Bachelor’s Degree in Aerospace Technology Engineering Bachelor Thesis
Project of designing and manufacturing a small horizontal axis wind turbine using 3D printing technologies
Document: REPORT
Author:
Guillem Vergés i Plaza
Supervisor:
Francesc Xavier Sanz Cano
Co-Supervisor:
Álvaro Luna Alloza
Delivery date: Presentation date: 27/04/2020 11-22/05/2020
Abstract
The goal of this project is to design and manufacture a horizontal axis wind turbine. Its main requirements are a diameter of 1 meter and a construction based on 3D printing. The design process is focused on the interaction between the torque produced by the rotor and the one demanded by the electrical generator. In order to optimize it, a BEMT code is developed and validated against QBlade. The design is also constrained by the starting behavior, which may be a critical point provided that the wind turbine must be controlled by passive means. After the aerodynamic study, the loads and the structure are evaluated following the small wind turbines guideline IEC 61400-2. The blades are printed in two parts using PETG and a carbon fiber beam. The other components of the wind turbine are also studied, as well as the aerodynamic noise produced by the rotor. Eventually, a final product is obtained, although there is still room for a more detailed analysis and further optimization. The use of 3D printing allows fast prototyping and enables extensive testing. Nevertheless, there are added difficulties in anticipating the structural properties, which is its main drawback during the design process.
L’objectiu d’aquest projecte és dissenyar i fabricar un aerogenerador d’eix horitzontal. Els requeriments principals són un diàmetre d’1 metre i una construcció basada en la impressió 3D. El procés de disseny se centra en la interacció entre el parell produït pel rotor i el que demanda el generador elèctric. Per optimitzar-lo, un codi BEMT s’ha desenvolupat i validat amb el software QBlade. El disseny també està restringit pel comportament d’arrancada, que pot ser un punt crític tenint en compte que tot l’aerogenerador serà controlat passivament. Després de l’estudi aerodinàmic, les càrregues i l’estructura són avaluades seguint la normativa de petits aerogeneradors IEC 61400-2. Les pales estan impreses en dues parts fent servir PETG i una biga de fibra de carboni. Els altres components de l’aerogenerador també estan estudiats, així com el soroll produït pel rotor. Al final s’ha obtingut un producte complet, tot i que encara hi ha possibilitat de fer anàlisis més complets i una millor optimització. L’ús de la impressió 3D permet prototipar ràpidament i fer una gran quantitat d’assajos. Tanmateix, hi ha dificultats afegides per caracteritzar les propietats estructurals de les peces, fet que esdevé el seu principal inconvenient durant el procés de disseny.
El objetivo de este proyecto es diseñar y fabricar un aerogenerador de eje horizontal. Los requerimientos principales son un diámetro de 1 metro y una construcción basada en la impresión 3D. El proceso de diseño se centra en la interacción entre el par producido por el rotor y el que demanda el generador eléctrico. Para optimizarlo, se ha desarrollado un código BEMT, validado mediante el software QBlade. El diseño también está restringido por el comportamiento de arranque, que puede ser un punto crítico teniendo en cuenta que todo el aerogenerador estará controlado pasivamente. Después del estudio aerodinámico, las cargas y la estructura son evaluadas siguiendo la normativa para pequeños aerogeneradores IEC 61400-2. Las palas están impresas en dos partes usando PETG y una viga de fibra de carbono. Los otros componentes del aerogenerador también se estudian, así como el ruido producido por el rotor. Al final se ha obtenido un producto completo, aunque todavía hay posibilidades de profundizar en los análisis y la optimización. La impresión 3D permite prototipar rápidamente y hacer una gran cantidad de ensayos. Sin embargo, hay dificultades añadidas en la caracterización de las propiedades estructurales de las piezas, lo que acontece el principal inconveniente durante el proceso de diseño. Declaration of honour
I declare that,
• the work in this Degree Thesis is completely my own work,
• no part of this Degree Thesis is taken from other people’s work without giving them credit,
• all references have been clearly cited.
I understand that an infringement of this declaration leaves me subject to the foreseen disci- plinary actions by the Universitat Politècnica de Catalunya - BarcelonaTECH.
Title of the Thesis: Project of designing and manufacturing a small horizontal axis wind turbine using 3D printing technologies
Student Name: Guillem Vergés i Plaza
Date: 27/04/2020
Signature: Contents
Contents i
List of Figures iii
List of Tables v
Symbols vi
1 Introduction 1 1.1 Aim...... 1 1.2 Scope...... 1 1.3 Requirements...... 3 1.4 Justification of the need...... 3
2 Background and review of the state of the art4 2.1 History and impact of small wind turbines...... 4 2.2 Advantages and disadvantages...... 6 2.3 Design solutions...... 7 2.4 State of the market...... 10
3 Approach and decision on possible solutions 12 3.1 General architecture...... 12 3.2 Design procedure...... 14
4 Electrical design 16 4.1 Introduction and general architecture...... 16 4.2 Generator selection...... 17 4.3 Electrical system architecture...... 19
5 Aerodynamic design 21 5.1 Airfoil selection...... 21 5.2 Blades aerodynamic design...... 27 5.2.1 Power curve calculation procedure...... 27 5.2.2 Theoretical approach and design challenge...... 29 5.2.3 Optimization procedure...... 33 5.2.4 Start-up analysis...... 37 5.3 Final results...... 43
i CONTENTS
6 Structural design 48 6.1 3D printing initial considerations...... 48 6.1.1 Printer characteristics...... 48 6.1.2 Filament selection...... 49 6.2 Loads calculation...... 50 6.3 Blades structural design...... 56 6.3.1 Beam study...... 56 6.3.2 Blade parts attachment...... 59 6.4 Hub design...... 62 6.4.1 Blade-hub joint...... 62 6.4.2 Hub-shaft joint...... 64 6.5 Printing properties...... 65 6.5.1 Blade...... 65 6.5.2 Pin joints...... 67 6.5.3 Hub...... 67 6.6 Tower assessment...... 69
7 Tail study 71 7.1 Analysis of an existing tail...... 71 7.2 Furling tail design for over-speed protection...... 75
8 Noise prediction 77 8.1 Noise mechanisms studied...... 77 8.2 Boundary layer parameters analysis...... 79 8.3 Noise calculation results...... 81 8.4 Tonality check...... 84 8.5 A-Weighting results...... 85
10 Summary of the results 89 10.1 Budget summary...... 89 10.2 Funding...... 89 10.3 Analysis and assessment of the environmental implications...... 89 10.4 Future lines of work...... 90 10.5 Planning and programming of the next stage...... 92 10.6 Conclusions...... 93
Bibliography 96
ii List of Figures
2.1 Total cumulative installed capacity of SWT by country...... 5 2.2 SWT installed capacity forecast...... 6 2.3 Upwind and downwind wind turbines...... 8 2.4 Power coefficient as a function of the number of blades and wind turbine type..9
3.1 Influence of the tip speed ratio on the centrifugal force...... 13 3.2 Design procedure...... 15
4.1 Different small wind turbine controllers...... 20
5.1 Reynolds number ranges...... 22 5.2 S1223 airfoil shape...... 25 5.3 S1223 airfoil polar curves...... 25 5.4 S1223 extrapolated lift coefficient curve...... 26 5.5 S1223 extrapolated drag coefficient curve...... 27 5.6 Power curve calculation procedure...... 28 5.7 Optimal chord distribution according to Betz and Schmitz...... 30 5.8 Power coefficient comparison between Betz’s and Schmitz’s blade geometries... 30 5.10 Blade geometry optimization procedure scheme...... 33 5.11 Optimization procedure first results...... 34 5.12 Chord and twist distribution for different optimized wind speeds...... 34 5.13 Operation results of the rotor optimized for λ = 2.2...... 35 5.14 Pitch influence on the power coefficient curve...... 35 5.15 Chord influence on the power coefficient curve...... 36 5.16 Torque curve considered for the starting procedure...... 38 5.17 Starting torque and AEP as a function of the pitch angle...... 39 5.18 Intersections between the rotor curve and the generator curve at low wind speeds. 41 5.19 Steady power curve at low wind speed with two intersection points per wind speed. 41 5.20 Rotor speed and torque during the starting sequence...... 42 5.21 Blade section behavior during the starting sequence...... 42 5.22 Final chord and twist distribution...... 43 5.23 Final adimensional power coefficient curves...... 44 5.24 Final aerodynamic design: Power curve, power coefficient and AEP contribution. 44 5.25 Final aerodynamic design: Rotor speed and tip speed ratio...... 45 5.26 Final aerodynamic design: Thrust and thrust coefficient...... 45 5.27 Final aerodynamic design: Angle of attack along the blade for different wind speeds. 46 5.28 Final aerodynamic design: Lift coefficient and efficiency along the blade...... 46 5.29 Final aerodynamic design: Sectional torque contribution...... 47
iii LIST OF FIGURES
6.1 Examples of layer separation using ASA...... 50 6.2 Connector that will be used between the beam and the hub...... 57 6.3 Available space inside the blade to fit the carbon fiber beam...... 59 6.4 Blade joint shape and dimensions...... 60 6.5 Bed adhesion issue...... 61 6.6 Insulating tape in the blade attachment...... 61 6.7 Hub-blade joint design...... 62 6.8 Blade root stress distribution...... 63 6.9 Hub-shaft joint design...... 64 6.10 Alternating extra wall and fill gap between walls settings...... 66 6.11 Screenshot of the sliced root part of the blade...... 68
7.1 Scheme of the main geometrical dimensions of the tail...... 72 7.2 Yaw misalignment time response...... 74 7.3 Basic furling geometry...... 75
8.1 Turbulent Boundary Layer - Trailing Edge noise mechanism...... 78 8.2 Laminar Boundary Layer - Vortex Shedding noise mechanism...... 78 8.3 Separated/Stalled Flow noise mechanism...... 78 8.4 Tip Vortex Formation noise mechanism...... 79 8.5 Trailing Edge Bluntness - Vortex Shedding noise mechanism...... 79 8.6 Boundary layer displacement thickness for different scenarios...... 80 8.7 Noise spectrum for each wind speed...... 81 8.8 Frequency spectrum of all noise mechanisms at 13 m/s...... 82 8.9 Frequency spectrum of all noise mechanisms at 9 m/s...... 82 8.10 Noise per section at 13 m/s...... 83 8.11 Noise per section at 9 m/s...... 83 8.12 Tonality study at 9 m/s...... 84 8.13 Final noise results per wind speed considering A-Weighting...... 85
9.1 Wind resource assessment of the possible installation site...... 87 9.2 Annual Energy Productions (AEP) predictions...... 87
10.1 Gantt diagram of the next stages of the project...... 92 10.2 Final wind turbine...... 95
iv List of Tables
1.1 Deliverable of each scope task...... 2
2.1 State of the market of small wind turbines...... 11
4.1 Generator selection: model and manufacturer of each option...... 18 4.2 Generator selection: characteristics of each option...... 18 4.3 Characteristics of the selected generator...... 19
5.1 Airfoils selected to be studied...... 23 5.2 Airfoil selection results...... 24 5.3 Intersection tip speed ratios obtained for each wind speed...... 34 5.4 AEP and start-up wind speed for different pitch angles...... 36 5.5 AEP and start-up wind speed for different chord offsets...... 37 5.6 Final parameters for the starting calculations...... 40
6.1 3D printer used (Ender-3) characteristics...... 48 6.2 Main characteristics of the filaments considered...... 49 6.3 Results of the filament comparison...... 49 6.4 Design load cases for the simplified load calculation method...... 51 6.5 IEC basic parameters for SWT class...... 51 6.6 Parameters used for the loads calculation...... 52 6.7 Loads obtained from DLC "I"...... 55 6.8 Final loads obtained in the blade and the rotor shaft using the SLM...... 55 6.9 Structural properties of the carbon fiber tube...... 57 6.10 Printing cost and time for each part...... 68 6.11 Characteristics of the tower analyzed...... 69
7.1 Tail dimensions...... 71 7.2 Inertia about the yaw axis...... 74
8.1 Noise parameters definition...... 81
9.1 Typical roughness length values...... 86 9.2 Annual Energy Production (AEP) and Discounted Payback Period (DPP).... 88 9.3 Discounted Payback Period for different average wind speeds...... 88
10.1 Project’s main costs...... 89
v Symbols
Symbol Description Unit a Axial induction factor - a0 Tangencial induction factor - 2 Ad Actuator disk section m 2 Aproj Projected area perpendicular to the incoming wind m 2 At Tail fin area m AEP Annual Energy Production W h AR Aspect Ratio - b Tail fin span m c Blade chord m c Tail fin chord m Cd Sectional drag coefficient -
Cds Stall drag coefficient - Cf Generic force coefficient - Cl Sectional lift coefficient - Cl,opt Optimum lift coefficient -
Cls Stall lift coefficient - CP Power coefficient - CQ Torque coefficient - CT Thrust coefficient - Cx Coefficient of blade element force normal to the rotor plane - Cy Coefficient of blade element force parallel to the rotor plane - dT,e Exterior tower diameter m dT,i Interior tower diameter m D Sectional drag in the tower N m−1 er Rotor eccentricity m E Aerodynamic efficiency - ET Tower elastic modulus Pa f Noise spectrum frequency Hz fk Characteristic material strenght Pa fT Tower first natural frequency Hz F Prandtl loss factor - Feq,adh Equivalent axial force at the beam root N Fx−shaft Axial force at rotor shaft N FzB Radial force at blade root N g Gravity acceleration m s−2 G Short-circuit torque factor - H Tower height m
vi Symbols
Symbol Description Unit i Tail fin indentation m 4 IB Blade beam area inertia m 4 IT Tower area inertia m 2 JR Rotor mass moment of inertia kg m 2 JY Yaw system mass moment of inertia kg m Lrb Distance from rotor centre to first bearing m Lrt Distance from rotor centre to yaw axis m Ln Nacelle length m mB Single blade mass kg mR Rotor mass kg mN Nacelle mass kg mT Tower mass kg mTT Tower top mass kg Mshaft Resultant bending moment on the rotor shaft Nm MxB In-plane moment at blade root Nm Mx−shaft Torsion moment on the rotor shaft Nm MyB Out-of-plane moment at blade root Nm N Number of blades - p Pressure N m−2 p Tail fin centre of pressure - yaw axis distance m −2 pd Pressure in the actuator disk N m P Power W PCR Euler’s critical load for buckling N Q Torque N m Qs Starting torque N m Qr Resistive or cogging torque N m r Local blade radius m re Exterior radius of the beam m ri Interior radius of the beam m R Total blade radius m Rcog Distance from blade centre of gravity to rotor axis m Re Reynolds number - S Airfoil surface m2 t Airfoil thickness (usually used as t/c) m ts Starting time s T Thrust N U Wind speed m s−1 −1 Ucut−in Wind speed for cut-in (start producing power) m s −1 Ud Wind speed in the actuator disk m s −1 Udesign Design wind speed for loads calculation m s −1 Ue50 50 years return wind speed for loads calculation m s −1 Uopt Wind speed for the optimization procedure m s −1 Uref Reference wind speed for the loads calculation m s −1 Us Wind speed for starting (spinning) m s −1 UT Total velocity at blade element m s −1 Uw Wind speed down-stream m s −1 U∞ Wind speed in the far-wake m s
vii Symbols
Symbol Description Unit α Angle of attack rad αopt Angle of attack - optimal rad αs Angle of attack - stall rad β Geometric twist τ plus pitch θ rad γf Partial safety factor for loads - γm Partial safety factor for material - δ Boundary layer thickness m δ∗ Boundary layer displacement thickness m ∆ Indicates amplitude of a fatigue load if preciding F or M - ζ Yaw system damping - θ Pitch angle rad θ Yaw misalignment angle rad λ Tip speed ratio - λr Local blade section tip speed ratio - λints Tip speed ratio of intersection with the generator curve - ρ Air density kg m−3 −3 ρb Blades density kg m σB Stress at blade beam root Pa σT Stress at tower bottom Pa σr Local blade solidity - µ Nondimensional local blade radius r/R - µ Kinematic viscosity of air m2 s−1 τ Geometric twist of the blades rad τadh Mean shear stress at beam-insert joint Pa φ Flow angle rad ϕ Wind direction angle in earth-fixed coordinates rad ψ Rotor azimuth angle rad ωn Yaw system natural frequency Hz −1 ωyaw,max Maximum yaw rate for loads calculation rad s Ω Rotor speed rad s−1
viii Chapter 1
Introduction
1.1 Aim
The objective of this project is to design and manufacture a small wind turbine using 3D printing technologies. The rotor design and optimization will be the main focus, and its structural and aerodynamic design will aim to maximize the power extracted and create a final design that can be easily 3D printed. The rest of the wind turbine components (hub, nacelle, generator, tail, and tower) will be studied and integrated in the global design in order to have a final product. The power produced in a possible installation site will be finally analyzed, as well as the noise generated by the blades.
1.2 Scope
The areas that this project intends to cover are summarized in this section.
1. Conceptual Design
1.1. Study the state of the market and the particularities of the small wind turbines. 1.2. Based on the preceding point, define the main characteristics of the product. 1.3. Arrange a design procedure for the complete wind turbine.
2. Electrical Design
2.1. Study the general architecture and possible integration options. 2.2. Select a suitable generator. 2.3. Define the complete electrical scheme.
3. Aerodynamic Design
3.1. Select an airfoil. 3.2. Create and validate a BEMT code to calculate the blades performance. 3.3. Define an optimization procedure and determine the chord and twist distribution. 3.4. Analyze the start-up. 3.5. Study the behavior and operation in all the wind speed range.
4. Structural Design
1 Scope
4.1. Analyze the 3D printing limitations and select a filament type. 4.2. Calculate the loads on the wind turbine. 4.3. Determine the blade structural design. 4.4. Determine the hub structural and mechanical design. 4.5. Select the printing settings for the 3D printed parts. 4.6. Study a possible tower.
5. Tail Study
5.1. Analyze an existing tail and its integration with the designed wind turbine. 5.2. Study the possibility of using a furling tail.
6. Noise Prediction
6.1. Create and validate a noise code to evaluate the design. 6.2. Analyze the influence of the boundary layer parameters. 6.3. Calculate and study the aerodynamic noise produced by the blades. 6.4. Determine whether there are tonality issues.
7. Wind Resource Assessment: analyze the wind availability and the economic feasibility of a possible installation site.
8. Manufacturing: Build the final design and assemble all the parts.
Table 1.1: Deliverable of each scope task.
Task Report Report Attachment Task Report Report Attachment 1.1 2 4.2 6.2 1.2 3.1 4.3 6.3 1.3 3.2 4.4 6.4 2.1 4.1 4.5 6.5 2.2 4.2 4.6 6.6 2.3 4.3 5.1 7.1 3.1 5.1 1.2 5.2 7.2 3.2 5.2.1 1.1 6.1 8.1 2.1, 2.3 3.3 5.2.2, 5.2.3 1.3.2 1.3.1 6.2 8.2 3.4 5.2.4 6.3 8.3, 8.5 2.2 3.5 5.3 6.4 8.4 4.1 6.1 7 9
The manufacturing process (point 8) is described in the technical sheets. The design of each component is justified in the respective section of the report, and all the dimensions are located in the drawings document.
2 Requirements
1.3 Requirements
The design requirements that will limit and constrain the design are the following:
1. A rotor diameter of 1 meter.
2. A completely passive operation, without any torque, pitch, or yaw control.
3. Maximize the 3D printing use in the manufacturing process.
1.4 Justification of the need
Although this project will focus on the wind turbine design, it is especially interesting to study to which extent the 3D printing technologies may be useful to achieve this objective. This can be the interaction between two highly growing areas: wind energy and 3D printing.
On one hand, wind power is leading the path to a more renewable energy generation. The temperature rise in the earth should be limited to below 2ºC this century to prevent highly devastating consequences like melting glaciers or crop failure. The current expectations are to have a rise between 3.6ºC and 5.3ºC. The power sector alone is responsible for about 40% of global CO2 emissions. Therefore, quick actions in this regard should be taken, and renewable energy deployment around the globe is required to mitigate it [1]. Wind energy plays a key role in this movement because it is already highly developed, it does not emit pollutants, has a minimal water usage footprint, and it is quick to install [2]. Although the main contributor to this change is the large scale wind power, the importance and growth perspective of small wind turbines is also highly remarkable [3–5]. Furthermore, an increase of small wind turbine energy would help to decentralize and democratize the power industry. It would also allow a better grid integration, because the power production will be closer to its consumption, and the system would be more stable, less affected by punctual disturbances, and less prone to blackouts if everything is integrated within a smart grid [6].
On the other hand, additive manufacturing (or colloquially: 3D printing) also has an increasing trend. Although its future as a mass production method remains uncertain, its use for rapid prototyping, iterative design, or DIY (Do It Yourself) projects is beyond discussion [7]. It is reducing its cost and improving its availability [8], and the DIY community is collaborating and sharing a lot of knowledge and content (e.g. [9,10]). Hence, it may be useful to explore whether this can help home-made wind turbines manufacturing. This would harmonize quite well with the latter point of the previous paragraph: the interest of building wind turbines at a very small scale, either by particulars or collaborative projects.
3 Chapter 2
Background and review of the state of the art
As the aim of the project is to design a new product, a good knowledge of the state of the art is necessary to have a starting point. In this section the current framework of small wind turbines will be described.
2.1 History and impact of small wind turbines
The first steps in the development of small and micro wind turbines took place during the thirties, with the objective of charging batteries in remote households. Manufacturers like Ja- cobs [11] or Parris-Dunn [12] produced this type of wind turbines in the United States. In the late forties, with the arrival of the electrical grid to the rural areas, this industry practically disappeared. It remained in hibernation until the seventies, when the petrol crisis created the need for alternative energy sources. The attention came back to the small wind turbine energy, not only in the United States but also in Europe, where, for example, the Bornay brothers started their company in Spain [13].
During the eighties this technology started to evolve, as the manufacturers began to abandon the DC dynamo generators and incorporated synchronous generators with permanent magnets (AC). In order to obtain DC current for charging batteries, rectifiers were needed. Over time these rectifiers were connected to inverters to be able to connect the wind turbines to the grid. Induction generators began to be used as well in order to connect them directly to the grid, but it was a difficult solution to implement in isolated applications due to the generator’s need to be excited from outside. The need for a gearbox also difficulted its success. The size and power produced started growing gradually, and before the ending of the eighties 50 kW was considered a small wind turbine, with diameters of more than 15 m. [5] The current regulations (IEC 61400-2 [14]) establish that the limit of a small wind turbine is given by a swept area smaller than 200 m2.
The small wind turbines technology has been evolving from the isolated applications to he mod- ern grid-connected installations, and has even entered into the residential and urban outline. These last applications have caused the increased use of vertical axis solutions. The most well known developments are the Savonius and Darrenius wind turbines, but also the Gorlov design and some combined schemes are being used [5].
4 History and impact of small wind turbines
Regarding the impact of the small wind energy, the last World Wind Energy Association (WWEA) report indicates, from 2014 data, that there were 945,000 small wind turbines in- stalled all over the world, producing almost 850 MW [3]. China and USA are clearly leading this market, and the biggest market in Europe is the UK. Unfortunately, developing countries have an anecdotal presence, even though this was a technology initially developed with the ob- jective of electrifying isolated regions, and the enormous wind power potential (especially in the eastern highlands of Africa) [15]. All of this can be seen in the following figure:
Figure 2.1: Total cumulative installed capacity of SWT by country. Retrieved from WWEA 2016 report [3].
