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energies
Review
Studies on Cup Anemometer Performances Carried
out at IDR/UPM Institute. Past and Present Research
Elena Roibas-Millan 1ID , Javier Cubas 1,2 ID and Santiago Pindado 1, 2, *ID
1Instituto Universitario de Microgravedad “Ignacio Da Riva” (IDR/UPM), ETSI Aeronáutica y del Espacio,
Universidad Politécnica de Madrid, Pza. del Cardenal Cisneros 3, 28040 Madrid, Spain;
elena.roibas@upm.es (E.R.-M.); j.cubas@upm.es (J.C.)
2Departamento de Sistemas Aeroespaciales, Transporte Aéreo y Aeropuertos (SATAA), ETSI Aeronáutica
y del Espacio, Universidad Politécnica de Madrid, Pza. del Cardenal Cisneros 3, 28040 Madrid, Spain
*Correspondence: santiago.pindado@upm.es; Tel.: +34-913-36-63-53
Received: 20 September 2017; Accepted: 9 November 2017; Published: 14 November 2017
Abstract:
In the present work, the research derived from a wide experience on cup anemometer
calibration works at IDR/UPM Institute (Instituto Universitario de Microgravedad “Ignacio Da Riva”)
is summarized. This research started in 2008, analyzing large series of calibrations, and is focused
on two main aspects: (1) developing a procedure to predict the degradation level of these wind
sensors when working on the field and (2) modeling cup anemometer performances. The wear and
tear level of this sensor is evaluated studying the output signal and its main frequencies through
Fourier analysis. The modeling of the cup anemometer performances is carried out analyzing first
the cup aerodynamics. As a result of this process, carried out through several testing and analytical
studies since 2010, a new analytical method has been developed. This methodology might represent
an alternative to the classic approach used in the present standards of practice such as IEC 64000-12.
Keywords:
cup anemometer; wind speed measurements; calibration process; Fourier analysis;
IDR/UPM Institute
1. Introduction
Since 1997, the IDR/UPM Institute (Instituto Universitario de Microgravedad “Ignacio Da Riva”) has
performed high level standardized calibrations to wind speed sensors, mainly for the wind energy
sector and Spanish meteorology institutions. LAC-IDR/UPM is the calibration laboratory within this
research institute, which is accredited according to ISO/IEC 17025 standard and is a member of the
Measuring Network of Wind Energy Institutes (MEASNET) since 2003.
The line of work related to wind speed sensors calibration represents, together with space
engineering [
1
–
11
], wind engineering [
12
–
17
], and different high education degree programs such
as the Master in Space Systems [
18
–
21
], the core of the activities being carried out by the IDR/UPM
research institute’s staff.
With regard to the aforementioned wind speed sensors calibration, this line of work has produced a
strong research, mainly focused on cup anemometers (see Figure 1) [
22
–
34
]. Additionally, some relevant
research devoted to sonic anemometers has been carried out at IDR/UPM [
35
–
39
]. Although other
wind speed sensors such as the aforementioned sonic anemometer, LIDAR, SODAR, and nacelle
anemometers, have been thoroughly developed and studied in order to substitute the cup anemometer
along the past decades [
40
–
59
], this old fashioned but robust and reliable instrument (see Figure 1)
developed by T.R. Robinson in the 19th century [60–63], remains the most demanded and used wind
sensor for meteorologists and within the wind energy sector.
Energies 2017,10, 1860; doi:10.3390/en10111860 www.mdpi.com/journal/energies
Energies 2017,10, 1860 2 of 17
Energies 2017, 10, 1860 2 of 18
Figure 1. Old Robinson cup anemometer (a) and Thies Clima 4.3350 cup anemometer (b).
In addition, it should be pointed out that the demand of cup anemometers might increase, as
the wind energy installed power has been continuously growing in the last years (see Figure 2). This
fact also involves a huge demand for calibration of these sensors because any lack of accuracy in
relation to the measured wind speed by an anemometer installed on a wind generator will have a
major impact on the economic revenue (the extractable wind power is proportional to third power of
the wind speed).
Figure 2. Installed wind power in some of the most relevant countries (a) and its annual growth (b).
Source: Global Wind Energy Council.
In this work, the research activities related to cup anemometer performance analysis carried out
at IDR/UPM are reviewed. The work is organized as follows: the experimental analyses and results
based on the huge calibrations database of the LAC-IDR/UPM are described in Section 2. In Section
(a) (b)
0
20
40
60
80
100
120
140
160
180
2004 2006 2008 2010 2012 2014 2016 2018
Installed
Wind Power
[GW]
Year
China
USA
Germany
Spain
India
UK
Canada
Brazil
Denmark
0.01
0.1
1
10
100
1000
2004 2006 2008 2010 2012 2014 2016 2018
Installed
Wind Power.
Annual
Growth
[GW]
Yea r
China
USA
Germany
Spain
India
UK
Canada
Brazil
Denmark
(a) (b)
Figure 1. Old Robinson cup anemometer (a) and Thies Clima 4.3350 cup anemometer (b).
In addition, it should be pointed out that the demand of cup anemometers might increase, as the
wind energy installed power has been continuously growing in the last years (see Figure 2). This fact
also involves a huge demand for calibration of these sensors because any lack of accuracy in relation to
the measured wind speed by an anemometer installed on a wind generator will have a major impact on
the economic revenue (the extractable wind power is proportional to third power of the wind speed).
Energies 2017, 10, 1860 2 of 18
Figure 1. Old Robinson cup anemometer (a) and Thies Clima 4.3350 cup anemometer (b).
In addition, it should be pointed out that the demand of cup anemometers might increase, as
the wind energy installed power has been continuously growing in the last years (see Figure 2). This
fact also involves a huge demand for calibration of these sensors because any lack of accuracy in
relation to the measured wind speed by an anemometer installed on a wind generator will have a
major impact on the economic revenue (the extractable wind power is proportional to third power of
the wind speed).
Figure 2. Installed wind power in some of the most relevant countries (a) and its annual growth (b).
Source: Global Wind Energy Council.
