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```									    WIND TURBINE FLOW ANALYSIS
Jean-Jacques Chattot
University of California Davis
OUTLINE
•   Challenges in Wind Turbine Flows
•   The Analysis Problem and Simulation Tools
•   The Vortex Model
•   The Hybrid Approach
•   Conclusion
GGAM Mini-Conference
Saturday, March 31, 2007
CHALLENGES IN WIND
TURBINE FLOW ANALYSIS
• Vortex Structure
- importance of maintaining vortex structure 10-20 D
- free wake vs. prescribed wake models
- separated flows and 3-D viscous effects
- yaw, tower interaction, earth boundary layer
CHALLENGES IN WIND
TURBINE FLOW ANALYSIS
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
REVIEW OF VORTEX MODEL
• Goldstein Model
• Simplified Treatment of Wake
- Rigid Wake Model
- “Ultimate Wake” Equilibrium Condition
- Base Helix Geometry Used for Steady and
• Application of Biot-Savart Law
• 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
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
CONDITIONS

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

S809 profile at Re=500,000 using XFOIL 0    20 deg
+ linear extrapolation to   90 deg
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
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
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
Power output comparison
RESULTS: YAWED FLOW
Time-averaged power versus velocity at different yaw angles

 =5 deg                                   =10 deg

 =20 deg                                  =30 deg
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
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.
CONCLUSIONS

• Vortex Model: simple, efficient, can be used for
design
• Stand-alone Navier-Stokes: too expensive, dissipates
wake, cannot be used for design
• Hybrid Model: takes best of both models to create
most efficient and reliable simulation tool
• Next Frontier: aeroelasticity and multidisciplinary
design
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
APPENDIX C
APPENDIX C
APPENDIX C