The forecast for new installations in this report predicted a big growth in the annual installed capacity. Unfortunately there is no data available or a newer WWEA report to check the last tendency of the market.
5 Advantages and disadvantages
Figure 2.2: Small Wind Turbines installed capacity forecast. Retrieved from WWEA 2016 report [3].
Analyzing the perspectives in Spain, the last Renewal Energy Plan (PER) established the ob- jective of reaching 300MW installed in 2020, predicting more than 50MW of new installations every year on from 2020 [4].
The investment in this kind of wind turbines is usually made by private individuals or small com- munities in order to partially or totally fulfill their demand for electricity or heating. However, a large portion of the buyers are disappointed by the actual energy obtained from these wind turbines. The main reason for this is the promotion of inaccurate and overstated information of the power output by manufacturers or installers. The satisfaction and reviews of this kind of products can spread very fast, and this type of feedback is reducing the confidence of this sort of economic investing, consequently slowing down this sector’s growth [16].
2.2 Advantages and disadvantages
The generation of electricity through small wind turbines has some particular advantages and disadvantages in comparison to larger wind turbines or other sources of renewable energy. In this section these particular characteristics will be enumerated [5, 17].
Advantages 1. Renewable energy: It is virtually inexhaustible and does not produce air emissions nor pollution.
6 Design solutions
2. It can coexist with other installations and land uses (for example agriculture).
3. Easy and fast installation: the study made in section 2.4 shows that a strong point of commercial SWTs is the possibility of an easy installation, which facilitates direct sale to the final user.
4. Suitable for isolated areas due to the possibility of battery charging applications and integration with other types of generation. It allows the possibility to achieve electric energy independence.
5. Energy is generated close to the consumption points, which reduces the transportation losses. It also does not require additional big installations for transportation and evacu- ation of electricity.
6. Reduced maintenance and operation costs, and high reliability.
7. Less environmental and visual impact.
8. Can be generally optimized for moderated wind speeds, which eliminates the need for complex viability studies and allows a better production in average installation sites.
Disadvantages 1. The wind is intermittent, uncontrollable, and relatively unpredictable, so other sources of energy are required to ensure enough electricity production.
2. The visual impact can still be a drawback.
3. The noise is important in residential areas.
4. Flickering: visual phenomena produced by the periodic projection of the blades shadow.
5. Lack of complex active control systems due to price limitations. SWTs are generally simpler than large wind turbines.
2.3 Design solutions
The design of any wind turbine in general has multiple options and solutions. In this and the following section these alternatives will be analyzed, first with an explanation of each solution and then with its presence and importance in the market. The main different approaches for small wind turbines will be explained below: the axis orientation (horizontal axis wind turbines (HAWTs) and vertical axis wind turbines (VAWTs)), the rotor position in relation to the tower (upwind and downwind), the addition of a duct (diffusor augmented wind turbines DAWTs), the number of blades, and the power control method.
Axis orientation The major classification of wind turbines is commonly made from the position of the rotor axis of revolution: HAWTs and VAWTs. The most used solution is the horizontal design. As the small wind energy world usually follows the developments of the large wind turbines industry, close to 75% of SWTs are HAWTs. However, VAWTs have some advantages: they are conceptually simpler (since they do not require a yawing mechanism), there are some structural
7 Design solutions and maintenance benefits (the generator and the gearbox are placed close to the ground), and they need a lower cut-in wind speed. VAWTs can be based on drag (Savonius) or on lift (Darrenius), which is a much more efficient approach. A lot a of research is being done in the latter, as the aerodynamics are much more complex than HAWTs, and the overall performance is growing. VAWTs have been gaining presence in the last years, especially in urban environments. [16, 18]
Rotor position The wind turbines can also be divided by the position of the rotor in relation to the tower. The most common solution is using upwind wind turbines, situating the blades (relatively to the wind) in front of the tower (windward). The other alternative is called downwind, where the rotor is located on the back side of the turbine.
Figure 2.3: Upwind (a) and downwind (b) wind turbines. Extracted from [16].
The upwind wind turbines are characterized by a higher efficiency, as the impact of the tower and the nacelle to the incoming wind is much smaller in this configuration. However, there is risk of collision between the rotor and the tower, so the blades are required to have a higher stiffness or either be placed with some angle or distance. Another drawback of this design is the need of a yaw system in order to keep the rotor facing the wind, as the natural trend of the rotor is to move to the downwind position. In the SWTs this is usually accomplished using a tail vane.
These special requirements of the upwind wind turbines are precisely one of the principal ad- vantages of the downwind design: they are simpler. The lack of these needs is also beneficial in regard to the structural dynamics and weight of the wind turbine. The main disadvantage is the influence of the tower and the nacelle to the incoming wind profile, which leads to fluctuations of momentum in the blades. The fatigue damage and the resonance risk are a real danger to take into account. The noise generated is higher, as the turbulence produced by the tower will impact the blades. [16]
Diffusor augmented wind turbines An innovative design for HAWTs is the usage of a circular duct that encapsulates the rotor. These wind turbines are called DAWT, compact wind acceleration turbine (CWAT) or wind lens. The objective of this solution is to accelerate and uniformize the incoming flow through
8 Design solutions the rotor. Some studies have shown in wind tunnel test the benefits of this system [19], but little results are obtained in real outside conditions. The added mass due to the diffusor puts more stress in the tower and makes the operation of the yaw system more difficult. However, it is not strange to see this kind of system in boat’s SWTs. [16]
Number of blades
The selection of the number of blades (only referring to HAWTs) is a compromise between different aspects. The effects of varying the number of blades can be analyzed from both an aerodynamic and a dynamic perspective.
From the aerodynamic point of view, the performance (power coefficient) increases with the number of blades, but this effect has less importance from 3 blades on. The optimal rotational speed, on the other hand, decreases with the number of blades, and this is important to take into account because the aerodynamic noise produced (the most predominant) scales with the fifth power of the blade tip speed.
From the dynamic point of view, the main goal is to reduce the rotating mass in order to dimin- ish the loads that the structure will have to support. The weight of each blade is important.
Figure 2.4: Power coefficient as a function of the number of blades and wind turbine type. Extracted from [17].
The dominant solution for multi-megawatts wind turbines is the three-bladed rotor. More variety is observed in the world of SWTs, but the most used design is composed of three blades as well. The main advantage of this design is a higher stability: the power output oscillates less during a turn, the gravitational and gyroscopic forces are better balanced (reduction of vibration problems), and a smoother operation is achieved. The noise and the visual impact are also reduced. However, they are heavier and more complex in general than two or one-bladed rotors, and the installation and control system are more complicated. [17]
9 State of the market
Power control Once the generator reaches nominal power, a control system is required in order to maintain this value. This control system is also necessary to protect the wind turbine in case of stronger winds. If the wind speed exceeds the one required to reach nominal power, this system will waste part of the excess energy in order to avoid damaging the wind turbine. This is achieved, typically, by either an active pitch control or a passive stall control.
In a passive stall control system, the blades are bolted into the hub at a fixed angle. As the actual angle of attack of the blades increases with the wind speed (if the rotor speed is constant), the fixed pitch and twist of the blade can be designed in order to get the blades to stall at a desired point. If the rotor stalls, the torque and power generated will diminish. This solution avoids the need of a complex variable pitch system, but higher loads will be experienced. An- other possible passive option is a furling tail that turns the rotor away at high wind speeds [20].
On a pitch controlled wind turbine, there is an electronic controller that receives the generator’s power output. If this magnitude becomes excessively high, the controller varies the pitch of the blades. The effective angle of attack is reduced, and the torque and power produced by the blades drop. [21]
2.4 State of the market
The table 2.1 indicates a sample of the small wind turbines that can be commonly found in the market nowadays. Some interesting conclusions can be extracted from it:
1. The dominant design is the horizontal axis wind turbine, as seen in the preceding section.
2. All of them use direct drive configuration (lack of gearbox).
3. All mention a low start torque resulting in a low start wind speed (between 2 m/s and 4 m/s). However, it has been seen that the power output at these wind speeds is also very low. The objective of this feature could be an automatic starting procedure.
4. The usage of UV protection coatings on the blades.
5. The installability and the low noise production are essential characteristics from a commercial point of view.
6. Almost all of them are configured for battery charging applications, and some of them have one version for grid connexion and another one for battery charging at 24/48 V.
7. Most of them require a tower of at least 10 m height to reach nominal power (by man- ufacturer indication). However, almost none of them include it. Some brands offer the tower separately from the wind turbine, which is sold at almost the same prize as the wind turbine itself.
10 State of the market - 41 29 34 10 34 10 10 125 Weight [kg] poles) magnet magnet magnet magnet magnet magnet magnet 3 phase 3 phase 3 phase 3 phase 3 phase 3 phase 3 phase 3 phase 3 phase magnet s Generator permanent permanent permanent permanent permanent permanent permanent permanent permanent magnet (30 - speeds system Furling Passive Control (torque) (torque) (torque) (torque) regulator pasive by controller controller controller controller Electronic Electronic Electronic Electronic Electronic two action inclination control with (torque) and Passive pitch fiber fiber alloy nylon nylon Nylon Nylon GFRP GFRP GFRP GFRP Technic Injected Material and glass and glass CFRP or Aluminum 800 300 400 400 [W] 1500 1900 3000 1000 1000 power Nominal - 12 12 11 10 11 13 13 7.6 wind [m/s] speed Nominal - - 600 500 250 300 525 300 400 rotor [rpm] speed Nominal [m] 2.86 1.75 3.80 3.90 0.34 1.20 2.50 1.22 1.40 Rotor (1.38m (1.60m height) height) diameter Table 2.1: State of the market of small wind turbines. 2 5 3 3 1 3 3 3 3 of blades Number self blade VAWT VAWT, Upwind Upwind Upwind Upwind HAWT, HAWT, HAWT, HAWT, HAWT, HAWT, HAWT, Helicoidal regulating regulating regulating Downwind, Upwind, self Upwind, self Architecture 1 [ 26 ] 800 [ 13 ] Aeolos V PRO [ 22 ] SD Wind MarsRock 300W [ 25 ] Enair E30 AutoMaxx and Model Bornay Bee DB-400 [ 27 ] ST-1000 [ 24 ] Smarttwister Bergey Excel Manufacturer Windmill [ 28 ] Bornay 13 [ 13 ] 400W Economy Energy SD3 [ 23 ]
11 Chapter 3
Approach and decision on possible solutions
In this section the design approach followed is discussed and justified.
3.1 General architecture
The general architecture of the wind turbine will be based on the tendencies seen in the state of the market.
1. Horizontal axis, upwind wind turbine: The horizontal axis option is selected because it is the most used and studied. Although the vertical axis is growing in importance, the classic concept is chosen. The rotor position will also follow the usual convention: an upwind wind turbine is selected. A downwind concept would simplify the yaw stabilization system, but it could also lead to big fatigue loads and dangerous aeroelastic coupling. As the loads calculation that will be performed does not involve a detailed aerolastic analysis, it is desirable to avoid these possible problems from the beginning.
2. Three blades: In Figure 2.4 the influence of the number of blades on the optimal tip speed ratio and maximum power coefficient is shown. Following the same reasoning that was discussed there (Section 2.3), it is desirable to increase the power coefficient by selecting a higher number of blades, however the cost in material and loads of this option are the main drawback. In a small wind turbine, the effect of the tip speed ratio should also be taken into account. The tip speed ratio is defined as:
ΩR λ = (3.1) U∞ Due to its small radius, if a high tip speed ratio is desired, the required angular velocity of the blades must be very high. Thus, the corresponding centrifugal forces will increase as well. An approximated magnitude of this effect is represented in the Figure 3.1. This illustrates the importance of being able to operate at the lower tip speed ratio possible. Hence, three blades are preferable rather than two, specially in this case. When it comes to the change between three and four blades, the decision is not as clear as for the former option. The increase in power coefficient and the decrease in rotor speed are smaller, and the rotor instability might be a source of problems. The hub design is also
12 General architecture
4000
3000 F C
2000
1000 Rotor speed [rpm] Centrifugal force [N]
0 0 2 4 6 8 10 Tip speed ratio [-] Figure 3.1: Influence of the tip speed ratio on the centrifugal force. Values estimated at 10 m/s for a wind turbine of 1 m diameter.
compromised (more blades to join, more space needed), and the blade cost is increased once more. An excessive reduction of the rotor speed would also compromise the generator selection, because more pairs of poles would be required and the price and weight would increase. Hence, this option is discarded and three blades will be the final choice, following the trend of the market.
3. 1.0 m rotor diameter: This requirement was actually set by the capacities of the 3D printer that will be used. The printer characteristics will be described in more detail in the section 6.1.1. The biggest restriction it imposes is the available printing space: 220x220x250 mm, which means that the blades will have to be built from more than one piece. It can be anticipated that the union between the different parts will be an added difficulty to the design, so it may be helpful to minimize the number of pieces it is comprised of. A blade made of two pieces is selected. This option will keep the material cost as low as possible but will still involve the challenge of joining two different pieces, and the study and methodology used could be extrapolated to join more pieces.
4. Entirely passive control system: Large commercial wind turbines have torque and pitch control systems, which allow them to reduce loads, being able to operate in a wider range of wind speeds, and ultimately increase their power production. On the other hand, small wind turbines seldom have a pitch controller, and the torque control is not a clearly dominant option. For this project, none of them will be developed. Although a torque controller would simplify the aerodynamic design (as the rotor speed could be practically selected for each wind speed), there are two major drawbacks. Firstly, the hardware would increase in cost (a different generator plus the variable speed drive) and the software would increase in complexity. Secondly, it is desirable to develop a design that could be easily reproduced by anyone with access to a 3D printer. If a control system is included, both with the hardware and software it involves, it will likely be more difficult to replicate.
5. Over-speed control by furling: This characteristic is highly related to the preceding one. An over-speed control is needed even though there is not a controller for the normal operation. This will allow the turbine to operate safely under extreme wind conditions, which will increase its life span and simplify the structural requirements. There are two main options for a passive over-speed control:
13 Design procedure
The first option is a furling mechanism, which turns the rotor away from the incoming wind flow. The rotor can be either rotated around the tower axis or around the axis perpendicular to the tower and contained in the rotor plane. This rotation is achieved through the higher thrust obtained at higher wind speeds, and the system should be designed in a way that this higher force creates a moment around the above-mentioned axis. The furling mechanism should be dimensioned so that the deviation occurs at the desired wind speed. The second option is a passive stall mechanism, which simply uses the reduction in lift coefficient and the increase in drag coefficient in the post-stall region to create a ceiling in the power level as the wind speed increases. The passive stall mechanism is a simpler option. However, it imposes big restrictions in the blade geometry, and it creates big uncertainties in the aerodynamic post-stall behavior. Most importantly, it is a requirement for applying this option that the angle of attack increases with the wind speed. In the section 5.2.2 it can be seen that this is not meet. Due to all these disadvantages, the furling mechanism approach is selected.
6. Permanent magnet generator: If one option was dominant in the state of the market, it was the usage of permanent magnet generators. It is especially interesting the low rotational speed they can operate at, which can help to avoid the use of a gearbox. This trend will be followed, and a permanent magnet generator will be used as well.
7. Direct drive: In the state of the market it has been seen that the tendency of the market is also to avoid the use of a gearbox, which adds weight, mechanical complications and decreases the efficiency. This preference will also be followed throughout this project.
3.2 Design procedure
In a wind turbine almost everything is coupled. Therefore, is difficult to isolate and design each part separately. To obtain a complete design which takes into account all its different aspects, a iterative process should be made. The Figure 3.2 shows the procedure that will be followed, as well as the different parts in which the design can be divided by.
The first step will be to select an electrical generator (Section 4.2), which will establish a torque curve for the aerodynamic design, and a shaft shape for the hub design. Using this curve and selecting an airfoil (Section 5.1), the blade geometry will be optimized (Section 5.2.3) and the necessary corrections for the start-up will be applied (Section 5.2.4). With that, the final power curve of the wind turbine will be defined (Section 5.3).
For the structural part of the blade design, a loads calculation will be required (Section 6.2). The main two inputs for that will be the computed power curve and some structural assumptions (the weight, for example). Taking into account the loads obtained and the previous consider- ations of the 3D printing manufacture, the blade structural design will be conducted (Section 6.3). The root part of the blade will be closely related with the hub-blade joint (Section 6.4.1). The joint with the generator shaft will be the second constraint of the hub (Section 6.4.2).
The design process will be focused on the rotor, and the other components will not be directly designed but will be selected from the market and integrated in the design. The tower will be assessed (Section 6.6) considering the previously calculated loads. The response of a determined
14 Design procedure
Figure 3.2: Design procedure. tail will also be calculated (Section7). Once the full wind turbine has been designed, the noise spectrum will be predicted (Section8) and the wind resource assessment of a possible installa- tion site will be made (Section9). The installation site will also set the final architecture of the electrical design.
The process shown above does not fully cover the iterative nature of this design. The scope has been adjusted to a feasible point, and a procedure has been defined such that no steps must be repeated. Nonetheless, further optimization would require to extend this procedure. The loads, for example, should be calculated from the existent design values and not from conservative assumptions. The blade design could also use the noise results to try to reduce the aerodynamic noise produced, or the blade could be optimize differently depending on the installation site. Moreover, some of the steps conducted here could be done in a more detailed manner with more time and resources. All the possible future tasks are detailed in the Section 10.4.
There are two processes that will require the development of a code to be completed. The blades aerodynamic design will need a BEMT code, and the noise calculation will be done with the BPM equations adapted to a wind turbine. The validation and source code of both is listed in the Report Attachment.
15 Chapter 4
Electrical design
4.1 Introduction and general architecture
These sections will provide an overview of the electrical system and how it will be designed. Firstly, the general configuration of the system will be described and justified, and the main components to be used will be presented. Then, the selection of the generator will be made based on the available options in the market. Finally, the future procedure to select the rest of the components will be described, paying special attention to the interaction of the generator with the rotor curves.
Overview and generator
The generator is the most key component of this system. The type of generator used will define a lot of the specifications and needs for the other parts. As it has been explained in the state of the art (Section 2.1), the initial developments of small wind turbines used dynamo DC genera- tors. Modern designs go for three-phase AC permanent magnet generators (PMG). This change is given both by consumer demands (more AC-powered products) and recent advances in power electronics. The three-phase generators are also more stable and have a better power-weight ra- tio. Other designs use induction generators (IG), which have lower cost, no cogging torque, and better ruggedness. The major drawback of this option is a lower efficiency compared to PMG. This is due to the high heat losses when decreasing the rotor size. This type of generators also need excitation capacitors before they can generate power, which adds complexity and risk, as they are prone to failure and this could lead to rotor overspeed. These disadvantadges prevent the induction generators to be a real alternative to permanent magnet generators (as seen in the state of the market (Table 2.1)), and therefore for this design the main option will be chosen, and a PMG will be selected [29].
The obtained AC power is usually rectified into DC and then inverted back to produce AC power of a determined and constant voltage and frequency. The great improvements in modern inverters (in cost and capabilities) have benefited these conversions. This can be combined with a controller system that tracks the maximum power point, which is usual for wind turbines above the micro category but has higher costs and complexity associated. Filtering can also be used to reduce the harmonic distortion, specially if the power will be supplied to the grid. The inverter should control the power factor, and more importantly: have a safe shutdown mechanism in case of a grid loss. An usual method to do so is to shorten the output, although there are potential problems like the demagnetization of the magnet [29].
16 Generator selection
Gearbox This design option is put here because it affects directly the generator to be used, as the presence or not of a gearbox would modify the rpm range the generator is working on. Because of the added complexity, noise, and maintenance issues, the gearbox is mostly avoided in small wind turbines design. Moreover, the increase in resistive torque is important compared to the cogging torque of the generator and the inertia of the rotor. As the frequency of the blades decrease with the rotor size (the smaller the wind turbine, the faster it will rotate), it is possible (and common practice) to design it without a gearbox. Larger wind turbines usually need it because they rotor speed is much lower (8-15 rpm), and therefore the number of poles that a generator would need without gearbox is very large, which results in a very expensive option. In this case, a design without gearbox is feasible, and it will avoid the above-mentioned prob- lems. Consequently, a gearbox will not be used, and the rotor shaft will be connected directly to the generator (direct-drive).
Rectifier The function of the rectifier is to convert the AC current into DC current. One of the sim- plest ways to achieve so is using a diode rectifier, as there is no need for control as they turn on and off following the current wave. The output voltage, however, would not be constant, as the rectification only makes it positive. Usually, the low power rectifiers include a capacitor in the DC bus to filter it. It charges up to a voltage close to the AC sinusoidal line-to-line voltage.
As the wind speed varies, the generator and therefore the rectifier will be working under a wide range of voltage. This has two major consequences: 1. The generator voltage at low wind speeds could be so low that the diode losses became significant (around 0.7-0.9 V). This may be overcome with a transistor rectifier instead of using diodes, but an electronic controller would be needed. 2. At low wind speeds, the output DC voltage may be too low for the inverter to produce the needed AC voltage. To solve it, the rectifier may be followed by a boost converter. The wind speed regime that a micro wind turbine will be working in involves a lot of time at very low wind speeds. Therefore, these two issues should definitely be taken into consideration for the final design.
Inverter If AC output is desired, the electrical scheme shall include an inverter to converter from DC current to AC power of a fixed frequency and voltage. Without any filtering, the output of the bridge would be a square wave. However, this approach is used for some low power applica- tions, because most electrical devices can be powered with square wave AC. To obtain a better approximation to a sinusoidal waveform, a filter may be used, or a complex PWM algorithm to control the switching of the inverter.
4.2 Generator selection
In this section the generator that will be used will be selected. As it has been decided in the preceding section, the generator selected will be a Permanent Magnet Generator (PMG). Two
17 Generator selection tables with the options considered and its characteristics may be found below. Note that the vast majority of the options available come from Chinese manufacturers. This is mainly given by the fact that China has most of the reserves of the rare magnetic materials necessary for their manufacture [29]. The characteristics table is not fully completed, because some resellers would not reply to the author’s inquires (possibly because only one unit would be bought). On average, the reply times of the manufacturers or the resellers was quite long, which has been an added difficulty for this selection.
Table 4.1: Generator selection: model and manufacturer of each option.
Option Manufacturer Model 1 Shangai Laisa New Energy Technology LS-500 2 China Top Grand TGET220 3 Qingdao Greef New Energy GDG-320 4 Qingdao HenryD Wind Power Equipment 500W 5 Mecc Alte Eogen 30/16 6 Ningbo Ginlong Technologies GL-PMG-500A
Table 4.2: Generator selection: characteristics of each option.
Rated Max Rated Rated Starting Weight Price Delivery Total Option Power Power Speed Torque Torque W W rpm Nm Nm kg € € € 1 500 536 600 7.96 0.42 6.1 113 122 235 2 500 - 500 9.55 <0.1 8 370 - ∼500 3 500 620 200 23.87 <0.1 20 702 0 702 4 500 750 500 9.55 0.4 12.5 162 - ∼280 5 500 - 415 11.51 - 21.2 - - - 6 500 - 450 10.61 <0.5 14.4 200 - ∼320
Unfortunately, this study was done before the 1.0 m rotor diameter was set as a constraint for the design. The first approach was based on selecting a generator and after that adapt the rotor geometry to that. This is the reason why this study was done at first place. However, the blades that a 500 W generator would need are larger than 1.0 m diameter, and the needed material would increase the costs of this project. The final approach is the other way around: select a generator based on a determined rotor diameter. The results of this study are very useful either way, because the generator characteristics are very similar within the same manufacturer. If a 500 W generator was too expensive or too heavy, it is very likely that its equivalent with different rated power will have the same traits.
