HELICOIDAL VORTEX MODEL FOR WIND TURBINE AEROELASTIC SIMULATION Jean-Jacques Chattot University of California Davis OUTLINE Challenges in Wind Turbine Flows The Analysis Problem and Simulation Tools The Vortex Model The Structural Model Some Results Conclusions Fourth M.I.T. Conference June 13-15, 2007

CHALLENGES IN WIND TURBINE FLOW ANALYSIS Vortex Structure - importance of maintaining vortex structure 10-20 D - free wake vs. prescribed wake models High Incidence on Blades - separated flows and 3-D viscous effects Unsteady Effects - yaw, tower interaction, earth boundary layer Blade Flexibility

THE ANALYSIS PROBLEM AND SIMULATION TOOLS Actuator Disk Theory (1-D Flow) Empirical Dynamic Models (Aeroelasticity) Vortex Models - prescribed wake + equilibrium condition - free wake Euler/Navier-Stokes Codes - 10 M grid points, still dissipates wake - not practical for design - expensive to couple with structural model Hybrid Models

REVIEW OF VORTEX MODEL Goldstein Model Simplified Treatment of Wake Rigid Wake Model “Ultimate Wake” Equilibrium Condition Base Helix Geometry Used for Steady and Unsteady Flows Application of Biot-Savart Law Blade Element Flow Conditions 2-D Viscous Polar

GOLDSTEIN MODEL Vortex sheet constructed as perfect helix with variable pitch

SIMPLIFIED TREATMENT OF WAKE No stream tube expansion, no sheet edge roll-up (second-order effects) Vortex sheet constructed as perfect helix called the “base helix” corresponding to zero yaw

“ULTIMATE WAKE” EQUILIBRIUM CONDITION Induced axial velocity from average power:

BASE HELIX GEOMETRY USED FOR STEADY AND UNSTEADY FLOWS Vorticity is convected along the base helix, not the displaced helix, a first-order approximation

APPLICATION OF BIOT-SAVART LAW

BLADE ELEMENT FLOW CONDITIONS

2-D VISCOUS POLAR S809 profile at Re=500,000 using XFOIL + linear extrapolation to

CONVECTION IN THE WAKE Mesh system: stretched mesh from blade To x=1 where Then constant steps to Convection equation along vortex filament j: Boundary condition

CONVECTION IN THE WAKE

ATTACHED/STALLED FLOWS Blade working conditions: attached/stalled

RESULTS: STEADY FLOW Power output comparison

RESULTS: YAWED FLOW Time-averaged power versus velocity at different yaw angles =5 deg =10 deg =20 deg =30 deg

STRUCTURAL MODEL Blade Treated as a Nonhomogeneous Beam Modal Decomposition (Bending and Torsion) NREL Blades Structural Properties Damping Estimated

NREL BLADES Structural Coefficients: - M’=5 kg/m - EIx=800,000 Nm2 - cfb=4 First Mode Frequency - f1=7.28 Hz (vs. 7.25 Hz for NREL blade)

TIME AND SPACE APPROACHES Typical Time Steps: - Taero=0.0023 s (1 deg azimuthal angle) - Tstruc=0.00004 s (with 21 points on blade) Explicit Scheme Large integration errors due to drifting Implicit Scheme Second-Order in time unstable First-order not accurate enough Modal Decomposition Very accurate. Integration error only in source term

NREL ROOT FLAP BENDING MOMENT COMPARISON V=5 m/s, yaw=10 deg

TOWER SHADOW MODEL DOWNWIND CONFIGURATION

TOWER SHADOW MODEL Model includes Wake Width and Velocity Deficit Profile, Ref: Coton et Al. 2002 Model Based on Wind Tunnel Measurements Ref: Snyder and Wentz ’81 Parameters selected: Wake Width 2.5 Tower Radius, Velocity Deficit 30%

SOME RESULTS V=5 m/s, Yaw=0, 5, 10, 20 and 30 deg Comparison With NREL Sequence B Data

