Wind pressure distributions and structural responses on
ground mounted scale solar arrays
Thesis Proposal Report
James Cook University
College of Science and Engineering
Wing Hong Leung – EG4012 – 6MAY2022
Table of Contents
1.0 Introduction ................................................................................................. 3
1.1 Aims ......................................................................................................... 4
2 Literature review .......................................................................................... 5
2.1 Single axis tracking system ....................................................................... 5
2.2 Fixed frame system ................................................................................... 7
2.3 Industry design approaches and current design data available ................... 8
2.4 Wind Loading on ground mounted Solar arrays ........................................ 9
2.5 Dynamic Response of SAT System......................................................... 12
3 Methodology ................................................................................................. 16
3.2 Ground Mounted Solar panel array structure ........................................... 16
References .................................................................................................... 18
1.0 Introduction
There has been significant growth in technological advancements and industry interest for large-scale
solar. Ground mounted solar panel structural systems typically are either a fixed frame system shown
in Figure 1.1 or single axis tracking system shown in Figure 1.2.
Figure 1.1: Fixed frame mounting structure in a solar farm setting (L David 2022)
Figure 1.2: Tracking structures at stowing position during construction (R Hamilton 2021).
The fixed frame system are steel frames which support various panel configuration to be mounted on
the structural system. The solar panels are orientated in a fixed angle and ground clearances are
allowed for the panels for maintenance and installation requirements. Fixed frame system failures are
typically caused by hail damage, water ingress issues related to natural disasters. Commonly, fixed
frame system failures are non-structural related, as the solar panel arrays become non-functional due
to excessive damage on them by wind borne debris or excessive water ingress.
A single axis tracking (SAT) system orientates the solar panel arrays in an optimum position for
maximum electricity generation. SAT systems can be 25% more efficient than fixed frame systems,
therefore deployment of fixed frames system is now less common within the industry. (Mackenzie,
2019) estimates SAT system will account for 43% of system deployed in the solar farming industry
by 2024.
A large quantity of arrays are needed within solar farms to generate targeted electricity threshold,
therefore the industry desires to deploy the maximum allowable operating units within a site. To
alleviate the cost of the structural system, functional specifications generally desire a cost-effective
design solution. This has led to design of solar array mounting structures to utilise simple construction
techniques and slender structural elements. Prior to the release of AS/NZ1170.2 2021 revision, there
was no standardised guidance for Australian designers to obtain the pressure distribution coefficient
for ground mounted solar arrays which were compatible to the wind loading code AS/NZ1170.2 2011.
Since the structure is unlike a common portal frame or awning, obtaining explicit design guidance
was difficult and the available data in the public domain is scant.
There is evidence of wind induced failures of solar arrays mounted on SAT system due to wind
induced dynamic excitation, as shown in Figure 1.3. These failures can occur when solar panels are
tracking the sun via an algorithm which can be aerodynamically undesirable and during the night
when the panels are stowed horizontally. The causes of these reported failures can be due to an error
in construction resulting the erected structure not meeting the manufacture’s recommendations; or the
established design process is flawed and there are currently insufficient design data available.
Regardless of the possible causes of the failures, published reports has indicated that common modes
of failures within the SAT systems are caused by dynamic excitation and aeroelastic fluttering forces
which causes the torque tubes to be loaded to failure.
Torque Tube
Figure 1.3: Structural failure caused by dynamic excitation known as Torsional Galloping on SAT systems (R
Hamilton 2021)
1.1 Aims
This study aims to obtain net pressure distributions on typical ground mounted solar array and
compare the data to the data in AS/NZ1170.2 2021. The structural responses of system are to be
analysed, and dynamics effects of the structure are to be discussed from a preliminary standpoint.
2 Literature review
The Figure 2.1 illustrates the notable characteristics of a ground mounted solar array structure which
influences the wind loads on the structural system
1.
2.
3.
4.
5.
6.