The first option will be selected because it is the cheapest one while keeping the weight and the starting torque to a minimum. For the 300 W variant of this generator, the following characteristics are provided by the manufacturer:
18 Electrical system architecture
Table 4.3: Characteristics of the selected generator.
Characteristic Unit Value Rated Power W 300 Maximum Power W 345 Rated Rotor Speed rpm 650 Rated Voltage V 12/24 Output current - Three phase AC Start torque Nm 0.28 Weight kg 4.3 Lifetime years >20 Shaft Material - Iron Shell Material - Aluminium alloy Magnets Material - NdFeB Working Temperature ºC -40 to +80
The cost of this generator "stand-alone" was 90 €. However, the final cost was 108 € because it was acquired together with a nacelle and a tail. This simplifies a lot the design and allows the scope to be reduced to a feasible length for this project duration. The nacelle is basically a frame for the generator and a connection with bearings with the tower top, allowing the turbine to freely rotate in the yaw axis. The tail is studied in the Section7.
4.3 Electrical system architecture
The permanent magnet generator chosen has a characteristic curve, which is the relation be- tween the rotor speed and the torque required to do so. The product between them will give the power produced. This curve will be highly important in the aerodynamic design in the Section 5. This curve may be understand as a resistance that fixes the relation between the voltage and the current of the generator. Provided that the voltage is just a function of the rotor speed V ∝ Ω, and the current is proportional to the torque I ∝ Q, this equivalent resistance is actually fixing a linear curve Q = f(Ω).
In the aerodynamic design section it will be explained that the rotor is designed and evaluated such that a linear and constant generator curve is assumed. The initial goal of the project was to test the generator in a laboratory bench and find the equivalent resistance that lead the assumed generator curve. This way, a dump load could be connected to the generator output, and the generator curve would therefore be fixed. This would allow a validation of the rotor behavior predicted. Unluckily, the generator was received just a few days before the CoVid-19 2020 lock-down begun, so it could not be tested.
There is, however, an approach that could lead to a higher power extraction. Using a MPPT (Maximum Power Point Tracking) could fix the generator curve on the fly during the operation, such that it is always operating at its most efficient point possible. Basically there are two ways to achieve so. The most inexpensive and common one is the so called "perturb and observe" operation. Given a rotor speed in a determined point of time, the MPPT modifies the current demanded to the generator, and therefore the torque required by the rotor, which eventually impacts the blades aerodynamics. If the result of this perturbation is a higher power output,
19 Electrical system architecture the MPPT will continue the perturbation in this direction, or will search an equilibrium point around it. Otherwise, if the outcome is bad, it will reverse the direction of the perturbation (increasing current instead of decreasing, or the other way around). The other MPPT type have the optimum rotor curve programmed. From the measured rotor speed, they know which is the best operational point at that condition, and they demand the corresponding generator current such that his operation is established [29].
Unfortunately, the electrical scheme has not been fully determined due to time constraints and uncertainties on the final installation site. However, a procedure going forward is planned. Firstly, the generator curve will be measured in an electrical testing bench, and the equivalent resistance that gives the assumed generator curve Q = f(Ω) will be found. The wind turbine will be installed and tested with a dump load such that the assumed generator curve is fixed. The calculated power curve will be validated this way. Then, the power curve will be measured again, but this time a MPPT will be connected to the generator output. The MPPT that will be used (Figure 4.1, borrowed by a kind colleague) is originally designed for the Bergey Excel 1 kW wind turbine [26], but the manufacturer has confirmed by email that it may also be used for other wind turbines. Its input expects DC current, so an inexpensive 3 phase diode rectifier will be bought (e.g. [30]). Comparing both power curves, it will be decided whether it is worth to buy an own MPPT (they are expensive) or it is better to select an electrical system such that it fixes the desired generator curve. Additionally, the LS-300 controller (Figure 4.1) will be tested as well. It is the controller sold by the generator manufacturer, and it is expected to fix the curve provided by the manufacturer, but no clear information of its operation is provided. Its output is expected to be constant DC voltage to charge a pack of batteries, and includes a braking function by means of generator shorting. It is a very important and valuable safety feature.
(a) Bergey Excel 1 kW controller. (b) LS-300 controller.
Figure 4.1: Different small wind turbine controllers.
The rest of the electrical system will be designed once an installation site is defined, because depending on the integration necessities the final components may vary. An inverter will not be needed if the output is used to charge batteries, but it will be necessary if it will be used directly to power appliance or other loads. In this case, the type of inverter may as well be different as a function on the maximum distortion acceptable of the current wave (e.g. connection to the grid).
20 Chapter 5
Aerodynamic design
This chapter will cover the aerodynamic design of the wind turbine, refereed as the exterior shape of the blades. The section of the blades will be firstly chosen by selecting an appropriate airfoil. Then, its variation of chord and twist along the blade will be studied and optimized. The start-up procedure will also be analyzed, and the final results will be discussedd in detail.
5.1 Airfoil selection
In this section, the selection of the airfoils for the blades will be made. Firstly, the desired characteristics will be defined. The low Reynolds influence will be described, and a study methodology will be defined according to it. Then, several existing airfoils will be studied and a selection criteria will be established. Finally, the elected airfoil will be characterized.
Desired characteristics The desired performance of the blades varies from root to tip. The optimal solution would be to have blades with aerodynamic twist and adapt the airfoil selection to the different circumstances of each section of the blade. However, this would difficult the optimization of the chord and geometric twist distribution. Moreover, it is common for small wind turbines to have the same airfoil for the whole blade span, so only one will be selected [29].
This selection is a compromise between aerodynamic and structural issues. Usually, a high relative thickness is used at the root (around 35%) and a lower one at the tip (18%). The biggest drawback of a single-airfoil blade is that this could not be done. The desired characteristics of the airfoil are enumerated in the following list: [17, 29]
1. Good performance at low Reynolds number.
2. High efficiency (Cl/Cd)max. 3. Margin between optimal and critical conditions (stall angle of attack far from the optimal angle of attack to be resistant to perturbations). 4. High lift coefficient: a higher lift coefficient would lead to a lower chord, resulting in less loads and costs. 5. Soft stall behaviour. 6. Insensitive to dirt (turbulent airfoils are more resistant).
21 Airfoil selection
Low Reynolds number and simulation parameters The Reynolds number in a wind turbine blade is defined as:
ρU c Re = T (5.1) µ
Where UT is the "total" velocity at the blade, c is the chord, ρ is the air density and µ the dynamic viscosity. Note that the first two variables change along the blade, and that the lower Reynolds value will be achieved when the blades are stationary and UT = Ud. The typical Re ranges for small wind turbines and other aerodynamic bodies can be found in the following table:
Figure 5.1: Reynolds number ranges for small wind turbines and other aerodynamic bodies. Retrieved from [29].
It is known that lift and drag coefficients depend on the Reynolds number. Although computa- tional analysis is very used for airfoil study, there are authors that state that these results can not be completely trusted at low Re [29]. There is also low accurate experimental data available for these cases (Re < 105) due to the small forces involved. Ideally, the airfoil selected would have been tested in the wind tunnel. Due to time constraints and the CoVid-19 lock-down, this will unfortunately remain as a future task, but it would have been very interesting to study further the influence of the Reynolds number, the surface coating, and the layer height when 3D-printing it (a parameter directly related to the roughness of the surface).
The airfoils will be studied using the XFOIL code with XFLR5 graphical user interface. It uses an inviscid linear-vorticity panel method, and it is known to show reliable results for low Re flows (it was initially intended for the calculation of model sailplanes) [31, 32]. The following parameters need to be defined to set up the simulation
1. Mach number: As XFOIL considers incompressible flow (M=0) any value below 0.3, this value is directly defined as M = 0.
2. Boundary layer transition: It will be assumed that the greatest part of the boundary layer will be turbulent due to the roughness of the blades and the turbulence of the
22 Airfoil selection
incoming flow. The former is presupposed given the surface finish of 3D printed parts, and the latter because of the hypothesis that the wind turbine will be installed at a low hub height, with a lot of influence from the close obstacles. XFOIL defines the transition based on the eN transition theory [31], so a Ncrit value must be selected. A value of 1, which is the most turbulent scenario, is chosen. This hypotheses will be revised in Section 8.2.
3. Reynolds number: Although reliability can be expected from XFOIL results, the error increases at significant low Reynolds. The following Reynolds will be studied: Re = 2·105, Re = 1.6 · 105, Re = 1.2 · 105, Re = 8 · 104, and Re = 4 · 104. It is observed that the effect of varying Ncrit is more important at the lower Reynolds numbers, and it is affecting specially the stall region.
Airfoils studied
The following table summarizes the airfoils that will be tested and studied. The airfoil coor- dinates and the values presented below has been obtained from airfoiltools.com [33], a useful website that uses UIUC’s airfoil database [34]. All the airfoils studied have been designed look- ing for a good performance in low Reynolds number operation. Some of them are specifically designed for small wind turbines: SG series (Selig-Giguere) and S833/4/5 airfoils designed by NREL are probably the first aerofoils designed for this purpose [29]. The other models have been selected by looking into low Reynolds airfoils studies [32, 35].
Table 5.1: Airfoils selected to be studied. All values are indicated in chord percentage.
Code Airfoil Maximum Position Maximum Position thickness [%] [%] camber [%] [%] 1 SG6040 16.0 35.3 2.3 60.5 2 SG6041 10.0 34.9 1.5 49.7 3 SG6042 10.0 33.5 3.3 51.5 4 SG6043 10.0 32.1 5.1 53.3 5 S833 18.0 36.3 2.5 78.8 6 S834 15.0 39.5 1.6 60.0 7 S835 21.0 30.5 2.4 78.0 8 S1210 12.0 21.4 6.7 51.1 9 S1223 12.1 19.8 8.1 49.9 10 S6063 7.0 29.4 1.3 43.8 11 S9037 9.0 28.5 3.3 42.4 12 S3010 10.3 25 2.3 43.3 13 SD8000 8.9 29.4 1.5 54 14 BW3 5.0 7.4 5.7 45.4 15 E387 9.1 31.1 3.2 44.8 16 E374 10.9 34.3 2.0 38.9 17 E62 5.6 26.2 5.0 49.3 18 RG15 8.9 30.2 1.8 39.7
The desired characteristics that have been defined before must be quantified in order to have a solid selection criteria. To do so, the following parameters will be analyzed for each airfoil:
23 Airfoil selection
1. Maximum efficiency E: An airfoil that produces the more lift possible with the minimum drag is desired.
2. ∆α = αs − αopt: It is important to have the optimum angle of attack far from the stall angle of attack, as this provides consistency to the design. dα 3. opt : The Reynolds range that the airfoil will work at makes desirable to have uniformity dRe around the optimal operating point. Hence, the lower variation of its location is searched. dE 4. : The same reason than the previous point. dRe dE 5. (α = α ): This parameter is also studied in order to provide consistency. Variations dα opt of α should not lead to huge changes in the efficiency.
6. Thickness t/c: The thicker the airfoil, the more space it has to contain a more resis- tant structural system. Usually the thickness is a compromise between the aerodynamic performance and the structural perspective.
7. Clopt: The higher the lift coefficient, the smaller the chord needed.
Selection results An explanation of how the data have been extracted from each airfoil can be found in the section 1.2 of the Report Attachment. The polar curves and data from each airfoil is also presented there with more detail. The results are summarized in the following table:
Table 5.2: Airfoil selection results.
Parameters Nº Airfoil 1 2 3 4 5 6 7 Emax αs − αopt dαopt/dRe dE/dRe dE/dα (t/c)max Clopt 1 SG6040 44.11 10.81 0.55 9.86 4.66 16.00 0.87 2 SG6041 42.46 6.02 0.36 7.50 2.14 10.00 0.89 3 SG6042 48.89 9.24 0.64 8.01 2.57 10.00 0.85 4 SG6043 57.73 10.96 0.94 11.87 5.59 10.00 0.97 5 S833 31.13 8.59 0.69 6.32 1.32 18.00 0.75 6 S834 32.30 7.62 0.33 5.96 1.32 15.00 0.69 7 S835 27.96 10.03 0.60 6.00 1.97 21.00 0.67 8 S1210 62.47 6.32 0.31 12.13 4.80 12.00 1.40 9 S1223 55.67 5.63 0.37 10.55 1.44 12.10 1.52 10 S6063 36.78 3.89 0.18 5.36 5.57 7.00 0.67 11 S9037 50.95 6.57 0.09 8.55 2.33 9.00 0.93 12 S3010 48.35 5.97 0.07 8.59 2.45 10.30 0.94 13 SD8000 42.76 5.35 0.06 7.24 2.15 8.90 0.84 14 BW3 45.99 6.27 0.49 5.89 2.96 5.00 1.08 15 E387 56.17 6.85 0.66 10.42 9.22 9.10 0.89 16 E374 44.81 7.98 0.56 7.04 6.69 10.90 0.71 17 E62 65.55 7.02 0.72 11.70 13.64 5.60 0.95 18 RG15 43.48 5.41 0.25 6.74 4.66 8.90 1.83
24 Airfoil selection
In order to select which airfoil will be used, the preceding table must be normalized, and each parameter should have a weight assigned. A common risk when comparing different possibilities is to select an option which stands out in a particular variable but is not the best option in average. To avoid so, a domination matrix will be used [36]. The matrices with normalization and the domination procedure may be found in the section 1.2.2 of the Report Attachment.
The final selected option is the airfoil S1223 (number 9), a high lift low Reynolds airfoil designed by Selig and Guglielmo [37]. It is a relatively thin airfoil with a lot of camber. Its shape and polar curves are presented in the following figures.
Figure 5.2: S1223 airfoil. Plotted using Airfoil Tools [33]
2.5 0.15 2 1.5 0.1 1 0.5 0.05 Lift Coefficient [-]
0 Drag Coefficient [-] -0.5 0 -10 -5 0 5 10 -10 -5 0 5 10 Angle of attack [º] Angle of attack [º]
80
Re=40k 60 Re=80k Re=120k 40 Re=160k Re=200k
Efficiency [-] 20
0 -10 -8 -6 -4 -2 0 2 4 6 8 10 Angle of attack [º]
Figure 5.3: S1223 airfoil polar curves.
Post-stall extrapolation
In wind turbine design it is important to have the polar curves characterized for the possible 360º of angle of attack, because the blades may work in very different regimes [17]. The wind tunnel testing is the best way to do so, although its measurements might not be very precise and can have large deviations in the reverse flow region. For conceptual or rapid design, extrap- olations are commonly used. Viterna and Corrigan proposed the following equations, which is the combination of experimental airfoil data with flat plate correlations [38].
25 Airfoil selection
cos2 α C = A sin 2α + A (5.2) l 1 2 sin α
2 Cd = B1 sin α + B2 cos α (5.3)
Where the first coefficients A1 and B1 are related with the maximum drag coefficient, found experimentally at α = 90º.
B A = 1 B = C C ≈ 1.11 + 0.018AR (5.4) 1 2 1 dmax dmax And the maximum drag coefficient is related to the aspect ratio AR = b2/S = b/SMC, where b is the span of the blade, S the blade area and SMC the standard mean chord. The parameters A2 and B2 are the result of substituting the previous constants in the first equations and solving for continuity with the polar curve data below stall:
sin αs A2 = (Cls − Cdmax sin αs cos αs) 2 (5.5) cos αs
2 Cdmax sin αs B2 = Cds − (5.6) cos αs Where the subscript s indicates the value of the constant at stall. Applying these equations on the polar curves of the airfoil selected leads to the following results:
2 Re=40k Re=80k 1.5 Re=120k Re=160k Re=200k 1
0.5
Lift Coefficient [-] 0
-0.5
-80 -60 -40 -20 0 20 40 60 80 Angle of attack [º] Figure 5.4: S1223 extrapolated lift coefficient curve.
26 Blades aerodynamic design
1.2
1
0.8
0.6
Re=40k 0.4 Re=80k Drag Coefficient [-] Re=120k 0.2 Re=160k Re=200k 0 -80 -60 -40 -20 0 20 40 60 80 Angle of attack [º] Figure 5.5: S1223 extrapolated drag coefficient curve.
The Viterna extrapolation is focused in the positive post stall region up to α = 90º. The empirical data used does not extend further to this region, so his equations will not be used either for the full ±180º. In addition, applying the CL equation for α = 180º would lead to an unrealistic infinite value. In this case, the extrapolation is only required for an steady BEMT calculation of normal operation, and therefore the full data is not completely required. It is also interesting to note that the continuity in the negative stall region is not included in the original equations, so a separate calculation of the constants depending on the limit of the linear curve has been included. The implementation may be seen in the Section 1.4.3 of the Report Attachment.
5.2 Blades aerodynamic design
In this section the whole aerodynamic design of the blades will be reviewed. Firstly, the method to compute the power curve of a given blade geometry will be described. After that, different methods to optimize it will be discussed, as well as the distinctive feature that this passive solu- tion should take into account. Finally, a blade geometry will be obtained, and its characteristics and performance will be described.
5.2.1 Power curve calculation procedure To be able to design the blade geometry, the first step is create a code to obtain the power curve from a given chord, pitch, and twist. These three will be the variables to be determined. With them, the goal is to maximize the Annual Energy Production (AEP) by means of the power curve.
If a generator is selected, the curve of torque vs rotor speed Q = f(Ω) may be fixed. This curve will also be the one that the wind turbine will follow. With that, it is already know how much torque the rotor will have to produce at each rotational speed in order to match the generator demand and achieve an equilibrium point. The remaining task is to compute at which wind speed these equilibrium points are obtained. If a Ω = f(U∞) function can be found, then these
27 Blades aerodynamic design
points can be traced into a Q = f(U∞) function and the desired power curve P = f(U∞) would be immediate to obtain. In order to do so, the following procedure has been defined:
Figure 5.6: Power curve calculation procedure. It includes the Matlab function created for each step, so the code is easier to analyze.
28 Blades aerodynamic design
5.2.2 Theoretical approach and design challenge Until this point, an airfoil has been selected and a calculation procedure to calculate the power curve has been defined. In parallel, a BEMT code has been developed and validated (Section 1.1.3 of the Report Attachment) for such purpose. The next step is determine the chord and twist distribution of the blades. In this section, the theoretical approaches to both parameters will be described, and the result of the first tests will be explained. The information exposed here will establish the foundations for the aerodynamic optimization carried out in the Section 5.2.3. The results exposed below are a summary of the full development shown in the Report Attachment (Sections 1.3.1 and 1.3.2).
Theretical optimal blade geometry Firstly, a comparison of the optimal blade geometry according to Betz and Schmitz will be dis- cussed [29,39]. They aim to optimize the power extracted, which is obviously very important but it is not the only thing that should be taken into account: the loads, the blade structural capabil- ities, and the noise are another typical constraints of the wind turbine design [17]. Nonetheless, in this case only the maximization of the power produced will be taken into consideration. The complete derivation of the equations is presented in the Section 1.3.1 of the Report Attachment, and the final results are summarized below. Firstly, the Betz geometry is obtained with the following equations:
2π 8/9 c(r) = R s (5.7) λNCl 2 2 4/9 + (λµ)2 1 + 9(λµ)2 2/3 β(r) = φ − α = arctan − α (5.8) 2 λµ 1 + 9(λµ)2 The Schmitz chord and twist distribution are represented by:
16πr R c(r) = sin2 arctan /3 (5.9) Cl λr 2 R β(r) = φ − α = arctan − α (5.10) 3 λr Basically both results come from imposing an optimal operation condition (a = 1/3 in Betz case and φ = φ1 · 2/3 in Schmitz equations) and a fixed airfoil operating point, therefore a fixed angle of attack α (usually the one leading to the highest efficiency E) and its corresponding lift coefficient Cl. With an appropriate α, only a design tip speed ratio λ should be selected to build the complete chord and twist distribution along the blade span. The future optimization procedure will be based on this parameter.
Both approaches have very similar results at high tip speed ratios λ. However, they differ significantly at low values, especially near the hub. This is important because it is likely the area that this designed blades will be working in. To check its importance, a comparison of the results obtained with both will be done. Although the preceding equations were derived without accounting for any losses, the results presented below include the drag effect, the Prandtl tip and root losses, and the Glauert correction (this is described in detail in the Section 1.1 of the Report Attachment).
29 Blades aerodynamic design
B = 1.0 0.4 S = 1.0 B = 2.0 S = 2.0 B = 3.0 0.3 S = 3.0
0.2 Chord [m]
0.1
0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Radius [m] Figure 5.7: Optimal chord distribution according to Betz and Schmitz for different tip speed ratios λ. The solid lines have been obtained with Betz’s approach (Equation (5.7)), and the dashed lines have used Schmitz’s equations (Equation (5.9)).
The difference between both approaches grows with the tip speed ratio and the closer the blade section is to the hub. In order to test the difference regarding the power produced by both geometries, the power coefficient CP has been computed for geometries optimized at different tip speed ratios. Each point in the plot below shows the CP of the optimal blade geometry for a determined λ value, analyzed at that same λ value. Therefore, according to Betz and Schmitz, each point is the maximum power coefficient that can be extracted for a given tip speed ratio. As this analysis takes into consideration several effects that have been neglected during the derivation of the geometries, the performance obtained is far from the theoretical maximum power coefficient CP,max = 16/27 ≈ 0.593.
0.45
0.4 P
0.35
0.3 Betz blade geometries 0.25 Schmitz blade geometries Power Coefficient C 0.2
0.15 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 Tip Speed Ratio Figure 5.8: Power coefficient comparison between Betz’s and Schmitz’s blade geometries.
As the tip speed ratio grows and the geometries are more similar, the power coefficients are also looking alike. In the lower region, however, the Betz’s geometries lead to higher power coefficients at a cost of higher chord values. In the following sections the need of optimizing at a low tip speed ratio will be seen. The maximum chord will be a constraint, because it is limited
30 Blades aerodynamic design by the 3D-printed bed size and the impossibility to have a hub too large to host such blades. The mass and the cost would also increase. Then, going with Betz or Schmitz is a compromise between a higher CP or a smaller chord at the root. If Betz theory is selected, however, it will not be possible to use it for a λ value sufficiently small, because the resultant chord values would be too high, and the rotor geometry would be optimized for a tip speed ratio larger than the one it usually operates at. Therefore, it is worth to go with Schmitz geometry, because the wind turbine will be optimized at a more useful operating point.
Initial approach and design challenge The first approach to the blade design was to use a genetic algorithm. A genetic algorithm is a numerical optimization method based in the natural selection principle of the evolution theory: only the better adapted individuals will survive. The code presented in Wood [29] was taken as the baseline. There, the fitness of the individuals (objective function) is the preponderate relative value of the power coefficient and the starting time. Each individual (blade) has a series of genes, which in this case are the chord and twist of each blade section. In this case, however, the code was modified to have as objective function the AEP (Annual Energy Production) and the maximum thrust. The main reason to do so is that a determined operational point cannot be selected to optimize at it, because it will depend on the intersection with the generator curve.