In this work, the research activities related to cup anemometer performance analysis carried out
at IDR/UPM are reviewed. The work is organized as follows: the experimental analyses and results
based on the huge calibrations database of the LAC-IDR/UPM are described in Section 2. In Section
(a) (b)
0
20
40
60
80
100
120
140
160
180
2004 2006 2008 2010 2012 2014 2016 2018
Installed
Wind Power
[GW]
Year
China
USA
Germany
Spain
India
UK
Canada
Brazil
Denmark
0.01
0.1
1
10
100
1000
2004 2006 2008 2010 2012 2014 2016 2018
Installed
Wind Power.
Annual
Growth
[GW]
Yea r
China
USA
Germany
Spain
India
UK
Canada
Brazil
Denmark
(a) (b)
Figure 2.
Installed wind power in some of the most relevant countries (
a
) and its annual growth (
b
).
Source: Global Wind Energy Council.
In this work, the research activities related to cup anemometer performance analysis carried out
at IDR/UPM are reviewed. The work is organized as follows: the experimental analyses and results
based on the huge calibrations database of the LAC-IDR/UPM are described in Section 2. In Section 3,
the analytical models and procedures developed at IDR/UPM to study the cup anemometer are
reviewed. Finally, conclusions are summarized in Section 4.
Energies 2017,10, 1860 3 of 17
2. Experimental Analyses of Cup Anemometer Performances
Historically, the first analyses of cup anemometer performance were carried out based on
experimental results, analyzing the performances [
64
–
67
] or searching for the optimum configuration
(number of cups, size
. . .
) [
68
–
71
]. A thorough review of the literature was carried out in previous
works [29,31].
In a first approach to anemometer performances, more than 3500 calibrations (performed at
IDR/UPM on 25 different cup anemometer models) were studied by Pindado et al. [
22
]. The calibration
of an anemometer involves the definition of its transfer function, which relates the measured wind
speed, V, to the cup anemometer’s output frequency, f.
V=Af+B. (1)
In the above equation, constants A (slope) and B (offset) are the ones that need to be defined by
means of a proper calibration. However, it should be pointed out that normally the output frequency
is not equal to the cup anemometer’s rotation frequency, f
r
, due to the different electronic systems used
to measure the rotation rate, which give a different number of pulses, m, along one turn of the rotor.
Therefore, Equation (1) should be referred to f
r
, in order to analyze the aerodynamic performances
properly (obviously, Ar=m·A in the above equation).
V=Arfr+B. (2)
In Figure 3, the results of two different calibration procedures, performed on the same Thies
4.3350 cup anemometer, are shown. The first procedure, the AC calibration procedure, strictly follows
MEASNET [
72
,
73
] requirements (13 measurement points taken within a wind speed bracket from
4 m
·
s
−1
to 16 m
·
s
−1
), whereas the second one, the AD calibration procedure, is an internal procedure
performed at the IDR/UPM Institute within a larger wind speed range and with less measurement
points taken (nine measurement points taken within a wind speed bracket from 4 m
·
s
−1
to 23 m
·
s
−1
).
This AD calibration procedure was developed at customers’ request.
Energies 2017, 10, 1860 3 of 18
3, the analytical models and procedures developed at IDR/UPM to study the cup anemometer are
reviewed. Finally, conclusions are summarized in Section 4.
2. Experimental Analyses of Cup Anemometer Performances
Historically, the first analyses of cup anemometer performance were carried out based on
experimental results, analyzing the performances [64–67] or searching for the optimum
configuration (number of cups, size…) [68–71]. A thorough review of the literature was carried out
in previous works [29,31].
In a first approach to anemometer performances, more than 3500 calibrations (performed at
IDR/UPM on 25 different cup anemometer models) were studied by Pindado et al. [22]. The
calibration of an anemometer involves the definition of its transfer function, which relates the
measured wind speed, V, to the cup anemometer’s output frequency, f.
A BVf=+
. (1)
In the above equation, constants A (slope) and B (offset) are the ones that need to be defined by
means of a proper calibration. However, it should be pointed out that normally the output frequency
is not equal to the cup anemometer’s rotation frequency, fr, due to the different electronic systems
used to measure the rotation rate, which give a different number of pulses, m, along one turn of the
rotor. Therefore, Equation (1) should be referred to fr, in order to analyze the aerodynamic
performances properly (obviously, Ar = m·A in the above equation).
In Figure 3, the results of two different calibration procedures, performed on the same Thies
4.3350 cup anemometer, are shown. The first procedure, the AC calibration procedure, strictly
follows MEASNET [72,73] requirements (13 measurement points taken within a wind speed bracket
from 4 m·s−1 to 16 m·s−1), whereas the second one, the AD calibration procedure, is an internal
procedure performed at the IDR/UPM Institute within a larger wind speed range and with less
measurement points taken (nine measurement points taken within a wind speed bracket from 4
m·s−1 to 23 m·s−1). This AD calibration procedure was developed at customers’ request.
Figure 3. Two different calibrations performed on the same Thies Clima 4.3350 cup anemometer (see
Figure 1): AC calibration (13 measurement points taken within a wind speed bracket from 4 m·s−1 to
16 m·s−1) and AD calibration (nine measurement points taken within a wind speed bracket from
4 m·s−1 to 23 m·s−1). The transfer function related to the AC calibration has been included in the graph.
The coefficient of determination related to this linear fitting, R2, is also included in the graph (AC
calibrations require high values of this coefficient).
Two important conclusions were derived as a result of this work:
V= 0.04759 f+ 0.26993
R
2
= 0.99998
0
5
10
15
20
25
0 100 200 300 400 500
V
[m s
−1
]
f[Hz]
AC-calibration
AD-calibration
AB
rr
Vf=+. (2)
Figure 3.
Two different calibrations performed on the same Thies Clima 4.3350 cup anemometer
(see Figure 1): AC calibration (13 measurement points taken within a wind speed bracket from 4 m
·
s
−1
to 16 m
·
s
−1
) and AD calibration (nine measurement points taken within a wind speed bracket from
4 m
·
s
−1
to 23 m
·
s
−1
). The transfer function related to the AC calibration has been included in the
graph. The coefficient of determination related to this linear fitting, R
2
, is also included in the graph
(AC calibrations require high values of this coefficient).
