeter 1 $ 29.00 $ 29.00 12 ERAU wind tunnel testing (hours) 3 $ 200.00 $ 600.00

Total $ 1,822.99


Page | 104

7.5 FEA study for prototype prior to wind tunnel testing

One of the main concerns with the prototype assembly was to ensure that the material and the design would withhold the forces created by the wind tunnel. Hence, an FEA study was conducted using SolidWorks COSMOS in order to analyze the stresses, deflections and factor of safety (FOS) in the assembly. The results are presented in the following figures.

In order to select the right material for the prototype, and FEA study was performed to validate that the selected material will stand the large amount of stresses and deformations due to the wind speeds and centrifugal force.

In order to produce an accurate FEA study of the prototype, a computational fluid dynamics simulation had to be done to input realistic wind pressures and velocities.

The CFD analysis setup consisted on the scaled wind turbine assembly in an external computational environment, simulating the case of the prototype sitting on an open site with no wall restrictions around.

Figure 111: Computational Domain for the Wind Turbine Prototype


Page | 105

The calculation were done in SolidWorks due to its simplicity and fast results, also sue to its great integration with a trustable FEA analysis system.

The analysis type for the FEA study was set as external type, indicating that the fluid domain consist of everything surrounding the turbine, and that the pressures around it are all atmospheric.

Also, in order to simulate the rotation of the wind turbine, the domain was set with a rotational behavior. The rotation was set around the Z axis with an angular velocity of 94.25 rad/sec which corresponds approximately to 900 rpm, the speed of the rotor in tests performed at the FIU Transport Phenomena Lab. The domain was set as a global rotating domain, which indicates that the whole fluid domain will rotate.

Figure 112: SolidWorks CFD Study Settings


Page | 106

The fluid selected for the study was air, with its original properties included in the SW library, and the fluid type was set as turbulent due to the high Reynolds Number obtained in the calculations.

As an initial condition, some velocity parameters were included simulating the real wind speed obtained at the FIU Transport Phenomena Lab. The wind speed was set at 18.8 m/s, specifically in the Z direction. Turbulence parameters were left with their default values.

Figure 113: SolidWorks CFD Study Settings

Since in the prototype the parts that are of more concern are the blades, these were set as real walls, simulating the interaction with the fluid. Everything else in the wind turbine assembly was ignored due to the lack of relevance in the CFD simulation.

The next step involves the creation of the mesh; this was set at level 5 in the scale that SolidWorks provide without any further change in its default settings. This completes the setup of the prototype so it can be set to run to obtain the desired results.


Page | 107

Since the results are saved in .fld format there is no need of further interaction with the CFD interface, everything can be imported into the FEA study and SolidWorks will take care of the pressures and velocities created by the fluid. For illustration purposes the images of the CFD study are shown below.

Figure 114: CFD Study for the Prototype


Page | 108

Figure 115: CFD Study for the Prototype, Pressure Profile

With the CFD done, the structural analysis if the blade can be started. Since the parts of the assembly that is important for this study is only the blades, to simplify the problem and reduce the calculation time, the other parts of the assembly were ignored from the structural study.

To simulate the connection between the blade and the t-mount, the root of the prototype blade was set as fix.


Page | 109

Figure 116: Fixed Components in Blade Prototype

The loads applied to the components in the study are the pressure of the fluid and the centrifugal force produced by the rotation of the system. The pressure of the fluid is loaded from the previous CFD study. This file will include all the data needed to calculate the stresses and strains in the model. In the case of the centrifugal force, the rotation speed was set to 94.27 rad/s which correspond to 900 rpm. Since there is no other important source of loads in the system the mesh can be created.

The mesh was created with a superfine specification for a higher accuracy in the calculations.

Figure 117: Mesh for Structural Analysis


Page | 110

The same procedure was done for both cases, the prototype that include winglets and the prototype that comes with a regular blade.

7.5.1 FEA Results

In the case of the turbine without the winglets the results for the analysis are as follows.

7.5.1.1 Results without winglet implementation

Figure 118: Von Mises Stresses without Winglet Implementation


Page | 111

Figure 119: Deflection without Winglet Implementation


Page | 112

Figure 120: Strain without Winglet Implementation

Table 12: Max and Min Stresses, Displacement and Strains for No Winglet Configuration

Name Type Min Max Stress VON: von Mises Stress 6.94223 x 10-5 N/m2 271496 N/m2

Displacement URES: Resultant Displacement 0 mm 0.0608007 mm Strain ESTRN: Equivalent Strain 2.10725 x 10-8 3.01639 x 10-5


Page | 113

7.5.1.2 Results with winglet

The results for the case of the blades with the implemented winglet are as follows.

Figure 121: Von Mises Stress with Winglet Implementation


Page | 114

Figure 122: Displacement with Winglet Implementation


Page | 115

Figure 123: Strain with Winglet Implementation

Table 13: Max and Min Stresses, Displacement and Strains for Winglet Configuration

Name Type Min Max

Stress VON: von Mises Stress 0.000153018 N/m2 387655 N/m2

Displacement URES: Resultant Displacement 0 mm 0.0653411 mm

Strain ESTRN: Equivalent Strain 2.70108 x 10-8 3.01695 x 10-5

One of the most important differences between the case with no winglet in the blades, and the case with the winglets implemented, is the substantial increase of Von Mises stresses in the blade. The increase is approximately 100 kPA more in the case with the winglets implemented. This high concentration of stresses is specifically located in the winglet.

