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WIND TURBINE FLOW ANALYSISJean-Jacques Chattot
University of California DavisOUTLINE
• Challenges in Wind Turbine Flows
• The Analysis Problem and Simulation Tools
• The Vortex Model
• The Hybrid Approach
• Conclusion
GGAM Mini-ConferenceSaturday, 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
• High Incidence on Blades
- separated flows and 3-D viscous effects
• Unsteady Effects
- yaw, tower interaction, earth boundary layer
• Blade Flexibility
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
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:
bbav uuadvR
P 23
53)1(4
2
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
jijiss
jijitt
vorticitysheds
vorticitytraileds
,,1
,1,
BLADE ELEMENT FLOW CONDITIONS
)()(cossin
)(costan)()()( 1 yt
ywadv
yyu
ytyy
2-D VISCOUS POLAR
S809 profile at Re=500,000 using XFOIL+ linear extrapolation to deg90
deg200
NONLINEAR TREATMENT
• Discrete equations:
• If
Where
)(21
jljjj Cqc
jjljj
j
Clj Cqc
)()( 21
max
jjj 1
NONLINEAR TREATMENT
• If
• is the coefficient of artificial viscosity
• Solved using Newton’s method
onpenalizatitsj Clj max)(..
)2()( 1121
jjjjljjj Cqc
0
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
3
1 10x
)100.2( 2
max
Ox20Tx
0)1(
xu
tjj
jj ,1)0(
CONVECTION IN THE WAKE
tt
n
ji
n
ji
n
ji
n
ji
,11
,1,1
, )1(
0)1(1
,1,
1
1,1
1,
ii
n
ji
n
ji
ii
n
ji
n
ji
xxxx
ATTACHED/STALLED FLOWS
Blade working conditions: attached/stalled
RESULTS: STEADY FLOW
Power output comparison
RESULTS: YAWED FLOWTime-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
Navier-Stokes
Vortex Method
)()( 1 jjj yy Vortex Filament
Biot-Savart Law (discrete)
j
Bound
Vortex
j
j
Vortex
Filament
j
r
rl
r
rlv
3
_
3
4
4
Boundary of Navier-Stokes Zone
Converged for …
51 10)()(
njnj yy
j jL Aj dAdsvy ..)( Bound Vortex
Fig. 1 Coupling Methodology
HYBRID 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.
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 AUAE Sequence Q
V=8 m/s pitch=18 deg CN at 80%
APPENDIX AUAE Sequence Q
V=8 m/s pitch=18 deg CT at 80%
APPENDIX AUAE Sequence Q
V=8 m/s pitch=18 deg
APPENDIX AUAE Sequence Q
V=8 m/s pitch=18 deg
APPENDIX BOptimum Rotor R=63 m P=2 MW
APPENDIX BOptimum Rotor R=63 m P=2 MW
APPENDIX BOptimum Rotor R=63 m P=2 MW
APPENDIX BOptimum Rotor R=63 m P=2 MW
APPENDIX BOptimum Rotor R=63 m P=2 MW
APPENDIX BOptimum Rotor R=63 m P=2 MW
APPENDIX BOptimum Rotor R=63 m P=2 MW
APPENDIX CHomogeneous blade; First mode
APPENDIX CHomogeneous blade; Second mode
APPENDIX CHomogeneous blade; Third mode
APPENDIX CNonhomogeneous blade; M’ distribution
APPENDIX CNonhomog. blade; EIx distribution
APPENDIX CNonhomogeneous blade; First mode
APPENDIX CNonhomogeneous blade; Second mode
APPENDIX CNonhomogeneous blade; Third mode
TOWER SHADOW MODELDOWNWIND CONFIGURATION