Energies 2017,10, 1860 4 of 17
Two important conclusions were derived as a result of this work:
•
The differences between the AC and AD calibration procedures were negligible in terms of both
wind speed (with 2.6%, 0.88%, and 0.31% deviation at 5 m
·
s
−1
, 10 m
·
s
−1
, and 15 m
·
s
−1
wind
speed for the Thies anemometer referred in Figure 3) and wind power generator Annual Energy
Production (AEP);
•
The slope of the calibration curve, A
r
, seemed (in that work) to have a direct relationship with the
cups’ center rotation radius, R
rc
, (that is, with the anemometer’s rotor radius). This relationship
was also proven with an analytical model of the cup anemometer performance.
This last conclusion was checked with further studies at the IDR/UPM Institute by
Pindado et al. [
24
] and Sanz-Andres et al. [
29
]. In these works, the calibration constants were proven to be
dependent on geometric parameters of cup anemometer rotors, the following equations being derived:
Ar=dAr
dRrc
Rrc +Ar0=dAr
dRrc
Rrc −Scζ+ηS−ξ
c, (3)
B=dB
dRrc
Rrc +B0=ε+φS−γ
cRrc −µS−ψ
c, (4)
where R
rc
is the cups’ center rotation radius, S
c
, stands for the cups front area, and R
c
is the cups radius
(see Figure 4). The other terms present in the above equations:
ζ η
,
ξ
,
ε
,
φ
,
γ
,
µ
, and
ψ
are parameters
to be extracted from experimental data.
Energies 2017, 10, 1860 4 of 18
• The differences between the AC and AD calibration procedures were negligible in terms of both
wind speed (with 2.6%, 0.88%, and 0.31% deviation at 5 m·s
−1
, 10 m·s
−1
, and 15 m·s
−1
wind speed
for the Thies anemometer referred in Figure 3) and wind power generator Annual Energy
Production (AEP);
• The slope of the calibration curve, A
r
, seemed (in that work) to have a direct relationship with
the cups’ center rotation radius, R
rc
, (that is, with the anemometer’s rotor radius). This
relationship was also proven with an analytical model of the cup anemometer performance.
This last conclusion was checked with further studies at the IDR/UPM Institute by Pindado et
al. [24] and Sanz-Andres et al. [29]. In these works, the calibration constants were proven to be
dependent on geometric parameters of cup anemometer rotors, the following equations being
derived:
where R
rc
is the cups’ center rotation radius, S
c
, stands for the cups front area, and R
c
is the cups
radius (see Figure 4). The other terms present in the above equations: ζ η, ξ, ε, φ, γ, μ, and ψ are
parameters to be extracted from experimental data.
Figure 4. Sketch of a cup anemometer. The more important dimensions of the rotor, the cups’ center
rotation radius, R
rc
, and the cups radius, R
c
, are indicated in the figure.
In the mentioned work by Pindado et al. [24], two anemometers (Climatronics 100075 and
Ornytion 107A, see pictures in Figure 5), were calibrated several times equipped with different
rotors (varying the size of the same conical-shape cups and their distance to the rotation axis, i.e.,
R
rc
). One of the most relevant conclusions of this study was that the slope dA
r
/dR
rc
only depends on
the cups shape and not on their size (see Figure 5). Furthermore, in the analysis carried out by
()
0
dA dA
AA
dd
rr
rrcr rccc
rc rc
RRSS
RR
−ξ
=+=−ζ+η
, (3)
()
0
dB
BB
d
rc c rc c
rc
RSRS
R
−γ −ψ
=+=ε+φ−μ
, (4)
Rrc
2·Rc
Figure 4.
Sketch of a cup anemometer. The more important dimensions of the rotor, the cups’ center
rotation radius, Rrc, and the cups radius, Rc, are indicated in the figure.
In the mentioned work by Pindado et al. [
24
], two anemometers (Climatronics 100075 and
Ornytion 107A, see pictures in Figure 5), were calibrated several times equipped with different rotors
(varying the size of the same conical-shape cups and their distance to the rotation axis, i.e., R
rc
).
One of the most relevant conclusions of this study was that the slope dA
r
/dR
rc
only depends on
Energies 2017,10, 1860 5 of 17
the cups shape and not on their size (see Figure 5). Furthermore, in the analysis carried out by
Sanz-Andres et al. [
29
], another important fact was revealed. The aerodynamic force on the cups
is not acting on their center and even more, the center of the cup is not the average location of the
aerodynamic center during one turn of the rotor (this has a quite important effect on the analytical
modeling of cup anemometer performances).
Energies 2017, 10, 1860 5 of 18
Sanz-Andres et al. [29], another important fact was revealed. The aerodynamic force on the cups is
not acting on their center and even more, the center of the cup is not the average location of the
aerodynamic center during one turn of the rotor (this has a quite important effect on the analytical
modeling of cup anemometer performances).
Figure 5. Climatronics 100075 with a R
c
= 30 mm and R
rc
= 100 mm rotor (a) and Ornytion 107A with a
R
c
= 30 mm and R
rc
= 40 mm rotor (b) cup anemometers. A
r
(c) and B (d) calibration coefficients (see
Equation (2)), in relation to the cups’ center rotation radius, R
rc
, for two different size conical cups (R
c
= 25 mm and R
c
= 80 mm).
y= 0.03x−0.2955
R² = 0.9998
y= 0.03x−0.4254
R² = 0.9997
0
1
2
3
4
20 40 60 80 100 120 140 160
A
r
R
rc
Rc = 25 mm
Rc = 80 mm
y= 0.0083x−0.1682
R² = 0.9933
y= 0.0019x+ 0.0306
R² = 0.9305
0
0.2
0.4
0.6
0.8
1
20 40 60 80 100 120 140 160
B
R
rc
Rc = 25 mm
Rc = 80 mm
(a) (b)
(c)
(d)
Figure 5.
