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					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:
           2 Pav
                   4adv (1  ub ) ub
                         3         2

          R3 5
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




   s t  trailed vorticity  t  i , j 1  i , j
   s s  shed vorticity  s  i 1, j  i , j
    BLADE ELEMENT FLOW
        CONDITIONS




                                                               
                                            cos   u ( y )    
 ( y )   ( y )  t ( y )  tan 
                                 1
                                                                  t ( y)
                                      sin  cos  y  w( y ) 
                                                    adv        
          2-D VISCOUS POLAR




S809 profile at Re=500,000 using XFOIL 0    20 deg
+ linear extrapolation to   90 deg
  CONVECTION IN THE WAKE
• Mesh system: stretched mesh from blade x1  10 3
To x=1 where xmax  O(2.0 10 2 )
Then constant steps to xT  20
• Convection equation along vortex filament j:
              j            j
                   (1  u )     0
               t            x
Boundary condition j (0)  1, j
             CONVECTION IN THE WAKE




                                             
       n                                  n
    i , j       inj
              1
                                  i 1, j  in1, j
                                              1

                   ,
                        (1   )              

               t                         t
                                                     
                                     n             n
                                  i , j       i 1, j
                                            1       1
                                                                     
                                                                    n      n

                                                        (1   )i, j
                                                                                0
                                                                          i 1, j

                                           xi  xi 1                xi  xi 1
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
• V=10 m/s, Yaw=0 and 20 deg
• V=12 m/s, Yaw=0, 10 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                                      Biot-Savart Law (discrete)
                                                                             Vortex   
                                                                      j             l  r 
                                                              v            
                                                                  j  4      Filament r    
                                                                                           3

                                                                                             
                                                                        _           Bound   
                                                                          j                 l  r 
                                                                                   r 3 
                                                    Boundary of       j  4         Vortex         
                                                    Navier-Stokes Zone                             


                                                          Vortex Method


( y j )   v.ds    .dA           Bound Vortex
           Lj             Aj


  Converged for …

    ( y j )n1  ( y j )n  105
                                         Vortex Filament
                                              j  ( y j 1 )  ( y j )

                                 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 pitch=18 deg CN at 80%
         APPENDIX A
       UAE Sequence Q
V=8 m/s pitch=18 deg CT at 80%
   APPENDIX A
  UAE Sequence Q
V=8 m/s pitch=18 deg
   APPENDIX A
  UAE Sequence Q
V=8 m/s pitch=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: j  1 c j q j Cl ( j )
                           2



                          j
• If  j  ( )Cl max           c j q j Cl ( j )  j
                                  1                  

                          
                                  2




Where      j   1  
                  j       j
  APPENDIX D: NONLINEAR
       TREATMENT
• If  j s.t. j  ( ) Cl max  penalization

     j  1 c j q j Cl ( j )   (j 1  2j  j 1 )
          2


•   0 is the coefficient of artificial
  viscosity
• Solved using Newton’s method

				
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posted:1/27/2013
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