Aspect ratio of panel array configurations (b/d)
Tilt angle 𝛼 in degrees with the horizontal to be taken as 00
Cord lengths of the panel arrays (d)
Array Rows spacing (s)
Ground clearances and array height (h)
Structure’s stiffness sequentially the natural frequency of the structure system
Panel Height (h)
Solar panels are mounted on either fixed frames or SAT systems. The panels mounted on the structure
is referred to as solar arrays or arrays for short. In solar farms, a long continuous units of arrays are
regarded as row seen in Figure 1.2. The tilt angle of the arrays is denoted by 𝛼 in degrees with the
horizontal to be taken as 00. Tilt angles are fixed for the fixed frames system while for SAT systems
can change throughout the day. The cord length ( is dependent on the solar array configuration and
chosen structural system. The panel height (h) is taken from the centroid point of the array.
Figure 2.1: Geometric terminology of typical ground mounted solar array systems
2.1 Single axis tracking system
Consider Figure 2.1, the shown SAT system is a slender structure where pillar supports stem from the
bearing units (Pivot device) or Drive mounts. The shaft which runs along the solar arrays is the torque
tube and it is sequentially connected via shaft joints to make one long tube to increase the row length.
The torque tubes pass through the bearings and gear drives that enables the system to track the path of
the sun via a power generation efficiency algorithm with additional site meteorology data. The solar
arrays are placed on supports which are sometimes a frame system as shown in Figure 2.1 where it
can be as simple as rows of purlins. The structure system is similar a torsional embedded beam where
its torsional constant is dependent on the geometry and materials property of the torque tube.
Figure 2.1: Parts of a typical single axis tracker structure
Foundations of SAT modules are typically directly driven steel piles as shown in Figure 2.2 to reach a
certain critical depth determined by a geotechnical investigation. Concrete piles and ground screw
footings are also commonly used by industry, but they are not as economical as directly driven piles.
Figure 2.2: On site direct driven support pillars on a solar farm site
The stowing angle is referred to as the preferred tilt positions of the array of the SAT system during
night times where there are no power generation from the modules. Stowing angles are selected with
the aim to reduce the angle of attack where it will be least susceptible to wind loading. The strategy to
position the arrays parallel to the ground aims to produce the minimal cross-sectional area for winds
to act on the structure which may result in the minimal stress induced into the torque tubes (Young et
al., 2020).
Depending on the model or make of the SAT system, there are guidelines on what geometric
configurations of solar panels that could be fitted on specific makes of SAT systems. The arrays can
be orientated on the system in portrait or landscape configuration which could enable more flexible
row spacing possibilities. Spacing of the tracker rows are given in terms of edge to edge of module
spacing at 00 tilt angle and pillar to pillar spacing. Spacing selections are chosen based on land usage
efficiency and shading losses caused by nearby systems creating a blocking effect during SAT
towards sunrise and sunset. The typical layout of a SAT configuration is shown in Figure 2.3.
Figure 2.3: Typical tracking system arrangements
The possible modules configurations will change the cord length, aspect ratio (array span to cord
length ratio) and row spacing of the system. Furthermore, depending on the nature of the site for sun
SAT requirements there will be a pre-determined range of module tilt angles allowed for the system
as specified in various data sheets. The mentioned are all critical parameters for obtaining the wind
loading on the SAT system.
2.2 Fixed frame system
Figure 2.4 (a) shows a fixed framed system consisting of an aluminium frame design made up of
struts. The frames are fixed on to strip footings via bolted braced brackets to form a pin connection as
shown in figure 2.4 (b). Vendors offers pre-certified fixed frames system depending on the wind
regions with compliance engineering certificate. The structural frames are erected on site with
necessary manufactures guidance.
(a)
(b)
Figure 2.4: (a) Fixed Frame Structural system for ground mounted solar arrays (S Griffin 2021)
(b) Footing to fixed frame connection (W Leung 2022)
The footings and foundations of the fixed frame systems can be mass concrete strip footings or bored
piers which requires excavations and concrete needs to be poured insitu. The design considerations of
the fixed frame systems consider the spacing of the rows to ensure service vehicles can travel between
the rows and panel blocking is minimised at operational time. The tilt of the arrays is chosen from an
efficiency study based on topographical and metrology data depending on the site of the solar farm.
