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HELICOIDAL VORTEX MODEL FOR WIND TURBINE AEROELASTIC SIMULATION
Jean-Jacques ChattotUniversity 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. ConferenceJune 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:
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
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
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 SchemeLarge integration errors due to drifting• Implicit SchemeSecond-Order in time unstableFirst-order not accurate enough• Modal DecompositionVery accurate. Integration error only in source term
NREL ROOT FLAP BENDING MOMENT COMPARISON
V=5 m/s, yaw=10 deg
TOWER SHADOW MODELDOWNWIND 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 MOMENTV=5 m/s, yaw=0 deg
RESULTS FOR ROOT FLAP BENDING MOMENTV=5 m/s, yaw=5 deg
RESULTS FOR ROOT FLAP BENDING MOMENTV=5 m/s, yaw=10 deg
RESULTS FOR ROOT FLAP BENDING MOMENTV=5 m/s, yaw=20 deg
RESULTS FOR ROOT FLAP BENDING MOMENTV=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
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.
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
APPENDIX D: NONLINEAR
TREATMENT• Discrete equations:
• If
Where
)(21
jljjj Cqc
jjljj
j
Clj Cqc
)()( 21
max
jjj 1
APPENDIX D: NONLINEAR TREATMENT
• If
• is the coefficient of artificial viscosity
• Solved using Newton’s method
onpenalizatitsj Clj max)(..
)2()( 1121
jjjjljjj Cqc
0