Some effects of large blade deflections on aeroelastic stability Bjarne S. Kallesøe Morten H. Hansen
Some effects of large blade deflections on aeroelastic stability Bjarne S. Kallesøe Morten H. Hansen.
Dec 26, 2015
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Some effects of large blade deflections on aeroelastic stabilityBjarne S. KallesøeMorten H. Hansen
6/01/2009Some effects of large blade deflections on aeroelastic stability2 Risø DTU, Technical University of Denmark
Introduction• Why? Does the deflection of turbine blades effect the
aeroelastic properties of the blades?
• What? Compare frequencies, damping and shapes of aeroelastic modes of motion for undeflected and steady state deflected blade
• How? Eigenvalue analysis 2nd order Bernoulli-Euler beam and time simulations with Risø’s in-house aeroelastic simulation tool, HAWC2
6/01/2009Some effects of large blade deflections on aeroelastic stability3 Risø DTU, Technical University of Denmark
Background• Large turbines with flexible
blade
6/01/2009Some effects of large blade deflections on aeroelastic stability4 Risø DTU, Technical University of Denmark
Blade Model #1• 2nd order Bernoulli-Euler beam (2nd B-E)1
– Similar to Hodges and Dowell2
– Extended to include the effects of pitch action, gravity and rotor speed variations
– Furthermore, models for pitch action and rotor speed are derived
– Quasi-static aerodynamic for non-linear steady state version– Unsteady dynamic stall model3 for linear unsteady version
1) Kallesoe, B., Equations of motion for a rotor blade, including gravity, pitch action and rotor speed variations, Wind Energy, Vol. 10, No. 3, 2007, pp. 209–230.
2) Hodges DH, Dowell EH. Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades. Technical Report TN D-7818, NASA, December 1974.
3) Hansen, M., Gaunaa, M., and Madsen, H., A Beddoes-Leishman type dynamic stall model in state-space and indicial formulation, Tech. Rep. Risø -R-1354(EN), Risø National Laboratory, (available from www.risoe.dk), August 2004.
6/01/2009Some effects of large blade deflections on aeroelastic stability5 Risø DTU, Technical University of Denmark
Blade Model #1 Edge-twist coupling of flapwise deflected blade
Part of nonlinear equation of motion for edgewise blade motion:
Linearized about deflected blade:
Part of nonlinear equation of motion for torsional blade motion:
Linearized about deflected blade:
6/01/2009Some effects of large blade deflections on aeroelastic stability6 Risø DTU, Technical University of Denmark
Blade Model #2• Risø’s in-house aeroelastic code (HAWC2)1,2
– Time domain simulations– Combined Beam-element and multi-body formulation– BEM theory, extended to handle dynamic inflow, dynamic
stall, skew inflow, shear effects on the induction and effects from large deflections
– Stiff turbine except for the blades– No induction and tip loss
1) Larsen, T., Hansen, A., and Buhl, T., Aeroelastic effects of large blade deflections for wind turbines, Proceedings of the special topic conference ”The Science of making Torque from Wind”, 2004, pp. 238–246.
2) Larsen, T., Madsen, H., Hansen, A., and Thomsen, K., Investigations of stability effects of an offshore wind turbine using the new aeroelastic code HAWC2, Proceedings of the conference ”Copenhagen Offshore Wind 2005”, 2005.
6/01/2009Some effects of large blade deflections on aeroelastic stability7 Risø DTU, Technical University of Denmark
Test case: Overspeed• NREL 5 MW reference turbine1
– 61.5 m blade– No structural damping– Rated rotor speed: 1.26 rad/s
• Operational conditions– wind speed: 10 m/s– 0 deg pitch– Stepwise increase of rotor speed
• Method– First; Computer steady state blade deflection at different rotor
speeds – Next; Compute aeroelastic frequencies and damping
1) Jonkman J., Nrel’s offshore baseline 5MW turbine. Technical report, NREL/NWTC, 1617 Cole Boulevard; Golden, CO 80401-3393, USA, 2005.