It can be concluded that give the material chosen, the prototype will withstand the testing that would be performed at Embry Riddle Aeronautical University. The deflection is practically zero and the FOS is much higher than expected. The design is safe for testing at the wind tunnel facility.


Page | 116

7.6 Test Results

As it is has been stated in previous sections, the motivation of this project is to enhance the productivity of a horizontal axis wind turbine by implementing and optimizing winglets in the tips of each blade. This implementation had not only to be simulated, build and tested, but also to be proven efficient and actually beneficial to the operation of a wind turbine. The objective of this project considered an estimated improvement in amount of wind energy production ranging between 1% and 3%.

The results of the wind tunnel test compare the power generation of a wind turbine with winglet, and of a wind turbine without winglet. The side-by-side comparison of the two tests can be seen in Figure 124.

Figure 124: Average improvement

On average, the improvement on the amount of power generation resulting from the implementation of a winglet is 1.57%. This percentage has been calculated by comparing the results of 4 tests conducted in each of the two wind turbine configurations. The amount of improvement is given as a function of the electrical load specified for teach turbine configuration on each test. The comparison between the resultant improvement and the load at each step of the test is given numerically by Table 14 and graphically by Figure 125.

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045

0

1000

2000

3000

4000

10000

15000

20000

25000

30000

40000

45000

60000

Power Generated (W)

Load

(Ω)

No Winglet

With Winglet


Page | 117

Table 14: Load vs. % Improvement

Resistance % Improvement 1000 1.23% 2000 0.17% 3000 0.76% 4000 0.51%

10000 1.61% 15000 0.54% 20000 1.42% 25000 0.46% 30000 0.53% 40000 2.37% 45000 1.80% 60000 7.48%

Average 1.57%

Figure 125: Load vs. % Improvement

A complete table of testing results can be found in Appendix E.

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

0 10000 20000 30000 40000 50000 60000 70000

Impr

ovem

ent

Load (Ω)


Page | 118

8 Conclusions and Recommendations

The winglet design process must come after an implementation of an optimized blade design that will be used to compare the improvement of a system with winglets over one without them.

The blade design of a wind turbine differs from an airplane wing design. Airplane wings usually have one airfoil design through all the length of the wing, in the case of wind turbines, around three or four different airfoil profiles are used in the same blade varying from the root to the tip of the wind. Also, another important difference can be found in the twist angle of a wind turbine blade. The blade is twisted in an special and optimized manner through the length of the blade, this do not happens on an airplane wing.

These differences make the analysis of a wind turbine blade more complicated than usual. Software and techniques used in airplane design must be altered in accordance to the needs.

For this study, several software packages were used independently to create and obtain an optimal blade design. The specific packages used include XFOIL, QBLADE, SolidWorks 2010 and ANSYS Fluent 12.1.

The blade design process was very time consuming, methods and techniques are being refined in order to produce fastest and more reliable designs. The implementation of the mentioned software packages reduces largely the load of the design process, and several other packages are in way to be implemented to improve the blade design and the calculations as much as possible.

It has been shown that winglets can effectively improve the performance of a conventional tip wind turbine blade. The results are in agreement with published research. This opens an area of analysis for other students to explore and further analyze with different winglet and blade designs which may lead to higher performance.

As recommendations, larger scale testing can be conducted at the Wall of Wind facility at Florida International University, which would provide better flow conditions in order to correctly compare the scaled prototype to the real scale wind turbine. Also, given the constant fluctuation of current and voltage output from the wind turbine prototype, the use of data acquisition systems (DAQ) is recommended.


Page | 119

9 Acknowledgements

The wind turbine winglet design team would like to thank Mr. Richard Zicarelli, from the FIU Engineering Manufacturing Center for his help with manufacturing the coupler and stepper motor mount for the prototype.

Prof. Snorri Gudmundsson, from Embry Riddle Aeronautical University who was very helpful and available to arrange the wind tunnel testing.

Mr. Stephen Wood and Dr. Agerneh Dagnew, graduates from the Mechanical Engineering and the Civil Engineering departments respectively for their friendship and excellent guidance, brainstorming, ideas and good humor in the field of computational fluid dynamics and computational meshing.

Mr. Nader Fateh for his help in learning the use of modeFRONTIER software for optimization purposes.

Ms. Catherine Alviz, Mr. Carlos Sousa, and Mr. Victor Polanco, all Electrical Engineering students and amazing friends who supported us and provided their assistance in setting up the electrical circuitry for the prototype.

Dr. George Dulikravich, Dr. Igor Tsukanov and Dr. Sabri Tosunoglu for their guidance, mentorship, help and thoughtful discussions on this project, mechanical engineering and lifelong learning.

Most importantly, thank you to our families, loved ones and close friends who gave us unconditional support throughout this project and our undergraduate careers.


Page | 120

References

[1] U.S. Department of Energy- EERE, "20% Wind Energy by 2030: Increasing Wind Energy's Contribution to U.S. Electricity Supply," Golden, CO, 2008.