RESULTS FOR ROOT FLAP BENDING MOMENT V=5 m/s, yaw=0 deg

RESULTS FOR ROOT FLAP BENDING MOMENT V=5 m/s, yaw=5 deg

RESULTS FOR ROOT FLAP BENDING MOMENT V=5 m/s, yaw=10 deg

RESULTS FOR ROOT FLAP BENDING MOMENT V=5 m/s, yaw=20 deg

RESULTS FOR ROOT FLAP BENDING MOMENT V=5 m/s, yaw=30 deg

NREL ROOT FLAP BENDING MOMENT COMPARISON V=10 m/s, yaw=0 deg

NREL ROOT FLAP BENDING MOMENT COMPARISON V=10 m/s, yaw=20 deg

NREL ROOT FLAP BENDING MOMENT COMPARISON V=12 m/s, yaw=0 deg

NREL ROOT FLAP BENDING MOMENT COMPARISON V=12 m/s, yaw=10 deg

NREL ROOT FLAP BENDING MOMENT COMPARISON V=12 m/s, yaw=30 deg

CONCLUSIONS Stand-alone Navier-Stokes: too expensive, dissipates wake, cannot be used for design or aeroelasticity Vortex Model: simple, efficient, can be used for design and aeroelasticity Remaining discrepancies possibly due to tower motion

HYBRID APPROACH Use Best Capabilities of Physical Models - Navier-Stokes for near-field viscous flow - Vortex model for far-field inviscid wake Couple Navier-Stokes with Vortex Model - improved efficiency - improved accuracy

HYBRID METHODOLOGY Navier-Stokes Vortex Method Vortex Filament Biot-Savart Law (discrete) Boundary of Navier-Stokes Zone Converged for … Bound Vortex Fig. 1 Coupling Methodology

RECENT PUBLICATIONS J.-J. Chattot, “Helicoidal vortex model for steady and unsteady flows”, Computers and Fluids, Special Issue, 35, : 742-745 (2006). S. H. Schmitz, J.-J. Chattot, “A coupled Navier-Stokes/Vortex-Panel solver for the numerical analysis of wind turbines”, Computers and Fluids, Special Issue, 35: 742-745 (2006). J. M. Hallissy, J.J. Chattot, “Validation of a helicoidal vortex model with the NREL unsteady aerodynamic experiment”, CFD Journal, Special Issue, 14:236-245 (2005). S. H. Schmitz, J.-J. Chattot, “A parallelized coupled Navier-Stokes/Vortex-Panel solver”, Journal of Solar Energy Engineering, 127:475-487 (2005). J.-J. Chattot, “Extension of a helicoidal vortex model to account for blade flexibility and tower interference”, Journal of Solar Energy Engineering, 128:455-460 (2006). S. H. Schmitz, J.-J. Chattot, “Characterization of three-dimensional effects for the rotating and parked NREL phase VI wind turbine”, Journal of Solar Energy Engineering, 128:445-454 (2006). J.-J. Chattot, “Helicoidal vortex model for wind turbine aeroelastic simulation”, Computers and Structures, to appear, 2007.

APPENDIX A UAE Sequence Q V=8 m/s Dpitch=18 deg CN at 80%

APPENDIX A UAE Sequence Q V=8 m/s Dpitch=18 deg CT at 80%

APPENDIX A UAE Sequence Q V=8 m/s Dpitch=18 deg

APPENDIX A UAE Sequence Q V=8 m/s Dpitch=18 deg

APPENDIX B Optimum Rotor R=63 m P=2 MW

APPENDIX B Optimum Rotor R=63 m P=2 MW

APPENDIX B Optimum Rotor R=63 m P=2 MW

APPENDIX B Optimum Rotor R=63 m P=2 MW

APPENDIX B Optimum Rotor R=63 m P=2 MW

APPENDIX B Optimum Rotor R=63 m P=2 MW

APPENDIX B Optimum Rotor R=63 m P=2 MW

APPENDIX C Homogeneous blade; First mode

APPENDIX C Homogeneous blade; Second mode

APPENDIX C Homogeneous blade; Third mode

APPENDIX C Nonhomogeneous blade; M’ distribution

APPENDIX C Nonhomog. blade; EIx distribution

APPENDIX C Nonhomogeneous blade; First mode

APPENDIX C Nonhomogeneous blade; Second mode

APPENDIX C Nonhomogeneous blade; Third mode

APPENDIX D: NONLINEAR TREATMENT Discrete equations: If Where

APPENDIX D: NONLINEAR TREATMENT If is the coefficient of artificial viscosity Solved using Newton’s method