May 1992 NREL/TP-442:-4822 iamics orizontal A.xis rrbines port A.C. Hansen University of Cia a Salt Lake City, Utah "'?tional Renewable Energy Laboratory bivision of Midwest Research Institute NREL/TP-442-4822 c.2 erated for the U.S. Department of Energy der Contract No. DE-AC02-83CH10093 INREL/TP-442-4822 UC Category: 261 DE92001245 Horizontal Axis A.C. Hansen University of Utuh 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 May 1992 , i iI h On September 16,1991, the Solar Energy Research Institute was designated a national laboratory, and its name was changed Renewable I- r to the National Energy Laboratory. t i NOTICE ! This repon was prepared as an account of work sponsored by 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 or implied, or assumes any legal liability or responsibility for the accuracy, corn- i pleteness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily can- stitute or imply its endorsement, recommendation, or favoring by the United States government or any agency thereof. 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Notice This report was prepared as an 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. t 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, Noman Siedschlag, Robert Schmepp, and Todd Boadus each assisted in the analysis, programming, validating and debugging, Without their help this work would not have ken possible. Papers, reports and theses which resulted from their efforts we listed at the end of the list of references, Work of this type cannot be completed without the efforts and cosperadsn of many individuals. The SERI technical monitor, contract officials, test personnel and management have all approached this task with the goal of getting ajob done in the most straigh$orward, cost-effective and reasonable manner. And many individuals at . the University of Utah have shared that approach and attitude. That spirit is gratefully and wdyacknowledged. Much of the material of Section 2.0 was originally commissioned by the Wind Turbine Company, Inc, Their permission to include this materid in this report is gratefully acknowledged. Table of Con tents Notice. .............................................................................................. ii... Fkface .......... :................................................................................... III ..................................................................................... List of Figures v ..a List of Tables ...................................................................................... wu 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 czdses 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 ValidationStudies .......................................................................... 35 5.1 Introduction ........................................................................ 35 5.2 Md-2 Wind Tunnel Test Comparisons ........................................ 35 5.3 SEN 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 Sensitivity 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 Appendix B Characteristics of the Wind Turbines ........................................... B1 Appendix C User's Guide to the YawDyn program ......................................... C1 iv I List of Figures Figure 2.1 Schematic view of the wind turbine showing the forces exerted by ome blade upon the hub....................................................... 7 Figure 2.2 Stdl hysteresis for the SEW Combined Experiment calculated by YawDyn, Wind speed 30 fds, yaw angle 30°, no whd shear or tower shadow. .................................................................... 11 Figure 2.3 Angle of attack of blades at two azimuth positions when the rotor operates with a yaw enor.. ...................................................... 12 Figure 2.4 Effect of vertical wind component on the angles of attack.. ................. 13 Figure 2.5 Effect of horizontd 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