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Hydrodynamic Analysis of Ocean Current Turbines Using Vortex Lattice Method

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HYDRODYNAMIC ANALYSIS OF OCEAN CURRENT TURBINES USING VORTEX LATTICE METHOD by Aneesh Goly A Thesis Submitted to the Faculty of The College of Engineering and Computer Science in Partial Fulfillment of the Requirements for the Degree of Master of Science Florida Atlantic University Boca Raton, Florida August 2010 ACKNOWLEDGEMENTS I would like to express my gratitude to my advisor, Palaniswamy Ananthakrishnan, for his support, patience, and encouragement throughout my graduate studies. It is not often that one finds an advisor who always finds the time for listening to the little problems that unavoidably crop up in the course of performing research. His technical and editorial advice was essential to the completion of this master’s thesis and has taught me innumerable lessons and insights. I would like to sincerely thank my committee members Dr. Dhanak, Dr. Hanson and Dr. Xiros for their valuable comments, suggestions and input to the thesis. My special thanks go to Ranjith for his encouragement and numerous fruitful discussions related to the research. I feel privileged to have been able to work with Zaqie, Waazim, Lakitosh and Baishali who were encouraging me all through my thesis. My deepest gratitude goes to my family for their unflagging love and support throughout my life. In the first place to my parents, Srinivas and Rajani for giving me everything in my life. Second, to my grandparents and aunt, Jaishanker, Pushpavathy and Rekha for their unparalleled love and care. Next, to uncle Ravi for his motivation throughout my thesis. Last but not the least, to my uncle Kumar Allady, who directed me in choosing this field and together with aunt, Vishala, has given me unparalleled love, affection and guidance. Finally, I express my gratitude to each and every member in my family, who finds joy in my every success as much. I am proud to have such a family. iii The financial support provided by the Center for Ocean Energy Technology of Florida Atlantic University to the author in the form of graduate student research assistantship and tuition waiver for the past two year is gratefully acknowledged. iv ABSTRACT Author: Aneesh Goly Title: Hydrodynamic Analysis of Ocean Current Turbines using Vortex Lattice Method Institution: Florida Atlantic University Thesis Advisor: Dr. Palaniswamy Ananthakrishnan Degree: Master of Science Year: 2010 The main objective of the thesis is to carry out a rigorous hydrodynamic analysis of ocean current turbines and determine power for a range of flow and geometric parameters. For the purpose, a computational tool based on the vortex lattice method (VLM) is developed. Velocity of the flow on the turbine blades, in relation to the free- stream velocity, is determined through induction factors. The geometry of trailing vortices is taken to be helicoidal. The VLM code is validated by comparing its results with other theoretical and experimental data corresponding to flows about finite ‐aspect ratio foils, swept wings and a marine current turbine. The validated code is then used to study the performance of the prototype gulfstream turbine for a range of parameters. Power and thrust coefficients are calculated for a range of tip speed ratios and pitch angles. Of all the cases studied, the one corresponding to tip speed ratio of 8 and uniform pitch angle 2 0 produced the maximum power of 41.3 [kW] in a current of 1.73 [m/s]. The v corresponding power coefficient is 0.45 which is slightly less than the Betz limit power coefficient of 0.5926. The VLM computational tool developed for the research is found to be quite efficient in that it takes only a fraction of a minute on a regular laptop PC to complete a run. The tool can therefore be efficiently used or integrated into software for design optimization. vi DEDICATION This thesis is dedicated to my wonderful family. “You have been with me every step of my way, through good and bad times. Thank you for all the unconditional love, guidance, and support that you have always given me, helping me to succeed and instilling in me the confidence that I am capable of doing anything I put my mind to. Thank you for everything. I love you all! ” HYDRODYNAMIC ANALYSIS OF OCEAN CURRENT TURBINES USING VORTEX LATTICE METHOD List of Figures .................................................................................................................x 1. Introduction .................................................................................................................1 1.1 Motivation..............................................................................................................3 1.2 Vortex Lattice Method ...........................................................................................7 1.3 Scope of the Thesis ................................................................................................8 2. Formulation of the problem .........................................................................................9 2.1 Potential Flow ...................................................................................................... 10 2.2 Biot - Savart Law ................................................................................................. 11 2.3 Horseshoe Vortex ................................................................................................. 12 2.4 Velocity Induced by a Horseshoe Vortex .............................................................. 12 2.5 Boundary Conditions ............................................................................................ 19 3. Vortex Lattice Method ............................................................................................... 21 3.1 Generation of Lattice ............................................................................................ 22 3.2 Description of Flow and Forces of a Turbine Blade .............................................. 24 3.3 Influence of Coefficient Matrix for Turbine Blade Analysis ................................. 26 3.4 Boundary Condition Vector .................................................................................. 27 3.5 Determination of Circulation Strengths and Other Quantities of Interest ................................................................................................................... 28 3.6 Special Case: Planar Wing.................................................................................... 29 3.7 Onset Flow at the Turbine .................................................................................... 32 3.8 Trailing Helical Vortices ...................................................................................... 33 viii 4. Validation Study ........................................................................................................ 37 4.1 Flow about a Flat Plate ......................................................................................... 38 4.2 Comparisons with Prandtl’s Lifting Line 3D Theory ............................................ 39 4.3 Flow past a Swept Wing ....................................................................................... 41 5. VLM Results for Turbine Flow .................................................................................. 44 5.1 VLM Analysis of a Turbine Designed for Alderney Race in Channel Islands .......................................................................................................... 45 5.2 Simulation of Gulf Stream COET Turbine............................................................ 47 6. Conclusion................................................................................................................. 58 Bibliography .................................................................................................................. 60 Appendix A ................................................................................................................... 62 Appendix B ................................................................................................................... 67 ix LIST OF FIGURES 1.1 The intensification of the gulf stream current .............................................................1 1.2 Proposed Gulf Stream turbine of Florida Atlantic University .....................................2 1.3 Actuator disk model of a wind turbine .......................................................................3 2.1 The horseshoe vortex with bound vortex AB and the trailing vortices A ∞ and B ∞. .. 13 2.2 The angles and magnitude distribution of the horseshoe vortex ................................ 14 2.3 Representation of the panel distribution on the cambered wing ................................ 20 3.1 Lattice configuration of 3 rows and 3 columns on the wing ...................................... 23 3.2 Showing the forces acting on the blade .................................................................... 25 3.3 Blade layout of the turbine ....................................................................................... 26 3.4 Showing the shedding of trailing vortices and the nomenclature. .............................. 34 4.1 CL vs alpha. The solid line represents VLM results from the code. The asterisk marks are calculated from the theoretical lift coefficient equation.......... 39 4.2 Prandtl’s lifting line and VLM aspect ratio theory comparison with VLM using (5x1) panels. ................................................................................. 40 4.3 Prandtl’s lifting line and VLM aspect
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