helicoidal vortex model for wind turbine aeroelastic simulation jean-jacques chattot university of...

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