A Comparison between Tip Speed Ratios (2, 4, 5) to Obtain ...
Transcript of A Comparison between Tip Speed Ratios (2, 4, 5) to Obtain ...
A Comparison between Tip Speed Ratios (2, 4, 5) to Obtain
the Fatigue Life of Horizontal Axis Wind Turbine Blades
Aiya Naseer Hussein, Basim Ajel Sadkhan
Mechanical Engineering Department, College Of Engineering, Almustansriyah University, Baghdad, Iraq.
Email Address:
Correspondence should be addressed to Aiya Naseer Hussein [email protected]
Received: 6 May 2021, Revised: 11 May 2021, Accepted: 26 May 2021, Online: 21 Jun 2021
Abstract
The power of the wind is considered the best source of non-pollution renewable energy. The wind turbine blade
is the major and costly part of the wind turbine system. The fatigue phenomena of the blade is a major design
condition to predict the wind turbine blade fatigue life. If the blade fails at serving time, the turbine system will
collapse and the cost will be high. This work aims to estimate the fatigue life for a wind turbine blade with
different tip speed ratios (2, 4, and 5). For obtaining the fatigue life of the blade, the Miner-Palmgren rule and
M-N curve were used. According to the results, at wind velocity (13.85 m/s, 10.96 m/s), it was found that TSR 2
has the highest fatigue life. It was found that three variables depend on each other and the changing in one of
them affects the others. So, the 3-Dimensional plots are useful tools to find the relationship between them.
Visual observation noticed that the damage in the wind turbine was found at the adhesive bounding joint for a
tip speed ratio of 4, and tip speed ratio 2; but, the tip speed ratio of 5 took a long time to fail.
Keywords: Renewable Energy, Fatigue Life, Damage, Tip Speed Ratio
1. Introduction
Wind energy is the fastest energy
technology growing because of its
inexhaustible and renewable source. Wind
energy was developed in the twentieth –
century because the price of oil was a
shock in the 1970s. The development of
wind turbine technology has found a
serious interest in many countries as a
clean source of energy. This technology is
still very new for approximately 25 years,
but the idea of using wind as a source of
energy has existed for centuries. A wind
turbine is a combination of devices and
systems used to extract the kinetic energy
from the wind and convert it into
mechanical energy by using a rotor system
for driving a generator producing electrical
energy, see figure (1). [1-3].
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Figure (1): wind turbine components.
Fatigue is the major mechanism of failure
for constructions beneath a cyclic loading,
which can be considered as an important
design parameter in some applications.
The failure passes in three phases as Crack
initiation, Crack growth, and Fracture of
the structure. Multiple factors can affect
the fatigue of a wind turbine blade as
material, operation speed, wind velocity
distribution, blade length, and the aerofoil.
These factors create seven forms of blade
damage which are an adhesive joint
failure, delamination, adhesive depending,
buckling, split into fibers, cracks in Gel-
coat, and sandwich debonding. [4, 5]
The fatigue phenomena of wind turbine
design were studied and researched with
many methods. (Basim Ajel Sadkhan,
2009) [6] studied the life of the fatigue of
the fiberglass composite blades of wind
turbine according to aerodynamic forces
using TSR (1.5). The air duct system was
used to obtain the experiment data as air
velocity, forces, amplitude moment, and
ultimate moment to estimate the number of
cycles to failure to form an M-N curve
(moment – number of cycle to failure).
The fatigue slope 12 was found as the best
slope to find the fatigue. The M-N
relationship and Palmgren -miner rule
were used to find the damage and fatigue
of the blade. In the experimental program,
fatigue was found at the adhesive joints.
(Amr Mohamed Metwally Ismaiel et al.,
2017) [7] studied the fatigue of full-scale
wind turbine blades by using traditional
theory, as well as probabilistic and
numerical techniques. FAST and M-Life
being utilized for finding the blade's
fatigue life. The fatigue analysis showed
the service life of blade until failure takes-
place. When the rotational speed reaches
36 rpm, the blade lifetime is 17 years, and
Hussein, A. N. & Sadkhan, B. A. Journal of Global Scientific Research (ISSN: 2523-9376) 2021/ 6 (6) 1484
when the rotational speed reaches 47, the
blade lifetime is 15.8 years. (Qiang Ma et
al., 2018) [8] studied a simplified load
spectrum. A full-scale test of fatigue is a
successful technique to obtain the behavior
of the blade's fatigue of a wind turbine.