Whereas the original code performs a single BEMT calculation for each individual in each gener- ation, the new approach supposed a dramatically increase in the number of calculations, because all the wind speeds should be analyzed for a different tip speed ratios to find the intersection points. For example, if the tip speed ratio was divided in 15 values, 10 different wind speeds were analyzed, the blade was divided into 20 sections (genes), and 50 individuals were studied during 25 generations, this would lead to 3.75·106 BEMT calculations. Although the BEMT cal- culation is very fast (0.06 seconds average in this case), this is still a very time-consuming process.
Nonetheless, some test were completed, but the results were inconclusive and confuse. It was decided to do an initial study to understand the general characteristics of the operation resultant from the intersection with the generator curve.The results will now be presented. An extensive development of this study is shown in the Section 1.3.2 of the Report Attachment. Several blade geometries have been tested to see the general behavior of the wind turbine and analyze trends.
To do so, the optimal geometry was generated for a range of tip speed ratio λ values. Addi- tionally, different pitch values (understood as an offset to the twist) were used. The procedure shown in the Section 5.2.1 was applied to all the different blade geometries to obtain the power curve. Then, the Annual Energy Production (AEP) was calculated using a Weibull wind speed distribution. The Weibull used, due to the lack of experimental data of a possible installation site, corresponds to the reference one used in the Small Wind Turbine Contest [40]: A = 4.5 m/s (Vave = 4.0 m/s) and k = 2. The blade geometry that lead to the higher AEP was selected, and now its characteristics are going to be analyzed. Note that this study was carried out before implementing all the losses in the code, so the results obtained have an overestimation of the power produced. However, this is acceptable given the objective of it, and its conclusions will be helpful for further design steps.
The full operation of the blade geometry selected is shown in the Section 1.3.2 of the Report Attachment. The most remarkable and surprising behavior is the angle of attack evolution with the wind speed. The Figure 5.9 shows the mean angle of attack along the blade in the
31 Blades aerodynamic design cut-in (about 3 m/s) and the value at the cut-out (approximately 13 m/s). As the angle of attack distribution varies less than 20º from tip to root, the blade would be stalled during all its operation. There is a change of more than 40º during all the operation curve. Then, the main question to be asked is: why a design like that appears to be the optimal one? It is surprising that the working region of the airfoils is outside the linear zone.
2 C L C D 1.5 Cut-out Cut-in 1
0.5
0 Aerodynamic Coefficients [-] -0.5
-80 -60 -40 -20 0 20 40 60 80 Angle of attack [º] Figure 5.9: Airfoil polar (Re=120k) with operation region indicated.
To understand why this operation is more beneficial, firstly it could be analyzed what would happen if the operation regime was located in the linear region. If the starting mean angle of attack were, for example, 20º, and the cut-out one were -20º, almost half of the operation would have a negative lift coefficient. The BEMT equations from which the axial induction factor is obtained may show the effect that this has:
Cl cos φ + Cd sin φ = Cx (5.11)
a σ = r C (5.12) 1 − a 4 sin2 φ x
The coefficient of sectional blade element force normal to the rotor plane Cx would be negative in that case, therefore the axial induction factor a would be less than zero as well. It should be constrained between 0 and 1, so this possibility cannot be studied with the BEM theory without reversing the rotational direction. It makes no sense to reverse the direction in the middle of the operation. Moreover, an operation like that would not match the generator curve, so it would not be possible.
However, if the operation is contained in the region shown in Figure 5.9, the lift coefficient variation is more stable. Furthermore, its value near the cut-out region (where the power produced is higher) is also larger, which is an advantage from a power coefficient point of view. It could be argued that operating from 60º to 20º, for example, would be more beneficial, because the operation would be as solid as the obtained one, and the lift coefficient values would be higher. Firstly, the influence of the flow angle φ should be taken into account with more detail, and secondly, the number of blade geometries tested was low (225), so it is likely that no geometry capable to operate at such regime was created. Nevertheless, this first study was intended to understand the design challenge that will be faced, as well as the general operating characteristics of the design, and this result is enough for that.
32 Blades aerodynamic design
Design challenge and conclusions To sum up, an operation like this is not feasible. The post stall region is very stochastic, unstable, and it could easily lead to high vibrations and aeroelastic instabilities. The drag is also unacceptable there. However, the behavior seen here is also obtained in other blade geometries analyzed, so it must be taken into consideration for further design. Two main conclusions are derived from this study. The two points presented below have not only been obtained for the shown case but for all the blade geometries tested. It is interesting to note that both effects are purely given by how the generator and the rotor curve intersect with each other.
1. Large angle of attack range: The angle of attack variation throughout the operation is very important. This is driven by the big range of rotor speeds that the wind turbine will be working in. This leads to a very different operation for distinct wind speeds.
2. Decreasing angle of attack wind the wind speed: When the wind speed increases, the angle of attack decreases. This is directly triggered by the equilibrium tip speed ratios from the intersection of the generator and the rotor curves. The λ at cut-in (0.71 in the exampled shown) is lower than at cut-out (2.44), which leads to a decrease in α. In the Report Attachment this is covered with more detail (Equation (1.79)). It is also interesting to note that a stall control could not be implemented. A typical stall regulated wind turbine works in a constant rotor speed. As the tip speed ratio is defined as λ = ΩR/U∞, as the wind speed increases, the tip speed ratio decreases, and it has been demonstrated that a lower tip speed ratio leads to a higher angle of attack. If it is design properly, the stall will be reached at the desired wind speed. Nonetheless, this effect may be beneficial from a loads point of view, because small values of the aerodynamic coefficients could be achieved at high wind speeds.
5.2.3 Optimization procedure In order to avoid the issues explained in the preceding section, a different optimization procedure will be followed. Instead of only looking to the AEP and selecting the rotor that apparently leads to the maximum power production, the blade geometry will be optimized for a given wind speed. The next figure summarizes the procedure to be followed:
Figure 5.10: Blade geometry optimization procedure scheme. Includes the Matlab function created for each step, so the code is easier to analyze.
33 Blades aerodynamic design
The results obtained may be found in the following figure:
300
U = 3 m/s opt 250 U = 5 m/s opt U = 7 m/s opt U = 9 m/s 200 opt U = 11 m/s opt Generator Curve 150 Power [W] 100
50
0 0 100 200 300 400 500 600 700 Rotor speed [rpm]
Figure 5.11: Optimization procedure first results for different selected wind speeds.
The intersection tip speed ratio λints is different for each wind speed. Once a design wind speed is fixed, the intersection tip speed ratio will provide an omptimum rotor geometry for this operating point. The different λints obtained and their corresponding chord and twist distributions are presented below.
Table 5.3: Intersection tip speed ratios obtained for each wind speed.
Uopt [m/s] 3 5 7 9 11 λints [-] 1.30 1.80 2.20 2.55 2.85
0.3 35
30 0.25
25 0.2 20
0.15 Twist [º]
Chord [m] U = 3 m/s 15 opt U = 5 m/s opt U = 7 m/s 0.1 opt 10 U = 9 m/s opt U = 11 m/s opt 0.05 5 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 Radius [m] Radius [m]
Figure 5.12: Chord and twist distribution for different optimized wind speeds.
The higher the selected wind speed for the optimization, the higher the intersection λ, which is translated into a more slender blade. The wind speed should be selected such that the rotor is optimized in the operational point that contributes the most to the total AEP production. This point depends on the wind turbine power curve but also on the Weibull distribution of the wind. With the Weibull selected in the preceding section, it has been seen that the wind speed
34 Blades aerodynamic design that has the biggest contribution to the total energy production is found around 7 m/s, so this will be the optimization wind speed. The operation results of this rotor are presented below:
5 3 5 600
4 4 Torque Lambda 2 400 3 3
2 2 1 200 lambda [-] Torque [Nm] 1 1 Omega [rpm]
0 0 0 0 0 200 400 600 Torque [Nm], lambda[-] 2 4 6 8 10 Omega [rpm] Wind speed [m/s]
300 0.4 15 0.45
0.3 200 10 0.4 0.2 100 5 0.35 Trhust [N] Power [W] 0.1 Power coefficient [-] 0 0 0 0.3 Thrust coefficient [-] 2 4 6 8 10 2 4 6 8 10 Wind speed [m/s] Wind speed [m/s]
Figure 5.13: Operation results of the rotor optimized for λ = 2.2.
This option has a bad response in the start-up region. The start-up wind speed is high (4.5 m/s), which is not recommendable for the range of wind speed that the wind turbine will be usually working in. The late start-up of the turbine is due to the high angles of attack seen there; the blade is in the stall region in the vast majority of its sections. Moreover, the power coefficient for the lowest tip speed ratios is very low (because of the stall). This can be modified by applying pitch to the blades:
0.4
0.35
[-] 0.3 P
0.25
0.2
0.15 0º Pitch 2.5º Pitch 0.1 5º Pitch
Power Coefficient C 7.5º Pitch 0.05 10º Pitch
0 0.5 1 1.5 2 2.5 3 3.5 4 Tip Speed Ratio [-]
Figure 5.14: Pitch influence on the power coefficient curve.
35 Blades aerodynamic design
The CP increases in the lower region if the pitch θ is increased. However, this effect comes with a significant CP descent in higher tip speed ratios. Is it worth to sacrifice production in the high λ region (at higher wind speeds) in return to a lower start-up wind speed? This is a decision based on the overall energy production, and therefore the AEP is the parameter that should be studied. Table 5.4: AEP and start-up wind speed for different pitch angles.
Pitch θ [º] 0 2.5 5 7.5 10 AEP [kWh] 101.3 109.6 113.6 112.8 108.8 Us [m/s] 4.5 4 3.5 3.5 3.5
The starting wind speed indeed decreases with the pitch angle. Being able to produce energy from a lower wind speed helps to the total AEP. However, from 5º on, Us is no longer reduced (at least not in a significant manner), and the losses in AEP begin to be more important. This can be explained by taking a look to the angles of attack at low wind speeds. With low pitch, the majority of the blade span is in stall, and from θ = 5º on, the blade is working at the linear region, and the starting wind speed cannot be reduced more because the wind would not carry enough energy. The starting will be analyzed with more detail in the next section.
Now, the chord will be slightly modified (just by applying an offset) to see its influence on the power coefficient curve, and study whether it can help to the starting region.
0.4
0.35
[-] 0.3 P
0.25 Baseline -1 cm 0.2 -2 cm +1 cm +2 cm 0.15
0.1 Power Coefficient C
0.05
0 0.5 1 1.5 2 2.5 3 3.5 4 Tip Speed Ratio [-]
Figure 5.15: Chord influence on the power coefficient curve.
The effect of increasing the chord is very similar to the effect of increasing the twist: the low λ region improves its production whereas the high λ region decreases it. Nevertheless, applying a twist to the blade does not modify the material costs nor the weight of the blade, and therefore it is a better option to achieve the same results. The different AEP results obtained with the blade geometries with a chord offset are presented below:
36 Blades aerodynamic design
Table 5.5: AEP and start-up wind speed for different chord offsets.
Chord offset ∆c [cm] -2 -1 0 +1 +2 AEP [kWh] 87.5 96.9 101.3 107.9 110.6 Us [m/s] 5 4.5 4.5 4 3.5
Conclusions An optimization goal was set to find the optimal blade geometry for a determined wind speed. This wind speed Uopt has been selected such that it has the highest contribution to the AEP. The chord and twist distributions have been obtained by using the Schmitz equations with the λints that lead to an equilibrium with the generator curve for the chosen wind speed.
Once an initial geometry has been calculated, the effect of modify the twist and chord has been studied. If the chord is increased, the performance gets better at low tip speed ratios, but decreases at high tip speed ratios. The same behavior is produced if a pitch is applied to the blades. It is desired to have a higher power coefficient at low tip speed ratios, because this is where the rotor will be working during more time. It has been decided that this will be achieved by modifying the twist and not the chord, because this way the cost, the mass, and the inertia of the blade will not increase. In order to decide which pitch should be used, the start-up procedure will be analyzed more deeply in the following section.
At this point, when the geometry of the blade was already defined, and only the pitch determi- nation was left, an error has been spotted in the simulation procedure. Each BEMT iteration takes into account the Reynolds number of the corresponding blade section, and interpolates the polar curve between the two closest Reynolds number available as inputs. In the input file, however, a manual error was made: the polar curves associated to Re = 40, 000 and Re = 80, 000 were actually filled with the data of the polar curve at Re = 120, 000. This has probably lead to an overestimation of the wind turbine behavior at low wind speeds. As the blade was already drawn in SolidWorks and the structural analysis was already performed, it has been decided to maintain the same blade design. The objective of the project is to design and build a complete wind turbine, and it is better to have a final product rather than spending excessive time in the rotor optimization.
Nonetheless, it has also been seen that the Reynolds values around the optimization point are higher or very close to 120,000, so the polar curves that have been used for the design are correct. The next section calculations and the final aerodynamic characteristics described in the Section 5.3 will be done with the correct polar curves.
5.2.4 Start-up analysis To obtain the results shown in the preceding section, an ideal torque curve has been considered. Due to the lack of experimental data, it has been assumed that the Q = f(Ω) curve is linear, and the two points considered are (0, 0) and (Ωrated,Qrated). Although it is a realistic approach, it might lead to an incorrect start-up wind speed determination. The static power curve found with the procedure described in the Figure 5.6 consists of the equilibrium points between the generator and the rotor for each wind speed. Nonetheless, when it comes to the starting wind speed, further analysis must be made, because it should be considered that the rotor comes from a static or idling state.
37 Blades aerodynamic design
The starting torque will now be taken into account. It is assumed that, until the starting wind speed, the rotor remains static (or idling with a negligible speed). The starting wind speed Us, then, is defined as the minimum wind speed capable to overcome the starting torque Qs and start spinning. In the IEC 61400-2 this is expressed as the "lowest mean wind speed at hub height at which the wind turbine produces power" [14]. The transition from the static position to the power production one will be analyzed in this section. The torque curve considered will be as follows: starting =0.28 Q s
Q Lineal generator curve Assumed curve for starting Generator torque [Nm] 0 0 starting Rotor speed Figure 5.16: Torque curve considered for the starting calculations.
The upper right corner values correspond to the equilibrium point between the generator and the rotor at the starting wind speed. No values are introduced yet because the equilibrium point will depend on the pitch angle chosen. It is a conservative approach because the frictional static starting torque of the generator is higher than the dynamic one [41].
The calculation of the torque produced by the rotor is not simple, because it mixes a dynamic analysis, the BEMT theory, and unsteadiness of the wind and the aerodynamics. Moreover, as there is not a pitch control system, the blades are in a deep stall region during the starting procedure, which includes more uncertainties to the calculations and decreases the overall effi- ciency of the rotor. On top of that, it is assumed that the rotor is facing the incoming wind speed, but significant yaw misalignment is expected during these low wind speeds. However, a simplified approach can be followed in order to estimate the torque. The procedure explained below uses the assumptions and definitions from D. Wood [29]. The torque generated on each blade element can be expressed as:
dQ 1 = NρU 2 c(C sin φ − C cos φ)r (5.13) dr 2 T l d Assuming that both a and a0 are small:
φ ≈ π/2, α ≈ π/2 − τ, sin α ≈ cos τ (5.14) Then, only lift is important in the torque generated on a stationary blade. Further simplifications can be extracted from the first assumption: the total wind speed will be UT ≈ (1 − a)U∞ ≈ U∞. Another effect of neglecting a and a0 is that the rotor does not extract power, but only its own rotational kinetic energy. This simplifies the analysis very much because the BEMT does not need to be applied. Nonetheless, it can only be used for small values of the ratio of the rotor kinetic energy at the end of the idling period (1/2NJΩ2) to the kinetic energy of the wind 3 2 (1/2ρUs πR Ts)[29].
38 Blades aerodynamic design
Now, the torque along the different blades can be integrated to compute the rotor angular acceleration.
dΩ J = Q (5.15) dt The calculation of the inertia J is described in more detail in the Section 1.3.3 of the Report Attachment, but basically is the result of the integration of the blades inertia plus the generator inertia. The generator contribution is the same, but the blades inertia depends on both the chord and the twist distribution.
Different pitch angles have been tested to asses its influence in the starting torque. The results are presented below:
0.4 102
0.38 100
0.36 98 0.34 96 0.32 94 0.3 92
Torque [Nm] 0.28 90 0.26 Rotor starting torque Qs Generator restistive torque Qr 88 0.24 Generator resistive torque Qr +10% Annual Energy Production [kWh] AEP points 0.22 AEP spline 86
0.2 84 0 2 4 6 8 10 12 Pitch [º]
Figure 5.17: Starting torque and AEP as a function of the pitch angle.
The starting torque Qs has been calculated for a starting wind speed of Us = 3.5 m/s, and the values represented above correspond the initial torque produced when the rotor is still static. The horizontal green lines show the static resistive torque of the generator (its nominal value and the same with a conservative increment of 10%). All the points at which the blue curve is below the green line indicate that the wind turbine would not be capable of starting at this wind speed. Ideally, a point over the dashed green line should be selected, because its starting would be more ensured.
The equilibrium at pitch θ = 10º is a good compromise, because the starting torque is already over the conservative minimum line, and the AEP is still very close to the maximum. The reason for selecting this point and not the absolute AEP maximum is because all the AEP calculations assume that the wind turbine will be able to start rotating and producing power from the very beginning of the operation, and this is not realistic because the static resistive torque of the generator is not taken into consideration there. Therefore, it is better to ensure that the wind turbine will be able to start even though there is a little loss of "theoretical" AEP.
39 Blades aerodynamic design
This will be the selected point, and now the starting procedure for this blade geometry will be described with more detail, following the equations shown before. A summary of the parameters used and calculated are found below: Table 5.6: Final parameters for the starting calculations.
Symbol Unit Value Description
Qr Nm 0.28 Generator resistive torque Qs Nm 0.31 Rotor starting torque JR kgm² 0.217 Rotor inertia
JRG kgm² 0.040 Generator inertia
JRB kgm² 0.177 Blades inertia −5 J1 kgm² 4.73 · 10 Blades radial inertia contribution −7 J2 kgm² 7.61 · 10 Blades second order inertia contribution ts s 11 Starting time Us m/s 3.5 Starting wind speed Ucut−in m/s 4.2 Cut-in wind speed ρb kg/m³ 1230 Blades density
The first integrand of the blade inertia (JRB = Nρb(J1 + J2)) is two orders of magnitude higher than the second one, which corroborates the assumptions used in the calculation of the latter (Section 1.3.3 of the Report Attachment). The generator contribution to the inertia is much lower than the blades one. The blades density used for the calculation is taken from the very conservative assumption that the blades will have the density of the material selected in the Section 6.1.2. This is not realistic, because they will be printed with a low infill, not completely solid, and therefore the blades density will be lower than the filament density. Nonetheless, the inertia calculation does not take into account the weight of the beam (its contribution would not be important either way), and the torque computation comes from a simplified analysis, so it is better to stay in the safety side here.
Before presenting the starting behavior, it is worth to justify briefly the election of a starting wind speed of Us = 3.5 m/s, and explain the difference between the starting wind speed and the cut-in wind speed. To do so, the intersection between the rotor and the generator curve in this region is shown in detail in the Figure 5.18. The following wind speeds have been defined:
• Starting wind speed Us: The lowest wind speed that allows the rotor to start turning.
• Cut-in wind speed Ucut−in: The lowest wind speed that allows the generator to start drawing power.
40 Blades aerodynamic design
1 U = 3 m/s 0.9 U = 3.2 m/s U = 3.4 m/s 0.8 U = 3.6 m/s U = 3.8 m/s 0.7 U = 4 m/s U = 4.2 m/s U = 4.4 m/s 0.6 U = 4.6 m/s Generator curve 0.5 Torque [Nm] 0.4
0.3
0.2
0.1 0 50 100 150 Omega [rpm]
Figure 5.18: Intersections between the rotor curve and the generator curve at low wind speeds.
Each wind speed curve has an inflection point at a determined value of rotor speed. This is directly related to the shape of CP = f(λ) relation (see Figure 5.14). Until approximately 4.0 m/s, the intersection of the curves take place in the positive slope areas, which means that the rotor will be working in a low tip speed ratio region with a low power coefficient. Then, the intersection takes place in the flat or negative slope region, which corresponds to a higher power coefficient value. In addition, there are determined wind speeds which curves intersect two times with the generator curve. Both points are stable equilibrium points, and therefore the static operation point will depend on the previous wind speed. This kind of behavior is experimentally observed in other passively controlled wind turbines:
Figure 5.19: Steady power curve at low wind speed with two intersection points per wind speed. In this case the bottom line shows unstable equilibrium points. Retrieved from [41].
It is desirable to avoid this behavior, because it increases the uncertainty of the wind turbine operation, and it is likely that it will be under-producing power in a situation that could be more beneficial. This behavior was also observed when studying and testing different generator curves. The slope of the motor curve will be directly related to the wind speed region that will
41 Blades aerodynamic design or will not be directly defined with one single point.
The starting wind speed will be 3.5 m/s, because in the Figure 5.17 it has been seen that it is enough to produce the necessary torque to start spinning. The cut-in wind speed will be defined as 4.2 m/s, because this is the first wind speed that only intersects with the generator one time, and it is found in the high performance area. The power produced before that will be neglected, because its operation can not be very well predicted and significant yaw misalignment may be expected. This way it is ensured that the power will not be overestimated.
With these final variables, the following starting behavior at 3.5 m/s is obtained:
50 0.55
40 0.5
30 0.45
20 0.4 Rotor Speed [rpm] Starting Torque [Nm] 10 0.35
0 0.3 1 2 3 4 5 6 7 8 9 10 Time [s] Figure 5.20: Rotor speed and torque during the starting sequence.
The rotor speed increases gradually, and its rotation increase the torque that it is generating. It may also be interesting to observe what is happening at the different blade sections:
70 1.2 [º] 60 1 50 r=0.15m r=0.25m 40 0.8 r=0.35m r=0.45m Lift coefficient Cl [-] Angle of attack 30 2 4 6 8 10 2 4 6 8 10 Time [s] Time [s] 10-3 5 1.5 4
3 1
2 0.5 1
Sectional torque [Nm/m] 2 4 6 8 10 2 4 6 8 10 Time [s] Aerodynamic efficiency E [-] Time [s]
Figure 5.21: Blade section behavior during the starting sequence.
42 Final results
As it has been anticipated, all the blade sections are in the stall region when the wind turbine is static. Once it starts to accelerate, the angle of attack decreases, and the blade sections located in the outermost part of the blade (which had the higher angles of attack at the beginning) have now a much lower one. It increases the lift coefficient in these sections and therefore its torque contribution. The efficiency has also been plotted to show how bad it looks even though the angle of attack decreases with the rotor speed. It also explains why the tip sections does not have the biggest contribution to the torque, as it is observed during the normal power produc- tion. They indeed have a higher contribution, but far from what is usually expected. Wright and Wood predicted this behavior [41].
The last two figures do not intend to represent accurately the starting behavior of the rotor, because they are based in simplified and conservative assumptions. The wind speed, in addition, will not be constant and non-turbulent during the starting. Nonetheless, with this study the performance of the turbine can be understood, and it can be checked that it will be able to start. As an extra checked, it has been calculated that the wind turbine would be able to start if the resistive torque were a 10% higher (the dashed line of Figure 5.17) with a starting time of 19 s.