The size and make of the racks to be used must be compatible with the chosen array systems. The
Alzone Solar panel mounting systems with pre certified wind region A mount kits are shown in
Figure 2.5.
Figure 2.5: Alzone Wind Region A fixed ground mounted solar ranking systems
2.3 Industry design approaches and current design data available
The governing design criteria for ground mounted solar arrays are wind loading and its associated
effects. In the past, designers have used Free Roofs aerodynamic shape factors (Appendix D3 of
AS/NZ 1170.2 2011 revision) to obtain the design pressure coefficients for ground mounted solar
panels. It is a flawed design assumption as the free roofs are commonly isolated and its ground
clearance is higher than ground mounted solar panels.
In the 2021 revision of AS/NZ1170.2, a new dedicated section (appendix B.6.2) provides the net
pressure coefficient induced by wind loads on ground mounted solar arrays with geometric
restrictions. The methodology and approaches where reported by (Ginger et al, 2019) where
aerodynamic shape factors for solar arrays are given in a form appropriate for AS/NZS 1170.2.
Designers are required to determine the design wind speeds for ultimate and serviceability events
based on:
1. Regional wind speeds
2. Site Terrain and topography
3. Design life and importance level
With the design wind speed and aerodynamic shape factor determined for a specific solar array
configuration, an idealised distributed load acting normally on the solar arrays can be derived. For
fixed frames systems, the tributary width of the ground mount rails can be determined and the
nominal loads on the frame system can be analysed in this simplified manner. For SAT system, the
non-uniform distributed load causes a force imbalance and induces a hinge moment to the torque tube.
Structural analysis reports for proposed solar farm project encompasses numerical simulations along
with scaled model testing and relevant design guidelines provided by Standards.
Designers typically uses computer finite element models built with reference to the proposed
structural system’s technical specification. Computer models allows designers to:
1.
2.
3.
4.
Simulate local stress and strains on specific elements of the structure like connections
Identify critical modes of failures of the specific elements of the structural system
Compute total deformations and deflections for critical load cases
Obtain critical mode shapes and natural frequencies of the structural system.
The computer analysis can be performed on popular simulation environments such as ANSYS.
Critical cases can be outlined, and critical checks of bending, torsion and lateral torsional buckling
can be outputted to a summary results report.
2.4 Wind Loading on ground mounted Solar arrays
Obtaining the pressure distribution and resultant forces acting on the solar panel arrays mounted on a
single axis SAT system, or a fixed frame system are dependent on many variables as mentioned in
section 2. The accepted industry approach is to obtain the pressure distribution data via a wind tunnel
testing of scaled models. However, most boundary layer wind tunnels are built to accommodate
models scale of 1:100 to 1:500 to models the wind loading effects for large to mega structures.
Therefore, the following difficulties as summarised by (Mousaad Aly and Bitsuamlak, 2013) to
develop a representative aerodynamic model are:
1. In the common scales which wind tunnel models are made, the individual solar arrays will
become too small to mount adequate pressure taps resulting in poor resolution of pressure
distribution data.
2. The model will not be within a representative portion of the boundary layer of fluid flow
which is required for similitude. A common problem for low rise models and close to ground
structures. As the height of the model can be less than of the floor roughness elements blocks
in the upstream of the wind tunnel which can induce high uncertainty in wind speeds
measurements.
3. Also due to scant availability of full-scale data of aerodynamic loading on ground mounted
solar arrays. Calibration or validation of wind tunnel data becomes difficult.
(Mousaad Aly and Bitsuamlak, 2013) investigated the use of different scales and its associated
effects on wind tunnel data. The study concluded that 1:5 to 1:10 scaled models do not achieve
modelling similitude while the scale of 1:50 was observed to suffer from model close to ground effect.