[2] E. F. Baerwald, G. H. D'Amours, B. J. Klug and R. M. Barclay, "Barotrauma is a significant cause of bat fatalities at wind turbines," Current Biology, vol. 18, no. 16, August 2008.

[3] Wikimedia Foundation Inc., April 2011. [Online]. Available: http://en.wikipedia.org/wiki/Wingtip_device.

[4] Global Wind Energy Council, March 2011. [Online]. Available: http://www.gwec.net/fileadmin/documents/Publications/GWEC_PRstats_02-02-2011_final.pdf.

[5] M. Gaunaa and J. Johansen, "Determination of the Maximum Aerodynamic Efficiency of Wind Turbine Rotors with Winglets," Journal of Physics: Conference Series, vol. 75, 2007.

[6] J. Johansen and N. N. Sorensen, "Aerodynamic investigation of Winglets on Wind Turbine Blades using CFD," Roskilde, 2006.

[7] J. Johansen and N. N. Sorensen, "Numerical Analysis of Winglets on Wind Turbine Blades using CFD," in European Wind Energy Conference, Milan, 2007.

[8] J. S. Merchant, J. M. Bondy and K. W. Van Treuren, "Wind tunnel analysis of a wind turbine with winglets," in ASME Early Career Technical Conference, Tulsa, 2010.

[9] P. M. Congedo and M. G. De Giorgi, "Optimizing of a wind turbine rotor by CFD modeling," in ANSYS Italy Conference , Mestre, 2008.

[10] M. O. Hansen, Aerodynamics of Wind Turbines, 2 ed., Sterling, VA: Earthscan, 2008.

[11] T. Burton, D. Sharpe, N. Jenkins and E. Bossanyi, Wind Energy Handbook, 1 ed., West Sussex: John Wiley & Sons, 2001.

[12] P. Gipe, April 2011. [Online]. Available: http://www.wind-works.org/photos/Smith-PutnamPhotos.html.

[13] Danish Wind Industry Association, April 2011. [Online]. Available: http://guidedtour.windpower.org/en/pictures/juul.htm.


Page | 121

[14] Wikimedia Foundation, Inc., April 2011. [Online]. Available: http://en.wikipedia.org/wiki/Wind_turbine_design.

[15] U.S. Department of Energy- EERE, March 2011. [Online]. Available: http://www1.eere.energy.gov/windandhydro/budget.html.

[16] U.S. Department of Energy, April 2011. [Online]. Available: http://www1.eere.energy.gov/windandhydro/m/budget.html.

[17] U.S. Department of Energy, April 2011. [Online]. Available: http://www.windpoweringamerica.gov/wind_installed_capacity.asp.

[18] Wikimedia Foundation, Inc., April 2011. [Online]. Available: http://en.wikipedia.org/wiki/Wind_turbine.

[19] J. F. Manwell, J. G. McGowan and A. L. Rogers, Wind Energy Explained: Theory, Design and Application, 2 ed., West Sussex: John Wiley & Sons, 2009.

[20] U.S. Department of Energy, April 2011. [Online]. Available: http://www1.eere.energy.gov/windandhydro/wind_how.html.

[21] M. D. Maughmer, "The design of winglets for high-performance sailplanes," 2001.

[22] J. L. Tangler and D. M. Somers, "NREL Airfoil Families for HAWTs," Golden, 1995.

[23] Anonymous MIT Students, "Wind Turbine Blade Design Optimization," Cambridge, 2011.

[24] L. Qunfeng, J. Chen, J. Chen, N. Qin and L. A. Danao, "Study of CFD simulation of a 3-D wind turbine," in International Conference for Renewable Energy & Environment (ICMREE), Shangai, 2011.

[25] D. Digraskar, "Simulations of Flow over Wind Turbines," University of Massachussets Amherst, May 2010.


Page | 122

Appendix A: Technical Drawings for Wind Turbine

NREL Blade 400 kW Family -With Winglet

DO NOT SCALE DRAWING SHEET 1 OF 1

UNLESS OTHERWISE SPECIFIED:

SCALE: 1:128WEIGHT:

REVDWG. NO.

ASIZE

TITLE:

NAME DATE

COMMENTS:

Q.A.

MFG APPR.

ENG APPR.

CHECKED

DRAWN

FINISH

MATERIAL

INTERPRET GEOMETRICTOLERANCING PER:

DIMENSIONS ARE IN INCHESTOLERANCES:FRACTIONALANGULAR: MACH BEND TWO PLACE DECIMAL THREE PLACE DECIMAL

APPLICATION

USED ONNEXT ASSY

PROPRIETARY AND CONFIDENTIALTHE INFORMATION CONTAINED IN THISDRAWING IS THE SOLE PROPERTY OF<INSERT COMPANY NAME HERE>. ANY REPRODUCTION IN PART OR AS A WHOLEWITHOUT THE WRITTEN PERMISSION OF<INSERT COMPANY NAME HERE> IS PROHIBITED.

