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Journal ArticleDOI

Wind loads on heliostats and photovoltaic trackers of various aspect ratios

01 Sep 2011-Solar Energy (Pergamon)-Vol. 85, Iss: 9, pp 2185-2201

AbstractFor the layout of solar trackers the wind loads on the structure have to be known. They can be calculated by using wind load coefficients given in literature. But so far these values are only valid for aspect ratios of the panel (width to height) of about 1.0. Therefore the wind load coefficients for heliostats of aspect ratios between 0.5 and 3.0 were determined to close this gap. As solar trackers are exposed to the turbulent atmospheric boundary layer the turbulence of the approaching flow has to be modeled. As a reliable method at reasonable cost wind tunnel measurements were chosen. Solar trackers of 30 m2 panel size were investigated at a model scale of 1:20. Wind direction and elevation angle of the panel were varied to investigate especially the constellations at which the highest wind loads are expected (critical load cases). By spires and roughness elements a wind profile and a turbulence intensity of the modeled wind according to typical sites for solar trackers were achieved. The loads were measured by a high frequency force balance placed underneath the models. Additionally measurements of the pressure distribution on a panel with aspect ratio of 1.2 were performed to better understand the effects that lead to the peak values of the wind load coefficients. A significant impact of the aspect ratio was measured. For the critical load cases the aspect ratio dependencies of the accordant peak wind load components were determined. By these the peak wind loads on solar trackers of varies aspect ratios can be calculated. Regarding the single solar tracker components the main results are: Higher aspect ratios are advantageous for the dimensioning of the foundation, the pylon and the elevation drive but disadvantageous for the azimuth drive.

Topics: Wind profile power law (63%), Wind direction (63%), Wind engineering (61%), Wind gradient (60%), Roughness length (60%)

Summary (4 min read)

1 Introduction

  • As photovoltaic (PV) and solar thermal power plants are getting more and more important for the world wide energy supply heliostats of central receiver power plants and PV trackers are build in rising quantities.
  • At the determination of the aspect ratio two contrary aims have to be taken into account:.
  • For a cost effective design of solar trackers therefore the impact of their aspect ratio concerning wind loads has to be known.
  • By their report the wind load coefficients for the main wind load components are available.

2.1 Selection of method

  • Theoretically, the wind loads could be determined at real scale heliostat models exposed to atmospheric wind.
  • Thus only simulation approaches at which at least the largest turbulence structures are captured are suitable (especially LES, Large Eddy simulation or DES, Detached Eddy Simulation) (Spalart, 2000).
  • For some cases it is possible to determine the peak loads by just multiplying the loads gained at attacking wind of no turbulence (measured or calculated) with the square of the gust factor R accordant to the turbulence intensity of the site (for a typical solar site turbulence intensity of 18% R=1.6) (Peterka and Derickson, 1992, pp. 5ff).
  • The second is the case for example for MHy at upright mirror orientation and frontal wind attack.
  • Also in this case CFD or wind tunnel measurements at attacking wind of no or low turbulence in combination with the gust factor approach would not lead to realistic results for the peak values.

2.2 Specifications

  • The mirror area (A=30m²) and the distance of the mirror plane to the ground at upright orientation (H-1/2h=0.4m) was the same for all aspect ratios.
  • This means that the elevation axis height H decreases with the aspect ratio.
  • Therefore H is explicitly given in the accordant formulas (table 2).
  • Nevertheless for ratios of ground distance to mirror area (H-1/2h)/A much different to the value of this study the results might not be valid.
  • The wind load components differ with the elevation of the panel α and of the wind direction β.

3.1 Similarity

  • In order to obtain realistic wind loads by means of wind tunnel tests the most significant modelling laws have to be accounted for.
  • For the determination in wind tunnels the micrometeorological fluctuations must be modeled according to the length scale.
  • The similarity of the approaching flow depends crucially on the upstream surface characteristics.
  • If the range of the frequencies of the actuating force would be in the range of the resonance frequency of the balance resonance raise would appear which would lead to too high measuring results.
  • With the force balance it is possible to determine the forces and moments at the pylon feet.