The study states scales of 1:20 to 1:30 are the preferred model scales and specific geometric
sensitivity analysis is recommended to better anticipate possible data deviations.
The common types of boundary wind tunnel studies either focuses on the wind loading effects on a
stand-alone solar array model or the inclusion of multiple panel arrays rows. Models with multiple
rows uses dummy blank models with no data recording capabilities. The studies performed by
numerous institutes adopts a boundary layer wind tunnel as its experimental component with a
Computational fluid dynamic model to compare the findings. The pressure distribution data of various
model configuration can be used to assist designers to determine the wind loads on the solar arrays.
The aspect ratio determined by the mounting style of the solar arrays can have a significant influence
on the pressure distribution as suggested by (Sakamoto and Arie 1983) and (Browne et al., 2020) in
their general study of wind loads on ground mounted solar arrays. (Pfahl et al., 2011) performed a
specific study on the effects of aspect ratio of the solar arrays on SAT structures. It was indicated for
trackers in stowed positions, hinge moment is reduced with increasing aspect ratios (b/d) when the
wind directions are at 𝜃= 0o or 1800. But when the wind direction is 𝜃= 90o or 2700, only a small
reduction of the hinge moment was observed.
From a first principles standpoint, the increase of aspect ratio restricts the length of lever arm of the
resultant force of the wind load from the torque tube. When the title angle of the model was 300 and
the wind direction was at 𝜃= 0o , (Pfahl et al., 2011) shown that the decrease of the level arm of
resultant force from a lower aspect ratio to one of higher was by a factor of the ratio of the cord length
of the lower aspect ratio to the one of higher aspect ratio. This implies that the hinge moment induced
onto the torque tube is proportional to the cord length of the solar array which is a similar proposal to
the (Peterka and Derickson, 1992) on their research on wind loads on ground mounted heliostats.
Figure 2.6: Linear pressure distribution for high aspect ratios on the left and low aspect ratio on the
right (Pfahl et al., 2011)
The tilt angle of the solar arrays changes the flow field characteristic, panel array pressure distribution
and the drag coefficients. (Yemenici & Aksoy, 2021) tested a standalone solar array model in a
different series of panel tilts ranging from (00 to 450) with an accompanying numerical wind load
result agreement. Their study suggested that the maximum positive and negative pressures acting on
the panels occurred at the leading edges of the panel for wind directions perpendicular to the panel
(wind direction of 00), and pressure decreases gradually at the trailing edges of the panel arrays due
flow detachment and vortex shedding. The pressure drops from the leading edges and trailing edges
are much more sudden on higher tilt angles, this is caused by the greater frontal aera of obstruction to
the oncoming wind flow. The negative pressure coefficients which act on leeward side of the panel
increases in magnitude as the tilt angle increases, causing larger suctions force.
(Browne 2020), (Yemenici and Aksoy 2021) and (Jubayer and Hangan 2016) also suggests that the
increase of panel inclination is directly corresponding to the increase of net wind loads on the solar
panel arrays. Such pattern is also found within the AS/NZ 1170.2 (2021) net pressure coefficients for
ground mounted solar arrays.
Models which study the effects of multiple array rows have all found that the first windward rows to
be suscept the highest wind loads in frontal wind and oblique wind directions (Jubayer and Hangan
2016). Rear rows become less shielded in the oblique wind directions of 450 and 1350, and it was
found that rows of 2 to 5 out of 5 becomes more susceptible to higher wind loads shown visually in
Figure 2.7 of mean velocity contours of (Jubayer and Hangan 2016) study.
Figure 2.7: Mean velocity magnitude contours with streamlines. (Jubayer and Hangan 2016) where α
is denoted as the wind direction in their study.
The array row spacing selection for solar farms is often not dependant on wind loading considerations
but land usage efficacies, serviceability, and operational standpoint. The AS/NZ1170.2 (2021) does
not consider the shielding effects of upstream panels as it is negligible suggested by (Ginger, 2019).
