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