5 4 3 2 1


Page | 123

Appendix B: Vestas V39 Technical specifications

WIND PIONEER LTD

BATCHWORTH HOUSE, BATCHWORTH PLACE, CHURCH STREET RICKMANSWORTH HERTS WD3 1JE TEL: 0800 955 3838 COMPANY NO. 07148454

TEL: 0800 9655 3838 [email protected] www.windpioneer.co.uk

PERFORMANCE At a particular location, the wind speed will vary about an annual mean value. The expected energy yields for the Vestas V39 at various annual wind speeds (AMWS) is shown below:

AMWS m/s Annual MWh Daily kWh

4 255 699 5 552 1512 6 785 2151 7 1114 3052 8 1672 4581 9 1999 5477

Note: The annual electricity consumption of a medium size home is in the region of 4-6MWh or 11-16 kWh per day. At 6 m/s wind speed the Vestas V39 can provide the annual energy needs for 190 homes.

TECHNICAL SPECIFICATION

Generator Rating 500kW @ 16 m/s

Rotor Speed 30 rpm nominal

Cut-in Wind Speed 4.5 m/s

Survival wind speed 50 m/s

Rotor diameter 39m

Rotor orientation Upwind

Number of blades 3

Blade material Fibreglass/polyester

Control system Pitch controlled

Gearbox Planetary/helical

Brakes Disc

Generator Asynchronous

Yaw control Powered

Tower height 40m

Tower Free standing

OVERVIEW A 500kW medium sized wind turbine suitable for powering larger farms, community projects and commercial properties.

PERFORMANCE The energy capture of the Vestas V39 turbine is exceptionally good across a wide range of wind speeds and comes installed on a 40m free-standing tower for maximum energy capture.

RELIABILITY The Vestas V39 turbine is intended for a range of harsh conditions, especially exposed locations. The remaining design life of these machines is in excess of 20 years.

V39 Wind Turbine – Technical Specification

Experts in Wind Power & Planning

mailto:[email protected]�

Wind Pioneer is meeting the ne

WIND PIONEER LTD BATCHWORTH HOUSE, BATCHWORTH PLACE, CHURCH STREET RICKMANSWORTH

HERTS WD3 1JE TEL: 0800 955 3838 COMPANY NO. 07148454 TEL: 0800 9655 3838 [email protected] www.windpioneer.co.uk

Experts in Wind Power & Planning Wind Pioneer is committed to the production of clean affordable energy with these remanufactured and upgraded wind turbines. Wind Pioneer is the exclusive distributor and installer for the Vestas V39 turbine, remanufactured by Halus Power Systems, which is the most efficient and cost effective in its class. The Vestas V39 wind turbine generates exceptional levels of power for its size, but is remarkably quiet. Wind Pioneer can supply, install and support the Vestas V39 turbine to help power semi-rural domestic properties and many more applications. Wind Pioneer works in partnership with site owners, financiers, suppliers and other stakeholders to guide projects through the process and beyond. Wind Pioneer also sells a range of larger turbines for less power hungry applications.

V39 Wind Turbine – Technical Specification

Experts in Wind Power & Planning

Halus Power Systems are the USA’s leading supplier of remanufactured wind turbines, specialising in turbines originally produced by Vestas. They have been manufacturing turbines for 10 years at there 5 acre facility in San Leandro, California. All turbines comes with a standard 5 year parts warranty and an expected life of 20yrs+ Wind Turbine Controller – All turbines come with a new advanced controller. Some of the features of our controllers are:

• Advanced soft-start motor control with user definable thyristor trigger angle and cut in slope

• Automatic motor start • Power factor control including user definable delay

for capacitor connection and capacitor discharging time

• Web-based TCP/IP control and monitoring system which can also be used on site

• Top box for ease of maintenance and service

mailto:[email protected]�


Page | 124

Appendix C: Material and Supplies Quotes

P430 ABS Material Properties

P430 ABS Material Properties 9 March 2007

A true industrial thermoplastic, ABS is widely used throughout industry. When combined with a Dimension Elite system, P430 ABS is ideal for 3D printing of models in the engineering office.

MECHANICAL PROPERTIES1

Test Method Imperial Metric Tensile Strength, Type 1, 2 in/min (51 mm/min), 0.125

ASTM D638 5,295 psi 36 MPa

Tensile Modulus, Type 1, 2 in/min (51 mm/min), 0.125 Tensile Elongation, Type 1, 2 in/mm 51 mm/min, 0.125

ASTM D638

ASTM D638

329,499 psi

4%

2,272 MPa

4%

Flexural Delamination Stratasys Standard 5,142 psi 35 MPa Flexural Strength ASTM D790 7,604 psi 52 MPa Flexural Modulus ASTM D790 319,737 psi 2,204 MPa IZOD Impact, Notched, 73˚F (23˚ C) ASTM D 256 1.8 ft-lb/in 96 J/m

THERMAL PROPERTIES Heat Deflection Temperature – unannealed 3

HDT, 66 psi (0.5 MPa) HDT, 264 psi (1.8 MPa) Melt Point

ASTM D648

204 ˚F 180 ˚F

Not Applicable2

96 ˚C 82˚C

Not Applicable

OTHER Specific Gravity 1.04 Vertical Burning Test3 HB, UL94 Coefficient of Thermal Expansion3 4.9E-05

APPEARANCE Natural

Stratasys, Inc. 14950 Martin Drive Eden Prairie, MN USA 55344 Ph: 952.937.3000 Fax: 952.937.0070 www.dimensionprinting.com

The information presented are typical values intended for reference and comparison purposes only. They should not be used for design specifications or quality control purposes. End-use material performance can be impacted (+/-) by, but not limited to, part design, end-use conditions, test conditions, etc. Actual values will vary with build conditions. Product specifications are subject to change without notice.

