Post on 25-Oct-2020
Evan GaertnerUniversity of Massachusetts, Amherst
egaertne@umass.edu
NAWEA 2015 Symposium
June 11, 2015
Modeling Dynamic Stall for a Free Vortex Wake Model of Floating
Offshore Wind Turbines
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]
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]
4
WInDS Vortex Structure Evolution
[6]
12 l
c U Cdy
Kutta-Joukowski
Theorem
Dynamic Stall Modeling for WInDS
6
Unsteady Aerodynamics
WInDS models an unsteady wake, but assumes quasi-steady airfoil behavior.
Wind turbine blades see highly unsteady flow
[3]
7
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 (°)
8
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]
9
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
10
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]
11
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
]
12
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
13
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
Ongoing and Future Work
15
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
16
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]
17
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
18
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
19
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
Questions?
Evan Gaertneregaertne@umass.edu
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!
21
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.
Supplemental Slides
23
Classical Lifting Line Theory
12 l
c U Cdy
Kutta-Joukowski
Theorem
[3]
24
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
25
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
26
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]
27
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
28
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]
29
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