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