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F Horizontal Axis Wind Turbines Final Report NREL/TP-442-4822 • UC Category" 261 * DE92001245 Yaw " f Horizontal Axis Wind Turbines NREL/TP--442-4822 Final Report DE92 001245 A.C. Hansen University of Utah Salt Lake City, Utah NREL Technical Monitor: Alan Wright National Renewable Energy Laboratory (formerly the Solar Energy Research Institute) 1617 Cole Boulevard Golden, Colorado 80401-3393 A Division of Midwest Research Institute Operated for the U.S. Department of Energy under Contract No. DE-AC02-83CH10093 Prepared under subcontract no: XL-6-05078-2 Ma r 1992 [_,,_j_- _ _ On September 16, 1991, the Solar Energy Research Institute was designated a national laboratory, and its name was changed to the National Renewable Energy Laboratory. NOTICE This reportwas preparedas an accountof work sponsoredby an agency of the United States government. Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, express orimplied,or assumes any legal liabilityor responsibilityfor the accuracy, com- pleteness, or usefulnessof any information,apparatus, product,or processdisclosed, or representsthat its use wouldnot infringeprivatelyowned rights. Reference hereinto any specificcommercial product,process, or serviceby trade name, trademark, manufacturer,or otherwise does not necessarilycon- stituteor imply itsendorsement, recommendation,or favoringby the United States government or any agency the(eof. The views and opinionsof authors expressed hereindo notnecessarilystate orreflectthose of the United States government or any agency thereof. Printed in the United States of America Availablefrom: NationalTechnical InformationService U.S. Department of Commerce 5285 Port Royal Road Spnngfield,VA 22161 Price: MicroficheA01 Printed Copy A09 Codes are used for pricingali publications. The code is determined by the number of pages in the publication.Informationpertainingto the pricingccdes can be found in the currentissue of the followingpublicationswhich are generally available in mostlibraries:Energy Research Abstracts (ERA); Govern- ment Reports Announcements and Index (GRA and I); Scientific and Technical Abstract Reports (STAR); and publicationNTIS-PR-360 availablefrom NTIS at the above address. Notice This report was prepared as a,n account of work sponsored by the Solar Energy Research Institute, a Division of Midwest Research Institute, in support of its Contract No. DE-AC02-83-CH10093 with the United States Department of Energy. Neither the Solar Energy Research Institute, the United States Government, nor the United States Department of Energy, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights. Preface This Final Report is a summary of work that has been performed at the University of Utah over the past five years. Several graduate students contributed to the research: Xudong Cui, Norman Siedschlag, Robert Schnepp, and Todd Dorius each assisted in the analysis, programming, validating and debugging. Without their help this work would not have been possible. Papers, reports and theses which resulted from their efforts are listed at the end of the list of references. Work of this type cannot be completed without the efforts and cooperation of many individuals. The SERI technical monitor, contract officials, test personnel and management have ali approached this task with the goal of getting a job done in the most straightforward, cost-effective and reasonable manner. And many individuals at the University of Utah have shared that approach and attitude. That spirit is gratefully and warmly acknowledged. Much of the material of Section 2.0 was originally commissioned by the Wind Turbine Company, Inc. Their permission to include this material iil this report is gratefully acknowledged. °.. lH Table of Contents Notice ............................................................................................... ii Preface .............................................................................................. iii List of Figures ..................................................................................... v List of Tables .............................................................. ......................... viii List of Symbols .................................................................................... ix 1.0 Introduction ................................................................................. 1 2.0 General Introduction to Yaw Loads ...................................................... 5 2.1 Introduction ........................................................................ 5 2.2 Hub forces and moments of a single blade ..................................... 5 2.3 Hub forces and moments from multiple blades ................................ 7 2.4 Stall hysteresis and dynamic stall ................................................ 9 2.5 Wind disturbances which cause yaw loads ..................................... 9 2.6 Other causes of yaw loads ........................................................ 15 2.7 Yaw dynamics of the teetering rotor ............................................. 16 3.0 Theoretical Foundation ..................................................................... 17 3.1 Prediction of Yaw Dynamics ..................................................... 17 3.2 Relation between yaw and flap moments for a rigid rotor .................... 22 3.3 Equations of motion of the teetering rotor ...................................... 24 3.4 Subsystem details .................................................................. 26 4.0 Numerical Solution ......................................................................... 32 4.1 Numerical integration ............................................................. 32 4.2 Initial conditions and trim solution .............................................. 32 4.3 Program structure and flow chart ................................................ 33 4.4 Computer requirements ........................................................... 33 5.0 Validation Studies .......................................................................... 35 5.1 Introduction ........................................................................ 35 5.2 Mod-2 Wind Tunnel Test Comparisons ........................................ 35 5.3 SERI Combined Experiment and FLAP Prediction Comparisons ........... 38 5.4 Free-yaw predictions and measurements from the Combined Experiment rotor ........................... ...................................................... 48 5.5 Teeter Predictions by YawDyn and STRAP .................................... 49 6.0 Sensitivi:y Studies .......................................................................... 52 6.1 Introduction ........................................................................ 52 6.2 Rigid-hub configuration .......................................................... 52 6.3 Teetering rotor configuration ..................................................... 61 6.4 A Comparison of the Free-Yaw Behavior of Rigid and Teetering Rotors.. 64 7.0 Conclusions and Recommendations ...................................................... 67 7.1 The YawDyn Model ............................................................... 67 7.2 Yaw Loads on a Rigid Rotor ..................................................... 68 7.3 Yaw Loads on a Teetering Rotor ................................................ 68 7.4 Yaw Motions of Rigid and Teetering Rotors................................... 69 7.5 Recommendations for Additional Research .................................... 69 References .......................................................................................... 71 Appendix A Derivations of the Equations of Motion ........................................ A1 AppendixB Characteristics of the Wind Turbines ........................................... B1 AppendixC User's Guide to the YawDyn program ......................................... C1 iv List of Figures Figure 2.1 Schematic view of the wind turbine showing the forces exerted by one blade upon the hub ....................................................... 7 Figure 2.2 Stall hysteresis for the SERI Combined Experiment calculated by YawDyn. Wind speed 30 ft/s, yaw angle 30°, no wind shear or tower shadow ..................................................................... 11 Figure 2.3 Angle of attack of blades at two azimuth positions when the rotor operates with a yaw error ........................................................ 12 Figure 2.4 Effect of vertical wind component on the angles of attack ................... 13 Figure 2.5 Effect of horizontal wind shear on the angles of attack ...................... 14 Figure 3.1 Schematic of the rotor showing the primary blade variables. The view on the right is looking into the wind ..................................... 18 Figure 3.2 Hinged blade with torsional spring ............................................. 19 Figure 3.3 Comparison of the measured yaw moment (data points) with the moment calculated using the measured blade flap moment and the lp rotor mass imbalance ......................................................... 24 Figure 3.4 Sketch of the teetering rotor, showing key parameters. Free teetering is permitted
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