Climatronics 100075 with a R
c
= 30 mm and R
rc
= 100 mm rotor (
a
) and Ornytion 107A with
aR
c
= 30 mm and R
rc
= 40 mm rotor (
b
) cup anemometers. A
r
(
c
) and B (
d
) calibration coefficients
(see Equation (2)), in relation to the cups’ center rotation radius, R
rc
, for two different size conical cups
(Rc= 25 mm and Rc= 80 mm).
Additionally, both the effect of the climatic conditions during the calibration process and cup
anemometer performance degradation after several months working on the field were analyzed in the
works by Pindado et al. [23,25]. The results of these analyses were as follows:
Energies 2017,10, 1860 6 of 17
•
Calibration constants, A and B, are affected by changes in air density, which, on the other hand,
is driven mostly by changes in air temperature;
•
These changes have a quite relevant impact on Annual Energy Production (AEP) estimations,
depending on the selected wind sensor. Deviations of AEP up to 18% and 8% at 4 m
·
s
−1
,
and 7 m
·
s
−1
wind speeds were calculated for 0.1 kg
·
m
−3
air density variations and first
class anemometers;
•The anemometers degrade in large storage periods;
•
Even showing a quite high level of wear and tear, it is quite difficult to establish degradation
patterns of anemometers working on the field.
The output signal of cup anemometers has been also thoroughly studied at IDR/UPM
Institute [26,30,31,34].
In steady wind the multi-pulse signal can be translated into a periodic rotation
speed that shows three accelerations (and three decelerations) per turn of the rotor (see Figure 6).
Therefore, from the pulsed-signal, it is possible to decompose the rotation rate of the anemometer,
ω
,
into a Fourier series within one rotation period (see Figure 6).
ω(t)=ω0+ω1sin(ω0t+ϕ1)+ω2sin(2ω0t+ϕ2)+ω3sin(3ω0t+ϕ3). . . =
ω0+
∞
∑
i=1
ωisin(iω0t+ϕi), (5)
where iis the number of the harmonic term,
ωi
its magnitude, and
φi
its phase angle (or
angular deviation).
In the above equation, two important facts should be taken into account. First of all, the most
relevant harmonic terms are the ones which are multiples of three, since due to the shape of the
rotor (equipped with three cups) it accelerates three times per turn. Besides, all the other terms are
noise due to turbulence or the wake downstream the anemometer’s body interaction with the rotor,
with the obvious exception of the constant term,
ω0
, that gives the average rotation speed, and the
first harmonic term,
ω1
, which reflects the perturbations that are repeated periodically once per turn.
See the previous works by IDR/UPM Institute researchers [26,30,31].
The analysis of this first harmonic term has revealed itself as a very promising way to monitor
the anemometer working condition. A quite relevant percentage of anemometers that are removed
from a wind power generator for a recalibration process are damaged [
74
]. In Figure 7, a damaged
A100 LK cup anemometer is shown, together with its calibration curve. This curve is compared to
the one obtained with the anemometer equipped with a non-damaged rotor. In the top-right graph
included in Figure 7, it can be observed that only a slight difference in the calibration curve is obtained,
although the economic impact of this tiny deviation on a wind power plant could be huge. On the
other hand, the damage is perfectly revealed by the first harmonic term (shown in the bottom-right
graph of the figure).
Furthermore, a damaged cup anemometer might remain in a static position, that is, not-rotating,
under normal or strong winds if one of the cups is missing or severely damaged. This can be a quite
relevant problem, as the anemometer could still generate a pulsed signal that might be translated
by the data-logger into a wind speed. The pulsed signal is generated by a small rotor-oscillation
movement produced by the wake of the anemometer’s neck interacting with the rotor. Even worse,
this completely wrong signal depends linearly on the wind speed and could induce a wind power
generator to work out of the maximum efficiency point in case this problem is not anticipated, as shown
by Pindado et al. [32].
Finally, the harmonic distribution of the rotor movement in steady wind speed represents a
signature that defines a cup anemometer. Analyzing large series of two commercial cup anemometers
calibrated at IDR/UPM facility, different patterns of the first and third harmonic terms statistical
distribution were observed [
34
] (see Figure 8). The analysis of these frequency histograms might
be used for quality control processes related to cup anemometer industrial production, as the best
Energies 2017,10, 1860 7 of 17
quality processes ensure a lower level of deviation among performances of different units of the same
model (that is, a larger deviation of the harmonic histograms indicates greater differences on the
unit’s performances).
Energies 2017, 10, 1860 7 of 18
statistical distribution were observed [34] (see Figure 8). The analysis of these frequency histograms
might be used for quality control processes related to cup anemometer industrial production, as the
best quality processes ensure a lower level of deviation among performances of different units of the
same model (that is, a larger deviation of the harmonic histograms indicates greater differences on
the unit’s performances).
Figure 6. Voltage output signal, u
out
, from a Climatronics 100075 cup anemometer (a). The rotation
rate derived from that signal is included in the (b) graph, whereas the Fourier series extracted from
the rotation rate is included in the (c) graph, where the harmonic terms, ω
i
/ω
0
, are compared (see also
Equation (5)).
Figure 7. Damaged A100 LK cup anemometer after service period (a). Calibration curve of this
anemometer compared to the one of that anemometer equipped with a non-damaged rotor (b).
Fourier series decomposition of the aforementioned cup anemometer rotation rate along one turn of
the rotor, see Equation (5) (c).
0.0
1.5
3.0
4.5
6.0
0 0.2 0.4 0.6 0.8 1
u
out
t/T
0.9
1.0
1.1
0 0.2 0.4 0.6 0.8 1
ω
/
ω
0
t/T
0.0
0.1
0246810
ω
i
/
ω
0
i
(a)
(b)
(c)
2
6
10
14
4 6 8 10 12 14 16
f
r
[Hz]
V[m s
−1
]
Damaged rotor
Non-damaged rotor
0%
1%
2%
3%
012345678910
ω
i
/
ω
0
i
Damaged rotor
Non-damaged rotor
(a)
(b)
(c)
Figure 6.