3.3 Pressure measurements

  • In addition to the measurements with the force balance pressure measurements were performed for a heliostat with the most common aspect ratio of 1.2 and with formed back structure .
  • The corresponding model was constructed using sophisticated three-dimensional printing technologies.
  • The mean and the fluctuating wind pressure on front and back side of the panel could be directly measured as a function of wind direction and elevation angle.
  • The measurements were performed simultaneously on front and back side and throughout the entire surface area of the panel in order to be able to determine the differential pressure directly.
  • For facet “A” the positions of the measuring points are given in table 1.

5.1 General

  • The values of Peterka and Derickson (1992) for ra = 1 are mostly considerably higher than measured by the authors.
  • If a heliostat model as described in (Peterka et al., 1986, p. 15) was used part of the reason would be the wide gaps between the three vertical facets.
  • The aspect ratio dependencies used in (16) and (17) and given in table 2 represent fitting curves of the measured data .

5.2 Fx – horizontal force perpendicular to elevation axis

  • For free standing plates on ground, the wind force coefficient decreases with the aspect ratio for aspect ratios < 5 (Sakamoto and Arie, 1983; Letchford and Holmes, 1994).
  • For slightly lifted plates this effect is little reduced .
  • In accordance (but more pronounced) a reduction of Fx for increasing aspect ratio was measured .
  • The effects causing the decrease of Fx with the aspect ratio at load case 1 are also valid in a reduced manner (because of the smaller area of attack of the projection of the panel in wind direction) for load case 2 .
  • Fy – horizontal force along elevation axis.

5.4 Fz – vertical force

  • The absolute values of Fz at load case 2 decrease slightly with the aspect ratio .
  • The reason might be that for bigger width b the gusts of maximal wind speed cover a smaller portion of the mirror plane.
  • Therefore the mean values of Fz are very low .
  • The peak values are caused by temporarily sideward wind attack which causes high pressure values at the frontal edge .
  • The high differences to (Peterka and Derickson, 1992) particularly at this case are not clear.

5.5 Mx - moment at pylon feet about x axis

  • For wind moments this leads to an almost constant aspect ratio dependency – also for at load case 5 .
  • Therefore they are missing in the diagram .
  • For a linear pressure distribution and different aspect ratios the lever arm of the resulting force is proportional to h whereas the value of the force itself remains the same because the mirror area is not varied.
  • For load case 4 the pressure distribution which leads to the peak value of MHy is different to load case 2 .
  • Presumably it is caused by a turbulence structure which just hits the mirror plane there.

5.7 My - moment at pylon feet about y axis

  • (18) For the peak values formula (18) leads to too high results because the peak values of Fx and MHy do not appear at the same point in time since they are caused by different flow conditions.
  • Therefore the modification of the formula of the load coefficient for My is the same as for Fx .
  • The peak values of My at load case 4 are caused by similar pressure distributions (not shown here) as the ones of the peak values of MHy .

5.8 Mz - moment about azimuth axis

  • As Peterka and Derickson (1992, p. 5, (5)) assume a squared mirror plane they could take for Mz the same correlation as for MHy for uniformity reasons.
  • But for varied aspect ratio a dependency on the width b instead of the height h of the mirror plane would be expected which is confirmed by the measurements, see figure 22.
  • The reason for the proportional increase of the absolute values of Mz with b is the approximately linear pressure distribution (not shown here) on the whole mirror plane along b comparable to MHy with h at load case 2 (see 5.6).