The main difficulty of this test is the way
to design its load. The traditional methods
for determining the load of test are
intricate and take a long period to process.
For that, an easy technique is used to
convert the blade's loads into the load of
test. Beam theory being employed for
obtaining the relation among the blade
stress, strain, and bending moment.
Assuming the concentration of stress and
the relation between stress and strain, the
M-N curves (Exerted Moment - No. of
cycles to failure) are described. The rule of
Miner is used to calculate the equivalent
damage. The computed outcomes error
between such technique and the
conventional technique is near to (5%),
and one can use this method for the test of
fatigue and to enhance the effectiveness of
the design of the load test. (C. Muyan and
D. Coker, 2020) [9] investigated the static
and fatigue analysis of a (5 m) RUZGEM
composite blade of a wind turbine without
and with a defect. When the defect of
debonding is presented at the side of
pressure, the blade will fail beyond a
loading of (69%), and the zone of defect,
where the debonding is applied, will be the
failure crack propagation laminate failure
region. The outcomes of fatigue expected
that the blade with no defect possesses the
required no. of cycles to failure, while the
blade failed after 85% of loading.
2. Methodology
2.1. Tip Speed Ratio (TSR)
TSR is defined as the relationship between
rotational speed and wind velocity. The
definition of “fast turbines” refers to
turbines with a high optimum TSR, while
the term “slow turbines” refers to turbines
with a low optimum TSR. [10]
In the design of the wind turbine blade, at
first, select a TSR. Usually, the TSR relies
on profile type and blades number. A
different number of blades could be chosen
for various speed ratios. The number of
blades is chosen as a function of design
TSR according to the table (1). In this
study, the number of blades was chosen (6,
4, and 3) according to TSR (2, 4, and 5).
Figure (2): shows the three types of rotors.
The wind turbine blade was made from
composite material as fiberglass and
polyester with 3mm thickness.
Table (1): The relation between TSR and the number of blades. [11]
TSR Number of blades
1 12-36
1.5 6-18
2 4-12
3 3-6
4 2-4
5-8 2-3
8-15 1-2
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Figure (2): The Model of the Rotor.
2.2. Load Spectrum Method and
Palmgren-Miner Rule
The load spectrum technique objective is
to derive a fatigue test of an analogous
impairment, which depends completely
upon the Design-Load spectrum method.
The geometry of the blade and the fatigue
characteristics of material aren't important.
Without affecting the conditions of the
test, the test material may deviate from the
intended design. This method stays at the
load range; for that, the stresses are not
important. Therefore, instead of the (S - N)
curve, the (M - N) curve (Applied Moment
– Number of Cycles to Failure) will be
used for the blade failure. [12] This curve
is defined by the following equation:
Ma=Mu* Nf(-1
m⁄ ) (1)
The damage related to every curve can be
studied via implementing Palmgren-
Miner's rule. The fatigure failure is
happened when the damage reach 1.
𝐃𝐚𝐦𝐚𝐠𝐞 = ∑𝐧𝐢
𝐍𝐢
𝐣𝐢=𝟏
(2)
To compute the number of cycles for
loading (i) the following equation is used:
ni = rpm * T (3)
The amplitude moment was found
according to the equation (4) which was
found according to the aerodynamic
analysis presented in [6]
Ma = F * ( L
3 + rR ) (4)
Where:
Ma = amplitude moment (N.m)
Mu = ultimate moment
Nf = number of cycle to failure.
m = fatigue slope.
ni = number of cycle for loading (i).
T = time of operation.
rpm = speed of the rotor.
F= force acts on the blade
L= length of the blade.
r = radius of the rotor.
3. Experiment procedure
3.1. The test rig
A full-size model testing is expensive and
requires a large foundation for the
modified model. For that, a prototype was
made for studying the fatigue life of the
wind turbine blade. Figure (3) shows the
test rig. The experiment test rig was used
to measure wind turbine speed according
to different wind velocities. It contains few
components as listed below:
1) Inverter (regulator or speed
controller) type LS-M100 (2hp, 200-240 v,
1Ф, 1-50Hz).
Hussein, A. N. & Sadkhan, B. A. Journal of Global Scientific Research (ISSN: 2523-9376) 2021/ 6 (6) 1486
2) Air Generator type GAMAK
(2800rpm, 1.1KW, 220V, 50Hz) with four
blades at 40°.