5.3 Final results
In this section, the final aerodynamic behavior and characteristics of the blade will be described. Firstly, this is the resultant chord and twist distribution:
0.18
0.16
0.14
Chord [m] 0.12
0.1 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Radius [m]
40
35
30 Twist [º] 25
20 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Radius [m]
Figure 5.22: Final chord and twist distribution.
With this blade geometry, the following CP = f(λ) is obtained. The curve is presented for different wind speeds, because the Reynolds number will depend on that and it has an effect on the aerodynamic characteristics of the airfoil.
43 Final results
0.35
0.3 U = 13 m/s U = 11 m/s 0.25 U = 9 m/s U = 7 m/s U = 5 m/s 0.2
0.15
0.1 Power Coefficient Cp 0.05
0 0 0.5 1 1.5 2 2.5 3 3.5 Tip Speed Ratio Figure 5.23: Final non-dimensional power coefficient curves. Although the results are non-dimensional, they have been obtained from the complete resolution of the equations to account for the Reynolds number influence.
The lower the wind speed, the lower the Reynolds number, and the "worst" the polar curves are (they were presented in the Figure 5.3). This effect is important for 5 and 7 m/s, but from 9 m/s on the curves are almost overlapped.
The power curve obtained is presented below. The power coefficient and the AEP contribution are also shown:
300 0.5 P 250 AEP 0.4 C P 200 0.3 150 0.2 100 Power coefficient [-] 0.1 50
Power [W], AEP contribution [kWh/10] 0 0 5 6 7 8 9 10 11 12 13 Wind speed [m/s] Figure 5.24: Final aerodynamic design: Power curve, power coefficient and AEP contribution.
It may be seen that the biggest part of the annual energy produced is found between 4 and 8 m/s. The blades have been optimized for a wind speed of 7 m/s (see Figure 5.10 for reference), so the design result is coherent with the initial assumptions. Regarding the power coefficient, the values obtained show a reasonable and stable behavior during all its operation. It is also important to state why the power curve is no longer characterized after 13 m/s. After this wind speed, the maximum rotor speed and power of the generator would be exceeded, and therefore it is necessary to control the production in a way that the generator speed is not further increased. This is achieved by means of generator output shorting (Section 4.3), and additional safety may be added with a furling tail capable of de-orientating the rotor (Section 7.2). Either way, it has been considered that it is not necessary to define the power curve in this region because the
44 Final results
AEP contribution is negligible. Then, it is a matter of structural safety rather than a power production issue. The AEP contribution shown in this figure uses the Weibull wind distribution defined by the Small Wind Turbine Contest [40], as explained in the Section 5.2.2.
Below, the rotational speed and the tip speed ratio as a function of the incoming wind speed is shown:
700 2.8
600 2.6
2.4 500 2.2 400 2 300
1.8 Tip speed ratio [-] Rotor speed [rpm]
200 1.6
100 1.4 5 6 7 8 9 10 11 12 13 Wind speed [m/s] Figure 5.25: Final aerodynamic design: Rotor speed and tip speed ratio.
In the Figure 5.23 it may be seen that the maximum power coefficient is obtained for a λ ≈ 2.1. Looking at the tip speed ratio variation when the wind speed is increased can explain why the maximum power coefficient in the Figure 5.24 is found around 7.5 m/s: this is the "optimal" tip speed ratio point. Regarding the thrust, the following is obtained:
35 0.5
30 0.45 25
0.4 20
15 0.35 Thrust [N] 10 Thrust coefficient [-] 0.3 5
0 0.25 5 6 7 8 9 10 11 12 13 Wind speed [m/s] Figure 5.26: Final aerodynamic design: Thrust and thrust coefficient.
The thrust will be important in the structural section. In the Table 6.8 it is shown that the static loading (which is shown in the preceding figure) is almost negligible compared to the extreme wind loading obtained during the 50-year extreme wind speed Ue50 (equation 6.17). Nonetheless, this value would have influence in the furling tail design [42].
Finally, the aerodynamic characteristics on the blade along the radius will be analyzed. The angle of attack seen by each section at different wind speeds is the following:
45 Final results
10
8
6
4
2
0
-2 Angle of attack [º] -4 U = 13 m/s U = 11 m/s -6 U = 9 m/s U = 7 m/s -8 U = 5 m/s
-10 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Radius [m] Figure 5.27: Final aerodynamic design: Angle of attack along the blade for different wind speeds.
These results are coherent with the behavior seen in the Section 5.2.2: the angle of attack decreases when the wind speed increases. The challenge was to found and operation such that the blades were in stall the minimum time possible. This has been achieved, and moreover it operates at efficient angles of attack. The aerodynamic efficiency and the lift coefficient are plotted in the following figure:
2 70
1.5 60
50 1 40 0.5 30 0 U = 13 m/s 20 U = 13 m/s Lift coefficient [-] U = 11 m/s U = 11 m/s -0.5 U = 9 m/s 10 U = 9 m/s U = 7 m/s Aerodynamic efficiency [-] U = 7 m/s U = 5 m/s U = 5 m/s -1 0
-1.5 -10 0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 Radius [m] Radius [m] Figure 5.28: Final aerodynamic design: Lift coefficient and efficiency along the blade.
The lift coefficient, as expected, follows the same trend as the angle of attack, and its value decreases with the wind speed. Regarding the efficiency, the highest values are found between 7 and 9 m/s. This behavior also makes sense, because those are the wind speeds that the blades are optimized for. The efficiency at 5 m/s is lower due to the lower Reynolds number, and the 13 m/s curve is highly impacted by the drag increase from α = −2º on.
46 Final results
The contribution of each section to the total torque is shown below:
0.025 U = 13 m/s U = 11 m/s 0.02 U = 9 m/s U = 7 m/s 0.015 U = 5 m/s
0.01
0.005
0
Sectional torque contribution [Nm/m] -0.005 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Radius [m] Figure 5.29: Final aerodynamic design: Sectional torque contribution.
As it was anticipated in the literature, the highest contributions are found around 80% of the radius [17][29]. In the 13 m/s case, however, its contribution decreases a bit due to the lower lift coefficient and efficiency seen by those sections. It is also remarkable the negative contribution of the outermost sections, highly influenced by the Prandtl tip losses.
47 Chapter 6
Structural design
The structural design will be carried out in this chapter. The 3D printer and filament that will be used will be firstly described in the Section 6.1. Then, the loads on the blade root and main shaft will be calculate according to the guideline IEC 61400-2 (Edition 3) in the Section 6.2. The main structural parts of the blade (the beam and the pin joint) will be design and analyzed in the Section 6.3 to withstand the aforementioned loads. This will also be the condition to design the hub in the Section 6.4. The printing properties that will be used for the different parts of the rotor will be described in the Section 6.5, and finally a quick assessment of a possible tower will be made in the Section 6.6.
6.1 3D printing initial considerations
6.1.1 Printer characteristics The 3D printer that will be used for this project is the Creality Ender-3. The reason is simple: this is the printer that the author already had in his house. It is known as one of the best cheap options in the market, and it was awarded as the "Best 3D Printer Under $200" in Amazon [43]. Moreover, the use of this printer also aims to show that a very complex equipment is not needed to make a project like this. Its main characteristics are described in the table below:
Table 6.1: 3D printer used (Ender-3) characteristics.
Characteristic Unit Value Printing volume mm 220x220x250 Layer height mm 0.12 - 0.32 Nozzle size mm 0.4 Filament diameter mm 1.75 Max. extruder temperature ºC 255 Max. heated bed temperature ºC 100 Closed print chamber - No
The printing volume available will be a limitation in the blade design. As it has been explained in the Section 3.1, the blades will be 0.5 m long, and therefore they will be built from more than one piece. The other important restriction imposed by the printer is the filament to be used. The maximum extruder and heated bed temperatures are not enough for some materials, and therefore they could not be used for the design. Furthermore, the printer is not enclosed in a chamber, which will add difficulties when using determined materials.
48 3D printing initial considerations
6.1.2 Filament selection In this section, the filament to be used will be selected. Several filaments will be compared, and the most suitable one will be chosen by considering the needs of this design.
Table 6.2: Main characteristics of the filaments considered. Data extracted from [44] except for the prices, which have been obtained from the local reseller of 3D printing material BCN Maker Shop [45].
Filament ABS PLA PETG Nylon ASA PP Ultimate strength 40 65 53 40-85 55 32 [MPa] Stiffness [-] 5 7.5 5 5 5 4 Durability [-] 8 4 8 10 10 9 Max service 98 52 73 80-95 95 100 temperature [ºC] Thermal expansion 90 68 60 95 98 150 coefficient [µm/mºC] Density [kg/m³] 1040 1240 1230 1060-1140 1070 900 Price [€/kg] 21 20 21 29 25 47 Printability [-] 8 9 9 8 7 4 Extruder 220-250 190-220 230-250 220-270 235-255 220-250 temperature [ºC] Bed temperature 95-110 45-60 75-90 70-90 90-110 85-100 [ºC] Heated bed Required Optional Required Required Required Required
After normalizing and comparing all the parameters (as it has been done in the Section 5.1 when selecting the airfoil), the following results are obtained:
Table 6.3: Results of the filament comparison.
1 PETG 6.70 2 Nylon 6.53 3 PLA 6.53 4 ASA 6.49 5 ABS 6.44 6 PP 5.20
All parameters have been considered to have the same weight in the comparison. However, is specially interesting that the PETG thermal expansion coefficient is the lowest one. This parameter is important in this case because it can indicate the ease of the print: when printing thin and long geometries such the trailing edge of an airfoil, a phenomena called delamination may happen. It means that two consecutive layers do not fuse well enough together and they eventually end up separated.
49 Loads calculation
(a) Leading edge layer separation. (b) Trailing edge layer separation.
Figure 6.1: Examples of layer separation using ASA. The massive delamination obtained in first place in both the LE and the TE (a) was reduced to isolated delamination in the TE (b) by building an enclosure around the 3D printer. By doing so, the mean temperature was higher and the cooling down was less sudden. The ASA was being tested due to the attractive possibility of printing with a material that would not require any post-processing given its environmental resistance. However, the layer separation could not be removed completely, so the use of this material was discarded.
This happens due to the contraction of the material once it cools down after being fused. How- ever, the lower the thermal expansion coefficient, the less it will expand when it is fused, and the less likely that delamination will happen. Although the thermal expansion effect will not (hopefully) cause layer separations, there are other consequences that can not be completely avoided. For example, it is expected that the flat surface that serves as the base of a print will end up slightly curved once it has cooled down. This may be a problem when joining the two parts of the blade, as it is shown in the Section 6.3.2.
To sum up, PETG has been selected, which is often described by the 3D printing community as an easy to print material that has better mechanical properties than the PLA. Even though it does not provide resistance to the environmental conditions that it will have to face (ASA has this property), this can be obtained by means of a surface coating.
6.2 Loads calculation
The loads created onto the wind turbine will be analyzed in this section. The following calcu- lations will be based on the blade geometry obtained in the section 5.3, and the equations used will be extracted from the IEC 61400-2:2013 (Edition 3) [14]. The derivation of the equations may be found in the Annex F on the guideline.
The guideline allows the analysis of the turbine structural safety through three mechanisms:
1. Simple Load Model (SLM): Simplified analytic equations for the main loads, where very high safety factors are applied due to its assumptions.
2. Aeroelastic computational modeling: Accurate modeling of the wind turbine loads
50 Loads calculation
in response to both stochastic and deterministic wind inputs. This is the method used in large wind turbine, and the codes commonly used are Flex5, Bladed, Adams, or Simpack.
3. Measurements and extrapolations for extreme conditions: This method requires a prototype and load measurements, and therefore it cannot be used in the design stage but rather for validating the loads obtained with the previous two methods.
Aeroelastic analysis are not common in small wind turbine due to the high cost of the software and the computational resources required. The SLM is unique to the small wind turbines guideline, and although it has a "cost" on high safety factors, it allows a fast loads calculation [29]. This will be the method followed in this section, and the following Design Load Cases (DLC) will be analyzed:
Table 6.4: Design load cases for the simplified load calculation method. Note that the nomenclature used in the IEC is slightly different, and it will be adapted here to the symbols that have been already used throughout all the project. Obtained from the IEC 61400-2:2013 [14].
Design situation Design Load Case Code Wind inflow Analysis
Normal operation A Udesign Fatigue Yawing B U Extreme Power production design Yaw error C 2.5 · Udesign Extreme Maximum thrust D - Extreme Maximum rotational speed E - Extreme Power production plus fault Short at load connection F Udesign Extreme Shutdown Shutdown (braking) G Udesign Extreme Extreme wing loading Extreme wind loading H Ue50 Extreme Parked and fault conditions Parked wind loading I Uref Extreme
The wind inflow columns shows the hub wind speed that should be applied for each DLC. The guideline defines the value of those depending on the wind class at which the wind turbine is going to certified:
Table 6.5: Basic parameters for SWT class. The special class (S) values would be specified by the designer. Obtained from the IEC 61400-2:2013 [14].
SWT class I II III IV S Uref [m/s] 50 42.5 37.5 30 * Uave [m/s] 10 8.5 7.5 6 *
As the Weibull distribution used in the optimization and the calculations has a Uave = 4.0 m/s (Section 5.2.2), the wind class IV is considered enough to cover the wind conditions that the wind turbine is designed to work in. Therefore, all the calculations will be made with the values defined in this category. From these values, some more inputs should be calculated prior to the complete loads assessment. Firstly, the design wind speed Udesign is defined as:
Udesign = 1.4 · Uave = 8.4 m/s (6.1)
Now, the design power Pdesign, the design rotational speed Ωdesign and the design shaft torque Qdesign should be determined such that they would be the values obtained at the Udesign. All
51 Loads calculation these values, and the other variables needed for the loads calculation, are presented in the table below: Table 6.6: Parameters used for the loads calculation. Note that some of the parameters are not shown in the units they have to be used in the following equations.
Symbol Unit Value Description
Pdesign W 63.0 Design power Qdesign Nm 1.57 Design torque Ωdesign rpm 383.6 Design rotor speed Ωmax rpm 650.0 Maximum rotor speed Ue50 m/s 42.0 50 year extreme wind speed ωyaw,max rad/s 3.0 Maximum yaw rate Aproj,B m² 0.0575 Total planform area of the blade Cd,max - 1.50 Maximum drag coefficient Cl,max - 2.00 Maximum lift coefficient CT - 0.889 Thrust coefficient JB kgm² 0.032 Second moment of inertia for each blade mB kg 0.67 Single blade mass mR kg 2.22 Rotor mass (blades+hub) Rcog m 0.27 Distance from blade centre of gravity to rotor axis Lrb m 0.15 Distance from rotor centre to first bearing Lrt m 0.3 Distance from rotor centre to yaw axis G - 2.0 Short-circuit torque factor er mm 2.5 Rotor eccentricity N - 3 Number of blades R m 0.5 Blade radius ρ kg/m³ 1.225 Air density g m/s² 9.81 Gravity acceleration
Design Load Case "A": Normal operation This is the only fatigue load case, and it covers the normal operation of the wind turbine. It is assumed that all the extreme events considered in the rest of DLCs have a very low frequency of occurrence, and therefore do not contribute to the fatigue life. The equations in this case compute the cyclical loads during normal operation. First of all, the centrifugal load is defined as:
2 ∆FzB = 2mBRcogΩdesign = 587.3 N (6.2)
Where Rcog is the radius of the center of gravity of the blade, which has been obtained using CAD software. The mass of the blade mB has been obtained the same way, considering that the blade will be completely solid (as in the table 5.6 when calculating the starting).
Now, the moments in the blade root plane are computed. MxB is moment in the direction of rotation of the blades (in-plane). MyB is the moment normal to the preceding one and contained in the rotor plane (out-of-plane). As the pitch angle is fixed in this case and has a very small value, they can also be directly understood as the edgewise and flapwise components of the moment, respectively.
52 Loads calculation
∆MxB = Qdesign/N + 2mBgRcog = 4.4 Nm (6.3)
∆MyB = λdesignQdesign/N = 2.1 Nm (6.4) This loads case also allows to compute the peak to peak fatigue loads on the turbine shaft. These loads are considered to be applied at the first shaft bearing (nearest to the rotor). First, the thrust force (in the axial direction of the shaft) is calculated:
∆Fx−shaft = λdesignQdesign/(2R) = 18.7 N (6.5) The torsion moment on the shaft is obtained with:
∆Mx−shaft = Qdesign + 2mrger = 2.7 Nm (6.6)
Where mr is the total mass of the rotor and er is the rotor eccentricity, taken as 0.005R as per the guideline (as there is not a built rotor yet, no real data is available). Finally, the bending moment on the shaft is calculated:
∆Mshaft = 2mrgLrb + R∆Fx−shaft/6 = 8.1 Nm (6.7)
Lrb is the distance between the rotor center and the first shaft bearing, and is obtained from the nacelle that will be used (Section 6.4.2).
Design Load Case "B": Yawing
For this design load case, the maximum yaw speed ωyaw,max is assumed to occur during Ωdesign. As the yaw system is completely passive and the swept rotor area is less than 2 m2, the maximum yaw rate is set to 3 rad/s. Firstly, the flapwise moment on the blade can be calculated as follows:
2 MyB = mBωyaw,maxLrtRcog + 2ωyaw,maxJR,BΩdesign + R∆Fx−shaft/9 = 9.3 Nm (6.8) | {z } | {z } | {z } Centrifugal term Gyroscopic load Wind shear
Where Lrt is the distance from the rotor to the yaw axis (tower-nacelle join), which is obtained from the geometry of the nacelle. Regarding the shaft loading, the guideline define this equation for a three or more bladed wind turbine:
Mshaft = Nωyaw,maxΩdesignJR,B + mRgLrb + R∆Fx−shaft/6 = 16.5 Nm (6.9) | {z } | {z } | {z } Gyroscopic load Rotor weight Axial load eccentricity
Design Load Case "C": Yaw error The yaw error is a common operational case, and the wind turbine will work under very different yaw angle and wind speeds. An extreme loading might occur if the angle of attack seen by the blades leads to the maximum lift. This analysis intends to represent this scenario, and the expression shown below comes from integrating the blade flap moment along the blades.
!2 1 3 2 4 1 MyB = ρAproj,BCl,maxR Ωdesign 1 + + = 6.2 Nm (6.10) 8 3λdesign λdesign
Aproj,B is the planform area of one blade, and Cl,max is the maximum lift coefficient of the blades.
53 Loads calculation
Design Load Case "D": Maximum thrust The maximum thrust that the blades will see can be simply calculated with a force coefficient combined with a dynamic pressure. This equation has been tuned using thrust loads predicted by aeroelastic simulations. The guideline recommends caution when using this expression with wind turbines that operate at high rotational speeds. They recommend the use of a CT = 8/9 instead of CT = 0.5 in this case, and therefore the former will be used. 1 F = C ρ(2.5U )2πR2 = 96.2 N (6.11) x−shaft T 2 ave
Design Load Case "E": Maximum rotational speed The rotational speed may be very high in a small wind turbine, and therefore the centrifugal load must be taken carefully into account. It can be calculated as:
2 FzB = mBΩmaxRcog = 843.2 N (6.12) This DLC might also be important for the bending moment in the shaft due to blade unbalances:
2 Mshaft = mrgLrb + mrerΩmaxLrb = 7.1 Nm (6.13) | {z } | {z } Rotor weight Unbalances
Design Load Case "F": Short at load connection If the output terminals of the generator were shorted, a large moment would be created on the turbine shaft. This is known as short circuit torque, and the IEC defines the following equations for this load case:
GQ M = design + m gR = 3.5 Nm (6.14) xB N B cog
Mx−shaft = GQdesign = 5.2 Nm (6.15) Where the multiplier is taken as G = 2 for a permanent magnet generator.
Design Load Case "G": Shutdown-braking This load case accounts for the loads produced when the brake is applied. In this design, the braking will be done by means of generator shorting, and therefore the associated loads already have been calculated in the preceding DLC.
Design Load Case "H": Extreme wind loading
The wind speed applied to this DLC is the 50-year extreme wind speed Ue50. In this condition, the rotor is expected to be controlled (either actively or passively) to avoid overspeed. This DLC distinguishes between a rotating parking and a stationary parking. In this design, the rotor will be controlled by furling, and therefore the blades will be in motion, and the equations that must be applied are the following:
1 M = C ρU 2 A R = 20.7 Nm (6.16) yB 6 l,max e50 proj,B
54 Loads calculation
Where it has been assumed that, due to variations on the wind direction, the maximum lift coefficient will occur on one of the blades. For the thrust on the shaft, this equation can be used:
2 2 Fx−shaft = 0.17NAproj,Bλe50ρUe50 = 95.0 N (6.17)
Design Load Case "I": Parked wind loading - maximum exposure If the yaw mechanism suffers a failure, the wind turbine may be exposed to the find from any direction, and therefore the worst case aerodynamic force on all the components must be calculated. The load on each component is given by:
1 F = C ρU 2 A (6.18) 2 f ref proj
The force coefficient Cf is tabulated for blunt bodies in the guideline depending on the charac- teristic length. The following loads are obtained for the different components:
Table 6.7: Loads obtained from DLC "I"
Component Cf Aproj F Blades 2.0 0.173 m2 190.2 N Hub 1.3 0.030 m2 21.5 N Tail bar 0.7 0.008 m2 2.9 N Tail fin 2.0 0.075 m2 82.7 N Tower 1.3 0.060 m 43.0 N/m
The blades load is very unlikely, because it is the result of having the three blades seeing the maximum lift coefficient at the same time. It is something that would be very difficult in normal operation at Uref provided that α decreases with the wind speed, but should be considered as an extreme event. It will be treated as a thrust force acting in the rotor center (Fx−shaft). The loads in the other components have been obtained considering the wind coming parallel to the rotor plane. The tower loading is calculated per unit length.
Final loads
Table 6.8: Final loads obtained in the blade and the rotor shaft using the SLM.
Fatigue Loads Extreme Loads Blade Sensor Value DLC Sensor Value DLC ∆FzB 587.3 N A FzB 843.2 N E ∆MxB 4.4 Nm A MxB 3.5 Nm F ∆MyB 2.1 Nm A MyB 20.7 Nm H Shaft Sensor Value DLC Sensor Value DLC ∆Fx−shaft 18.7 N A Fx−shaft 190.2 N I ∆Mx−shaft 2.7 Nm A Mx−shaft 5.2 Nm F ∆Mshaft 8.1 Nm A Mshaft 16.5 Nm B
55 Blades structural design
The preceding table summarizes the worst case load for each sensor, and which is the design load case that it comes from.
At first glance it is surprising that the fatigue peak-to-peak edgewise moment is higher than the extreme load. Comparing the equations (6.3) and (6.14), it is found that this will be the case always that (G − 1)Qdesign/N is higher than mBgRcog. In the Simplified Load Model there is not a DLC that takes into consideration the normal operation regarding extreme loads (as the Extreme Turbulence Model in the aeroelastic modeling, for example), so these kind of strange results can be obtained, and the meaning is that the edge loads are mainly constrained by the normal operation. Other than that, observing at the results it can be seen how the high rotational speed (DLC "E") drives the maximum centrifugal force, and the extreme wind loading at Ue50 (DLC "H") leads to a very high moment in the flapwise direction.
