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Evan GaertnerUniversity of Massachusetts, Amherst
NAWEA 2015 Symposium
June 11, 2015
Modeling Dynamic Stall for a Free Vortex Wake Model of Floating
Offshore Wind Turbines
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2
Platform Motion
Complex platform motion coupled to the wind and waves
• 6 transitional and rotational DoF
Platform motion creates an effective velocity at the blade element
• Significantly increases unsteadiness in the flow
Not accounted for by typical methods such as
• Blade Element Momentum (BEM) Theory
• Dynamic Inflow Methods[1]
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3
Wake Induced Dynamic Simulator (WInDS)
A free-vortex wake method
• Developed to model rotor-scale unsteady aerodynamics
By superposition, local velocities are calculated from different modes of forcing
Previously neglected blade section level, unsteady viscous effects
induced platformU U U U
[2]
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WInDS Vortex Structure Evolution
[6]
12 l
c U Cdy
Kutta-Joukowski
Theorem
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Dynamic Stall Modeling for WInDS
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Unsteady Aerodynamics
WInDS models an unsteady wake, but assumes quasi-steady airfoil behavior.
Wind turbine blades see highly unsteady flow
[3]
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Dynamic Stall Flow Morphology
Stage 1 Stage 2 Stage 2-3 Stage 3-4 Stage 5
[3]
Lift
Coef, C
L
Dra
g C
oef, C
D
Mom
ent
Coef, C
M
Angle of Attack, α (°) Angle of Attack, α (°) Angle of Attack, α (°)
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Modeling Dynamic Stall: Leishman-Beddoes (LB) Model
Semi-empirical method
• Use simplified physical representations
• Augmented with empirical data
Model Benefits
• Commonly used, well documented
• Ex.: AeroDyn
• Minimal experimental coefficients
• Computationally efficient
[3]
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Example 2D LB validation: S809 Airfoil, k = 0.077, Re = 1.0×106
10 15 20 25 30
0.5
1
1.5
2
Coef. o
f Lift, C
l
Angle of Attack, []
mean
=20, amplitude
=10
10 15 20 25 30
0.5
1
1.5
2
Coef. o
f Lift, C
l
Angle of Attack, []
mean
=20, amplitude
=10
5 10 15 20 25
0.5
1
1.5
2
Coef. o
f Lift, C
lAngle of Attack, []
mean
=14, amplitude
=10
5 10 15 20 25
0.5
1
1.5
2
Coef. o
f Lift, C
lAngle of Attack, []
mean
=14, amplitude
=10
0 5 10 15 20
0
0.5
1
1.5
Coef. o
f Lift, C
l
Angle of Attack, []
mean
=8, amplitude
=10
0 5 10 15 20
0
0.5
1
1.5
Coef. o
f Lift, C
l
Angle of Attack, []
mean
=8, amplitude
=10
LB model validated against 2D pitch oscillation data
10 15 20 25 30
0.5
1
1.5
2
Coef. o
f Lift, C
l
Angle of Attack, []
mean
=20, amplitude
=10
10 15 20 25 30
0.5
1
1.5
2
Coef. o
f Lift, C
l
Angle of Attack, []
mean
=20, amplitude
=10
5 10 15 20 25
0.5
1
1.5
2
Coef. o
f Lift, C
l
Angle of Attack, []
mean
=14, amplitude
=10
5 10 15 20 25
0.5
1
1.5
2
Coef. o
f Lift, C
l
Angle of Attack, []
mean
=14, amplitude
=10
0 5 10 15 20
0
0.5
1
1.5
Coef. o
f Lift, C
l
Angle of Attack, []
mean
=8, amplitude
=10
0 5 10 15 20
0
0.5
1
1.5
Coef. o
f Lift, C
l
Angle of Attack, []
mean
=8, amplitude
=10
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LB Model integration and 3D Validation
LB model integrated with WInDS to calculate sectional loads along blade span.