Voltage output signal, u
out
, from a Climatronics 100075 cup anemometer (
a
). The rotation
rate derived from that signal is included in the (
b
) graph, whereas the Fourier series extracted from the
rotation rate is included in the (
c
) graph, where the harmonic terms,
ωi
/
ω0
, are compared (see also
Equation (5)).
Energies 2017, 10, 1860 7 of 18
statistical distribution were observed [34] (see Figure 8). The analysis of these frequency histograms
might be used for quality control processes related to cup anemometer industrial production, as the
best quality processes ensure a lower level of deviation among performances of different units of the
same model (that is, a larger deviation of the harmonic histograms indicates greater differences on
the unit’s performances).
Figure 6. Voltage output signal, u
out
, from a Climatronics 100075 cup anemometer (a). The rotation
rate derived from that signal is included in the (b) graph, whereas the Fourier series extracted from
the rotation rate is included in the (c) graph, where the harmonic terms, ω
i
/ω
0
, are compared (see also
Equation (5)).
Figure 7. Damaged A100 LK cup anemometer after service period (a). Calibration curve of this
anemometer compared to the one of that anemometer equipped with a non-damaged rotor (b).
Fourier series decomposition of the aforementioned cup anemometer rotation rate along one turn of
the rotor, see Equation (5) (c).
0.0
1.5
3.0
4.5
6.0
0 0.2 0.4 0.6 0.8 1
u
out
t/T
0.9
1.0
1.1
0 0.2 0.4 0.6 0.8 1
ω
/
ω
0
t/T
0.0
0.1
0246810
ω
i
/
ω
0
i
(a)
(b)
(c)
2
6
10
14
4 6 8 10 12 14 16
f
r
[Hz]
V[m s
−1
]
Damaged rotor
Non-damaged rotor
0%
1%
2%
3%
012345678910
ω
i
/
ω
0
i
Damaged rotor
Non-damaged rotor
(a)
(b)
(c)
Figure 7.
Damaged A100 LK cup anemometer after service period (
a
). Calibration curve of this
anemometer compared to the one of that anemometer equipped with a non-damaged rotor (
b
).
Fourier series decomposition of the aforementioned cup anemometer rotation rate along one turn of
the rotor, see Equation (5) (c).
Energies 2017,10, 1860 8 of 17
Energies 2017, 10, 1860 8 of 18
Figure 8. First and third harmonic terms, ω1/ω0 and ω3/ω0, histograms from large series of two first
class cup anemometers calibrated at Instituto Universitario de Microgravedad “Ignacio Da Riva”
(IDR/UPM): Anemometer-1 and Anemometer-2.
3. Modeling Cup Anemometer Performances
As far as the authors’ knowledge, the first analytical model developed to study cup
anemometer performances was proposed by Chree by the end of the 19th century [75]. After that,
Schrenk [76] developed the classic model that was initially used by the IDR/UPM staff to study the
cup anemometer behavior [22,29]. Since 2012, a new analytical model that takes into account the
aerodynamic forces on the three cups of the rotor has been developed at IDR/UPM Institute
[24,27,31,33]. At this point, it might be necessary to underline the importance of the analytical
models. These models reproduce the behavior of complex processes (related to mechanics,
thermodynamics, fluid mechanics, etc.), with quite simple equations that preserve the physics of the
problem. In the present case, the goal is to analyze the performance of a rotor based on the cups’
aerodynamics.
The aforementioned model, developed in our previous works, is derived from the equation that
defines the performance, that is, the rotation rate, ω, of a cup anemometer.
where I is the moment of inertia of the rotor, QA is the aerodynamic torque, and Qf is the frictional
torque that depends on the air temperature and the rotation rate [31]. The frictional torque is
normally neglected, as its effect is only important at very low wind speeds (out of the calibration
d
d
A
f
IQQ
t=+
ω
, (6)
0%
10%
20%
30%
40%
50%
4 m/s
7 m/s
10 m/s
16 m/s
0%
10%
20%
30%
40%
50%
4 m/s
7 m/s
10 m/s
16 m/s
0%
10%
20%
30%
40%
50%
4 m/s
7 m/s
10 m/s
16 m/s
0%
10%
20%
30%
40%
50%
4 m/s
7 m/s
10 m/s
16 m/s
Anemometer 1: ω1/ω0 Anemometer 2:
ω
1/
ω
0
Anemometer 1:
ω
3/
ω
0 Anemometer 2:
ω
3/
ω
0
Figure 8.
First and third harmonic terms,
ω1
/
ω0
and
ω3
/
ω0
, histograms from large series of two
first class cup anemometers calibrated at Instituto Universitario de Microgravedad “Ignacio Da Riva”
(IDR/UPM): Anemometer-1 and Anemometer-2.
3. Modeling Cup Anemometer Performances
As far as the authors’ knowledge, the first analytical model developed to study cup anemometer
performances was proposed by Chree by the end of the 19th century [
75
]. After that, Schrenk [
76
]
developed the classic model that was initially used by the IDR/UPM staff to study the cup anemometer
behavior [
22
,
29
]. Since 2012, a new analytical model that takes into account the aerodynamic forces
on the three cups of the rotor has been developed at IDR/UPM Institute [
24
,
27
,
31
,
33
]. At this point,
it might be necessary to underline the importance of the analytical models. These models reproduce
the behavior of complex processes (related to mechanics, thermodynamics, fluid mechanics, etc.),
with quite simple equations that preserve the physics of the problem. In the present case, the goal is to
analyze the performance of a rotor based on the cups’ aerodynamics.
The aforementioned model, developed in our previous works, is derived from the equation that
defines the performance, that is, the rotation rate, ω, of a cup anemometer.