6.3 Blades structural design
6.3.1 Beam study It is important to have the material properties well characterized when designing the structural end of the blades. This project initially intended to design a fully 3D printed wind turbine, specially regarding the blades. Nonetheless, it has been very difficult to find reliable informa- tion or characterization of the printed material properties. The mechanical attributes of the raw materials used in 3D printing are well known (e.g. [46]), but they are not the same when 3D printed. Not only the composition of the filament is different, but the properties highly depend on the printing settings. The extrusion temperature, speed, orientation, layer height, etc., are responsible of different mechanical behavior of the final print. There are several papers and studies that have addressed the problem, or at least that have determined the properties of one specific set of settings (e.g. [47–50]), but there is not a lot of information available yet.
Therefore, in order to the be in the safety side and avoid material characterization errors, a beam will be used in the blade. It will be considered that the loads are transmitted to the hub by this beam, and this will be the primary and critical structural element of the blade. The 3D printed structure will be neglected.
A carbon fiber beam will be used due to its excellent weight-resistance relation. There is also a large availability of pre-made carbon fiber beams in the market, for example in the website www.clipcarbono.com [51]. In order to select it, it is important to pay attention to the amount of space available in the cross sections of the blades, to the loads that it will have to withstand, and to the way that it will be attached to the hub. Regarding the latter, a common way to join carbon fiber tubes is by using inserts. This is a metallic connector that is glued to the inside part of the tube. In the afore-mentioned website, the smallest joint at sale has an interior diameter of 12 mm and an outside diameter of 15 mm. These connectors cost 9.90 € each.
56 Blades structural design
Figure 6.2: Connector that will be used between the beam and the hub. Obtained from [51].
The tube to be used must have the same interior and exterior diameter than the connector. If these dimensions are enough to withstand the calculated loads, and there is sufficient space available in the blade, the beam selection will be completed. These tubes are made of bidirec- tional 3K carbon fiber Sagra sheets of 200 g/m2. The specifications of the tube or the carbon fiber sheets are not provided by the reseller in its website, but looking to another manufacturer of the same type of tubes (www.tapplastics.com [52]), the following values are found:
Tensile strength 2.3 GPa Tensile modulus 134 GPa Compressive strength 1.9 GPa Compressive modulus 131 GPa Shear strength 41 MPa
Table 6.9: Structural properties of the carbon fiber tube.
The loads calculated before will be now assessed taking into account these properties. The maximum stress on the blade root is a combined bending and axial load problem in a circular section, and it can be calculated as shown below. Firstly, the fatigue loads will be assessed. The torsional load has been neglected, as it is indicated in the guideline.
q M 2 + M 2 FzB xB yB (σB)fat = + = 34.15 MPa (6.19) AB WB | {z } | {z } 9.23 24.92
Where the cross-section area of the beam is AB = 63.62 mm², and WB has been obtained as:
π 4 4 IB 4 (re − ri ) 3 WB = = = 195.6 mm (6.20) re re
57 Blades structural design
This equivalent fatigue stress should be compared with the ultimate fatigue damage of the material after the number of cycles that will be go through during its lifetime. There is not an S-N curve available, and the guideline recommends to use the following equation in this case:
fk σB ≤ (6.21) γmγf
Where fk is the characteristic material strength, γm is the partial safety factor for materials, and γf is the partial safety factor for loads. If no S-N is used, a γf = 10 should be used, but the guideline also allows to use a partial safety factor for material of γm = 3.7 if carbon fiber is used, and this includes the conversion from ultimate strength to fatigue strength. Then, the latter will be used, and a γf = 1 will be considered (this is the value to be used if the fatigue strength is well characterized). This leads to the following result:
" # f k = 18.2 (6.22) σ γ γ B m f fat This result means that, even after applying safety factors, the selected beam would be capable of resisting 18 times the stress that it will be usually working with. This overdimensioning is driven by the lack of smaller inserts to attach the blade to the hub. It could have two main drawbacks: an increase of price and mass. Regarding the former, it is true that a smaller tube in diameter would be cheaper, but a tailored-made insert for it would be much more expensive. Regarding the mass, it is considered that the mass assumptions that have been made in the loads calculation are very conservative, and the final blade mass will be less than that no matter which beam is used. Nonetheless, it is said in the guideline that the analytic method tends to underestimate the fatigue loads, so it is preferable to have a big margin like that [14].
The extreme loads will now be assessed. The radial force FzB and the flapwise moment MyB have been calculated from the maximum rotational speed and the extreme wind loading at Ue50 respectively (Table 6.8). In the latter, it is assumed that the rotor is spinning at its maximum rotational speed, therefore both loads would be contemporaneous. The corresponding edgewise moment MxB will be calculated using the same equation as in the DLC "A" (eq. (6.3)) but substituting the design rotor torque for the maximum one.
MxB = Qmax/N + 2mBgRcog = 5.0 Nm (6.23) These 3 loads will be combined as it has been done for the fatigue loads. The maximum stress in the beam at the blade root is now:
q M 2 + M 2 FzB xB yB (σeqB)ext = + = 122.11 MPa (6.24) AB WB | {z } | {z } 13.25 108.86 The centrifugal contribution is approximately 50% higher than in the fatigue case, but the biggest difference is found in the bending moment contribution, which has increased an order of magnitude. The safety factors to be used in this case are γf = 3 fo the loads and γm = 1.1 for the material. So, in this case, the net safety factor of the beam is:
" # f k = 5.7 (6.25) σ γ γ eqB m f ext
58 Blades structural design
Which shows that the structural design is drived by the extreme loads rather than the fatigue ones, and that the beam is conservatively designed but not very overdimensioned.
The last requirement that must be considered, after analyzing the resistance and the attachment to the hub, is the available space inside the blade. The maximum thickness of the blade (found at 19.8% chord) is shown in the figure below. In yellow, the remaining thickness (available t minus beam re) is shown. Not only the beam must fit inside the tube, but it should be enough space available for the walls of the blades to be printed. The recommended default settings are a minimum of 2 walls of 0.4 mm thickness each. In the flapwise direction there are a total of 4 group of walls to be printed: the suction surface, the top part of the beam hole, the bottom part of it, and the pressure surface. Therefore, a minimum space of 0.4 · 2 · 4 = 3.2 mm should be available.
20
15
Thickness at 19.8% chord 10 Beam thickness Remaining thickness Wall requirement Thickness [mm] 5
0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Radius [m]
Figure 6.3: Available space inside the blade to fit the carbon fiber beam.
From this figure it is decided that the beam will be extended until r = 0.3 m, because it is approximately where the wall requirement is not met, and in this way the beam will be attached to both parts of the blade.
6.3.2 Blade parts attachment
The joint between the two parts of the blade will be studied now. They will be connected only by means of an adhesive. Each part will be also glued to the beam, which will provide more reinforcement, but this will not be taken into consideration for determining the joint.
Firstly, the adhesive to be used will be selected. Usually, it is considered that PP, PE and PTFE are the common polymers that are harder to bond. In most commercial typical glues (such as cyanoacrylate or super glue) the technical data sheet indicates that its use is not recommended on such materials. This is because those are the polymers with the lowest solid surface energy. The material used for printing the blades is PETG (polyethylene terephthalate glycol-modified), which is a polyester based copolymer. It has a solid surface energy of 44.6 mN/m, significantly bigger that PP, PE and PTFE (30.1, 35.3 and 35.7 mN/m, respectively) [53]. Therefore, it is not necessary to go for a specific expensive adhesive for plastics which are hard to glue. In addition, a primer will be applied to the surface before the gluing process, which reinforces the
59 Blades structural design hypothesis of a surface with a "not-low" solid surface energy.
Aiming to use a state of the market common adhesive, the properties of the Araldite Standard are evaluated (an universal two component epoxy adhesive). From its technical data sheet [54], it is found that the average shear strength for PVC joints is slightly more than 4 MPa. As PVC is another amorphous thermoplastic with similar solid surface energy, it can be taken as a reference due to the lack of data for PET. However, a safety factor of 2 will be applied, and a shear strength of only 2 MPa will be considered. It will be assumed that the joint only will be withstanding centrifugal force. In the equation (6.24) this seems to be an unrealistic assumption, and therefore a very large safety factor (γf = 9) will be applied. In addition, the centrifugal force considered will be the one that has been calculated in the blade root for the worst case scenario. The centrifugal force that the mid section of the blade will actually see would be much lower, so it is reasonable to use the assumption that only the centrifugal force will be applied in the joint if all these corrections are utilized. To sum up, the necessary contact area will be:
γ γ F 2 · 9 · 843.2 S = m f zB = = 3794.4 mm2 (6.26) τmax 4 The first approach tested involved a "male-female" connection. The root part had a receptacle that held the "male" part of the joint. This option has a main problem: the male connector has to be printed in the same direction than the blade (radially: each layer is a blade section). The weaker part of a 3D printed object is the joint between two different layers. The centrifugal force will be withstood by the adhesive, but the bending moment will affect the adhesion between the layers. After a few tests, it has been seen that only a small bending moment (approximately 0.5 Nm) was necessary to break the pin.
The second and final option implies that both parts of the blade will have "female" receptacles, and the pin joint will be printed separately. By doing so, the printing direction can be adapted to the loads conditions. Moreover, the pin may be printed with more infill and number of perimeters, which will additionally increase its resistance. The joint shape designed is shown in the following figure:
Figure 6.4: Blade joint shape and dimensions (root section). Equivalent holes are present in the tip part.
60 Blades structural design
The tolerance between the pieces will be 0.20 mm, which has been determined after a trial and error process with simpler pieces. It allows a tight contact while keeping some space for the glue. The adhesive data sheet recommends a layer of approximately 0.10 mm, which will be the space available between the two pieces (considering the expansion and the uncertainties of the 3D printed objects). The perimeter of this joint is approximately 110 mm, and multiplying it for its height (35 mm), the necessary contact surface is obtained. The hole is slightly deeper than the male part to prevent a possible small separation between the two parts of the blade given by the tolerance of the pins.
Figure 6.5: Bed adhesion issue.
Nonetheless, the thermal expansion of the 3D printed parts (Figure 6.5) will create a small gap between the two parts. This issue does not have any impact in the structural area, because the pin joint behavior is not jeopardized, but would affect the aerodynamics of the blade. Therefore, it is necessary to fill this gap somehow. This will be done by placing insulating tape fully covering the aperture (Figure 6.6). Extra glue will be applied to ensure that it does not unstick, and the paint cover will also help to hold it in place. Either way, in the unlikely event that the insulating tape starts to get loose, it can be very easily replaced.
Figure 6.6: Insulating tape in the blade attachment.
61 Hub design
6.4 Hub design
6.4.1 Blade-hub joint In the preceding sections the use of a carbon fiber beam has been explained. In order to attach it to the hub, the so called inserts shall be used (Figure 6.2). In this section, the joint between them and both the beam and the hub will be studied. Moreover, the general design of the attachment will be described.
The design will use two aluminum inserts: the first one will be glued to the beam, and the second one will be joint to the hub by means of a M12 thread. The connection between them will be done by a M8 thread. The next figure shows the arrangement of these components:
Figure 6.7: Hub-Blade joint design. From right to left: blade beam, beam insert, hub insert, and hub. Over the hub there are two M4 bolts to tighten the joint and avoid tolerances. Their corresponding nut is not represented. The blade has been omitted for clarity.
This will allow a solid load transmission into the hub. The assembly process will be the following:
1. Print the blade and the hub. 2. Secure the hub insert in the hub with an Allen key. The tolerance will be very small to ensure a great tight contact. 3. Glue the blade insert inside the beam. Ensure good surface preparation, sufficient adhesive quantity, and enough curing time. 4. Screw the blade insert inside the hub insert. The beam will then be joint to the hub. 5. Glue the blade to the beam. This way the blade pitch will be fixed by the hub shape acting as a clamp.
62 Hub design
6. To avoid a wobbly joint, screw two M4 bolts in the exterior hub holes. This will solve any possible tolerance issue.
The threaded hub insert will provide excellent pull-out resistance according to the Handbook of Plastic Joining [55]. After testing it by simply holding a weight, it has been proven that it will be capable of holding the radial force calculated before (Table 6.8). The drawbacks of this option are a low torque resistance and a difficult process of finding an acceptable tolerance between the plastic and the insert. The low torque resistance is not worrying provided that the torsional load created by the blades is negligible, and the difficult process has been suffered; it was necessary to have a trial and error process until determining that an exterior hole of 12.1 mm created the best joint.
The joint between the beam and the insert may be more problematic, and therefore it requires more attention. It should be capable of transmitting the loads seen by the beam root to the beam insert. The stress distribution in the beam root looks like this:
Figure 6.8: Blade root stress distribution. The scheme is not in the actual scale.
This is the resultant stress of a deviated bending moment and an axial force problem (the flapwise and edgewise moments, and the centrifugal force). To compute the shear stress that will be transmitted to the insert by means of the adhesive, an equivalent force may be calculated. It will be assumed (to be in the conservative side) that the demanded side of the beam (the left side in the upper figure) is the stress that every projection of the root section will see. This is obviously incorrect, because this distribution has been obtained looking precisely to the worst projection. However, it is useful to have an equivalent load and ensure that the adhesive will be able to withstand the necessary shear stress in all the contact surface. This fictitious equivalent force is then calculated as:
r − r F = 2πr e i (σ + σ ) = 6288.2 N (6.27) eq,adh i 2 1 2 Which leads to the following shear stress to be held by the adhesive:
63 Hub design
Feq,adh τadh = = 8.34 MPa (6.28) 2πril Where l is the insert longitude inside the beam (20 mm). The value obtained is low because the insert and beam selected have a very large contact area. If a smaller pair of tube-insert had been available for purchase, it would have been selected, but the limited offer was a constraint. Nonetheless, a small shear value will tolerate a cheapest and non-specific adhesive, which is the positive side of this trade-off.
Once the extreme shear stress is calculated, an adhesive must be selected such that its maximum strength is greater than the computed value. This is not easy, because the joint strength of aluminum-carbon fiber is not stated in the vast majority of the commercial adhesives’ technical data-sheet. It only appears in the most specific ones, and even in those cases it is said that this value could not be treated as a specifications, and tests should be made. However, after erasing this question to Ceys technical department (a manufacturer of adhesives and glues [56]), they have confirmed that Araldite Standard should work for this case.
6.4.2 Hub-shaft joint The generator shaft is a M16 threaded bar of 20 mm. The initial thought was to place a M16 insert in the hub and screw the shaft using some thread locking glue. This option, however, would create large difficulties in the event of a rotor replacement. The glue can be removed, but it is a difficult process that it is better to avoid [57]. It is a likely scenario for future designs or improvements. Therefore, an alternative have been designed.
Figure 6.9: Hub-Shaft joint design. From right to left: threaded rod connector, threaded rod extension, downwind hub insert, hub, upwind hub insert, fixing nut. The blades have been omitted for clarity. 3 M4 screws to tighten the last section of the hub are not shown. The generator shaft would be coupled to the connector rod at the right.
The concept is similar than the blade-hub joint, as inserts will be used again to connect the printed parts to the metal components. The inner threads used are M16, whereas the exterior threads of the inserts are M22. In this case, one insert will be place in each extreme of the
64 Printing properties hub, and the shaft extension will be placed all the way in the rotor central axis. In the upwind extreme, it will be fixed by a nut that will fix its rotation. In the downwind extreme, the threaded rot will be screwed and glued with thread locking adhesive into a threaded connector. This connector will be also screwed and glued to the generator shaft in its other end. With this design, the main shaft will be extended such that a rotor replacement may be easily made by just removing the fixing nut and unscrewing the hub.
6.5 Printing properties
Once a part has been designed, a software called Slicer must be used to prepare it for 3D printing. It is able to generate the G-Code, a common Computer Numerical Control (CNC) programming language, that the printer will read and execute. The Slicer that will be used is Ultimaker Cura [58], a widely used free software which combines a user friendly interface and the possibility of using advanced settings. The inputs to the Slicer are the part to be printed and a series of settings that will define how the printing process will be conducted. The main printing properties used will be described in this section. Its selection must address two principal compromises: firstly, the infill of the part is a trade-off between strength and weight. Secondly, the layer height is a decision between surface quality and printing time. The properties will be different depending on the part to be printed, so they will be treated separately. The information found below has been obtained from own tests or from 3D-printing reference websites as [10] or [58]. The difficulties in justifying quantitatively some decisions has been already addressed in the beginning of the Section 6.3.1.
6.5.1 Blade
1. Orientation: radial. They will be printed in the radial direction, such that each layer will be a blade section. This will ensure the quality of the airfoil shape, and minimize the roughness in the flow direction.
2. Layer height: 0.32 mm. Using a 0.4 mm nozzle allows to use a layer height between 0.12 mm and 0.32 mm. The lower the layer height, the higher the printing time and surface quality. After some coating tests, it has been decided that it is worth to go for 0.32 mm to minimize the time, because the surface can be homogenized and smoothed afterwards.
3. Shell: The shell is referred as the exterior part of the part, and its settings will be important for both the quality and the strength.
3.1. Wall line count: 3. The number of perimeters that the print will have. Increasing it improves the rigidity and the layer adhesion of the part with less cost (mass and time) than doing so by an infill increase. 3.2. Z seam alignment: sharpest corner. The starting point of each consecutive layer may create a seam in the exterior perimeter present in the vertical direction. The option sharpest corner is selected, which will initialize each layer in the Trailing Edge. The drawback is that the thickness of the TE will be increased (1.5 mm), but it is assumed that the flow has already worked throughout all the chord length, and the aerodynamic implications are negligible. It may have effect in the noise production, however this possibility has been analyzed in detail in the Section8 and no implications are seen.
65 Printing properties
3.3. Walls order: inner first. After some testing, it has been determined that printing the inner walls first leads to the best surface finish and layer adhesion. 3.4. Alternating extra wall. It adds an extra wall every other layer, which will help the infill to adhere better to the walls. Some tests shown that having this option activated could lead to delamination in the trailing edge, so it has been finally deactivated. 3.5. Fill gaps between walls. There will be gaps thinner than the nozzle size, which would be left empty if this setting was not activated. It will increase the printing time but the layer adhesion at the Trailing Edge (a critical point) will be better.
(b) Fill gaps between walls scheme.
(a) Alternating extra wall scheme.
Figure 6.10: Alternating extra wall and fill gap between walls settings. Retrieved from [58].
4. Infill: The remaining space inside the shell will be filled out with a determined pattern and density depending on this properties.
4.1. Infill pattern: Cubic subdivision. This pattern changes every layer to provide an isotropic strength. The subdivision variant is selected to reduce time and material. 4.2. Infill density: 25%. This option has been considered enough to ensure layer adhe- sion, to provide sufficient stiffness, and a good load transmission to the hub. However, the criteria is not very clear and the decision is based on qualitative tests, so this settings would require further study.
5. Material: Temperature settings are usually more based on the printer and material used rather than the part to be printed.
5.1. Printing temperature: 225ºC. It has been selected after running a temperature tower (a test print that increases the nozzle temperature with the height so the most indicated temperature for the material used can be easily identified) and printing several typical test parts. 5.2. Build plate temperature: 70ºC. Although it is a high temperature that may lead to base deformation during cool down and print removing, the slenderness of the blade asks for it. Otherwise the print base may warp or not have the proper base adhesion.
6. Speed: It is a trade-off between quality and time. It can be increased at those places where the quality is not that important, like the infill. The settings detailed below have been obtained after testing and trial and error.
66 Printing properties
6.1. Outer wall speed: 20 mm/s. 6.2. Inner wall speed: 25 mm/s. 6.3. Infill speed: 50 mm/s. 6.4. Initial layer speed: 20 mm/s. 6.5. Travel speed: 150 mm/s.
7. Travel: A retraction distance of 7 mm is set. With less distance, a lot of stringing was present in the prints.
8. Build plate adhesion: These settings are important to ensure that the print is well attached to the plate. In addition, lacquer spray has been applied to the bed to improve even more the adhesion.
8.1. Build plate adhesion type: Brim. This setting adds a single layer flat area around the base of the part to prevent warping. 8.2. Brim line count: 35. The print has failed by bed separation when setting a low value here (5-10). 35 lines has been enough to have successful prints.
6.5.2 Pin joints Only the most important settings are listed below.
1. Layer height: 0.2 mm. Smaller resolution is needed for the rounded ends of the pins. This will allow a better matching.
2. Infill density: 90 %. A very high value is selected to ensure the maximum strength possible. An infill density of 100 % is not usually recommended due to shrinkage and residual stresses.
3. Infill speed: 80 mm/s. As the part uses a lot of infill, it is desirable to maximize its printing speed.
4. Slicing tolerance: inclusive. When slicing diagonal surfaces, the layer will contain the parts that are completely within the model. Usually the layer is generated with the middle point, but in this case this setting has provided the best fitting with the blade holes.
6.5.3 Hub As with the pin joints, just the most determining settings are detailed in the following list.
1. Layer height: 0.32 mm. The highest possible layer height was used again for the seek of time.
2. Wall line count: 4. Stronger and bigger walls are desired because of the direct interaction with the inserts.
3. Infill density: 50 %. Compromise between strength, printing time, and weight.
4. Infill speed: 60 %. Although a lot of infill will be needed, the lower it is printed, the more strength it will have, so it will now be printed slower than before.
67 Printing properties
5. Support material: activated. Because of the shape of the hub, it can not be fully held by its own base, so supports are needed. This is extra material printed where overhangs or bridges will be placed, and it should be removed once the print is completed. A support overhang angle of 50º is set, and the pattern will be "Zig Zag" with only 7 % density.
Figure 6.11: Screenshot of the sliced root part of the blade.
A summary table of the final printing cost for each part is shown below.
Table 6.10: Printing cost and time for each part.
Part Time Weight Length Cost Blade root 13h 32’ 156 g 52.47 m 3.13 € Blade tip 12h 33’ 149 g 49.83 m 2.97 € Pin joints 2h 17’ 22 g 7.43 m 0.44 € Hub 26h 43’ 378 g 126.76 m 7.56 € Total 111h 49’ 1359 g 455.95 m 27.18 €
68 Tower assessment
6.6 Tower assessment
The tower will be analyzed in this section. A first order linear study will be made for a tubular monopole tower, and the maximum stress, the natural frequency, and the top displacement will be calculated. The buckling will be assessed as well. For the static analysis, the loads that will be considered are the thrust and bending moment at the main shaft, and the drag force acting on the tower. The weight of the nacelle, rotor, and tower will be taken into account as well. For the dynamic analysis, the tower is modeled a flagpole in cantilever with a top mass. The foundation stiffness will not be considered.
The tower that will be assess is a 6 m height steel tube that the nacelle manufacturer can also provide. With that, the nacelle-tower top joint would be also determined. The main characteristics are shown in the next table:
Table 6.11: Characteristics of the tower analyzed.
Symbol Unit Value Description H m 6 Height dT,e mm 60 Exterior diameter dT,i mm 54 Interior diameter 2 AT mm 537.2 Section area 4 5 IT mm 2.19·10 Area inertia 3 ET MPa 200·10 Young modulus (steel [59]) 3 ρT kg/m 8000 Density (steel [59]) fk MPa 450 Yield strength (steel [59]) mT kg 25.8 Tower mass mTT kg 9.2 Tower top mass
The bending moment on the tower as a function of the height y can be calculated as:
2 MT (y) = Mshaft + Fx−shaft · y + D(y) · y (6.29) Where the first two quantities have been obtained in the loads calculation (Table 6.8) and the drag actuating in the tower D(y) will be taken from the Table 6.7. It is a function of the height because the wind shear could be taken into account, but as a conservative approach the wind speed will be considered constant and equal to Uref , and therefore D(y) = D.