1 Build orientation is on side edge 2 Due to amorphous nature, material does not display a melting point 3 Injection molded properties

DSM Somos®1122 St. Charles Street

Elgin, IL 60120 USATel: 800.223.7191 (in USA)

Tel: 847.697.0400 (outside USA)Fax: 847.468.7785

DSM Desotech bv 3150 AB Hoek van Holland

The NetherlandsTel: +31 1743.15391

Fax: +31 1743.15530

www.dsmsomos.com

Email:[email protected]@dsmsomos.info

[email protected]

DSM Somos®1122 St. Charles Street

Elgin, IL 60120 USATel: 800.223.7191 (in USA)

Tel: 847.697.0400 (outside USA)Fax: 847.468.7785

DSM Desotech bv 3150 AB Hoek van Holland

The NetherlandsTel: +31 1743.15391

Fax: +31 1743.15530

www.dsmsomos.com

Email:[email protected]@dsmsomos.info

[email protected]

2/08

DS

M S

om

os ®

DescriptionNanoTool produces strong, stiff, high temperature resistant composite parts on conventional stereolithography machines. This third generation of Somos® ProtoComposite materials is heavily filled with non-crystalline nanoparticles allowing for faster processing. It exhibits superior sidewall quality, along with excellent detail resolution as compared to other composite stereolithography materials.

ApplicationNanoTool’s smooth surface quality and high initial modulus make it an excellent resin for metal plating, a growing application which saves time and money as an alternative to fully metal prototypes. It’s also ideal for creating strong, stiff parts that need to resist high temperatures, including wind tunnel models for aerospace and automotive applications. A third major application area is rapid tooling for injection molding.

Physical Properties – Liquid Appearance Off White Viscosity ~2,500 cps at 30°CDensity ~1.65 g/cm3 at 25°C

Optical Properties at 355 nmEc 8.3 mJ/cm2

[criticalexposure]

Dp 0.11 mm (0.0043 inches) [slopeofcure-depthvs.ln(E)crve]

E10 84 mJ/cm2

[exposurethatgives0.254mm(0.010inch)thickness]

Somos® NanoTool™

Third Generation ProtoComposite™ Material for High Strength, High Temperature Applications

®

.

Mechanical Properties (Metric)Description

Tensile Strength

Tensile Modulus

Elongation at Break

Poisson’s Ratio

Flexural Strength

Flexural Modulus

Izod Impact-Notched

Hardness (Shore D)

Water Absorption

Somos® NanoTool UV Postcure

ASTMMethod

D638M

D790M

D256A

D2240

D570-98

Thermal & Electrical Properties (Metric)Description

C. T. E. -40°C – 0°C

C. T. E. 0°C – 50°C

C. T. E. 50°C – 100°C

C. T. E. 100°C – 150°C

Dielectric Constant 60Hz

Dielectric Constant 1KHz

Dielectric Constant 1MHz

Dielectric Strength

Tg

HDT@ 0.46 MPa

HDT @ 1.82 MPa

ASTMMethod

E831-00

D150-98

D149-97a

E1545-00

D648-98c

N/A: Not Available

N/A: Not Available

61.7 - 78.0 MPa

11,000 - 11,400 MPA

0.7 - 1.0 %

0.34 - 0.38

79 - 121 MPa

10,200 - 10,800 MPa

0.12 - 0.15 J/cm

94

0.23 %

25.3 - 26.0 μm/m-°C

30.4 - 32.4 μm/m-°C

75.9 - 87.4 μm/m-°C

90.0 - 95.7 μm/m-°C

4.0

3.9

3.6

15.6 - 16.8 kV/mm

225 °C

85 - 90 °C

66.3 - 80.3 MPa

10,400 - 11,200 MPa

0.7 - 1.0 %

0.29 - 0.36

103 - 149 MPa

9,960 MPa - 10,200 MPa

0.14 - 0.16 J/cm

94

TheProtoFunctional®MaterialsCompany

DSM Somos® DSM2/08

57 - 62 °C

Somos® NanoTool UV & Thermal Postcure



0.15 - 0.16 %

25.0 - 25.7 μm/m-°C

25.5 - 31.3 μm/m-°C

57.0 - 58.9 μm/m-°C

95.2 - 99.6 μm/m-°C

3.9

3.8

3.6

16.1 - 16.9 kV/mm

258 - 263 °C

104 °C

86 - 89 °C

.