6/01/2009Some effects of large blade deflections on aeroelastic stability8 Risø DTU, Technical University of Denmark
Steady state blade deflection• 2nd B-E
– Full non-linear beam– Quasi-static aerodynamic– Finite difference
discretisation of spatial derivatives
• HAWC2– High structural damping to
suppress any modes with negative aerodynamic damping
6/01/2009Some effects of large blade deflections on aeroelastic stability9 Risø DTU, Technical University of Denmark
Unsteady blade motion • 2nd B-E
– Linearized blade model– Linear unsteady dynamic stall model– Two cases:
• Linearized about the undeflected blade• Linearized about the steady state deflected blade
– Finite difference discretisation of spatial derivatives– Solve eigenvalue problem to compute aeroelastic frequency
and damping
• HAWC2– Measuring decay or growth of blade vibration amplitude, and
measuring the dominating frequency
6/01/2009Some effects of large blade deflections on aeroelastic stability10 Risø DTU, Technical University of Denmark
1 1.5 2 2.5
-0.2
0
0.2
0.4
0.6
0.8
rotor speed [rad/s]
log
arit
mis
ke d
ekr
em
en
t [-]
1 1.5 2 2.50
1
2
3
4
5
rotor speed [rad/s]
fre
qu
en
cy [H
z]
Aeroelastic frequencies and damping
Circles: undeflected bladeStars: steady state deflected bladeSquares: HAWC2
Frequency Damping
6/01/2009Some effects of large blade deflections on aeroelastic stability11 Risø DTU, Technical University of Denmark
Second mode (First edgewise mode)
1 1.5 2 2.50
0.2
0.4
0.6
0.8
1
rotor speed [rad/s]
mod
al c
onte
nt [
- ]
edgeflaptwist
Circles: undeflected blade
Stars: deflected blade
6/01/2009Some effects of large blade deflections on aeroelastic stability12 Risø DTU, Technical University of Denmark
0 20 40 60-0.5
0
0.5
1
Radius [m]
am
plit
ud
e [-
]
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
edge [-]
flap
[-]
1 1.5 2 2.50
1
2
3
4
5
rotor speed [rad/s]
fre
qu
en
cy [H
z]
1 1.5 2 2.5
-0.2
0
0.2
0.4
0.6
0.8
rotor speed [rad/s]
log
arit
mis
ke d
ekr
em
en
t [ -
]Second mode (First edgewise mode)
Green: undeflectedBlue: deflected
Wind
Circles: undeflectedStars: deflected
Blue: edgeGreen: flapRed: twist
6/01/2009Some effects of large blade deflections on aeroelastic stability13 Risø DTU, Technical University of Denmark
0 20 40 60-0.5
0
0.5
1
Radius [m]
am
plit
ud
e [-
]
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
edge [-]
flap
[-]
1 1.5 2 2.50
1
2
3
4
5
rotor speed [rad/s]
fre
qu
en
cy [H
z]
1 1.5 2 2.5
-0.2
0
0.2
0.4
0.6
0.8
rotor speed [rad/s]
log
arit
mis
ke d
ekr
em
en
t [ -
]Second mode (First edgewise mode)
Green: undeflectedBlue: deflected
Wind
Circles: undeflectedStars: deflected
Blue: edgeGreen: flapRed: twist
6/01/2009Some effects of large blade deflections on aeroelastic stability14 Risø DTU, Technical University of Denmark
0 20 40 60-0.5
0
0.5
1
Radius [m]
am
plit
ud
e [-
]
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
edge [-]
flap
[-]
1 1.5 2 2.50
1
2
3
4
5
rotor speed [rad/s]
fre
qu
en
cy [H
z]
1 1.5 2 2.5
-0.2
0
0.2
0.4
0.6
0.8
rotor speed [rad/s]
log