3) Anemometer type (MT-4615).
4) Duct.
5) Wind Turbine made of blades, hub,
bearings, and shaft.
6) Tachometer type (DT-2234C+).
7) Oil.
Figure (3): the test rig.
3.2. Bending Test
The bending test is used to extract the flexibility behavior of the material. The bending
specimen was made according to the materials and dimensions of the blade (230x20x3 mm).
Figure (4) shows the specimen before and after the test. A 3-point bending test was applied to
find the maximum bending load was extracted from this test.
Figure (4): bending specimen before and after the test.
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3.3. Fatigue Test
Fatigue test machine type (Avery 7305),
speed 1400 rpm was used for this test as
seen in the figure (5). A reverse bending
test is associated with this machine. The
fatigue specimen was made according to
standard (ASTM D 3479/D 3479M–96)
for flat polymer matrix composite
materials and the manual of the fatigue
machine [13]. Figure (6) shows the
geometries and dimensions of the
specimen. Figure (7) shows the fatigue
specimen before and after the test. The test
was done under variable amplitude
moment. The specimen materials were
made from the same material as the blade.
The number of cycle to failure was found
from the mechanical cycles counter.
Figure (5): fatigue test machine.
Figure (6): dimension of the fatigue specimen.
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Figure (7): Fatigue Specimen Before and After the Test.
4. Results
4.1. Bending Test Results
According to equation (1), the applied moment (Ma) was found as a function of the ultimate
moment (Mu) of the blade, and the number of cycles to failure (Nf). The maximum bending
load was found 0.325 KN before the fracture took place. The test device gives the load and
extension as shown in figure (8). The ultimate moment for simply supported beam was found
by equation (5) [14]:
Mu=Fmax*L
4 (5)
Mu = 0.325*103 * 230*10
-3 /4
Mu = 18.6875 N.m
Where:
Fmax = maximum load.
L = length.
Hussein, A. N. & Sadkhan, B. A. Journal of Global Scientific Research (ISSN: 2523-9376) 2021/ 6 (6) 1489
Figure (8): the load- extension chart of the bending test.
4.2. M-N Curve and Damage Results
The M-N curve was found according to the equation (1) and the ultimate moment from the
bending test with fatigue slope m=12 according to reference [9]. The M-N curve equation
takes the final form as follows:
Ma = 18.6875 * Nf-0.083333
Where m = 1/0.083333 = 12.
Tables (2), (3), and (4) show the results for three types of TSR.
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Table (2): Results of TSR 2
rpm Vair (m/s) F (N) M (N.m) Nf ni Damage
43 1.24 0.0392 0.012 2.112E+38 928800 4.3986E-33
113 1.74 0.1525 0.0465 1.772E+31 2440800 1.3777E-25
288 2.36 0.3443 0.105 1.008E+27 6220800 6.1694E-21
393 3.24 0.7143 0.2179 1.588E+23 8488800 5.3478E-17
489 3.77 0.9924 0.3027 3.068E+21 10562400 3.4958E-15
594 4.5 1.4435 0.4403 3.42E+19 12830400 3.7866E-13
698 5.2 1.9502 0.5948 9.251E+17 15076800 1.6677E-11
774 5.75 2.3991 0.7317 7.698E+16 16718400 2.3385E-10
882 6.45 3.0353 0.9258 4.577E+15 19051200 4.3958E-09
980 7.25 3.8511 1.1746 2.63E+14 21168000 8.4881E-08
1071 7.94 4.6309 1.4124 2.878E+13 23133600 8.8873E-07
1178 8.87 5.7933 1.767 1.958E+12 25444800 1.3882E-05
1270 9.35 6.4434 1.9652 5.466E+11 27432000 6.4069E-05
1369 10.2 7.6782 2.3418 6.667E+10 29570400 0.0005076
1462 10.96 8.8728 2.7062 1.176E+10 31579200 0.0031935
