HELICOIDAL%20VORTEX%20MODEL%20FOR%20WIND%20TURBINE%20AEROELASTIC%20SIMULATION%20Jean-Jacques%20Chattot%20University%20of%20California%20Davis%20OUTLINE

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HELICOIDAL VORTEX MODEL FOR WIND TURBINE
AEROELASTIC SIMULATIONJean-Jacques
ChattotUniversity of California DavisOUTLINE

• 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
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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

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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

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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

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GOLDSTEIN MODEL
Vortex sheet constructed as perfect helix with
variable pitch
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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

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ULTIMATE WAKE EQUILIBRIUM CONDITION
Induced axial velocity from average power
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BASE HELIX GEOMETRY USED FOR STEADY AND UNSTEADY
FLOWS
Vorticity is convected along the base helix, not
the displaced helix, a first-order approximation
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APPLICATION OF BIOT-SAVART LAW
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BLADE ELEMENT FLOW CONDITIONS
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2-D VISCOUS POLAR
S809 profile at Re500,000 using XFOIL linear
extrapolation to
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CONVECTION IN THE WAKE

• Mesh system stretched mesh from blade
• To x1 where
• Then constant steps to
• Convection equation along vortex filament j
• Boundary condition

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CONVECTION IN THE WAKE
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ATTACHED/STALLED FLOWS
Blade working conditions attached/stalled
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RESULTS STEADY FLOW
Power output comparison
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RESULTS YAWED FLOW
Time-averaged power versus velocity at different
yaw angles
10 deg
5 deg
20 deg
30 deg
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STRUCTURAL MODEL

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

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NREL BLADES

• Structural Coefficients
• - M5 kg/m
• - EIx800,000 Nm2
• - cfb4
• First Mode Frequency
• - f17.28 Hz (vs. 7.25 Hz for NREL blade)

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TIME AND SPACE APPROACHES

• Typical Time Steps
• - Taero0.0023 s (1 deg azimuthal angle)
• - Tstruc0.00004 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

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NREL ROOT FLAP BENDING MOMENT COMPARISONV5 m/s,
yaw10 deg
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TOWER SHADOW MODELDOWNWIND CONFIGURATION
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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

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SOME RESULTS

• V5 m/s, Yaw0, 5, 10, 20 and 30 deg
• V10 m/s, Yaw0 and 20 deg
• V12 m/s, Yaw0, 10 and 30 deg
• Comparison With NREL Sequence B Data

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RESULTS FOR ROOT FLAP BENDING MOMENTV5 m/s,
yaw0 deg
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RESULTS FOR ROOT FLAP BENDING MOMENTV5 m/s,
yaw5 deg
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RESULTS FOR ROOT FLAP BENDING MOMENTV5 m/s,
yaw10 deg
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RESULTS FOR ROOT FLAP BENDING MOMENTV5 m/s,
yaw20 deg
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RESULTS FOR ROOT FLAP BENDING MOMENTV5 m/s,
yaw30 deg
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NREL ROOT FLAP BENDING MOMENT COMPARISONV10
m/s, yaw0 deg
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NREL ROOT FLAP BENDING MOMENT COMPARISONV10
m/s, yaw20 deg
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NREL ROOT FLAP BENDING MOMENT COMPARISONV12
m/s, yaw0 deg
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NREL ROOT FLAP BENDING MOMENT COMPARISONV12
m/s, yaw10 deg
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NREL ROOT FLAP BENDING MOMENT COMPARISONV12
m/s, yaw30 deg
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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

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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

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HYBRID METHODOLOGY
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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, 14236-245 (2005).
• S. H. Schmitz, J.-J. Chattot, A parallelized
  coupled Navier-Stokes/Vortex-Panel solver,
  Journal of Solar Energy Engineering, 127475-487
  (2005).
• J.-J. Chattot, Extension of a helicoidal vortex
  model to account for blade flexibility and tower
  interference, Journal of Solar Energy
  Engineering, 128455-460 (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, 128445-454 (2006).
• J.-J. Chattot, Helicoidal vortex model for wind
  turbine aeroelastic simulation, Computers and
  Structures, to appear, 2007.

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APPENDIX AUAE Sequence QV8 m/s Dpitch18 deg
CN at 80
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APPENDIX AUAE Sequence QV8 m/s Dpitch18 deg
CT at 80
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APPENDIX AUAE Sequence QV8 m/s Dpitch18 deg
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APPENDIX AUAE Sequence QV8 m/s Dpitch18 deg
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APPENDIX BOptimum Rotor R63 m P2 MW
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APPENDIX BOptimum Rotor R63 m P2 MW
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APPENDIX BOptimum Rotor R63 m P2 MW
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APPENDIX BOptimum Rotor R63 m P2 MW
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APPENDIX BOptimum Rotor R63 m P2 MW
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APPENDIX BOptimum Rotor R63 m P2 MW
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APPENDIX BOptimum Rotor R63 m P2 MW
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APPENDIX CHomogeneous blade First mode
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APPENDIX CHomogeneous blade Second mode
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APPENDIX CHomogeneous blade Third mode
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APPENDIX CNonhomogeneous blade M distribution
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APPENDIX CNonhomog. blade EIx distribution
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APPENDIX CNonhomogeneous blade First mode
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APPENDIX CNonhomogeneous blade Second mode
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APPENDIX CNonhomogeneous blade Third mode
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APPENDIX D NONLINEAR TREATMENT

• Discrete equations
• If
• Where

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APPENDIX D NONLINEAR TREATMENT

• If
• is the coefficient of artificial
  viscosity
• Solved using Newtons method