5.9 Comparison of aspect ratio dependencies without impact of wind profile

  • In table 2 the quasi aspect ratio dependencies of Peterka and Derickson (1992, p. 10) and the aspect ratio dependencies representing fitting curves to the values of the peak load measurements (see 5.1) of this study are assorted.
  • But at load case 4 the cross bar is exposed directly to the wind and is of higher impact on the wind loads than for the other load cases.
  • Therefore the wind moment would be constant for varied aspect ratio.
  • In fact the aspect ratio dependencies are less pronounced as it would be the case if the relevant pressure distributions would be linear which would lead to aspect ratio dependencies similar to the ones implicitly given by Peterka and Derickson (1992), see figures 16, 19 and 21.
  • The accordant characteristic lever arms of Peterka and Derickson (1992) in table 2 h and H decrease with the aspect ratio.

6 Conclusions

  • The wind load components vary partly significantly with the aspect ratio of the panel.
  • Therefore the aspect ratio must be considered at the layout of the components of solar trackers.
  • The main components are the foundation, the pylon, the panel, the elevation and the azimuth drive.
  • For stow position with wind direction along with the panel height h (load case 5) only a small reduction with the aspect ratio was measured.
  • The elevation drive is loaded by the hinge moment MHy.

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* Corresponding author: Tel.: ++49 711 6862 479, Fax: ++49 711 6862 8032,
E-Mail: Andreas.Pfahl@dlr.de
Wind loads on heliostats and photovoltaic trackers of
various aspect ratios
A. Pfahl
a,*
, M. Buselmeier
b
, M. Zaschke
b
a
German Aerospace Center (DLR)
Solar Research
Pfaffenwaldring 39-40
D – 70569 Stuttgart
Germany
b
Wacker Ingenieure
Wind Engineering Consultants
Gewerbestraße 2
D 75217 Birkenfeld
Germany
Available online at http://www.sciencedirect.com/science/article/pii/S0038092X1100209X
© 2011 The Authors. Published by Elsevier Ltd.
Solar Energy Vol. 85, Issue 9, Sept. 2011, pp 21852201
doi:10.1016/j.solener.2011.06.006
Abstract
For the layout of solar trackers the wind loads on the structure have to be known.
They can be calculated by using wind load coefficients given in literature. But so
far these values are only valid for aspect ratios of the panel (width to height) of
about 1.0. Therefore the wind load coefficients for heliostats of aspect ratios
between 0.5 and 3.0 were determined to close this gap.
As solar trackers are exposed to the turbulent atmospheric boundary layer the
turbulence of the approaching flow has to be modelled. As a reliable method at
reasonable cost wind tunnel measurements were chosen. Solar trackers of 30
panel size were investigated at a model scale of 1:20. Wind direction and
elevation angle of the panel were varied to investigate especially the
constellations at which the highest wind loads are expected (critical load cases).
By spires and roughness elements a wind profile and a turbulence intensity of the
modelled wind according to typical sites for solar trackers were achieved. The
loads were measured by a high frequency force balance placed underneath the
models. Additionally measurements of the pressure distribution on a panel with
aspect ratio of 1.2 were performed to better understand the effects that lead to
the peak values of the wind load coefficients.
A significant impact of the aspect ratio was measured. For the critical load cases
the aspect ratio dependencies of the accordant peak wind load components were

