Flutter analysis of two wind turbines was correlated with experimental data for flutter of Darrieus blades

Ham, N. D.

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FLUTTER OF DARRiEUS WIND TURBINE BLADES: CORRELATION OF THEORY AND EXPERIMENT
Norman D. Ham
Department of Aeronautics and Astronautics
Massachusetts Institute of Technology
Cambridge, Mass. 02139
Acquisition of frequency data for the Alcoa 17-M
- __ LC and 1238229 wind turbines has permitted some
limited correlation of the flutter analysis of
Ref. l with experimental data for flutter of
_ Darrieus blades from Ref. 2.
=
The natural frequencies of the non-rotating
critical blade bending modes can be written as
where
ElF
_20 = _2 /mR-_ rad./sec.
g20 = %2 / GJ rad./sec.
mR4
_2' _2 are frequency parameters, and
i_
==
ElF = blade flatw_se bending stiff-
ness, Ib-ft_
GJ = blade torsion stiffness, lb-ft_
m = blade running mass, slugs/ft.
R = radius of circular arc portion
of blade
Also, the effect of turbine rotational speed Q is
_iven by
2 +
c°2 : _0 K2_2
-2 -2 R2_72m : m 0 +
where K2, R2 are Southwell coefficients.
Data provided by Alcoa has made possible the
following tabulation for turbines of h/b = 1.5:
TABLE I
TYPE _2 _2 K2 K2
17-Meter LC 5.72 23-.7 2.74 4.57
1238229 lO.O 23.5 4.32 3.99
Proceedings of the Second DOE/NASA Wind Turbine
Dynamics Workshop, Cleveland, February 1981.
199
The bracing struts of Type 1238229 appear to
have a significant effect on the flatwise bending
parameters _ and Kp. It is suspected that
significant _ode shape variations may also be
related to the clamping effect of the struts.
Experimental flutter data for wind tunnel models
of Darrieus wind turbines of h/D = l .5 are shown
in Fig. l taken from Ref. 2. The correlating
parameters are the reduced _utter speed
Uc_ PB
J
t G
where Uc : blade tangential velocity at
flutter = _FRc
: blade length
t = blade section maximum thickness
PB = blade material density
G = blade material torsion modulus
and the density ratio
PBAB
_2
_c
where AB = blade material cross-section area
o = air density
c : blade chord
These parameters were calculated for the 17-
Meter LC and 1238229 wind turbines using their
theoretical flutter speeds _F of I08 rpm and
57 rpm respectively as calculated by the method
of Ref. I. The results are plotted in Fig. I.
The theory is seen to give a conservative
prediction of flutter speed.
An attempt was made to predict the experimental
flutter speed directly for the particular case
of the aluminum blade of 0012 section of Fig. l,
using blade frequencies estimated by means of the
parameters tabulated in TABLE I for the 17-Meter
LC turbine, and the flutter parameter values
C = -6.5 and m_/m 6 = 0.75 for that strutless
t_rbine. Again,_th_ theoretical prediction is
seen to be conservative.
https://ntrs.nasa.gov/search.jsp?R=19820015830 2020-03-21T17:05:18+00:00Z
l °
2,
REFERENCES
Ham, N.D., "Flutter of Darrieus Wind Turbine
Blades", from "Wind Turbine Structural
Dynamics", NASA Publication C0NF-2034,
November 1977.
Templin, R.J. and South, P., "Canadian Wind
Energy Program", Proc. of the VAWT Technology
Workshop, SAND76-5686, Sandia Laboratories,
Albuquerque, N.M., July 1976.
90.
-i- v-6-
20
IO
0
0
Ix
SOLID SYMBOLS SHOW DATA
FOR BLADES SUPPORTED AT 2/3 R
FLAGGED SYMBOLS ARE WITH WIND ON
AT V/U : O.T,, I
IO0 200
PI A •
_pc a
I
A I kYM.o,lV, t *','.1 ','.. I _,,o..]
+ h I I o I_ool _'1""'1 "°' I
/ I u I ,43 I 6s I "'"I '" I
---_ 1--1 _ I _ I _' I "' I "°' I
/ I o I 63 I 6' I"'"1 "°' I
0 I I r_ I 50 I 138 I sh_.l I flat I
A/ _ IA I _,1 _,1.,..,I ,,., I
I T LA.J_ 6, I AI.JNA 
I ® 17-t"1 LC _YSTEM ( ,I )
• t238229 SYSTEH ( ,, )
AL OO12 ( ,, )
300
Fig.1. Variation of blade flutter parameter with density
ratio for turbine with h/d = 1.5.
200


Flutter of Darrieus wind turbine blades: Correlation of theory and experiment

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