3-3
DESCRIPTION
flutterTRANSCRIPT
Dynamic Stall Model for Investigating Stall Flutter
Motivation
Discussion of flutter has often been put off – until the next generation of larger, more flexible blades
For large offshore wind turbines designers are pushing the boundaries:• Higher tip speeds• More flexible blades• More varied lay-up designs• Advanced control designs which sacrifice some rotor speed control for other benefits
At what point do we meet the limit of blade aeroelastic stability?
And what margin do we need to have to avoid flutter in all design situations?
Overview
Unsteady attached flow aerodynamic model
Classical flutter analysis
Dynamic stall model
Stall flutter
4
Theodorsen, working at NACA wrote a paper in 1934 on solving the linearised potential flow loading solution for a flat plate aerofoil with a flap
The aim was the understanding of the phenomenon known as flutter
Attached flow aerodynamics – Theodorsen’s Theory
Theodore Theodorsen
(January 8, 1897 –November 5, 1978)
5
The results included equations for the force and moment on the aerofoil section depending on the angle of attack, plunging motion and flap angle as well as their first and second derivatives
These equations, along with the Theodorsen function, C, which is a function of the reduced frequency of the motion can be used to construct an approximation to the attached flow aerodynamics of aerofoils
Attached flow aerodynamics – Theodorsen’s Theory
6
A quasi-static assumption for the lift coefficient of an aerofoil is:
Whereas the full result for an oscillating angle of attack is
F+iG is the complex Theodorsenfunction
k = ωc/2V is the reduced frequency
Theodorsen’s function
πα2=lC
++=2
2k
iiGFCl απ 1/k for the NREL blade torsional mode at rated
0
2
4
6
8
10
0 20 40 60 80
distance along blade [m]
1/k
0.5 1 1.5 2 2.5 3
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Time [s]
Normal force coefficient
Circulatory normal force coefficientNon-circulatory normal force coefficient
7
The Theodorsen function is frequency dependent
Wagner formulated an approximation in the time domain
ønc models the effects from pressure forces accelerating the fluid; øc models the creation of circulation around the aerofoil
The parameters are the number of semi-chords travelled, s = tc/2V, and the Mach number, M
Time-domain model: Wagner’s indicial response
Step change angle of attack (2m blade section at 10m/s)
( ) ( ) ( )MsMsM
sCcncn ,
2,
4αα φ
βπφ
αα +=
8
Bladed’s model has been tested against the results from Beddoes and Leishman’s experiments
From version 4.3, Bladed will include dynamic variation of the drag and pitching moment coefficients for the first time
This is important for the torsionalstability of wind turbine blades…
Attached flow: validation
-1.0
-0.5
0.0
0.5
1.0
1.5
-10 -5 0 5 10 15
Angle of Attack, deg
CN
- 0 .1
- 1 0 - 5 0 5 1 0 1 5
A n g l e o f A t t a c k , d e g
- 0 .1
- 1 0 - 5 0 5 1 0 1 5
A n g l e o f A t t a c k , d e gC
D
Overview
Unsteady attached flow aerodynamic model
Classical flutter analysis
Dynamic stall model
Stall flutter
10
On the right frequency domain results for flutter showing the system on the limit of stability at 163m/sBelow, results of a time-domain simulation with a slow ramp in wind speed
Flutter: NREL 5MW blade
Blade geometry
In order to simulate flutter at wind speeds closer to the wind turbine design envelope, the blade was modified by moving the mass axis aft
Not an exercise in blade design – the aim was to change as few parameters as possible while achieving the desired results
Blade Planform: Chord, Pitch axis (black)m
Distance along pitch axis (m)
-0.5-1.0-1.5-2.0
0.00.51.01.52.02.53.0
20 40 60 80
Blade Planform: Chord, Pitch axis (black)
m
Distance along pitch axis (m)
-0.5-1.0-1.5-2.0
0.00.51.01.52.02.53.0
20 40 60 80
Modified NREL blade planform
Original NREL blade planform
12
Moving the mass axis toward the trailing edge decreases the flutter onset wind speed
Both time-domain and frequency domain models predict the same decrease for the modified structural model
Flutter: Modified 5MW blade
Overview
Unsteady attached flow aerodynamic model
Classical flutter analysis
Dynamic stall model
Stall flutter
14
Every aerofoil has a point at which the pressure generated by the circulation around the aerofoil causes the flow to detach
At this point, lift forces stop increasing so quickly and drag forces increase
But the transition from one state to the other can’t be instantaneous
Trailing edge stall
15
The model of stall is a specific case of Kirchoff flow around a plate – a steady wake region separated from the potential flow around a body by a vortex sheet
The value of normal force is approximated as
Where f is defined as the separation and obtained from the steady aerofoil data
Trailing edge stall
Gustav Robert Kirchhoff
(12 March 1824 –17 October 1887)
απ2
2
12
+=
fCN
16
In the dynamic theory, the motion of the separation position is delayed according to deficiency functions with time period Tf which is assumed to be the time taken to travel 3 semi-chords
Or a two metre section in travelling at 75m/s, this is 0.08 seconds
A short time but it still can cause significant increase in loading compared to the steady aerofoil data (and the time will be longer for the inboard sections of a blade)
Trailing edge stall
Liftcoefficient
Dragcoefficient
Pitchingmomentcoefficient
[.]
Angle of attack for blade 1 [deg]
-0.2
-0.4
-0.6
-0.8
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2 4 6 8 10 12 14 16 18 20
17
The most severe kind of stall
Pressure becomes so high at the leading edge that a vortex forms and detaches
Sudden increase in lift and drag followed by sudden loss of lift
Wind turbine aerofoils are designed with the aim of avoiding this phenomenon
Vortex detachment – leading edge stall
0.0
0.5
1.0
1.5
2.0
0 5 10 15 20
Angle of Attack, deg
CN
18
Model also developed according to the Beddoes-Leishman paper
Difficulties lie in producing a generic model for drag and pitching moment agreement
Results can also be aperiodic
Leading edge stall - validation
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0 5 10 15 20
Angle of Attack, deg
CD
Overview
Unsteady attached flow aerodynamic model
Classical flutter analysis
Dynamic stall model
Stall flutter
20
Experimental work was done in the 1940s by Mendelson at NACA
A similar model was recreated in Bladed
Qualitatively similar results are obtained with differences assumed to be due to different aerofoil characteristics and structural differences
Stall flutter: comparison with experiment
21
Analysis of stall flutter was carried out for the NREL blade with modified mass axis
This showed a 15% drop in flutter windspeed at moderately stalled angles of attack
Stall flutter: wind turbine blade
0
10
20
30
40
50
60
70
80
90
100
-10 0 10 20 30
Angle of attack, degF
lutte
r w
ind
spee
d, m
/s
Bladed
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Attached flow and dynamic stall models have been implemented for a commercial wind turbine code
Flutter has been analysed in the attached flow regime with both frequency domain and time domain methods
Drop in flutter onset wind speed with stall angle can be significant
Turbulence may take part or all of a wind turbine blade into stall and this could be combined with an overspeed for a variable speed turbine
More work is required to establish how general the behaviour of stall flutter is across a range of blade designs including:
• Pre-bend• Sweep
• Range of torsional stiffness, mass and shear centre locations
Conclusions
Thank you for listening
Further Information
• Visit our website: www.gl-garradhassan.com
• Contact us:
James Nichols
Turbine Loads Analysis Department
Tel. +44 117 972 9772