Taking the maximum bending moment at tower bottom, and adding the axial loading given by the weight and the maximum radial force of a blade pointing downwards, the resultant maximum stress is:
MT (y = H)dT,e FzB + (mT + mTT )g σT = + = 26.55 MPa (6.30) 2IT AT Which is way under the maximum yield stress. However, note that the upwind face is in tension and the downwind in compression, so the tower could buckle and this should be assessed. The Euler critical load will be calculated considering a beam in cantilever with one free end [60]:
π2E I P = T T = 3000 N (6.31) CR 4H2
69 Tower assessment
The conservative maximum axial load on the tower would be FzB + (mT + mTT )g = 1186.6 N. there is some margin but more attention should be paid to this possible failure. The second order effects must be considered, and the assumption of the radial blade force contributing to the tower axial load should be revised. To calculate this axial load it has been considered that the all the tower mass is actuating, which is a false and conservative assumption.
The tower top displacement will now be calculated to discuss the accuracy of the first order model. It must remain small to justify that the structural shape is not highly modified under the loads and does not alter it. According to the standard beam theory:
Mshaft 2 Fx−shaft 3 D 4 2 · H + · H + · H d x MT (y) 2 6 12 2 = → x(y = H) = = 0.58 m (6.32) dy ET IT ET IT Which is about 10% of the tower length. It would be interesting to have a more detailed analysis and verify whether the small displacements assumption can be used.
Regarding the dynamic analysis, Tempel and Molenaar proposed an analytical equation to calculate the tower first natural frequency considering the nacelle as a punctual mass, the tower as a distributed mass and the tower bottom as a fixed extreme [61]: s 1 3.04ET IT fT ≈ 2 3 = 1.018 Hz (6.33) 2π (mTT + 0.227mT H )H The towers are usually characterized as soft-soft, soft-stiff, or stiff-stiff depending on the relation between its first natural frequency and the 1P frequency at rated speed. As the 1P in this case is 383.6 rpm = 6.4 Hz, this would be considered a soft-soft tower. Another check can be made with the similarly derived equation from Wood [29]: s 1 KT fT ≈ = 0.998 Hz (6.34) 2π mTT + 0.23mT
Where KT is the stiffness of the tower, obtained as KT = T/x, where x is the displacement generated by the thrust force T . It leads to a value very close to the other approach, so it may be considered a solid result.
To reduce the buckling risk, add additional safety, and simplify the erection procedure, some guys could be added to the tower. If placed in the middle section, they would reduce the tower 0 buckling length to the half, leading to a 4 times higher critical load PCR = 4PCR. This option may be modeled as explained in the reference [62].
70 Chapter 7
Tail study
The calculations of power extraction and starting behavior done until this point have assumed steady flow perpendicular to the rotor plane. However, the unsteadiness are important, especially when it comes to the yaw behavior and the capability of the wind turbine to face the incoming wind. It has a remarkable effect because a yaw error θ reduces the power produced by the ratio cos2 θ [29]. Not only the power reduction is important, but also the loads created by the gyroscopic forces, which is an important term in the driving load that dimensions the rotor shaft (Equation (6.9) and Table 6.8). In this section, the behavior of the original tail that came with the generator and the nacelle will be analyzed, a description of the furling tail technology will be done, and a procedure to design a furling tail will be proposed.
7.1 Analysis of an existing tail
Firstly, the geometrical properties of the tail will be described. The tail fin is simply a flat plate acting as a wing. The shape of the existing tail is slightly unconventional, but for a simplified analysis it is similar enough to a typical arrow form, so an equivalent arrow shape will be con- sidered. Both geometries are represented in Figure 7.1.
2 The equivalent geometry has been obtained by imposing the same fin area (At = 0.065 m ) and 2 aspect ratio AR = b /At = 1.58, where b = d3 + d4. The indentation i = d5 and the chord c have also been fixed. With that, the only unknown is the new span of the tail b, which may be obtained with the aspect ratio and area relation:
bc bi b2 c − i − = A = → b = AR = 213 mm (7.1) 2 2 t AR 2 The center of pressure r may be assimilated to the one of a delta wing, so a distance of 2c/3 from the apex will be taken. All the dimensions are summarized in the Table 7.1.
Table 7.1: Tail dimensions.
r 600 mm d1 100 mm x 400 mm d2 245 mm c 300 mm d3 240 mm b 213 mm d4 80 mm i 30 mm d5 30 mm
71 Analysis of an existing tail
Figure 7.1: Scheme of the main geometrical dimensions of the tail. The upper figure shows the equivalent geometry, and the lower one the actual tail dimensions. The rounded edges of the real geometry have been neglected.
The yaw performance will be modeled as a second order differential equation. It is derived by applying the unsteady slender body theory (USB) [63]. Although it is only valid for small angles and has neglected the drag, it is useful and commonly used [29].
¨ ˙ 0 ¨ JY θ = K1(θ − φ) + K2θ − K2ϕ˙ + K3θ (7.2) Where θ is the angle between a non-rotatory inertial system and ϕ is the wind direction in the same coordinates (with an arbitrary origin). JY is the total inertia moment around the yaw axis, and the K constants are defined as:
1 K = πρb2U 2r (7.3) 1 4 Which is the steady lift of the tail fin applied in its center of pressure. The following two constants are related to the instantaneous down-wash: the movement of the flow caused by the voracity generated by the lift.
1 K = πρKU(c + x)2 (7.4) 2 4
1 K0 = πρb2U(c2/4 + cx/3) (7.5) 2 4 Finally, the last term accounts for the added mass of the air moved with the yawing tail fin [29].
1 K = πρb2c(c2/5 + x2/3 + cx/2) (7.6) 3 4
72 Analysis of an existing tail
If the added mass can be neglected (an usual approximation), the natural frequency and damping ratio for the case where the wind direction does not change may be represented by the following equations [29]. s ρA Kr ω = U t (7.7) n w 2I s ρA K ζ = (c + x)2 t (7.8) 8Ir Where K may be obtained from the studies of Polhamus [64], who computed the behaviour of arrowhead planforms, and tabulated the lift slope value for different indentation values:
K = AR(KP 0 + AR · KP 1) (7.9)
Where KP 0 and KP 1 are constants that depend on the indent factor. For the current case, i/c = −0.1 (indendation is defined negative in the "arrow" direction). The result is then K = 6.259 rad−1, very similar to the classical flat plate slope 2π = 6.283 rad−1. The two remaining unknowns are the wind speed in the near-wake Uw and the yaw axis inertia JY . The latter will be calculated below, and for the former, an optimal operation will be assumed and then Uw = U∞(1 − a), where U∞ is the undisturbed wind speed and a = 1/3.
The mass inertia will be divided between the contributions of the rotor, the tail fin, the tail boom, and the nacelle JY = JY,R + JY,T F + JY,T B + JY,N . Firstly, the rotor inertia may be calculated as:
2 2 2 2 JY,R = mRLrt + JR,B[sin (ψ) + sin (ψ + 120) + sin (ψ + 240)] (7.10) Which is dependent on the rotor position for an individual blade but not for the whole rotor, because the addition of all sin2 terms is equal to 1.5. The tail boom inertia about the yaw axis can be calculated as:
3 JY,T B = ρtbAtbr /3 (7.11) And the tail fin contribution can be computed as if it had a delta planform:
2 2 JY,T F = ρtf bct(x /2 + 2xc/3 + c /4) (7.12) 3 Where ρtb = ρtf = ρsteel = 8000 kg/m (from [59]), and the tail boom has a cross-sectional area 2 of Atb = 490.9 mm (circular shape). The thickness of the tail fin is t = 3 mm. Lastly, the nacelle inertia will be computed as a rod with the center of mass located in the yaw axis.
2 JY,N = mN Ln/12 (7.13)
Where the nacelle length is Ln = 0.3 m and the nacelle mass is estimated to be the mass of the generator plus a steel cover mN = mG + 2πrntnρsteel = 5.9 kg. All the results are summarized in the Table 7.2.
Now, all the necessary variables are established to go back to Equations (7.7) and (7.8) and compute the natural frequency and the damping of the response.
ωn = 0.4384 · Uw [Hz] ζ = 0.179 (7.14)
73 Analysis of an existing tail
Table 7.2: Inertia about the yaw axis.
2 JY,R 0.174 kgm 2 JY,T B 0.283 kgm 2 JY,T F 0.280 kgm 2 JY,N 0.044 kgm 2 JY 0.781 kgm
The damping is fully determined by the geometry and the yaw inertia, but the natural frequency depends on the incoming wind speed. To recap a little bit, Equation (7.2) will be now solved neglecting the air mass moved (last term) and assuming a steady wind misalignment. Therefore it can be rewritten as:
¨ ˙ 2 2 θ + 2ζωnθ + ωnθ = ωnϕ (7.15) To have a centered response (0º = no yaw misalignment), the wind direction ϕ is set to zero, and the boundary conditions are set by θ, which will be the perturbation, and θ˙ = 0, which is set arbitrarily to be able to solve the equation. The time response of the system is presented in the Figure 7.2 for different U∞ and yaw misalignment ϕ.
50 50 Wind speed = 5 m/s Initial yaw error = 10 deg 40 Wind speed = 7 m/s 40 Initial yaw error = 20 deg Wind speed = 9 m/s Initial yaw error = 30 deg 30 Wind speed = 11 m/s 30 Initial yaw error = 40 deg Wind speed = 13 m/s Initial yaw error = 50 deg 20 20
10 10
0 0
-10 -10
-20 -20 Yaw misalignment [deg] Yaw misalignment [deg] -30 -30
-40 -40
-50 -50 0 5 10 15 20 25 30 0 5 10 15 20 25 30 Time [s] Time [s]
Figure 7.2: Yaw misalignment time response. The left plot has been obtained for a yaw error of 30º, and the right plot for a wind speed of 9 m/s.
The natural frequency dependence on the incoming wind speed is clearly seen in the left plot. The slower response is found in the lower wind speeds, which can jeopardize and slow down the starting. The right plot shows that the correction time is the same for any perturbation, but the amplitude of the damped oscillations depends on it. Overall, the damping obtained seem acceptable, and the capability of this tail to respond to low-frequency wind direction variations in this simplified analysis is good. This is an important relief, because increasing the damping of the tail is not trivial. In Equations (7.7) and (7.8) (or (7.3) and (7.4)), it is seen that the damping depends on the same parameters than the natural frequency, and any change in the
74 Furling tail design for over-speed protection
lengths (c or x) would be counteracted by an opposite change in the inertia JY . A higher natural frequency is not aimed either, because it is not desired to react to high-frequency wind direction changes [29].
7.2 Furling tail design for over-speed protection
Furling is an common design option used to provide passive aerodynamic over-speed control using the tail. Its basics will be described in this section, and a design process will be proposed. The mechanism is based on an eccentric positioning of the rotor or the tail with respect to the yaw axis. If it is designed properly, the tail will keep the rotor oriented to the wind in low and moderate wind speeds, but at higher wind speeds the thrust will create a moment that will turn the rotor out of the wind. The recovery to the oriented position once the wind speed has reduced is usually achieved by a spring in the furling hinge [42].
Figure 7.3: Basic furling geometry. The origin of coordinates indicates the yaw axis, and the other hinge is the furling tail axis. Retrieved from [42].
A detailed analysis of this technology is given in [20], and a mathematical framework for mod- eling a furling system is proposed in [42]. It is based on a Lagrangiane formulation using Euler angles to consider all degrees of freedom under different frames of reference. They have also studied the critical parameters for the design process, and observed hysteresis between onset and return positions. The wind speed associated to both processes is found to be linearly dependent to the tail mass and the lateral inclination of the furl axis, which therefore are good design parameters to tune for achieving the desired operation. The eccentricity lengths and the tilt angle of the furl axis have a lot of influence, and small variations may have a dramatic impact. Additionally, the open-source aerolastic code FAST (Fatigue, Aerodynamics, Structures, and Turbulence) from NREL can also model the furling effect [65]. An approach could be to design
75 Furling tail design for over-speed protection the system with the simplified "stand-alone" modeling of the yaw mechanism, and then validate it and observe second order effects with the full aeroelastic simulation. This remains as future work and may be too much work for a small wind turbine: a common design procedure after a basic equilibrium calculations is the trial and error [29]. Moreover, furling tails were used before the 20th century in the high solidity water pumpers [66], and it is unlikely that they used an aeroelastic code to design it.
In practice, there are a number of drawbacks associated. The hysteresis condition above- mentioned, or a gusty incoming wind, may result in the tail continually furling and unfurling, without a complete shut down. Furthemore, when the turbine is producing power in normal conditions, the thrust offset usually creates a small yaw misalignment, which can reduced the power extracted around 10% from the oriented case. Lastly, the design is not purely related to the thrust seen by a high wind speed, because the over-speed can happen in another scenario. If the generator losses its load, the blades will accelerate indefinitely unless the rotor is turned out of the wind, which will be achieved when the thrust coefficient grows enough due to the increased rotor speed [29].
To sum up, a furling mechanism could provide a safe passive over-speed control, but its design requires either testing or complex modeling. It remains as future work to be done, and designing it would help to accomplish the requirement set in the Section 1.3 that the operation should be completely passive. The alternative over-speed control would be done my means of a generator shorting once a determined voltage value is exceeded. The voltage is directly related to the rotor speed as seen in the Section 4.3, and the controller shown in the Figure 4.1 should accomplish this mission. The main problem of this option is that it is not fail-safe, as a problem in the generator-controller connection would probably result in an over-speed and maybe a complete failure.
76 Chapter 8
Noise prediction
In this section, the noise generated by the rotor blades will be analyzed. The type of noise sources that will be computed will be quickly described below, and the method and code used for the calculation will be further detailed in the Report Attachment (Section2). The valida- tion of the code may also be found there. The aerodynamic noise is usually divided between the airfoil-self noise and the turbulence inflow noise. In this case, only the airfoil-self noise will be taken into account, because it is more directly related with the blades design, and it can be determined whether future steps to reduce it are necessary.
A good noise assessment is important because it is one of the most annoying implications of the wind turbines [17]. Based on the results presented here and the possible reduction options for each noise mechanism, a future design iteration could take actions to mitigate it. The inflow should be also taken into account in the future to have the overall perspective of the noise produced by the rotor.
8.1 Noise mechanisms studied
There are several models available that allow to compute the aerodynamic airfoil self-noise (Grosveld, Brooks et al., or Glegg et al.), and they provide scaling laws derived from theoretical developments complemented with aerodynamic and aeroacoustic measurements [67]. The model that will be used for this section is from Brooks, Pope, and Marcolini (BPM) [68], which comes from a set of experiments done in several NACA 0012 airfoils with different chord lengths. They came up with a series of equations that allow to compute the Sound Pressure Level (SPL) as a function of the boundary layer parameters and several adimensional variables like the Reynolds, the Mach, and the Strouhal numbers. These equations must be applied to all the different blade sections in order to account for the individual flow conditions seen by them.
The noise mechanisms that will be calculated are explained below (from [17, 67–71]):
1. Turbulent Boundary Layer - Trailing Edge Noise (TBL-TE): The turbulent eddies of the boundary layer at low Mach numbers are inefficient sound sources. However, if there is a sharp edge close to them, they will be amplified and become more important. Therefore, trailing edges (TE) are a significant origin of noise. This is usually perceived as a swishing sound (broad-band), and it is typically one of the main sources of the total noise. It depends strongly on the angle between the eddy path and the TE, and therefore it can be reduced by giving the TE a serrated shape.
77 Noise mechanisms studied
Figure 8.1: Turbulent Boundary Layer - Trailing Edge noise mechanism. Retrieved from [67].
2. Laminar Boundary Layer - Vortex Shedding Noise (LBL-VS): If the laminar flow region of an airfoil extends up to the trailing edge, a resonant interaction of the TE with the unstable laminar-turbulent transition can happen, and it could travel upstream resulting in a tonal noise. It is a phenomenon to take into account when the major part of the chord has a laminar boundary layer, and it can be avoided by tripping the boundary layer. It is especially present in the pressure side of the airfoil.
Figure 8.2: Laminar Boundary Layer - Vortex Shedding noise mechanism. Retrieved from [67].
3. Separated/Stalled Flow (SSF) Noise: When the angle of attack increases, the size of the suction side boundary layer grows drastically. Large-scale unsteady eddies may form and cause sound radiation from the trailing edge. When deep stall is reached, this is even more amplified and the radiation takes places from the whole chord.
Figure 8.3: Separated/Stalled Flow noise mechanism. Retrieved from [68].
78 Boundary layer parameters analysis
4. Tip Vortex Formation Noise (TVF): This is a three-dimensional noise source based on the interaction between the tip vortex and the blade tip itself plus the trailing edge near the tip. It is a broad-band source and it is mainly influenced by the convection speed of the vortex and its spanwise extent. It can be mitigated by varying the tip shape.
Figure 8.4: Tip Vortex Formation noise mechanism. Retrieved from [68].
5. Trailing Edge Bluntness - Vortex Shedding Noise (TEB-VS): Depending on the TE bluntness and shape, vortex shedding can occur and lead to a Von Karman vortex street. These alternating vortices create high surface pressure fluctuations close to the TE at a specific frequency, and the noise generated is largely determined by its geometry. This will become specially important if the thickness of the TE is in the same order of magnitude as the boundary layer thickness. If the TE thickness is reduced the frequency peak will move towards higher frequencies and decrease its intensity.
Figure 8.5: Trailing Edge Bluntness - Vortex Shedding noise mechanism. Retrieved from [67].
8.2 Boundary layer parameters analysis
All the noise sources are highly dependent on the boundary layer (BL) parameters, and therefore it is worth to go through them carefully. Although BPM have proposed a set of equations to compute the BL thickness δ and the BL displacement thickness δ?, they are based on measure- ments of the NACA 0012 airfoil and, unlike the noise equations, it is not reliable to apply them to a different airfoil.
It is possible to quickly extract the BL displacement thickness from the software XFOIL, but the simulations done for the airfoil study (Section 5.1) must be revised. There, it had been assumed that most of the boundary layer would be turbulent, and a very low Ncrit value was
79 Boundary layer parameters analysis set. This assumption was based on the expected high turbulence of the incoming flow and the roughness of the surface finish of the blades. However, a wind tunnel validation was pending and unfortunately could not be completed. After some testing applying coatings to the blades, it has been seen that a very smooth surface may be obtained, and therefore a laminar BL might be more likely that it has been anticipated. Moreover, the low Reynolds number of most of the operation would help so. In the following figure, a comparison of the boundary layer displacement ? thickness δs is shown to highlight the importance of such calculation and transition behavior ? differences. The TE δs value is studied because it is the input needed for the BPM equations.
0.3 0.3
0.25 Transition at 0.05c 0.25 Ncrit = 1 Ncrit = 9 BPM (BL tripped) 0.2 BPM (BL not tripped) 0.2 * at TE [x/c] * at TE [x/c] 0.15 0.15
0.1 0.1 Suction side Pressure side
0.05 0.05
0 -10 -5 0 5 10 -10 -5 0 5 10 Angle of attack [º] Angle of attack [º]
Figure 8.6: Boundary layer displacement thickness δ? for different calculation methods and transition properties at Re=120k. The XFOIL data has been obtained from the S1223 airfoil used in the blades, and the BPM data use the equations extracted from NACA 0012.
First of all, it should be mentioned that the BPM equations are only defined from α = 0º on, because they are obtained from a symmetric airfoil. To apply them, it has to be considered that the negative angles of attack are treated equally to the positive ones but inverting the suction and the pressure sides. The BPM results in both figures are then symmetrical.
In general, the trend of all plots is the same: the boundary layer thickness increases with the angle of attack, and the slope gets larger when it approaches the stall region. The biggest dif- ference between the XFOIL and the BPM results is obtained in the pressure side at negatives angle of attack. This is likely due to the small radius of the S1223 leading edge and its large camber (Figure 5.2), which makes very difficult for the flow to remain attacked. Figure 8.6 intends to show the variability of δ? depending on the characteristics of the boundary layer, and therefore the differences that could appear in the noise calculations. For coherence with the design process, the data obtained from XFOIL at Ncrit=1 will be used. It will be tabulated for different Reynolds numbers, and interpolated for each blade section at each different operation point.
80 Noise calculation results
8.3 Noise calculation results
Different wind speeds will be studied, and the blade will be discretized with a sinusoidal spacing (the same way it was done for the aerodynamic design (Figure 1.6 of the Report Attachement)). The variables that are non-dependent on the operation are summarized below:
Table 8.1: Noise parameters definition.
TE Thickness h [mm] 1.5 TE Angle Ψ [deg] 8.8 Observer Φ [deg] 90 Observer Θ [deg] 90 Observer distance r [m] 1
The trailing edge thickness has been measured from the printed blades, and the angle has been obtained from the airfoil geometry. The observer variables have been defined as such arbitrarily, because the aim of this study is to have a comparative idea of the different mechanisms of noise at several operation regimes, and not a detailed prediction from a specific point. The results for different wind speeds are shown below. The frequency spectrum used is 1/3 octave, without any filtering.
Total noise for each wind speed 80 Wind speed = 5 m/s [OASPL = 40.6 dB] Wind speed = 7 m/s [OASPL = 58.3 dB] 70 Wind speed = 9 m/s [OASPL = 65 dB] Wind speed = 11 m/s [OASPL = 64 dB] 60 Wind speed = 13 m/s [OASPL = 64.9 dB]
50
40
30
20 Sound Pressure Level (SPL) [dB] 10
0 102 103 104 Frequency [Hz] Figure 8.7: Noise spectrum for each wind speed.
All the detailed plots of this calculation may be find in the Report Attachement (in the Section 2 the results are shown per noise mechanism and blade section), and here only the results for 9 m/s and 13 m/s will be discussed. At first glance, it may be surprising that the highest Overall Sound Pressure Level (OASPL) is found at 9 m/s and not at the highest wind speed studied. Taking a look at the driving noise mechanisms may help to explain it:
81 Noise calculation results
Frequency spectrum of all noise mechanisms at 13 m/s 80 Total Noise Laminar Boundary Layer - Vortex Shedding 70 Turbulent Boundary Layer - Trailing Edge (p) Tip Vortex Formation Turbulent Boundary Layer - Trailing Edge (s) Trailing Edge Bluntness - Vortex Shedding Separation Noise 60
50
40
30
20 Sound Pressure Level (SPL) [dB] 10
0 102 103 104 Frequency [Hz] Figure 8.8: Frequency spectrum of all noise mechanisms at 13 m/s.
Frequency spectrum of all noise mechanisms at 9 m/s 80 Total Noise Laminar Boundary Layer - Vortex Shedding Turbulent Boundary Layer - Trailing Edge (p) Tip Vortex Formation 70 Turbulent Boundary Layer - Trailing Edge (s) Trailing Edge Bluntness - Vortex Shedding Separation Noise 60
50
40
30
20 Sound Pressure Level (SPL) [dB] 10
0 102 103 104 Frequency [Hz] Figure 8.9: Frequency spectrum of all noise mechanisms at 9 m/s.