Idω
dt=QA+Qf, (6)
where Iis the moment of inertia of the rotor, Q
A
is the aerodynamic torque, and Q
f
is the frictional
torque that depends on the air temperature and the rotation rate [
31
]. The frictional torque is normally
neglected, as its effect is only important at very low wind speeds (out of the calibration range). If the
three cups of the rotor are taken into account the previous equation can be rewritten as follows:
Idω
dt=1
2ρScRrcV2
r(θ)cN(α(θ)) +1
2ρScRrcV2
r(θ+120◦)cN(α(θ+120◦))+
+1
2ρScRrcV2
r(θ+240◦)cN(α(θ+240◦))
, (7)
Energies 2017,10, 1860 9 of 17
where V
r
is the wind speed relative to the cups, c
N
is the aerodynamic normal force coefficient,
α
is the
wind direction with respect to the cups, and
θ
is the angle of the rotor with respect to a reference line
(see sketch in Figure 9). The relative-to-the-cup wind speed can be expressed as:
Vr(θ)=qV2+(ωRrc)2−2VωRrc cos(θ). (8)
Energies 2017, 10, 1860 10 of 18
Figure 9. Normal aerodynamic force coefficient, c
N
, of the Brevoort & Joyner Type-II (conical)
cups [77]. See in the sketch the variables involved in the rotation of an anemometer cup: normal
aerodynamic force on the cup, N, wind speed, V, relative wind speed to the cup, V
r
, rotor rotation
angle, θ, rotor rotational speed, ω, and wind direction with respect to the cup, α. The 1-harmonic
term Fourier series approximation (Equation (12)) to the Type-II cup has been plotted, together with
the more accurate 6-harmonic terms Fourier series approximation.
Besides, the relationship between α and θ angles, previously defined by Equation (9), can be
approximated as follows:
() () () ()
23
01 2 3
cos cos cos cos ...
αηη θη θ η θ
=+ + +
(13)
where:
Taking into account the above equations, the following expression can be derived from (7) in
order to relate the anemometer factor, K, to the aerodynamic coefficients of the rotor cups:
In Figure 10 the anemometer factor of several cases that were measured in wind tunnel (one
anemometer, Climatronics 100075, equipped with different rotors in which the characteristics of the
2
01 23
22
22 2 2
111
; ; ;
11
11 1 1
KKK
KK
KK K K
ηη ηη
−
==−==−
−−
++ + +
. (14)
2
11
2 2
22
00
11111 34
01 1
24 1
11
cc
KK
Kc cK K
KK
−
=+ − − +
−
++
. (15)
Figure 9.
Normal aerodynamic force coefficient, c
N
, of the Brevoort & Joyner Type-II (conical) cups [
77
].
See in the sketch the variables involved in the rotation of an anemometer cup: normal aerodynamic
force on the cup, N, wind speed, V, relative wind speed to the cup, V
r
, rotor rotation angle,
θ
,
rotor rotational speed,
ω
, and wind direction with respect to the cup,
α
. The 1-harmonic term Fourier
series approximation (Equation (12)) to the Type-II cup has been plotted, together with the more
accurate 6-harmonic terms Fourier series approximation.
On the other hand, it is possible to derive an equation that correlates both the wind direction
angle, α, and the position angle θ.
tan(α)=Ksin(θ)
Kcos(θ)−1. (9)
In the above equation, the constant K is called the anemometer factor and it represents the ratio
between the wind speed and the speed of the center of the cups.
K=V
ωRrc
=Arfr+B
2πfrRrc
=Ar
2πRrc
1
1−B
V. (10)
Taking into account that the offset B is below 0.6 m
·
s
−1
for most commercial anemometers in the
wind energy sector [22], it can be assumed that
K=Ar
2πRrc . (11)
Energies 2017,10, 1860 10 of 17
The aerodynamic force coefficient related to the cups, c
N
, can be obtained, in a first
approximation, from static measurements (that is, with no rotation of the cup) in wind tunnel [
77
].
However, this approach does not take into account the aerodynamic effect produced by the rotating
flow over the cup. The aerodynamic force coefficient, c
N
, can be expressed in terms of Fourier series,
as it is a periodic function. See in Figure 9the 1-harmonic and 6-harmonic terms Fourier series
compared to the coefficient related to a conical cup experimentally measured. If the 1-harmonic
equation is considered,
cN(α)=c0+c1cos(α). (12)
Besides, the relationship between
α
and
θ
angles, previously defined by Equation (9), can be
approximated as follows:
cos(α)=η0+η1cos(θ)+η2cos(θ)2+η3cos(θ)3. . . (13)
where:
η0=−1
√1+K2;η1=K
√1+K2−1
K2−1;η2=1
√1+K2;η3=K2
K2−1−K
√1+K2. (14)
Taking into account the above equations, the following expression can be derived from (7) in
order to relate the anemometer factor, K, to the aerodynamic coefficients of the rotor cups:
0=1+1
K21−1
2
c1
c0
1
√1+K2−1
4
c1
c0
1
KK
√1+K2+3K2−4
K2−1. (15)
In Figure 10 the anemometer factor of several cases that were measured in wind tunnel (one
anemometer, Climatronics 100075, equipped with different rotors in which the characteristics of the
cups have been varied) are compared to the above equation. Results from of Equation (15) seem to
reflect the tendencies shown by the testing results, with 13% average error [27].
Energies 2017, 10, 1860 11 of 18
cups have been varied) are compared to the above equation. Results from of Equation (15) seem to
reflect the tendencies shown by the testing results, with 13% average error [27].
Figure 10. Results of the developed analytical model (Equation (15)), compared to testing results. In
the graph, the anemometer factors, K, measured and calculated from anemometers equipped with
the same rotor varying only the aerodynamic characteristics of the cups, are plotted as a function of
those aerodynamic characteristics c0/c1 (see Equation (12)).
However, this model presents a drawback, as it gives a single value of K without taking into
account the geometric characteristics of the rotor (that affects the anemometer performance, as
shown by Equations (3) and (4)). This was already observed in previous research campaigns at
IDR/UPM, in which the effect of the ratio of the cups’ radius, Rc, to the cups’ center rotation radius,
Rrc, defined as:
was observed. In order to improve the model two effects were considered after an analysis campaign
carried out by using Computer Fluid Dynamics (CFD) [78]. First of all, a phase angle δ was
considered in relation to the aerodynamic force coefficient.
Additionally, the aerodynamic force on the cup was not considered to be applied on the cups
center, a deviation from the center (see sketch in Figure 11) being introduced in the model instead
This deviation d was also considered to be displaced a phase angle γ with respect to the cup position
angle α in relation to the wind.