2
determined. By these the peak wind loads on solar trackers of varies aspect
ratios can be calculated.
Regarding the single solar tracker components the main results are: Higher
aspect ratios are advantageous for the dimensioning of the foundation, the pylon
and the elevation drive but disadvantageous for the azimuth drive.
Keywords
heliostat, wind load, aspect ratio, PV tracker, central receiver, solar tower plant
Nomenclature
A mirror area [m²]
b width of mirror plane [m]
c wind load coefficient [-]
c
F,meas,ra
measured wind force coefficient of aspect ratio r
a
[-]
c
F,Pet
wind force coefficient according to [-]
Peterka and Derickson (1992), only for r
a
= 1
c
M,meas,ra
measured wind moment coefficient of r
a
[-]
c
M,Pet
wind moment coefficient according to [-]
Peterka and Derickson (1992), only for r
a
= 1
c
Py
wind force coefficient of circular cylindrical pylon [-]
D diameter of pylon [m]
d
ra
aspect ratio (r
a
) dependency of peak values [-]
d
ra,F,meas
r
a
dependency of force gained by measurements, [-]
see table 2
d
ra,F,Pet
r
a
dependency of force according to [-]
(Peterka and Derickson, 1992), see table 2
d
ra,M,meas
r
a
dependent effective lever arm of moment gained [m]
by measurements, see table 2
d
ra,M,Pet
r
a
dependent effective lever arm of moment according [-]
to (Peterka and Derickson, 1992), see table 2
F force caused by wind [N]
F
dram,ra
calculated wind force of aspect ratio r
a
[N]
based on measurements with various r
a
F
meas,ra
measured wind force of aspect ratio r
a
[N]
F
Pet,ra
wind force of aspect ratio r
a
according to [N]
(Peterka and Derickson, 1992)
F
ra
wind force at certain aspect ratio [N]
F
xPa
horizontal wind force of panel [N]
F
xPy
horizontal wind force of pylon [N]
h height of mirror plane [m]
H height of elevation axis [m]
H
P
height of elevation axis not wind shaded by panel [m]
i indication of x, y, Hy or z

3
l characteristic lever arm [m]
M moment caused by wind [Nm]
M
dram,ra
calculated wind moment at aspect ratio r
a
[Nm]
based on measurements with various r
a
M
meas,ra
measured wind moment at aspect ratio r
a
[Nm]
M
Pet,ra
wind moment at aspect ratio r
a
according to [Nm]
(Peterka and Derickson, 1992)
M
ra
wind moment at certain aspect ratio [Nm]
n exponent of power law describing wind profile [-]
p
dyn
dynamic pressure [N/m²]
R gust factor (peak wind speed / mean wind speed, for [-]
2-3 sec. gusts and 18% turbulence intensity R = 1.6)
r
a
= b / h aspect ratio width to height of mirror plane [-]
v mean wind speed at elevation axis height H [m/s]
v
ref
mean wind speed at mean wind tunnel height (100cm)[m/s]
v(z) mean wind speed at height z [m/s]
x coordinate, horizontal, perpendicular to elevation axis, at base
y coordinate, horizontal, along elevation axis, at base
z coordinate, vertical upwards (azimuth axis); height [m]
z
ref
reference height [m]
α
elevation angle of mirror plane, 0° when horizontal [°]
β wind direction, 0° when perpendicular to elevation axis[°]
ρ density of air [kg/m³]
1 Introduction
As photovoltaic (PV) and solar thermal power plants are getting more and more
important for the world wide energy supply heliostats of central receiver power
plants and PV trackers are build in rising quantities. The higher the quantities the
more significant is a cost effective design of the structure. For their dimensioning
the wind loads are decisive and therefore should be known as precise as
possible.
An important characteristic of solar trackers is the aspect ratio of the panel. At
the determination of the aspect ratio two contrary aims have to be taken into
account: First, to reduce the height of the solar tracker and thus the average wind
speed, wide panels would be favourable. Second, to avoid long lever arms and
for to reach high field densities (assuming that the distance between the solar
trackers is determined by the diagonal of the panel), square panels would be
best. From investigations of simple plates it is known that the aspect ratio can
have a significant influence on the wind loads (Sakamoto and Arie, 1983). For a
cost effective design of solar trackers therefore the impact of their aspect ratio
concerning wind loads has to be known.