NREL’s Unsteady Aerodynamics Experiment (UAE) Phase VI
• Full scale, heavily instrumented wind turbine tests in the NASA/Ames wind tunnel
• Span-wise CN and CA available along blade from chord-wise pressure taps (no angle of attack data)
Steady and Unsteady (yawed) test cases[7]
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UAE Steady: Avg. Thrust and Torque per Blade
10 15 20 25400
600
800
1000
1200
1400
1600
1800
2000
2200
Wind Speed, U [m/s]
Ae
ro. T
hru
st o
n B
1, T
[N
]
10 15 20 25100
200
300
400
500
600
700
800
Wind Speed, U [m/s]
Ae
ro. T
orq
ue
on
B1
, Q
[Nm
]
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0 90 180 270 360
1
1.5
2
2.5
Azimuth Angle []
CN
r/R = 0.30
0 90 180 270 3600.8
1
1.2
1.4
1.6
1.8
Azimuth Angle []
CN
r/R = 0.466
0 90 180 270 360
0.9
1
1.1
1.2
1.3
Azimuth Angle []
CN
r/R = 0.633
0 90 180 270 360
0.8
0.9
1
1.1
Azimuth Angle []
CN
r/R = 0.80
0 90 180 270 360
0.6
0.7
0.8
0.9
Azimuth Angle []
CN
r/R = 0.95
UAE Unsteady: Normal Force, U=10m/s, Yaw=30°0 90 180 270 360
0
0.2
0.4
0.6
Azimuth Angle []
CA
r/R = 0.30
0 90 180 270 360
0
0.1
0.2
0.3
0.4
Azimuth Angle []
CA
r/R = 0.466
0 90 180 270 360
0.1
0.15
0.2
0.25
Azimuth Angle []
CA
r/R = 0.633
0 90 180 270 360
0.08
0.1
0.12
0.14
0.16
Azimuth Angle []
CA
r/R = 0.80
0 1 20
0.5
1
1.5
2
UAE Data
WInDS - Baseline
WInDS - DS
FAST
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UAE Unsteady: Rotor Thrust and Torque, U=10 m/s, Yaw=30°
0 90 180 270 360
550
600
650
700
750
800
850
900
Azimuth Angle []
Ae
ro. T
hru
st o
n B
1, T
[N
]
0 90 180 270 360
400
450
500
550
600
650
Azimuth Angle []
Ae
ro. T
orq
ue
on
B1
, Q
[Nm
]
0 90 180 270 360
550
600
650
700
750
800
850
900
Azimuth Angle []
Ae
ro. T
hru
st o
n B
1, T
[N
]
0 0.5 1 1.5 20
0.5
1
1.5
2
UAE Data WInDS - Baseline WInDS - DS
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Ongoing and Future Work
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FAST Integration
WInDS was originally written as a standalone model in Matlab
• Decouples structural motion and the aerodynamics
Integrated into FAST v8 by modifying the aerodynamic model, AeroDyn
• Fully captures the effects of aerodynamics and hydrodynamics on platform motions changes the resulting aerodynamics
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Sample Floating Test Case
Spar buoy in rated conditions
Full degrees of freedom
Simulated time: 60s
Wind
Speed,
U∞
[m/s]
Sig. Wave
Height,
Hs
[m]
Peak Spec.
Period,
Tp
[s]
Rated 11.40 2.54 13.35OC3/Hywind
Spar Buoy [4]
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Span-wise Unsteadiness
0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
Blade Span, r/R
Ave
rag
e R
ed
uce
d F
req
ue
ncy, k
Spanwise k
Quasi-steady line
AoA predominately varying cyclically with rotor rotation, driven by:
• Mean platform pitch: ~4-5°
• Rotor shaft tilt: 5°
0.2 0.4 0.6 0.8 1
0.05
0.1
0.15
Blade Span, r/R
CL S
tan
da
rd D
evia
tio
n
LB Model
Static Data
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Dynamic Stall
10 12 14 16 18
1.3
1.4
1.5
1.6
1.7
1.8
Angle of Attack, ()
Lift C
oe
f., C
L
Span Location r/R = 0.186
LB Model
Static Data
5 6 7 80.9
1
1.1
1.2
1.3
1.4
Angle of Attack, ()
Lift C
oe
f., C
L
Span Location r/R = 0.381
LB Model
Static Data
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Future Work
Characterization of floating platforms using the combined FAST/WInDS tool
• Prevalence and severity of dynamic stall
• Floating platform motion
Reduce computational intensity of the far wake
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Questions?
Evan [email protected]
This work was supported in part by the
NSF-sponsored IGERT: Offshore Wind Energy Engineering, Environmental Science, and Policy
and by the Edwin V. Sisson Doctoral Fellowship
Thank You!