2
4
6
8
10
12
14
234567
K
c
1
/c
0
Analytical
3-cup model
Porous
h/R
c
= 0.48
Porous
h/R
c
= 0.38
Elliptical
a/b= 1.920
Elliptical
a/b= 1.440
Elliptical
a/b= 1.166
Conical
c
r
rc
R
rR
=, (16)
() ( ) () () () ()
() ()
01 01 1
011 12
cos cos cos sin sin
cos sin
N
ccc cc c
cc c
ααδδαδα
αα
=+ + =+ − =
+− . (17)
() ( ) () ( ) () ( )
() ()
11 12
sin cos sin sin cos
sin cos
c
dee e
R
ee
ααγ γ α γ α
αα
=+= + =
+
. (18)
Figure 10.
Results of the developed analytical model (Equation (15)), compared to testing results. In the
graph, the anemometer factors, K, measured and calculated from anemometers equipped with the
same rotor varying only the aerodynamic characteristics of the cups, are plotted as a function of those
aerodynamic characteristics c0/c1(see Equation (12)).
However, this model presents a drawback, as it gives a single value of Kwithout taking into
account the geometric characteristics of the rotor (that affects the anemometer performance, as shown
Energies 2017,10, 1860 11 of 17
by Equations (3) and (4)). This was already observed in previous research campaigns at IDR/UPM,
in which the effect of the ratio of the cups’ radius, R
c
, to the cups’ center rotation radius, R
rc
, defined as:
rr=Rc
Rrc , (16)
was observed. In order to improve the model two effects were considered after an analysis campaign
carried out by using Computer Fluid Dynamics (CFD) [
78
]. First of all, a phase angle
δ
was considered
in relation to the aerodynamic force coefficient.
cN(α)=c0+c1cos(α+δ)=c0+c1cos(δ)cos(α)−c1sin(δ)sin(α)=
c0+c11 cos(α)−c12 sin(α). (17)
Additionally, the aerodynamic force on the cup was not considered to be applied on the cups
center, a deviation from the center (see sketch in Figure 11) being introduced in the model instead.
This deviation dwas also considered to be displaced a phase angle γwith respect to the cup position
angle αin relation to the wind.
d(α)
Rc
=esin(α+γ)=ecos(γ)sin(α)+esin(γ)cos(α)=
e11 sin(α)+e12 cos(α)
. (18)
This approach takes into account the aerodynamic forces produced by cup rotation, together
with the aforementioned forces derived from the cup direction with respect to the wind (that is,
the aforementioned aerodynamic forces measured in static position). Making reasonable assumptions,
this model was compared to testing results [
33
]. As it can be observed in Figure 11, the model was
able to predict cup anemometer performances quite accurately, taking into account the effect of the
geometric variable r
r
. Furthermore, it is also fair to mention that the model seems to be less accurate
for r
r
> 0.45, that is, for rotors in which the cups are closer to the rotation axis (in relation to the cups
size). In these cases, the rotation produces higher variations on the local wind speed around the cups,
and probably causes this deviation.
Energies 2017, 10, 1860 12 of 18
This approach takes into account the aerodynamic forces produced by cup rotation, together
with the aforementioned forces derived from the cup direction with respect to the wind (that is, the
aforementioned aerodynamic forces measured in static position). Making reasonable assumptions,
this model was compared to testing results [33]. As it can be observed in Figure 11, the model was
able to predict cup anemometer performances quite accurately, taking into account the effect of the
geometric variable r
r
. Furthermore, it is also fair to mention that the model seems to be less accurate
for r
r
> 0.45, that is, for rotors in which the cups are closer to the rotation axis (in relation to the cups
size). In these cases, the rotation produces higher variations on the local wind speed around the
cups, and probably causes this deviation.
Figure 11. (a) Sketch of the variables involved in the rotation movement of an anemometer’s cup. See
that the normal aerodynamic force, N, is considered to be deviated from the center of the cup.
(b) Anemometer factors, K, measured from anemometers equipped with different rotors (varying the
cups’ radius, R
c
, and the cups center rotation radius, R
rc
), in relation to the geometric ratio r
r
= R
c
/R
rc
.
In the graph, the results from the analytical model developed (Equation (15)) and its improved
version (Equations (17) and (18)) are included.
Going back to the cup anemometer’s signal in steady wind and bearing in mind the work
carried out in [31], it should be also pointed out that its Fourier series decomposition (Equation (5))
can be introduced in the general equation of the cup anemometer (Equation (7)), generating an
interesting equation that takes into account the third harmonic term.
As it is obvious, the second term at the right side of the above equation is indeed the
Equation (15), which gives the average rotation speed of the cup anemometer as a function of the
ratio c
1
/c
0
. Additionally, the remaining terms give information on the third harmonic term of the
rotation rate. The following equation can then be derived:
()
()
()
()
()
03
03
22
33
22
3
1
010 2 11 3
24
2
1
32
2
3
dsin 3
d
11
1
12
1cos3
4
crc crc
I
It
SRV t SRV
cc c
KK
c
KK
ωω
ωωϕ
ρρ
ηη ηη
ηη θ
=− +
=+ + + − +
++ −
. (19)
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0 0.2 0.4 0.6 0.8 1
K
r
r
Aanalytica (eq. (15)
Analytical (improved)
Rc = 20 mm
Rc = 25 mm
Rc = 30 mm
Rc = 35 mm
Rc = 40 mm
(
a
)
(
b
)
Figure 11.
(
a
) Sketch of the variables involved in the rotation movement of an anemometer’s cup.
See that the normal aerodynamic force, N, is considered to be deviated from the center of the cup.
(
b
) Anemometer factors, K, measured from anemometers equipped with different rotors (varying the
cups’ radius, R
c
, and the cups center rotation radius, R
rc
), in relation to the geometric ratio r
r
=R
c
/R
rc
.
In the graph, the results from the analytical model developed (Equation (15)) and its improved version
(Equations (17) and (18)) are included.