1560 11.72 10.153 3.0966 2.333E+09 33696000 0.01763503
1651 12.3 11.187 3.4121 728335733 35661600 0.06659816
1755 13.24 12.969 3.9557 123581284 37908000 0.37334364
1856 13.85 14.196 4.3298 41786631 40089600 1.33273183
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Table (3): Results of TSR 4
rpm Vair (m/s) F (N) M (N.m) Nf ni Damage
37 2 0.226 0.0689 1.577E+29 692640 4.3933E-24
54 2.36 0.3443 0.105 1.008E+27 1010880 1.0069E-21
108 3.24 0.7143 0.2179 1.588E+23 2021760 1.2736E-17
227 3.77 0.9924 0.3027 3.068E+21 4249440 1.3977E-15
450 4.5 1.4435 0.4403 3.42E+19 8424000 2.4772E-13
696 5.2 1.9502 0.5948 9.251E+17 13029120 1.4332E-11
870 5.75 2.3991 0.7317 7.698E+16 16286400 2.259E-10
1004 6.45 3.0353 0.9258 4.577E+15 18794880 4.3319E-09
1136 7.25 3.8511 1.1746 2.63E+14 21265920 8.5189E-08
1249 7.94 4.6309 1.4124 2.878E+13 23381280 8.9764E-07
1388 8.87 5.7933 1.767 1.958E+12 25983360 1.4165E-05
1498 9.35 6.4434 1.9652 5.466E+11 28042560 6.547E-05
1604 10.2 7.6782 2.3418 6.667E+10 30026880 0.00051585
1724 10.96 8.8728 2.7062 1.176E+10 32273280 0.00326078
1877 11.72 10.153 3.0966 2.333E+09 35137440 0.01832009
1980 12.3 11.187 3.4121 728335733 37065600 0.0692109
2102 13.24 12.969 3.9557 123581284 39349440 0.38762028
2220 13.85 14.196 4.3298 41786631 41558400 1.38215847
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Table (4): Results of TSR 5
rpm Vair (m/s) F(N) M (N.m) Nf ni Damage
32 2.36 0.3443 0.105 1.008E+27 622080 6.1692E-22
82 3.24 0.7143 0.2179 1.588E+23 1594080 1.0042E-17
168 3.77 0.9924 0.3027 3.068E+21 3265920 1.0744E-15
312 4.5 1.4435 0.4403 3.42E+19 6065280 1.7843E-13
591 5.2 1.9502 0.5948 9.251E+17 11489040 1.2598E-11
791 5.75 2.3991 0.7317 7.698E+16 15377040 2.1235E-10
912 6.45 3.0353 0.9258 4.577E+15 17729280 4.0855E-09
1030 7.25 3.8511 1.1746 2.63E+14 20023200 8.0218E-08
1162 7.94 4.6309 1.4124 2.878E+13 22589280 8.6515E-07
1287 8.87 5.7933 1.767 1.958E+12 25019280 1.3641E-05
1404 9.35 6.4434 1.9652 5.466E+11 27293760 6.3575E-05
1520 10.2 7.6782 2.3418 6.667E+10 29548800 0.00050678
1642 10.96 8.8728 2.7062 1.176E+10 31920480 0.0032217
1764 11.72 10.153 3.0966 2.333E+09 34292160 0.01791874
1881 12.3 11.187 3.4121 728335733 36566640 0.06812449
1992 13.24 12.969 3.9557 123581284 38724480 0.38147679
2103 13.85 14.196 4.3298 41786631 40882320 1.35983564
(a)
Figures (9(a, b, c)) show the M-N curve for the three TSRs. As found from these figures and
tables (2), (3), and (4), TSR 2 as expected has a high fatigue strength as compared with
TSR4, TSR5.
Hussein, A. N. & Sadkhan, B. A. Journal of Global Scientific Research (ISSN: 2523-9376) 2021/ 6 (6) 1493
(b)
(c)
Figure (9): M-N curve for ((a) TSR2, (b) TSR4, (c) TSR5).
4.3. 3D Plots
It was found that 3D plots are useful tools
to explain the relationship between three
variables. There are a few remarkable
points has been noticed from the results;
so, 3D plots were used to present them.
The remarkable points are listed as
follows:
1. The increase in wind velocity leads
to an increase in the amplitude moment
effect on the blades. This will reduce the
number of cycle to failure. Figures (10(a,
b, c)) show the relationship between the
wind velocity, amplitude moment, and the
number of cycle to failure of the wind
turbine blade for TSR (2, 4, and 5). For
example; by taking wind velocity of 8 m/s
it was found that the amplitude moment
was 4.6 N.m and the number of cycle to
failure was 2.878*1013
for TSRs 2, 4, 5.
