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Vortex Lattice Modelling of Winglets on Wind Turbine Blades

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Vortex Lattice Modelling of Winglets on Wind Turbine Blades RIS0 Vortex Lattice Modelling of Winglets on Wind Turbine Blades Mads D0ssing Ris0-R-1621(EN) Ris0 National Laboratory Technical University of Denmark Roskilde, Denmark August 2007 Author: Mads Dossing Ris0-R-1621(EN) Mek-FM-EP 2007-04 Title: Vortex Lattice Modelling of Winglets on Wind Turbine August 2007 Blades Departments: Wind Energy Department - Riso & Department of Mechanical Engineering - DTU 3rd version. 18 oct. 2007 Abstract: ISSN 0106-2840 The power production of wind turbines can be increased by ISBN 978-87-550-3633-8 the use of winglets without increasing the swept area. This makes them suitable for sites with restrictions in rotor diameter and in wind farms. The present project aims at understanding how winglets influences the flow and the aerodynamic forces on wind turbine blades. A free wake vortex lattice code and a fast design algorithm for a horizontal axis wind turbine under steady conditions has been developed. 2 winglet designs are threated in detail. Information Service Department Riso National Laboratory Technical University of Denmark P.O.Box 49 DK-4000 Roskilde Denmark Telephone +45 46774004 biblfgirisoe.dk Fax +45 46774013 www.risoe.dk Summary The power production of wind turbines can be increased by the use of winglets without increasing the swept area. This makes them suitable for sites with restrictions in rotor diameter and in wind farms. The present project aims at understanding how winglets influences the flow and the aerodynamic forces on wind turbine blades. A free wake vortex lattice code and a fast design algorithm for a horizontal axis wind turbine under steady conditions has been developed. 2 winglet designs are threated in detail. II Resume Vindm 0llers energi-produktion kan 0ges ved brug af en winglet, uden at det bestrpgne areal 0ges. Dette g 0r dem egnede til brug pa anlaeg, hvor der er restriktioner pa rotorens diameter. Formalet med naervaerende projekt er at opna en forstaelse for, hvorledes en winglet pavirker strpmningnen og krafterne pa en vindmplle vinge. En vortex-lattice kode og en hurtig design algoritme er blevet udviklet for en horisontal mplle under tidsuafhaengige forhold. 2 winglet design er behandlet i detaljer. IV Preface This thesis was prepared at the Wind Energy Department at Risp in collabora ­ tion with the Department of Mechanical Engineering, the Technical University of Denmark in partial fulfillment of the requirements for acquiring the M.Sc. degree in engineering. The thesis deals with different aspects of mathematical and numerical modeling of wind turbine aerodynamics. The main focus is on development of methods for prediction the performance of turbine blades with winglets. I thank my supervisors Mac Gaunaa and Robert Flemming Mikkelsen for their aid and support. Kongens Lyngby, August 2007 Mads Dpssing VI Contents Summary i Resume iii Preface v 1 Introduction 1 1.1 Motivation ...................................................................................... 1 1.2 Winglet Description ....................................................................... 2 1.3 Overview of the Methods Applied ................................................... 3 1.4 Outline of the Thesis........................................................................ 5 2 Theory 7 2.1 Definition of Coordinate Systems................................................... 7 2.2 Definition of Blade and Winglet Geometry .................................... 8 2.3 Dimensionless Variables 9 VIII CONTENTS 2.4 Governing Equations ........................................................................ 10 2.5 The General Solution and Boundary Conditions ........................... 10 2.6 The Kutta Condition ........................................................................ 12 2.7 Singularity Elements........................................................................ 13 2.8 Kutta-Joukowsky and Helmholz Theorems.................................... 15 2.9 Wake Strength................................................................................ 15 2.10 Wake Shape...................................................................................... 16 2.11 The Unsteady Bernoulli Equation ................................................... 16 3 Numerical Lifting Line Model 19 3.1 Description ...................................................................................... 19 3.2 Classic Analytical Lifting Line Results.......................................... 22 3.3 Validation ......................................................................................... 23 3.4 Effect of Winglet Height and Curve Radius ................................. 24 3.5 Optimum Circulation distribution on Wings ................................. 25 3.6 Generalization of Wing Results to Turbines ................................. 27 3.7 Force and Viscous Drag Calculation Using Lifting Line Data . 27 3.8 Conclusions ...................................................................................... 30 4 A Free wake, Vortex Lattice and Panel Method 31 4.1 Freewake Model ................................................................................ 35 4.2 Evaluation of Forces ........................................................................ 37 4.3 Calculation of Wing Geometries for Vortex Lattice Simulations . 39 CONTENTS IX 4.4 Grid Generation .............................................................................. 41 4.5 Reference Blade Data......................................................................... 41 4.6 Validation ......................................................................................... 43 4.7 Conclusions ...................................................................................... 47 5 Blade and Winglet Design 49 5.1 Defining Bound Circulation ............................................................ 50 5.2 Calculating Velocities ..................................................................... 52 5.3 Summary of Method ....................................................................... 56 5.4 Validation ......................................................................................... 57 5.5 General Design Results..................................................................... 60 5.6 Conclusions ...................................................................................... 62 6 Final Designs 63 6.1 Conservative Winglet Design ......................................................... 63 6.2 Optimum Winglet Design ............................................................... 68 6.3 Conclusions ...................................................................................... 71 7 Conclusion 73 A Appendix 75 A.l Constant Strength Source Panel (3 Nodes) 75 X CONTENTS Part 1 Introduction The present report describes the mathematical methods and the results obtained regarding winglets mounted on windturbines. The main emphasis is on the aerodynamics and the associated forces, thus neglecting any elastic behavior of the blades. Efficient mathematical models for simulation of winglets on turbines were not available at the beginning of this project and the original idea was to make Vortex Lattice simulations in order to study the physical properties. Severe shortcomings of the method soon appeared and this project evolved into a study of numerical methods and the general properties of winglets. Eventually a modified Vortex Lattice method was used for simulation and a nearwake design method was developed which is considered more accurate. 1.1 Motivation Winglets increases the efficiency of wind turbine rotors by increasing the power production for a given blade length, making them attractive on sites with design restrictions on the rotor radius. On sites without restrictions the easiest way to increase the power is by using a longer traditional flat blade, but in wind farms this may have a negative impact on the total production due to the increased sweept area. Therefore, even if there are no design restrictions, winglets may still be attractive. Since a blade with a winglet is more expensive than a flat blade 2 Introduction and the manufacturing process is not well established, a clear understanding of the aeroelastic properties is needed in order for the industry to verify whether a production is profitable or not. 1.2 Winglet Description Winglets are essentially extensions of the main wing. The cant, sweep and height describes the overall shape of a straight winglet, and the local shape is described by the chord, twist angle and 2D profile. The bend has a curve radius which is also important. The winglets threated in this work has zero sweep and cant angle, leaving the curve radius of the bend, the height and the twist and chord distribution as geometrical parameters. The chord and twist distribution are very important for the winglet efficiency and determining them is the aim of the design process. The winglet height can be considered a design parameter. The efficiency increases with height until the viscous drag outbalances the benefits of the winglet and usually there is an optimum winglet height around 3-4% of the blade length. On airplanes the winglet works by decreasing the induced drag on the main wing. The induced drag is the component of lift in the direction opposite to the movement and despite its name it is therefore not associated with any viscous effects but instead to the change in inflow angle. On airplanes the inflow is angled down thereby tilting the force vector back. This change in
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