The main difference between both is the presence of a Laminar Boundary Layer - Vortex Shed- ding peak at 9 m/s in the high frequency region that is not appearing at 13 m/s. To understand this, it may be helpful to refresh the angle of attack distribution shown in Figure 5.27. On one hand, looking at 9 m/s, the angles of attack are located between 2º and 0º in approximately
82 Noise calculation results the 60% of the blade, which is translated into a good attachment of the pressure side boundary layer (as per Figure 8.6). Therefore, the LBL-VS noise can happen and indeed it shows a very important contribution. On the other hand, the angle of attack is negative for the whole blade at 13 m/s, which leads to a very early transition and detachment of the BL, and therefore the LBL-VS should not be calculated. Other than that, all the other sources are higher at 13 m/s, which is a direct consequence of higher flow speeds in all blade sections.
Blade section contribution of all noise mechanisms at 13 m/s 70 Total Laminar Boundary Layer - Vortex Shedding 60 Turbulent Boundary Layer - Trailing Edge (p) Tip Vortex Formation Turbulent Boundary Layer - Trailing Edge (s) Trailing Edge Bluntness - Vortex Shedding 50 Separation Noise
40
30
20
10 Sound Pressure Level (SPL) [dB] 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Blade Radius [m] Figure 8.10: Noise per section at 13 m/s.
Blade section contribution of all noise mechanisms at 9 m/s 70 Total Laminar Boundary Layer - Vortex Shedding Turbulent Boundary Layer - Trailing Edge (p) Tip Vortex Formation 60 Turbulent Boundary Layer - Trailing Edge (s) Trailing Edge Bluntness - Vortex Shedding Separation Noise 50
40
30
20
10 Sound Pressure Level (SPL) [dB] 0 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Blade Radius [m] Figure 8.11: Noise per section at 9 m/s.
Looking at the noise distribution per blade section, it is confirmed that the LBL-VS contribution is coming from the part of the blade at low positive angles of attack. Other than that, the TBL- TE noise is dominating in all the sections for both cases. The Tip Vortex noise is only calculated for the last blade section, and it is only driving the lower frequencies with a very small value. Regarding the TEB-VS, although it is not the highest mechanism in absolute noise for any section, looking at the frequency spectrum it may appear as a tonal sound at high frequencies. The TE could be sanded to mitigate this noise source, but its contribution is not worrying and
83 Tonality check can be accepted.
8.4 Tonality check
Tonality issues are usually coming from other sources other sources like the generator or the gearbox, and it is required to check it in the field. Moreover, the BPM equations do not have enough precision to predict the tonality. Nonetheless, as an extra safe check, it will be ensured that the LBL-VS peak around f = 2 · 103 is not leading to a tonality problem.
The behavior at 9 m/s will be studied because it is considered the worst case. It will be treated according to the guideline for wind turbine noise (IEC 61400-11 [70]). Firstly, all the noise spectrum has been analyzed with a 10 Hz resolution to find exactly the highest peak, and to be sure that there is not any hidden peak in a narrower band. The highest value has been obtained for f = 1825 Hz. Then, the critical bandwidth is computed as indicated in the guideline, and the noise is again evaluated with 5 Hz bands instead of 1/3 octave.
61.6
61.5
61.4 SPL [dB] 61.3
61.2 1700 1750 1800 1850 1900 1950 Frequency [Hz]
Figure 8.12: Tonality study at 9 m/s. Total noise with 5 Hz resolution. The dashed horizontal line shows the mean value without the highest band and its two adjacent ones.
To know whether this is a possible tone, the mean value of the critical band excluding the high- est point and its two adjacent ones should be computed. If the maximum is 6 dB higher than the calculated average, a possible tone is found. It is far from being the case here; although in the Figure 8.9 it looked like an isolated peak, putting it in non-logarithmic scale shows that it is actually a very broad peak. The regulations also allow to vary the critical band considered in this case, and some tests have been made (the Figure 8.12 is showing a band two times bigger than the calculated one), but there is not any case with a similar critical band that leads to a possible tone [70, 71].
84 A-Weighting results
8.5 A-Weighting results
Lastly, the noise results per wind speed will be calculated again but filtering it with the A- weighting, which is the typical approximation used to account for the actual loudness perceived by the human ear. It considers that the low audio frequencies are more difficult to be heard, so it decreases the SPL a lot in the lowest frequencies and slightly increases it around 103 and 5·103 [17]. In the following figure, the obtained results are shown together with the A-Weighting curve used.
Total noise for each wind speed (A-Weighting)
60
40
20
0
Wind speed = 5 m/s [OASPL = 37.4 dB] -20 Wind speed = 7 m/s [OASPL = 59.2 dB] Wind speed = 9 m/s [OASPL = 65.9 dB]
Sound Pressure Level (SPL) [dBA] Wind speed = 11 m/s [OASPL = 63.8 dB] Wind speed = 13 m/s [OASPL = 61.3 dB] -40 A-Weighting
102 103 104 Frequency [Hz] Figure 8.13: Final noise results per wind speed considering A-Weighting.
The weighted results are very similar with the previous ones, because there is not almost any difference in the region where the highest peaks were found. There is a slight increase in the OASPL at 9 m/s and decreases at the other wind speeds, but nonetheless this may be neglected, because it is considered that differences below 3 dB are not noticeable [67].
Conclusions
To sum up, the airfoil self-noise of the wind turbine designed has been obtained using the Brooks, Pope, and Marcolini method. The blades have been divided into several sections and the equations have been applied for those under different wind speed conditions. Previously, the code used had been validated against the software NAFNoise. The influence of the boundary layer properties has also been discussed. The results obtained have been analyzed, and the possible tonality issue has been studied. Finally, the noise results considering A-Weighting have been calculated.
85 Chapter 9
Wind resource assessment
The design process of the wind turbine has considered a theoretical Weibull distribution de- scribed in the Small Wind Turbine Contest [40]. However, the real wind distribution of the installation site will not necessarily look like that. In order to have a better approximation to the real one, the data from a possible installation site has been extracted from the Global Wind Atlas [72]. It allows the user to select an area and download a GWC (Generalized Wind Climate) file that contains the parameters for the Weibull distribution at different heights, rough- ness length, and wind directions. These values are extracted from satellite data over a large area (minimum 9 km2), so it still is a large approximation.
The roughness length z0 is a parameter found in the equation that approximates the shear of the wind speed near the ground, and it is indicative of the surface roughness of the terrain.
U¯(z) ∝ ln(z/z0) (9.1) Several typical values are defined in the literature [18]:
Table 9.1: Typical roughness length values.
Type of terrain Roughness length z0 [m] Cities, forests 0.7 Suburbs, wooden countryside 0.3 Villages, countryside with trees and hedges 0.1 Open farmland, few trees and buildings 0.03 Flat grassy plains 0.01 Flat desert, rough see 0.001
A possible installation site of the wind turbine would be in the middle of Barcelona (z0 = 0.7m) at approximately 18 m of hub height. The data downloaded has been interpolated to these values, and the results are presented in the Figure 9.1. There is more wind probability at higher wind speeds (from 6 m/s on) and at very low wind speed (0-1 m/s), but the approximate shape is significantly similar to the wind distribution used for the design. This indicates that the initial Weibull distribution used can be representative of several sites where a small wind turbine may be installed.
86 0.3 0º 0 330 0.15 30 30º 60º 300 0.1 60 0.2 90º 120º 0.05 150º 180º 270 0 90 0.1 210º Probability [-] 240º 270º 240 120 0 300º 0 5 10 15 330º 210 150 180 Wind Speed [m/s]
0.25
0.2 Installation Site Wind Distribution 0.15 Design Wind Distribution
0.1 Probability [-] 0.05
0 0 5 10 15 Wind Speed [m/s]
Figure 9.1: Wind resource assessment of the installation site. Data extracted from [72] and interpolated for z0 = 0.7m and hub height of 18m.
The Annual Energy Production (AEP) can be now recalculated with a more realistic wind dis- tribution. The previous AEP made in the aerodynamic design assumed that all the mechanical torque in the rotor was transformed to electrical power. They did not include the electrical sys- tem losses. Unfortunately, the generator has not been tested, and no real values of the efficiency curve are available, and there is no clear information whether the power curve provided by the supplier took the losses into account. An efficiency of 70 % will be taken based on generators described by Wood [29]. An efficiency of 85 % for the rest of the electrical system will be used. This will be the conservative approach, but the case with no losses will be calculated as well to see the range of possible outcomes.
20 400
300 15
200
10 AEP [KW/h] 100 AEP contribution [kW/h] 5 0 6 8 10 12 2 4 6 8 10 12 Wind Speed [m/s] Average Wind Speed [m/s] Figure 9.2: Annual Energy Productions (AEP) predictions.
87 The left plot in Figure 9.2 shows the AEP contribution with the wind distribution shown in Figure 9.1, and the right plot presents the AEP for different Vave and the Weibull parameter k = 2.0. They take into account and efficiency of 70 % and 85 % for the generator and the electrical system, respectively.
The Annual Energy Production obtained is presented in the Table 9.2 for the optimistic and pessimistic cases. Considering an electricity price after taxes of 0.24 €/kWh (from [73]), the annual saving is also calculated. To calculate the payback time, the following equation is used:
1 ln 1 − O · r/CF DPP = (9.2) ln(1 + r) Where DPP is the Discounted Payback Period, O is the initial investment (Outflow), r is the money yearly ratio of decrease (set to 1.1 % taking the mean of the latest three years from [74]), and CF is the annual incoming CashFlow [75]. The initial investment O considered here is only the cost of the wind turbine, and does not include all the design process and manhours work detailed in the Budget document and in table 10.1.
Table 9.2: Annual Energy Production (AEP) and Discounted Payback Period (DPP)
Case AEP Annual savings DPP Conservative 129.3 kWh 31,1 € 11.7 years Optimistic 217.3 kWh 52,2 € 6.8 years
The same method can be used to calculate the DPP for different average wind speeds, so the feasibility of other possible installation sites can be analyzed. The following table shows the DPP obtained from the different AEP calculated in Figure 9.2. The installation is hardly feasible for any average wind speed smaller than 5 m/s. To define it more properly, it would be necessary to know with more detail the lifetime of the wind turbine. However, it is difficult to define the behavior and resistance of the 3D printed parts. The lifetime may be set to 20 years (it is the minimum expected life of the non-printed components), and the event of changing a worn down blade must be considered as a likely possibility.
Table 9.3: Discounted Payback Period for different average wind speeds.
Average wind Conservative Optimistic speed [m/s] DPP [years] DPP [years] 3 268.2 75.7 4 29.3 16.3 5 12.6 7.3 6 7.5 4.4 7 5.4 3.2 8 4.5 2.7 9 4.2 2.4 10 4.0 2.4 11 4.0 2.4 12 4.2 2.5
88 Chapter 10
Summary of the results
10.1 Budget summary
All the project’s costs are detailed in the Budget document. In this section, only the summary table is presented.
Table 10.1: Project’s main costs.
Concept Cost Design process 123,54 € Wind turbine built 339,01 € Working hours 2.400,00 € Total 2.862,55 €
In the Budget document these concepts are broken down into individual expenses. In addition, the cost of the final wind turbine divided by components is also presented.
A quick feasibility study has been made in the Section9, showing a Discounted Payback Period between 6.8 and 11.7 years for a possible installation site wind conditions. The final energy production will depend on the wind distribution, so the DPP is also calculated for different average wind speeds.
10.2 Funding
This project was awarded a 560 € scholarship from the Terrassa City Hall. These scholarships are annually given to selected Degree’s/Master’s Thesis or PhD from Terrassa universities [76].
10.3 Analysis and assessment of the environmental implications
The whole life-cycle should be studied to determine precisely the environmental impact. It should be detailed how the raw materials are extracted and then processed, manufactured, dis- tributed, used, and disposed. It is out of the scope to study in detail all the process, so an overview of the implications will be made by looking at the estimated CO2 eq. saved by the wind turbine, the possible recycling of the materials, the shipping process of the generator and the tower, and the noise generated by the blades.
89 Future lines of work
From the estimated Annual Energy Production (AEP) of the designed wind turbine on a possible installation site, the saving in CO2 emissions may be calculated. It is estimated that 0.293 kg of CO2 eq. (equivalent) are saved for each kWh produced from a carbon-free source of electricity. This value is based on the emissions generated by the current power stations, and includes other gases such as methane or nitrous oxide, which are converted into their carbon dioxide equivalent CO2 eq. [77]. Using the AEP calculated in Section9, the CO 2 eq. resultant would be between 36.6 and 61.5 kg per year.
Regarding the recyclability of the wind turbine, the different materials are analyzed separately: 1. PETG: It is excluded from being processed by most recycling centers programs, so it is likely that it is not recycled even if thrown away in the plastic bin [10]. However, there are specialized plants and business dedicated to the recycling of this material [78]. 2. Mechanical metallic components: The mechanic metallic parts used in the wind turbine (mainly the tower but also the inserts, screws, bars, and nuts) are made either from steel or aluminium, which are two of the metals with higher recyclability rate after the end of its use. It is approximated that the recycling percentage exceeds 50 % [79]. 3. Magnetic metallic components: The permanent magnet generator uses NdFeB magnets. The recycling of these rare earth elements is still in its early stages, so it is currently far from being feasible on an industrial scale [80]. 4. Carbon fiber: As the previous point, the recyclability of carbon fiber materials is an ongoing process, which is not fully developed and standardized given the particularities of the material. However, as the rare magnetic materials, there is a lot of interest and effort put into those investigations [81]. The delivery of the generator and the tower should be taken into account, because they were shipped by plane from China. Taking into account a report of the UK Government [82], the emissions for a long haul cargo aircraft may be calculated with the conversion factor 0.6 kg CO2/Tkm. Given a package weight of 39 kg and a 9000 km flight (Shangai-Barcelona), the resultant emissions are 210.6 kg CO2. Comparing this result with the savings computed before (36.6-61.5 kg CO2/year), it is obtained an "environmental" payback time similar to the economic one: between 3.4 and 5.8 years. Unfortunately it is very difficult to buy a generator like that in a closer place, but it would have been better to search for a similar tower somewhere closer.
Overall, the environmental print of this project will depend on where the wind turbine is finally installed. If the power produced (and therefore the emissions saved) are enough to overcome the initial CO2 cost, the balance will be positive. Either way, for future iterations it would be desirable to bet for materials easier to recycle, and avoid long flights to deliver parts.
The visual impact and biological implications should also be analyzed. The noise should be assessed with more detail, considering the convenient observer positions and including the inflow noise in the calculations. The implications of these factors will depend a lot on the installation site.
10.4 Future lines of work
A design like this is an iterative process. All the knowledge and calculations done until this point may be used to re-design the wind turbine with more detail. Several actions and future
90 Future lines of work lines of work may be defined:
1. Aerodynamic design
1.1. Experimental airfoil study: test the selected airfoil in the wind tunnel. Study the effect of applying coatings in the surface. Characterize properly the boundary layer and its transition with different surface roughness. Understand more deeply its effect on the loads, the energy production, and the noise. 1.2. Further blade design: Study the influence of a cone or a tilt angle. If a installation site is defined, adapt the optimization to its Weibull distribution. Study the effect of a sweep angle and possible tip designs.
2. Structural design
2.1. Loads reiteration: Recalculate the loads using the final characteristics of the first design and not conservative assumptions. As a further step, an aeroelastic model could be built in FAST to have more realistic (and less conservative) results. 2.2. 3D printing structure: Study further the mechanical behavior of the printed parts. Experimental tests may provide values of maximum strains and stresses in different directions. Special attention must be paid to the adhesion between different layers. 2.3. More optimized blade design: Depending on the outcome of the last two points, a blade without any beam could be predicted and it may be feasible. 2.4. Hub study: Perform a FEM structural study of the hub to identify and reinforce possible critical points. 2.5. Dynamic analysis: A more detailed analysis of the frequency response of the wind turbine should be made. The natural frequencies of all the components may be calculated to study how they interact with the excitation frequencies (the multiples of the rotor speed).
3. Electrical design
3.1. Generator testing: Test the electrical generator in a lab bench to determine more precisely its characteristics. 3.2. System integration: Once a final installation site is determined, study and select the necessary remaining components. Basically, an inverter if it will be connected to the grid, or a charge controller if it will be used to charge batteries.
4. Component design
4.1. Tail: Design a furling tail to add over-speed safety. As explained in the Section 7.2, a simplified model could be built based on the methodology described in [42]. As a further and detailed step, the aerolastic code FAST also allows to set a furling degree of freedom [65]. 4.2. Nacelle: It may be useful to design an own nacelle to facilitate the introduction of the furling tail. Nonetheless, the existent nacelle may have the tail disassembled, so it still could be used. 4.3. Tower: More deep assessment of the tower, exploring the possibility of adding cables in the middle section to reduce the buckling analysis.
91 Planning and programming of the next stage
5. Installation, testing, and validation 5.1. Wind assessment: Measure the wind speed distribution on the installation site. 5.2. Commissioning and assembly: Determine an installation procedure, especially the tower raising process. Compute the foundation characteristics accordingly. Assembly and install all the parts. 5.3. Measure power curve: Measure the power curve with the original charge controller (or the necessary equivalent resistance described in Section 4.3). Validate the power curve predicted. Then, measure it will the MPPT (Maximum Power Point Tracking) controller installed (Figure 4.1). Assess the power production increase. 5.4. Validate loads: As a further step, measure the strains in key parts of the wind turbine (blade root, main shaft, or tower top) and compare them against the predicted loads.
10.5 Planning and programming of the next stage
The tasks defined in the preceding section are distributed and programmed in the following Gannt diagram:
Figure 10.1: Gantt diagram of the next stages of the project.
92 Conclusions
10.6 Conclusions
The main goal of this project was to design and manufacture a wind turbine. The requirements were a diameter of 1 meter, a completely passive operation, and manufacturing based on 3D printing. This has been achieved, and each step will be quickly summarized below.
Firstly, a review of the current state of the art was conducted in the Section2, and the different design options were described. Based on this, the general architecture of the wind turbine was defined in the Section3. The selected configuration consisted of a horizontal axis, three blades, an upwind rotor, and a permanent magnet generator. A design procedure was established ac- cordingly.
The next step was the electrical design, which was carried out in the Section4. The required parts of said system were described, and different possible generators were studied. As it is desired to keep the rotor speed as low as possible to avoid the need for a gearbox and minimize loads, the number of magnet pairs of poles should be high, which increases the generator cost and weight. A generator was selected among the studied possibilities, based on the equilibrium between price, rotor speed, and starting torque. The influence of the generator curve on the aerodynamic design and the possibility of using MPPT controllers was also described.
Once a generator was selected, the aerodynamic design (Section5) was executed, which started with an airfoil selection. For that, the most important airfoil parameters were determined such that the efficiency was maximized while keeping a consistent operation across different condi- tions (Re, α). These parameters were studied for an extensive selection of possible airfoils, and the better overall option was found to be S1223. The Viterna extrapolation was applied to have the polar curves for the deep stall region. In parallel, a BEMT code was developed and validated against the software QBlade (Section 1.1.3 of the Report Attachment). A procedure to calculate the power curve was also defined, which was based on the equilibrium points between the generator and the rotor curves. This has been the foundation of the blade design.
In order to determine the chord and twist distribution, the Betz and Schmitz blade geometries were studied and evaluated. The comparison between them shown that at low tip speed ratios the Betz geometries lead to higher power coefficients. However, it came with the cost of too large chords, so the Schmitz blade geometries were finally selected for the optimization. An initial study was carried out to understand the particularities of the design, which revealed a constant and important decrease of the angle of attack with the wind speed. This is a consequence of how the rotor and generator curves intersect with each other. A design procedure was finally proposed such that the blade was optimized for the wind speed with the highest AEP contribu- tion. A final study of the starting behavior was done to adjust the pitch angle (an offset to the twist distribution). The main characteristics of the resultant blade were finally discussed.
With the blade fully characterized, the first step of the structural design (Section6) was calculat- ing the loads that the structure should withstand. This was done using the Simple Loads Model of the small wind turbine guideline IEC 61400-2. The extreme loads were more demanding than the fatigue ones. The design driving loads were the centrifugal force (coming from the DLC E: maximum rotational speed) and the flapwise bending moment (from DLC I: parking with yaw failure). A carbon fiber beam was assessed assuming that all the loading is held by it, and the 3D printed blade structure was neglected. The blade should be divided into two pieces given the di-
93 Conclusions mensions of the printer, so a pin joint was designed and analyzed to attach them. The blade-hub joint was designed using aluminum inserts in both the beam and the hub, taken into considera- tion an easy mounting process and ensuring low tolerances in the pitch degree of freedom. The joint with the generator shaft also employed aluminum inserts. For the printed parts (blades and hub), the printing settings were studied and selected considering the compromise between printing time, weight, surface finish, and strength. Finally, a 6 meter tower was assessed by calculating its maximum stresses, the buckling risk, and its natural frequency. As the buckling was the most demanding failure mode, the use of cables in the middle section was recommended.
In order to simplify the design and reduce the scope to a feasible point, the nacelle and the tail were bought together with the generator. The original tail was studied in the Section7, and its response to yaw errors was analyzed. Even though the results were acceptable, it was seen that a furling tail would add additional safety against over-speed.
The airfoil self-noise was evaluated in detail in the Section8. To do so, the blade was dis- cretized into several sections, and the BPM equations were applied in each station with their corresponding flow conditions coming from the BEMT calculations. The noise frequency spec- trum was analyzed for different wind speeds. A high contribution of Laminar Boundary Layer - Vortex Shedding noise was observed around 9 m/s, a direct consequence of the angle of attack distribution at that wind speed. The possible tonality was checked, and the overall sound pres- sure level considering A-weighting was finally calculated.
Finally, the wind resource assessment of a possible installation site was undertaken in the Sec- tion9. The wind speed distribution was estimated interpolating satellite data from the Global Wind Atlas, and the Annual Energy Production (AEP) was calculated. Ultimately, a payback time between 7 and 11 and years was obtained. The reimbursement time was also calculated for different average wind speeds, which indicates the feasibly of distinct installation sites.
Ultimately, a final product has been obtained. Nonetheless, a design like this is an iterative pro- cess, and there is room for more detailed analysis and further optimization. The tools created, the design processes described, and the studies made can hopefully set up the foundation of a future iteration that requires fewer assumptions and conservatism. An extensive list of farther tasks to continue the project is presented in the preceding section.
This thesis also aimed to study to which extent the use of 3D printing was feasible for a small wind turbine manufacturing. Although it allows fast prototyping and enables extensive testing, there are added difficulties in anticipating the structural properties. This has been the main drawback during the design process, and a better characterization of the material would have reduced costs and weight because fewer conservative hypotheses would had taken. Either way, the most expensive part of the wind turbine turned out to be the generator, which high cost comes from the great quantity of rare magnetic material it requires.
The manufacturing was also a big objective of this project. It was probably the most important requirement of the design process, because it meant that almost anything cannot be excluded from the scope. One partial goal was to design a product that could be easily reproduced. The poor characterization of the 3D printed material lead to the use of a carbon fiber beam, which makes it difficult to replicate the product with ease. Nonetheless, the products selected are widely available in the market to minimize this effect. The manufacturing process is detailed
94 Conclusions in the Technical Sheets document, together with the main characteristics of the final design. The detailed drawings of the 3D-printed parts may be found in the Drawings document. In the following figure the complete wind turbine is shown as the culminating conclusion of the project.
Figure 10.2: Final wind turbine.
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