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References
[1] Sebastian, T. 2012. “The aerodynamics and near wake of an offshore floating horizontal axis wind turbine.” PhD Thesis presented to the University of Massachusetts, Amherst.
[2] Sebastian, T. 2012. “Wake simulation of NREL 5-MW Turbine on pitching OC3-Hywind Spar-Buoy in 18m/s winds.” Accessed at http://youtu.be/eAF54Vi12aU
[3] Leishman, J.G. 2006. “Principles of Helicopter Aerodynamics.” Cambridge University Press: New York, NY.
[4] Jonkman, J.M. 2010. “Definition of the Floating System for Phase IV of OC3.” NREL/TP-500-47535.
[5] Sebastion, T., Lackner, M.A. 2012. “Analysis of the Induction and Wake Evolution of an Offshore Floating Wind Turbine.” Energies, 5, pp. 968-1000.
[6] Anderson Jr., J. D. 2007. “Fundamentals of Aerodynamics.” 4th Ed. McGraw-Hill: New York, NY.
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Supplemental Slides
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Classical Lifting Line Theory
12 l
c U Cdy
Kutta-Joukowski
Theorem
[3]
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WInDS Fixed Point Iteration Algorithm
Data: Turbine geometry and wake properties
Results: Updated bound circulation strength
1 while ΔΓbound ≥ tolerance
2 Use Biot-Savart law to compute induced velocities
3 Compute span-wise angles of attack
4 Compute/table look-up Cl and Cd
5Compute new bound circulation strength via Kutta-
Joukowski theorem
6 Relax new bound circulation strength as % of previous
7 Update shed and trailed filaments
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Model Coupling Considerations
Shed vorticity into wake is double counted
• During induced velocity calculations, shed vortices for a given node are ignored
Dynamic stall nonlinearities can prevent fixed point iteration convergence
• Reduce relaxation factor and increase max number of iterations
• Longer simulation run time
• Detection of loops and override
DS model threshold exceeded, non-linear
ΔCL
Dramatic change in Γbound and
Uinduced
DS model no longer passed
threshold, non-linear
ΔCL
Dramatic change in Γbound and
Uinduced
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Quasi-Steady Aerodynamics
Aerodynamic properties of airfoils determined experimentally in wind tunnels
Lift increases linearly with angle of attack (α)
At a critical angle, flow separates and lift drops
• “Stall”
WInDS uses quasi-steady data
[6]
[6]
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Preprocessor: Kirchhoff-Helmholtz Model
Model is highly sensitive to correctly identifying constants from the steady airfoil data
• TE separation point curve fits most importantly
• f is the separation point as a ratio of the chord, f=0 is fully separate, f=1 is fully attached
1
2
3
1 11
2 2 1 2
23 3
,
,
,
S
S
S
c a e
f c a e
c a e
2
1,
2n nf
C f C
2,a e nC f C f
Calculate ffrom steady Cn and α data
Fit Piece-Wise function f and α data
Cn and Ca Calculated as functions of
f and α
2
2 1n
n
Cf
C
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Dynamic Stall Flow Morphology
Stage 1 Stage 2 Stage 2-3 Stage 3-4 Stage 5
•Static stall angle exceeded
•Flow reversals begin in boundary later
•Flow separation at leading edge
•Formation of spill vortex
•Vortex convectsdown the chord
• Induces additional lift and move center of pressure aft
•Vortex reaches trailing edge
•Stalled flow, fully separated
•When angle of attack is low enough, flow reattaches
[3]
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5 10 15 20 25
0
0.5
1
Coef. o
f D
rag, C
d
Angle of Attack, []
mean
=14, amplitude
=10
0 5 10 15 20-0.2
0
0.2
0.4
Coef. o
f D
rag, C
d
Angle of Attack, []
mean
=8, amplitude
=10
10 15 20 25 30
0
0.5
1
Coef. o
f D
rag, C
d
Angle of Attack, []
mean
=20, amplitude
=10
10 15 20 25 30
0
0.5
1
Coef. o
f D
rag, C
d
Angle of Attack, []
mean
=20, amplitude
=10
5 10 15 20 25
0
0.5
1
Coef. o
f D
rag, C
d
Angle of Attack, []
mean
=14, amplitude
=10
0 5 10 15 20-0.2
0
0.2
0.4
Coef. o
f D
rag, C
d
Angle of Attack, []
mean
=8, amplitude
=10
S809 Airfoil, k = 0.077, Re = 1.0×106