Mechanical Properties (Imperial)

Thermal & Electrical Properties (Imperial)Description

C. T. E. -40°F – 32°F

C. T. E. 32°F – 122°F

C. T. E. 122°F – 212°F

C. T. E. 212°F – 302°F

Dielectric Constant 60Hz

Dielectric Constant 1KHz

Dielectric Constant 1MHz

Dielectric Strength

Tg (TMA)

HDT@ 66 psi

HDT @ 264 psi

ASTMMethod

E831-00

D150-98

D149-97a

E1545-00

D648-98c

N/A: Not Available

8.9 - 11.3 ksi

1,590 - 1,650 ksi

0.7 -1.0 %

0.34 -0.38

11.5 - 17.5 ksi1,480 - 1,570 ksi

0.23 - 0.29 ft-lb/in

93 - 95

14.1 - 14.4 µin/in-°F

16.9 - 18.0 µin/in-°F

42.2 - 48.6 µin/in-°F

50.1 - 53.2 µin/in-°F

4.0

3.8 -3.9

3.6 - 3.7

396 - 427 V/mil

437 °F

185 - 193 °F

9.6 - 11.6 ksi

1,510 - 1,620 ksi

0.7 -1.0 %

0.29 -0.36

14.9 - 21.6 ksi

1,440 - 1,480 ksi

0.26 - 0.31 ft-lb/in

TheProtoFunctional®MaterialsCompany

DSM Somos® DSM2/08

135 - 144 °F

Description

Tensile Strength

Tensile Modulus

Elongation at Break Poisson’s Ratio

Flexural Strength

Flexural Modulus

Izod Impact-Notched

Hardness (Shore D)

Water Absorption

ASTMMethod

D638M

D790M

D256A

D2240

D570-98

N/A: Not Available





0.23 %

93 - 94

0.15 - 0.16 %

13.9 - 14.3 µin/in-°F

14.2 - 17.4 µin/in-°F

31.7 - 32.7 µin/in-°F

52.9 - 55.3 µin/in-°F

3.9

3.8

3.6

408 - 428 V/mil

496 - 506 °F

220 °F

187 - 192 °F

VisiJet® EX200 Plastic Material for 3-D Modeling

• ExpandyourmodelingandfitandfunctiontestingapplicationswithVisiJet®EX200,amaterialthatistougherandmoredurable.

• Materialtransparencyallowsyoutoviewinternalgeometriesandstructures–tobetterevaluateyourproductdesigns.

• Thefinestfeatures,sharpestedgesandsmoothestcurvesavailablein3-Dprinting.

• Quickly,andwithoutgeometriclimitations,createconsistent,repeatableandhighqualityparts.

• Simple,melt-awaysupportsandnoadditionalpostprocessingensuresthatyourproductdesignprojectsstayonschedule.

• VisiJet®EX200andtheProJet™3-DProductionSystemformacompletesolutionthatfitsyourbudgetwithuser-friendly,automaticoperationinanofficeenvironment.

Properties Condition VisiJet® EX200

Composition UVCurableAcrylicPlastic

Color Natural

CaseQuantity 8cartridges,0.5kgea

NetWeight(percase) 4.0kg

Density@80°C(liquid),g/cm3 ASTMD4164 1.02

TensileStrength,MPa ASTMD638 42.4

TensileModulus,MPa ASTMD638 1283

ElongationatBreak,% ASTMD638 6.83

FlexuralStrength,MPa ASTMD638 TBD

FlexuralModulus,MPa ASTMD790 1159

IzodNotchedImpact,kJ/m2 ASTMD256 2.5

GlassTransitionTemperature,Tg@1Hz 52.5

3D Systems333 Three D Systems CircleRock Hill, SC 29730 USATelephone +1(803) 326-4080

TollFree (800) 889-2964

Warranty/Disclaimer: The performance characteristics of these materials may vary according to product application, operat-ing conditions, material combined with, or with end use. 3D Systems makes no warranties of any type, express or implied, including, but not limited to, the warranties of merchantability or fitness for a particular use.© 2009 by 3D Systems, Inc. All rights reserved. Specifications subject to change without notice. ProJet is a trademark and VisiJet, 3D Systems and the 3D logo are registered trademarks of 3D Systems, Inc.

PN 70742 Issue Date May 2009

Revolutionize your functional testing and bring your general purpose Rapid Design to the next level. A truly flexible 3-D printing material.

[email protected]

NASDAQ:TDSC

High definition, hard plastic parts to expand your modeling applications

- Good impact strength - No additional curing required- Absorbs paint, can be machined, drilled,

chrome-plated or used as a mold- Elongation at break enables snap fit

Tensile Strength Elongation at breakModulus of Elasticity Flexural Strength Flexural Modulus Izod Notched Impact Heat Distortion Temperature

Compression Strength Rockwell

D-638D-638D-638D790D790D256D648@ 0.45Mpa (66psi)@ 1.82Mpa (264psi)

D695Scale M

42.3 MPa 15%-25%2000 MPa 70.6 MPa 1978 MPa 25-38 J/m 110º F (43º C)115º F (46º C)

69.4 MPa 81.0

Property Standard Procedure Value

© 2005 Stratasys, Inc. All rights reserved. Specifications subjectto change without notice. FullCure materials for Eden systems aresold by Stratasys in North America only. FC700 1/05

Ash Content: The ash content of the FullCure 720 is < 0.01% at 1000º C Resin Density: Liquid model resin(RT) 1.092 gr/cc Coefficient of Thermal Expansion: @ 30-35ºC: (34.6 ± 4.7) X 10-6 m/mºC @40-70ºC: (60.8± 9.5) X 10-6 m/mºC @ 75-90ºC: (104.4 ± 8.5) X 10-6 m/mºC @ 95-110ºC (122.2 ± 4.0) X 10-6 m/mºC

For more information about Stratasys systems and materials, contact your representative or visit www.stratasys.com

Part of an expanded line of proprietary photopolymer resins, FullCure™ 700 Series are designed for precise jetting in super fine layers by PolyJet™ technology inside the Eden333 and 260 fromStratasys. Both model and non-toxic, gel-like support materials come in sealed, easy to handle 2kgcartridges easily replaced through a front-loading door.

