1. Some effects of large blade deflections on aeroelastic stability Bjarne S. Kallesøe Morten H. Hansen

2. 6/01/2009Some effects of large blade deflections on aeroelastic stability2Risø DTU, Technical University of Denmark Introduction Why? Does the deflection of turbine blades effect the aeroelastic properties of the blades? What? Compare frequencies, damping and shapes of aeroelastic modes of motion for undeflected and steady state deflected blade How? Eigenvalue analysis 2 nd order Bernoulli-Euler beam and time simulations with Risø’s in-house aeroelastic simulation tool, HAWC2

3. 6/01/2009Some effects of large blade deflections on aeroelastic stability3Risø DTU, Technical University of Denmark Background Large turbines with flexible blade

4. 6/01/2009Some effects of large blade deflections on aeroelastic stability4Risø DTU, Technical University of Denmark Blade Model #1 2 nd order Bernoulli-Euler beam (2 nd B-E) 1 –Similar to Hodges and Dowell 2 –Extended to include the effects of pitch action, gravity and rotor speed variations –Furthermore, models for pitch action and rotor speed are derived –Quasi-static aerodynamic for non-linear steady state version –Unsteady dynamic stall model 3 for linear unsteady version 1) Kallesoe, B., Equations of motion for a rotor blade, including gravity, pitch action and rotor speed variations, Wind Energy, Vol. 10, No. 3, 2007, pp. 209–230. 2) Hodges DH, Dowell EH. Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades. Technical Report TN D-7818, NASA, December 1974. 3) Hansen, M., Gaunaa, M., and Madsen, H., A Beddoes-Leishman type dynamic stall model in state-space and indicial formulation, Tech. Rep. Risø -R-1354(EN), Risø National Laboratory, (available from www.risoe.dk), August 2004.

5. 6/01/2009Some effects of large blade deflections on aeroelastic stability5Risø DTU, Technical University of Denmark Blade Model #1 Edge-twist coupling of flapwise deflected blade Part of nonlinear equation of motion for edgewise blade motion: Linearized about deflected blade: Part of nonlinear equation of motion for torsional blade motion: Linearized about deflected blade:

6. 6/01/2009Some effects of large blade deflections on aeroelastic stability6Risø DTU, Technical University of Denmark Blade Model #2 Risø’s in-house aeroelastic code (HAWC2) 1,2 –Time domain simulations –Combined Beam-element and multi-body formulation –BEM theory, extended to handle dynamic inflow, dynamic stall, skew inflow, shear effects on the induction and effects from large deflections –Stiff turbine except for the blades –No induction and tip loss 1) Larsen, T., Hansen, A., and Buhl, T., Aeroelastic effects of large blade deflections for wind turbines, Proceedings of the special topic conference ”The Science of making Torque from Wind”, 2004, pp. 238–246. 2) Larsen, T., Madsen, H., Hansen, A., and Thomsen, K., Investigations of stability effects of an offshore wind turbine using the new aeroelastic code HAWC2, Proceedings of the conference ”Copenhagen Offshore Wind 2005”, 2005.

7. 6/01/2009Some effects of large blade deflections on aeroelastic stability7Risø DTU, Technical University of Denmark Test case: Overspeed NREL 5 MW reference turbine 1 –61.5 m blade –No structural damping –Rated rotor speed: 1.26 rad/s Operational conditions –wind speed: 10 m/s –0 deg pitch –Stepwise increase of rotor speed Method –First; Computer steady state blade deflection at different rotor speeds –Next; Compute aeroelastic frequencies and damping 1) Jonkman J., Nrel’s offshore baseline 5MW turbine. Technical report, NREL/NWTC, 1617 Cole Boulevard; Golden, CO 80401-3393, USA, 2005.

8. 6/01/2009Some effects of large blade deflections on aeroelastic stability8Risø DTU, Technical University of Denmark Steady state blade deflection 2 nd B-E –Full non-linear beam –Quasi-static aerodynamic –Finite difference discretisation of spatial derivatives HAWC2 –High structural damping to suppress any modes with negative aerodynamic damping

9. 6/01/2009Some effects of large blade deflections on aeroelastic stability9Risø DTU, Technical University of Denmark Unsteady blade motion 2 nd B-E –Linearized blade model –Linear unsteady dynamic stall model –Two cases: Linearized about the undeflected blade Linearized about the steady state deflected blade –Finite difference discretisation of spatial derivatives –Solve eigenvalue problem to compute aeroelastic frequency and damping HAWC2 –Measuring decay or growth of blade vibration amplitude, and measuring the dominating frequency