4
Peterka and Derickson (1992) have extensively investigated the wind loads on
heliostats through boundary layer wind tunnel tests. By their report the wind load
coefficients for the main wind load components are available. But they explicitly
remark that the tested heliostats were nearly square in shape and that the impact
of the aspect ratio is not known from the tests leading to their report (p. 13). Also
recent publications are based only on heliostats with aspect ratio around 1
(Wang and Li, 2008; Wu et al., 2010). Therefore the aspect ratios (width/height)
0.5, 1.0, 1.2, 1.5, 2.0 and 3.0 (see figure 1) were investigated. Although aspect
ratios of 0.5 and 3.0 are usually not chosen for solar trackers these values were
investigated to achieve more pronounced results which help to clearer
understand the effects that are causing the aspect ratio dependencies.
Figure 1: Heliostat models with aspect ratio 0.5, 1.0, 1.2, 1.5, 2.0 and 3.0
Background of the investigations is the development of a heliostat with hydraulic
drive and a mirror area of 30m² (HydroHelio
TM
). Before these investigations it
was not possible to decide in a profound way which aspect ratio for the mirror
plane should be chosen.
For uniformity reasons the coordinate system and the characteristic lengths are
according to (Peterka and Derickson, 1992, p. 11), see figure 2.
Figure 2: Coordinate system and characteristic lengths (Peterka and Derickson, 1992)

5
2 Selection of method and specifications
2.1 Selection of method
Theoretically, the wind loads could be determined at real scale heliostat models
exposed to atmospheric wind. But the low reproducibility of the wind conditions
would make it almost impossible to compare the results of heliostats with
different aspect ratio. At numerical calculations (computational fluid dynamics,
CFD) and at physical wind tunnel tests in model scales this problem is avoided.
For the layout of solar trackers the peak values of the wind loads are decisive.
Therefore CFD is only hardly suitable because especially the peak values of the
wind load components are highly sensitive to turbulence (gustiness) in the
attacking wind, as Peterka and Derickson (1992, p. 2) observed in their wind
tunnel tests and which is also known for other structures (Hucho, 2002, chapter
3.7). Hence it is important that the turbulence of the attacking wind is
appropriately modeled. For CFD this means that a turbulent inflow must be
generated. Fröhlich (2006, pp. 207ff) gives an overview of possible methods. A
method for synthetic turbulence generation which is already implemented at a
commercial tool is the vortex method (Sergent, 2002; Mathey et al. 2006).
Further more it must be ensured that the turbulence doesn’t dissipate before
reaching the investigated body. At the common RaNS (Reynolds averaged
Navier-Stokes) simulations the averaging eliminates turbulence structures in the
flow (Fröhlich, 2006, p. 16ff). The used turbulence models account for this only at
micro scale. Thus only simulation approaches at which at least the largest
turbulence structures are captured are suitable (especially LES, Large Eddy
simulation or DES, Detached Eddy Simulation) (Spalart, 2000). Further more it is
necessary to run the simulation for at least 10 min in real scale to determine the
peak values of the wind load coefficients (Cook and Mayne 1980). In combination
with the fine grid which is necessary for LES or DES this would mean a not
feasible high amount of computational time.
For some cases it is possible to determine the peak loads by just multiplying the
loads gained at attacking wind of (almost) no turbulence (measured or
calculated) with the square of the gust factor R accordant to the turbulence
intensity of the site (for a typical solar site turbulence intensity of 18% R=1.6)
(Peterka and Derickson, 1992, pp. 5ff). But this approach does not work well for
cases at which a wind load component is sensitive first to a change of the
wind direction or second to an unequal pressure distribution on the mirror
plane.
The first is the case for example for the hinge moment M
Hy
at stow position
(horizontal mirror plane). The mean value for this position is near zero while the
peak value caused by a temporarily sideward (to the panel) wind attack is not.
Peterka and Derickson (1992, p. 18) measured a ratio of peak to mean value of
10 for this case while R² was only 2.56. Also mean values can be sensitive to the

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Frequently Asked Questions (1)
Q1. What have the authors contributed in "Wind loads on heliostats and photovoltaic trackers of various aspect ratios" ?

In this paper, the effect of the aspect ratio of a solar tracker on the wind load was investigated using wind tunnel measurements at a model scale of 1:20.