POLYJET TECHNOLOGY > MATERIALS

FullCure™ 700 SeriesPhotopolymer Materials

QuoteDate

11/10/2011

Estimate #

4097

Name / Address

FIUDiego Moreno Ferguson Ferguson

3251 Progress DriveSuite B2Orlando, FL 32826

Project

11-10-11 Objet/FDM

Thank you for the opportunity to potentially assist with your project.

For questions or inquiries, please contact at:Phone: 407.737.1991Fax: [email protected]

Description Qty Rate (each) Total

Prototype(s) Option 1:Description: Prototype Set (see below)Material: High-res Photopolymer

Quantity Part Name

6 SCALE 1-75 BLADE WITH WINGLET1 nose cone SCALE 1-751 t-mount simple SCALE 1-75

1 380.00 380.00

Prototype(s) Option 2:Description: Prototype Set (see below)Material: ABS (FDM Process)Color: Any

Quantity Part Name

6 SCALE 1-75 BLADE WITH WINGLET1 nose cone SCALE 1-751 t-mount simple SCALE 1-75

1 260.00 260.00

-Project duration of 3 - 5 business days is ARO (at receipt of order)and based on having all required information and owner furnsiheditems from the customers to begin work.

-Shipping & Handling via TBD

Page 1

QuoteDate

11/10/2011

Estimate #

4097

Name / Address



Project

11-10-11 Objet/FDM




Project Notes:

**The tapered edge in the "SCALE 1-75 BLADE WITHWINGLET" model will not fully resolve in standard prototypingprocesses**

-To initiate the project, job terms must be established with MydeaTechnologies Corporation along with a formal Purchase Order. Otherwise a 50% deposit and authorized credit card on file isrequired to start the project.

Page 2

QuoteDate

11/15/2011

Estimate #

4109

Name / Address



Project

11-15-11 SLA Nanotool




Prototype(s):Description: Prototype Set (see below)Material: SLA Nanotool, built in 0.002" layersColor: Any

Quantity Part Name

1 Blade Prototype Assembly SCALE 1-75 - nose coneSCALE1-75-11 Blade Prototype Assembly SCALE 1-75 - t-mountsimpe SCALE 1-75-1.stl 3 Prototype Blade-With Winglet (Scaled 1 - 75)3 Prototype Blade-Without Winglet (Scaled 1 - 75)

1 990.00 990.00

Prototype(s):Description: Prototype Set (see below)Material: SLA Nanotool, built in 0.004" layersColor: Any

Quantity Part Name

1 Blade Prototype Assembly SCALE 1-75 - nose coneSCALE1-75-11 Blade Prototype Assembly SCALE 1-75 - t-mountsimpe SCALE 1-75-1.stl 3 Prototype Blade-With Winglet (Scaled 1 - 75)3 Prototype Blade-Without Winglet (Scaled 1 - 75)

660.00 660.00

Page 1

QuoteDate

11/15/2011

Estimate #

4109

Name / Address



Project

11-15-11 SLA Nanotool




-Project duration of 3 - 5 business days is ARO (at receipt of order)and based on having all required information and owner furnsiheditems from the customers to begin work.

-Shipping & Handling via TBD

General notes:

-To initiate the project, job terms must be established with MydeaTechnologies Corporation along with a formal Purchase Order. Otherwise a 50% deposit and authorized credit card on file isrequired to start the project.

Page 2


Page | 125

Appendix D: Technical Drawings for Prototype

t-mount



SCALE: 1:32 WEIGHT:

REVDWG. NO.

ASIZE

TITLE:

NAME DATE

COMMENTS:

Q.A.

MFG APPR.

ENG APPR.

CHECKED

DRAWN

FINISH

MATERIAL



APPLICATION

USED ONNEXT ASSY


5 4 3 2 1

set screw mount



SCALE: 1:64 WEIGHT:

REVDWG. NO.

ASIZE

TITLE:

NAME DATE

COMMENTS:

Q.A.

MFG APPR.

ENG APPR.

CHECKED

DRAWN

FINISH

MATERIAL



APPLICATION

USED ONNEXT ASSY


5 4 3 2 1

Prototype Blade-Without Winglet (Scaled 1 - 75)



SCALE: 1:2 WEIGHT:

REVDWG. NO.

ASIZE

TITLE:

NAME DATE

COMMENTS:

Q.A.

MFG APPR.

ENG APPR.