arit
mis
ke d
ekr
em
en
t [ -
]Second mode (First edgewise mode)
Green: undeflectedBlue: deflected
Wind
Circles: undeflectedStars: deflected
Blue: edgeGreen: flapRed: twist
6/01/2009Some effects of large blade deflections on aeroelastic stability15 Risø DTU, Technical University of Denmark
Fourth mode (Second edgewise mode)
1 1.5 2 2.50
0.2
0.4
0.6
0.8
1
rotor speed [rad/s]
mod
al c
onte
nt [
- ]
edgeflaptwist
Circles: undeflected blade
Stars: deflected blade
6/01/2009Some effects of large blade deflections on aeroelastic stability16 Risø DTU, Technical University of Denmark
Fourth mode (Second edgewise mode)
0 20 40 60-0.5
0
0.5
1
Radius [m]
am
plit
ud
e [-
]
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
edge [-]
flap
[-]
1 1.5 2 2.50
1
2
3
4
5
rotor speed [rad/s]
fre
qu
en
cy [H
z]
1 1.5 2 2.5
-0.2
0
0.2
0.4
0.6
0.8
rotor speed [rad/s]
log
arit
mis
ke d
ekr
em
en
t [ -
]
Green: undeflectedBlue: deflected
Wind
Circles: undeflectedStars: deflected
Blue: edgeGreen: flapRed: twist
6/01/2009Some effects of large blade deflections on aeroelastic stability17 Risø DTU, Technical University of Denmark
Fourth mode (Second edgewise mode)
0 20 40 60-0.5
0
0.5
1
Radius [m]
am
plit
ud
e [-
]
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
edge [-]
flap
[-]
1 1.5 2 2.50
1
2
3
4
5
rotor speed [rad/s]
fre
qu
en
cy [H
z]
1 1.5 2 2.5
-0.2
0
0.2
0.4
0.6
0.8
rotor speed [rad/s]
log
arit
mis
ke d
ekr
em
en
t [ -
]
Green: undeflectedBlue: deflected
Wind
Circles: undeflectedStars: deflected
Blue: edgeGreen: flapRed: twist
6/01/2009Some effects of large blade deflections on aeroelastic stability18 Risø DTU, Technical University of Denmark
Fourth mode (Second edgewise mode)
0 20 40 60-0.5
0
0.5
1
Radius [m]
am
plit
ud
e [-
]
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
edge [-]
flap
[-]
1 1.5 2 2.50
1
2
3
4
5
rotor speed [rad/s]
fre
qu
en
cy [H
z]
1 1.5 2 2.5
-0.2
0
0.2
0.4
0.6
0.8
rotor speed [rad/s]
log
arit
mis
ke d
ekr
em
en
t [ -
]
Green: undeflectedBlue: deflected
Wind
Circles: undeflectedStars: deflected
Blue: edgeGreen: flapRed: twist
6/01/2009Some effects of large blade deflections on aeroelastic stability19 Risø DTU, Technical University of Denmark
Fourth mode (Second edgewise mode)
0 20 40 60-0.5
0
0.5
1
Radius [m]
am
plit
ud
e [-
]
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
edge [-]
flap
[-]
1 1.5 2 2.50
1
2
3
4
5
rotor speed [rad/s]
fre
qu
en
cy [H
z]
1 1.5 2 2.5
-0.2
0
0.2
0.4
0.6
0.8
rotor speed [rad/s]
log
arit
mis
ke d
ekr
em
en
t [ -
]
Green: undeflectedBlue: deflected
Wind
Circles: undeflectedStars: deflected
Blue: edgeGreen: flapRed: twist
6/01/2009Some effects of large blade deflections on aeroelastic stability20 Risø DTU, Technical University of Denmark
Fourth mode (Second edgewise mode)
0 20 40 60-0.5
0
0.5
1
Radius [m]
am
plit
ud
e [-
]
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
edge [-]
flap
[-]
1 1.5 2 2.50
1
2
3
4
5
rotor speed [rad/s]
fre
qu
en
cy [H
z]
1 1.5 2 2.5
-0.2
0
0.2
0.4
0.6
0.8
rotor speed [rad/s]
log
arit
