TOWER SHADOW MODELIZATION WITH HELICOIDAL VORTEX METHOD Jean-Jacques Chattot University of...
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Transcript of TOWER SHADOW MODELIZATION WITH HELICOIDAL VORTEX METHOD Jean-Jacques Chattot University of...
TOWER SHADOW MODELIZATION WITH HELICOIDAL VORTEX METHOD
Jean-Jacques ChattotUniversity of California Davis
OUTLINE
• Motivations
• Review of Vortex Model
• Tower Shadow Model
• Conclusion
45th AIAA Aerospace Sciences Meeting and Exhibit26th ASME Wind Energy Symposium, Reno, NV, Jan.8-11, 2007
MOTIVATIONS
• Take Advantage of Model Simplicity and Efficiency for Analysis of Unsteady Effects with Impact on Blade Fatigue Life and Acoustic Signature
- Include Tower Interference Model (Upwind 2006)
- Include Tower Shadow Model (Downwind 2007)
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
ywadvyyu
ytyy
2-D VISCOUS POLAR
S809 profile at Re=500,000 using XFOIL+ linear extrapolation to deg90
deg200
FLEXIBLE BLADE MODEL
• Blade Treated as a Nonhomogeneous Beam
• Modal Decomposition (Bending and Torsion)
• NREL Blades Structural Properties
• Damping Estimated
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%
SIMPLIFIED MODEL
)'''
'1(
''
')',','(
222222
ZYX
Z
YX
XVaZYX
LINE OF DOUBLETSPERTURBATION POTENTIAL
•If |Y’|>2.5 a, Outside Wake, Use Where:
•If |Y’|<2.5 a, Inside Wake:
0,3.0 ''' ZYX UUVU
RESULTS
• V=5 m/s, Yaw=0, 5, 10, 20 and 30 deg• V=7 m/s, Yaw=0, 5, 10 and 20 deg• V=10 m/s, Yaw=0, 5, 10 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
EFFECT OF ROTOR INDUCED VELOCITY ON WAKE
V=5 m/s, yaw=30 deg
RESULTS FOR ROOT FLAP BENDING MOMENTV=5 m/s, yaw=30 deg
deg4.3yaw
NREL ROOT FLAP BENDING MOMENT COMPARISON
V=7 m/s, yaw=0 deg
NREL ROOT FLAP BENDING MOMENT COMPARISON
V=7 m/s, yaw=5 deg
NREL ROOT FLAP BENDING MOMENT COMPARISON
V=7 m/s, yaw=10 deg
NREL ROOT FLAP BENDING MOMENT COMPARISON
V=7 m/s, yaw=20 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=5 deg
NREL ROOT FLAP BENDING MOMENT COMPARISON
V=10 m/s, yaw=10 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
• Simple model for tower shadow easy to implement• Good results obtained for “downwind” configuration• Some remaining unsteady effects possibly due to
tower motion• Vortex Model proves very efficient and versatile
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 DKUTTA-JOUKOWSKI LIFT THEOREM
)]([)()(21
)( yCyqycy l
APPENDIX DNONLINEAR TREATMENT
• Discrete equations:
• If
Where
)(21
jljjj Cqc
jjljj
j
Clj Cqc
)()( 21
max
jjj 1
APPENDIX DNONLINEAR TREATMENT (continued)
• If
• is the coefficient of artificial viscosity
• Solved using Newton’s method
onpenalizatitsj Clj max)(..
)2()( 1121
jjjjljjj Cqc
0
APPENDIX ECONVECTION 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(
APPENDIX ECONVECTION IN THE WAKE (continued)
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
APPENDIX FBlade working conditions: attached/stalled
APPENDIX GSTEADY FLOW
Power output comparison
APPENDIX HYAWED FLOW
Time-averaged power versus velocity at different yaw angles
=5 deg
=10 deg
=20 deg =30 deg