CHECKED

DRAWN

FINISH

MATERIAL



APPLICATION

USED ONNEXT ASSY


5 4 3 2 1

Prototype Blade-With Winglet (Scaled 1 - 75)



SCALE: 1:2 WEIGHT:

REVDWG. NO.

ASIZE

TITLE:

NAME DATE

COMMENTS:

Q.A.

MFG APPR.

ENG APPR.

CHECKED

DRAWN

FINISH

MATERIAL



APPLICATION

USED ONNEXT ASSY


5 4 3 2 1

DO NOT SCALE DRAWING

nose cone

SHEET 1 OF 1


SCALE: 1:64 WEIGHT:

REVDWG. NO.

ASIZE

TITLE:

NAME DATE

COMMENTS:

Q.A.

MFG APPR.

ENG APPR.

CHECKED

DRAWN

FINISH

MATERIAL



APPLICATION

USED ONNEXT ASSY


5 4 3 2 1

3.125

120.00° 1.781

1.563

.120

1.000

Heavy Hex Flat Jam Nut_AI



SCALE: 1:2 WEIGHT:

REVDWG. NO.

ASIZE

TITLE:

NAME DATE

COMMENTS:

Q.A.

MFG APPR.

ENG APPR.

CHECKED

DRAWN

FINISH

MATERIAL



APPLICATION

USED ONNEXT ASSY


5 4 3 2 1


Page | 126

Appendix E: Data from Testing

Results for test with winglets

Test 1 Test 2 Resistance Voltage Current (mA) Power (W) Voltage Current (mA) Power (W)

0 7.91 0 0 7.92 0 0 1000 6.56 6.59 0.043230 6.53 6.55 0.042772 2000 7.15 3.59 0.025669 7.05 3.53 0.024887 3000 7.35 2.46 0.018081 7.18 2.39 0.017160 4000 7.46 1.87 0.013950 7.37 1.83 0.013487

10000 7.65 0.75 0.005738 7.65 0.75 0.005738 15000 7.7 0.49 0.003773 7.5 0.49 0.003675 20000 7.76 0.37 0.002871 7.58 0.36 0.002729 25000 7.73 0.28 0.002164 7.68 0.28 0.002150 30000 7.8 0.24 0.001872 7.67 0.24 0.001841 40000 7.8 0.17 0.001326 7.71 0.18 0.001388 45000 7.77 0.15 0.001166 7.67 0.15 0.001151 60000 7.77 0.11 0.000855 7.64 0.1 0.000764


0 7.92 0 0 7.91 0 0 1000 6.51 6.55 0.042641 6.51 6.52 0.042445 2000 7.06 3.54 0.024992 7 3.53 0.024710 3000 7.3 2.44 0.017812 7.25 2.42 0.017545 4000 7.36 1.82 0.013395 7.36 1.84 0.013542

10000 7.56 0.74 0.005594 7.58 0.74 0.005609 15000 7.52 0.49 0.003685 7.6 0.49 0.003724 20000 7.52 0.35 0.002632 7.61 0.36 0.002740 25000 7.62 0.28 0.002134 7.66 0.29 0.002221 30000 7.57 0.23 0.001741 7.55 0.23 0.001737 40000 7.66 0.17 0.001302 7.61 0.17 0.001294 45000 7.63 0.15 0.001145 7.61 0.15 0.001142 60000 7.61 0.13 0.000989 7.6 0.1 0.000760


Page | 127

Results for test without winglets


0 7.91 0 0 7.92 0 0 1000 6.4 6.45 0.041280 6.53 6.58 0.042967 2000 7.09 3.56 0.025240 7.09 3.54 0.025099 3000 7.31 2.44 0.017836 7.24 2.42 0.017521 4000 7.37 1.84 0.013561 7.4 1.84 0.013616

10000 7.6 0.75 0.005700 7.52 0.74 0.005565 15000 7.68 0.49 0.003763 7.6 0.49 0.003724 20000 7.69 0.37 0.002845 7.64 0.37 0.002827 25000 7.7 0.28 0.002156 7.65 0.28 0.002142 30000 7.68 0.25 0.001920 7.61 0.24 0.001826 40000 7.75 0.17 0.001318 7.6 0.17 0.001292 45000 7.75 0.15 0.001163 7.66 0.15 0.001149 60000 7.73 0.1 0.000773 7.66 0.1 0.000766


0 7.92 0 0 7.91 0 0 1000 6.49 6.51 0.042250 6.51 6.53 0.042510 2000 7.08 3.56 0.025205 7.05 3.53 0.024887 3000 7.27 2.42 0.017593 7.16 2.39 0.017112 4000 7.38 1.85 0.013653 7.29 1.82 0.013268

10000 7.57 0.74 0.005602 7.47 0.73 0.005453 15000 7.54 0.49 0.003695 7.49 0.48 0.003595 20000 7.67 0.36 0.002761 7.49 0.36 0.002696 25000 7.64 0.29 0.002216 7.56 0.28 0.002117 30000 7.62 0.23 0.001753 7.52 0.23 0.001730 40000 7.6 0.17 0.001292 7.56 0.17 0.001285 45000 7.68 0.15 0.001152 7.55 0.14 0.001057 60000 7.67 0.11 0.000844 7.51 0.1 0.000751

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