Energies 2017,10, 1860 12 of 17
Going back to the cup anemometer’s signal in steady wind and bearing in mind the work carried
out in [
31
], it should be also pointed out that its Fourier series decomposition (Equation (5)) can be
introduced in the general equation of the cup anemometer (Equation (7)), generating an interesting
equation that takes into account the third harmonic term.
I
3
2ρScRrcV2
dω
dt=−I3ω0ω3
3
2ρScRrcV2sin(3ω0t+ϕ3)
=1+1
K2(c0+c1(η0+1
2η2)) −1
Kc1(η1+3
4η3)
+1+1
K2η3−2
Kη2c1
4cos(3θ)
. (19)
As it is obvious, the second term at the right side of the above equation is indeed the Equation (15),
which gives the average rotation speed of the cup anemometer as a function of the ratio c
1
/c
0
.
Additionally, the remaining terms give information on the third harmonic term of the rotation rate.
The following equation can then be derived:
ω3
ω0=π
8ρR5
rc
I
K2+1η3−2Kη2
c1r2
r
≈π
8ρR5
rc
I0.5308c1
c0−1−1.599
−0.5c1r2
r
(20)
This is an important result that suggests the existence of a theoretical minimum for this third harmonic
term for c1/c0≈2.05.
Finally, the importance of modeling cup anemometer performances should be emphasized in
order to produce new improvements and designs that could increase the accuracy of the wind speed
measurements. In this sense, it is worth mentioning the work by Dahlberg et al. [
79
] that produced
in 2001 a new rotor design (Patent No.: US 2004/0083806 A1 [
80
], see Figure 12), or the one from
Thies Clima (Patent No.: EP 1489427 B1 [
81
]), or the more recent development by Hong in 2012 [
82
]
(Patent No.: US 2012/0266692 A1, see Figure 12).
Energies 2017, 10, 1860 13 of 18
This is an important result that suggests the existence of a theoretical minimum for this third
harmonic term for c1/c0 ≈ 2.05.
Finally, the importance of modeling cup anemometer performances should be emphasized in
order to produce new improvements and designs that could increase the accuracy of the wind speed
measurements. In this sense, it is worth mentioning the work by Dahlberg et al. [79] that produced in
2001 a new rotor design (Patent No.: US 2004/0083806 A1 [80], see Figure 12), or the one from Thies
Clima (Patent No.: EP 1489427 B1 [81]), or the more recent development by Hong in 2012 [82] (Patent
No.: US 2012/0266692 A1, see Figure 12).
(a) (b)
Figure 12. Examples of cups anemometer rotor design. Design by Dahlberg (Patent No.: US
2004/0083806 A1) (a), and design by Hong (Patent No.: US 2012/0266692 A1) (b).
4. Conclusions
In the present work, the research on cup anemometer performances carried out at IDR/UPM
has been summarized. This research has been focused on the following two aspects, although both
are related:
• The analysis of the performance based on experimental results as follows:
o Force on isolated cups;
o Calibrations performed on both commercial anemometers and anemometers equipped
with special-design rotors;
o The output signal of the cup anemometers.
• The analytical study of the cup anemometer performances with a new methodology developed
consequently. All expertise gained with the analysis of testing results was a fundamental basis
()
()
5
22
3
321
0
1.599
5
2
1
1
0
12
8
0.5308 1 0.5
8
rc
r
rc
r
RKKcr
I
Rccr
Ic
ωρ
πηη
ω
ρ
π
−
=+−
≈−−
. (20)
Figure 12.
Examples of cups anemometer rotor design. Design by Dahlberg (Patent No.:
US 2004/0083806 A1) (a), and design by Hong (Patent No.: US 2012/0266692 A1) (b).
Energies 2017,10, 1860 13 of 17
4. Conclusions
In the present work, the research on cup anemometer performances carried out at IDR/UPM has
been summarized. This research has been focused on the following two aspects, although both are
related:
•The analysis of the performance based on experimental results as follows:
#Force on isolated cups;
#
Calibrations performed on both commercial anemometers and anemometers equipped
with special-design rotors;
#The output signal of the cup anemometers.
•
The analytical study of the cup anemometer performances with a new methodology developed
consequently. All expertise gained with the analysis of testing results was a fundamental basis
for this analytical work. It should be underlined the importance of analytical models in order to
produce better sensors in the future, as by using these models, a reduction of costs (measured in
time and calculation resources) can be achieved in the first stages of the designing process.
For future works, some of them being in progress at the IDR/UPM Institute, it could be interesting
to analyze the performances of working-on-the-field cup anemometers, taking into account the
evolution of the rotation rate harmonic terms after long service periods of the wind sensor. Besides,
it should be also of great interest to understand the aerodynamic forces and pressure distribution on
rotating cups by means of experimental testing and CFD analysis.
Acknowledgments:
The authors are indebted to Enrique Vega, Alejandro Martínez, and Luis García for the
support in relation to the research work on cup anemometers. The authors are also grateful to Angel Sanz for
his contributions to the analytical studies on cup anemometers and all his work to create what is today the most
important wind speed sensors calibration facility in Spain.
Concerning international collaboration, Santiago Pindado is grateful to Chris Lacor and Alain Wery,
from Vrije Universiteit Brussel, for the support in several testing campaigns.
The authors are indebted to Victor Orozco and Daniel García, from Kintech Engineering, for their support
and collaboration in relation to the research on cup anemometer performance degradation.
The authors are also indebted to Anna María Ballester for her kind help in improving the style of the text.
The authors are grateful to the reviewers for their wise comments that helped us to improve the manuscript.
Finally, the present work is dedicated to the memory of Encarnación Meseguer, our beloved colleague who
was the LAC-IDR/UPM accounting manager and responsible for its quality assurance system. Thanks to her
courageous attitude, LAC-IDR/UPM became the most important wind speed sensors calibration facility in Spain.
We truly miss her each day.
Author Contributions:
All authors were equally involved in this work. Santiago Pindado selected the different
works to be reviewed. Elena Roibas-Millan and Javier Cubas wrote the text. Santiago Pindado revised the work in
order to organize it.
Conflicts of Interest: The authors declare no conflict of interest.
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