mis
ke d
ekr
em
en
t [ -
]
Green: undeflectedBlue: deflected
Wind
Circles: undeflectedStars: deflected
Blue: edgeGreen: flapRed: twist
6/01/2009Some effects of large blade deflections on aeroelastic stability21 Risø DTU, Technical University of Denmark
Fourth mode (Second edgewise mode)
0 20 40 60-0.5
0
0.5
1
Radius [m]
am
plit
ud
e [-
]
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
edge [-]
flap
[-]
1 1.5 2 2.50
1
2
3
4
5
rotor speed [rad/s]
fre
qu
en
cy [H
z]
1 1.5 2 2.5
-0.2
0
0.2
0.4
0.6
0.8
rotor speed [rad/s]
log
arit
mis
ke d
ekr
em
en
t [ -
]
Green: undeflectedBlue: deflected
Wind
Circles: undeflectedStars: deflected
Blue: edgeGreen: flapRed: twist
6/01/2009Some effects of large blade deflections on aeroelastic stability22 Risø DTU, Technical University of Denmark
Fifth mode (Third flapwise mode)
1 1.5 2 2.50
0.2
0.4
0.6
0.8
1
rotor speed [rad/s]
mod
al c
onte
nt [
- ]
edgeflaptwist
Circles: undeflected blade
Stars: deflected blade
6/01/2009Some effects of large blade deflections on aeroelastic stability23 Risø DTU, Technical University of Denmark
0 20 40 60-0.5
0
0.5
1
Radius [m]
am
plit
ud
e [-
]
-0.5 0 0.5-1
-0.5
0
0.5
1
edge [-]
flap
[-]
1 1.5 2 2.50
1
2
3
4
5
rotor speed [rad/s]
fre
qu
en
cy [H
z]
1 1.5 2 2.5
-0.2
0
0.2
0.4
0.6
0.8
rotor speed [rad/s]
log
arit
mis
ke d
ekr
em
en
t [ -
]Fifth mode (Third flapwise mode)
Green: undeflectedBlue: deflected
Wind
Circles: undeflectedStars: deflected
Blue: edgeGreen: flapRed: twist
6/01/2009Some effects of large blade deflections on aeroelastic stability24 Risø DTU, Technical University of Denmark
0 20 40 60-0.5
0
0.5
1
Radius [m]
am
plit
ud
e [-
]
-0.5 0 0.5-1
-0.5
0
0.5
1
edge [-]
flap
[-]
1 1.5 2 2.50
1
2
3
4
5
rotor speed [rad/s]
fre
qu
en
cy [H
z]
1 1.5 2 2.5
-0.2
0
0.2
0.4
0.6
0.8
rotor speed [rad/s]
log
arit
mis
ke d
ekr
em
en
t [ -
]Fifth mode (Third flapwise mode)
Green: undeflectedBlue: deflected
Wind
Circles: undeflectedStars: deflected
Blue: edgeGreen: flapRed: twist
6/01/2009Some effects of large blade deflections on aeroelastic stability25 Risø DTU, Technical University of Denmark
0 20 40 60-0.5
0
0.5
1
Radius [m]
am
plit
ud
e [-
]
-0.5 0 0.5-1
-0.5
0
0.5
1
edge [-]
flap
[-]
1 1.5 2 2.50
1
2
3
4
5
rotor speed [rad/s]
fre
qu
en
cy [H
z]
1 1.5 2 2.5
-0.2
0
0.2
0.4
0.6
0.8
rotor speed [rad/s]
log
arit
mis
ke d
ekr
em
en
t [ -
]Fifth mode (Third flapwise mode)
Green: undeflectedBlue: deflected
Wind
Circles: undeflectedStars: deflected
Blue: edgeGreen: flapRed: twist
6/01/2009Some effects of large blade deflections on aeroelastic stability26 Risø DTU, Technical University of Denmark
Conclusion• Large blade deflection do effect the aeroelastic stability of
a turbine blade • Flapwise steady state blade deflection couples edgewise
and torsional motion• The extra torsional motion changes the aerodynamic
forces, such that more flapwise motion is introduced in the edgewise modes
• The stability limit is reduced, but still well above normal operation.
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