10. 6/01/2009Some effects of large blade deflections on aeroelastic stability10Risø DTU, Technical University of Denmark Aeroelastic frequencies and damping Circles: undeflected blade Stars: steady state deflected blade Squares: HAWC2 Frequency Damping

11. 6/01/2009Some effects of large blade deflections on aeroelastic stability11Risø DTU, Technical University of Denmark Second mode (First edgewise mode) Circles: undeflected blade Stars: deflected blade

12. 6/01/2009Some effects of large blade deflections on aeroelastic stability12Risø DTU, Technical University of Denmark Second mode (First edgewise mode) Green: undeflected Blue: deflected Wind Circles: undeflected Stars: deflected Blue: edge Green: flap Red: twist

13. 6/01/2009Some effects of large blade deflections on aeroelastic stability13Risø DTU, Technical University of Denmark Second mode (First edgewise mode) Green: undeflected Blue: deflected Wind Circles: undeflected Stars: deflected Blue: edge Green: flap Red: twist

14. 6/01/2009Some effects of large blade deflections on aeroelastic stability14Risø DTU, Technical University of Denmark Second mode (First edgewise mode) Green: undeflected Blue: deflected Wind Circles: undeflected Stars: deflected Blue: edge Green: flap Red: twist

15. 6/01/2009Some effects of large blade deflections on aeroelastic stability15Risø DTU, Technical University of Denmark Fourth mode (Second edgewise mode) Circles: undeflected blade Stars: deflected blade

16. 6/01/2009Some effects of large blade deflections on aeroelastic stability16Risø DTU, Technical University of Denmark Fourth mode (Second edgewise mode) Green: undeflected Blue: deflected Wind Circles: undeflected Stars: deflected Blue: edge Green: flap Red: twist

17. 6/01/2009Some effects of large blade deflections on aeroelastic stability17Risø DTU, Technical University of Denmark Fourth mode (Second edgewise mode) Green: undeflected Blue: deflected Wind Circles: undeflected Stars: deflected Blue: edge Green: flap Red: twist

18. 6/01/2009Some effects of large blade deflections on aeroelastic stability18Risø DTU, Technical University of Denmark Fourth mode (Second edgewise mode) Green: undeflected Blue: deflected Wind Circles: undeflected Stars: deflected Blue: edge Green: flap Red: twist

19. 6/01/2009Some effects of large blade deflections on aeroelastic stability19Risø DTU, Technical University of Denmark Fourth mode (Second edgewise mode) Green: undeflected Blue: deflected Wind Circles: undeflected Stars: deflected Blue: edge Green: flap Red: twist

20. 6/01/2009Some effects of large blade deflections on aeroelastic stability20Risø DTU, Technical University of Denmark Fourth mode (Second edgewise mode) Green: undeflected Blue: deflected Wind Circles: undeflected Stars: deflected Blue: edge Green: flap Red: twist

21. 6/01/2009Some effects of large blade deflections on aeroelastic stability21Risø DTU, Technical University of Denmark Fourth mode (Second edgewise mode) Green: undeflected Blue: deflected Wind Circles: undeflected Stars: deflected Blue: edge Green: flap Red: twist

22. 6/01/2009Some effects of large blade deflections on aeroelastic stability22Risø DTU, Technical University of Denmark Fifth mode (Third flapwise mode) Circles: undeflected blade Stars: deflected blade

23. 6/01/2009Some effects of large blade deflections on aeroelastic stability23Risø DTU, Technical University of Denmark Fifth mode (Third flapwise mode) Green: undeflected Blue: deflected Wind Circles: undeflected Stars: deflected Blue: edge Green: flap Red: twist

24. 6/01/2009Some effects of large blade deflections on aeroelastic stability24Risø DTU, Technical University of Denmark Fifth mode (Third flapwise mode) Green: undeflected Blue: deflected Wind Circles: undeflected Stars: deflected Blue: edge Green: flap Red: twist

25. 6/01/2009Some effects of large blade deflections on aeroelastic stability25Risø DTU, Technical University of Denmark Fifth mode (Third flapwise mode) Green: undeflected Blue: deflected Wind Circles: undeflected Stars: deflected Blue: edge Green: flap Red: twist

26. 6/01/2009Some effects of large blade deflections on aeroelastic stability26Risø DTU, Technical University of Denmark Conclusion Large blade deflection do effect the aeroelastic stability of a turbine blade Flapwise steady state blade deflection couples edgewise and torsional motion The extra torsional motion changes the aerodynamic forces, such that more flapwise motion is introduced in the edgewise modes The stability limit is reduced, but still well above normal operation.