This means that the wind velocity has the
same effect on the wind turbine blade.
2. The increase at the moment leads
to a decrease in the number of cycle to
failure and an increasing in damage.
Figures (11 (a, b, c)) show the relationship
between the amplitude moment, the
Hussein, A. N. & Sadkhan, B. A. Journal of Global Scientific Research (ISSN: 2523-9376) 2021/ 6 (6) 1494
number of cycle to failure, and the damage
occurs at the wind turbine blade for TSR
(2, 4, and 5). For example; by taking
amplitude moment 4.3298 N.m the number
of cycle to failure was found 41786631 for
the three TSRs but the damage will be
1.3327, 1.38215, and 1.3598 for TSR 2, 4,
and 5 respectively.
3.
(a)
(b)
(c)
Figure (10): The relationship between the wind velocity, amplitude moment, and the number
of cycles to failure for (a) TSR 2, (b) TSR 4, (c) TSR5.
Hussein, A. N. & Sadkhan, B. A. Journal of Global Scientific Research (ISSN: 2523-9376) 2021/ 6 (6) 1495
(a)
(b)
(c)
Figure (11): The relationship between the moment, number of cycles to failure, and damage
for (a) TSR 2, (b) TSR 4, (c) TSR 5.
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4.4. Damage, Time and Fracture Location
Three, four, and six blades were operated by the test rig at the higher speed in this study,
which is (13.85 m/s) for 12 hours/day. Figure (12) shows that TSR2 has a higher fatigue life
as compared with TSR4, TSR5. The TSR2 fails after 30 days/12 hours; while TSR4 fails 26
days/12 hours and TSR5 fails 27 days/12 hours. Figure (13) shows a comparison between the
three TSRs at wind velocity (10.96 m/s). This velocity was in the range of wind velocity in
Iraq. The damage reaches 1 at 16 years for TSR2, 15 years for TSR5, and 14 years for TSR4.
If the blades rotate at a wind velocity of less than 10.96 m/s, it will have an infinity life.
Figure (12): A comparison between the three TSRs at 13.85 m/s.
Figure (13): A comparison between the three TSRs at 10.96 m/s.
The damage was found at the bounding joints between the ring and the blades as shown in the
figures (14) and (15). The adhesive material was made from the same material as the blades.
Its failure leads to excessive vibration and cyclic loading that acts on the wind turbine. TSR 5
with 3 blades does not fail after 27 days/12 hours. So, the blade takes a long time to fail.
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Figure (14): The Failure in 6 Blades Wind Turbine.
Figure (15): The Failure in 4 Blades Wind Turbine.
4.5. Fatigue Results
The five steps increasing loading program (4.5, 5, 5.5, 6, and 6.5). The number of cycles.
Figure (16) shows the block representation and damage results with the amplitude moment of
the test. From the increasing load program, it was noticed that the damage increase by
increasing the load on the specimen. The test gives a damage value of more than one.
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Figure (16): Increasing block diagram of fatigue test.
5. Conclusions
Power from wind is considered the best
source of non-pollution renewable energy.
A prototype of the blade was used to find
the effect of the three Tip Speed Ratios on
the fatigue life of wind turbine blades. The
results were obtained for three Tip Speed
Ratios (2, 4, 5) with a different number of
blades (6, 4, 3) respectively. It was
concluded:
1. The behavior of the M-N curve shows
that tip speed ratio TSR2 has high fatigue
strength and fatigue life as compared with
tip speed ratios 4 and 5.
2. The damage increases by increasing
the number of loading cycles after a time.
3. When the wind speed reaches 10.96
m/s, tip speed ratios 2, 4, 5 will fail in 16,
14, 15 years respectively because of the
increase in the rotational speed and
moment and decreases in the number of
cycle to failure.
4. Tip Speed Ratio 2 has been damaged
at 13.85 m/s wind speed after 30 days; but,
Tip Speed Ratio 4, 5 have been damaged
after 26 and 27 days respectively at the
same wind speed.
5. The damage was found at the
bounding joints between the ring and the
blades.
For future work, using vertical axis wind
turbine and other types of blades
manufactured from composite materials
with different tip speed ratios.
6 .Acknowledgment
The authors would like to thank Al-
Mustansiriyah University, College of
Engineering / Mechanical Engineering
Department for academic guidance and
support and the electromechanical
engineering department and the material
engineering department at the university of
technology.
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