However (Warsido et al., 2014) studied the effects of array row spacing (longitudinal and lateral
spacings) and as shown in Figure 2.8 pressure distribution was collected data of a model of a solar
farm array.
Figure 2.8: (Warsido et al., 2014) configurable wind tunnel model which can change the location of
the instrumented panels.
In the cases where the instrumented panels were in the leading edges of the tested model in respect to
the wind direction, the net pressures experienced by the front row panels was more than the 2nd row of
panels. The greatest reduction of wind loading was observed to be in the 2nd row, but further net
pressure reduction is not as great and becomes minimal by the 4th row of panel arrays. The outer
arrays of the models were also observed to experience a significant net pressure increase compared to
the ones in the middle of the model. The change of the lateral spacing between the solar arrays
reported little effects on the nominal pressure’s coefficient. The wind load coefficients increased long
with longitudinal spacing implying the inter panel array shielding effects becomes less prominent as
the longitudinal spacing of the arrays increased. (Warsido et al., 2014) compared pressure data of the
group array model to a stand-alone array in the wind tunnel, and it concluded that the arrays in groups
in practice would experience less wind loads to a standalone individual solar array.
2.5 Dynamic Response of SAT System
There has been a surge of industry interest on the wind induced dynamic effects of ground mounted
solar arrays specifically for SAT systems. Dynamic effects and responses caused by wind loading
have been analysed via specialist consultants such as CPP Wind engineering. Aeroelastic instabilities
studies can be performed to determine the site-specific optimum stowing angle and configurations.
Preliminary attempts at modelling the fluid to structure dynamic interaction has been akin to a basic
flat plate of various geometry in the past. Behaviour of inclined flat plates in turbulent flows has been
extensively studied especially on high Mach number flow regime within the aerospace research
sector. Translation of the established research findings are often incompatible as typical aspect ratios
between airplane foils thickness, cord length (d) and leading to trailing edge distances are immensely
different to the ones typically found within SAT systems. A SAT system can be considered as a
simple buff body with notable separation points and distinctive wake regions identifications.
The characteristics of buff bodies are the ability to induce Von Karman streets within the wake region
upon fluid interaction. The nature of the vortex shedding phenomena was first studied by (Vincenc
Strouhal 1878) where Strouhal proposed a relationship:
Strouhal number: 𝑆𝑡 =
𝑓𝐿
𝑈
Where f is the vortex shedding frequency within the wake region of the buff body, U is the mean wind
speed and L is the characteristic length. Refinement of Strouhal’s research focused on inclined flat
plates with infinite spans has been studied by (Fage & Johansen, 1927), and it was proposed that the:
“Vortex shedding frequencies increases as the inclination of the plate decreases. The frequency is
proportional to the wind speed at a constant inclination.”
A more contemporary study by (Chen & Fang, 1996) suggested that the modelling range of the plates
for the angle of attack should ideally be separated into 3 discrete ranges. This is due to the tilt angle of
00 -50 having immensely different fluid to structure behaviour because of boundary layer reattachment
mechanisms making the Strouhal number sensitive to the Reynolds number. The sudden jump of
higher shedding frequency occurs in the range of 5-100 in agreement to (Fage & Johansen, 1927)
research findings. For the 100 -900 the flow is fully separated where Strouhal number is insensitive to
Reynolds number, and it agrees of a universal Strouhal number of 0.160 ± 0.003 which (Matty, 1979)
and (Fage & Johansen, 1927) both initially suggested.
A simplified vortex shedding mechanism proposed by (Cain et al., 2015) that the characteristic length
in Strouhal number is the vertical projection of the solar array cord length. Therefore, for a given tilt
angle (𝛼) and cord length (d) the characteristic length is defined by:
𝐿 = 𝑑 × sin 𝛼
This implies that for a known Strouhal number such as a universal one proposed by(Chen & Fang,
1996) of 0.16 ± 0.003 for tilt angle range from 100 to 900, with the mean wind velocity (u) of the site
and projection length determined. The estimated frequency which the vortices can shed at the wake of
the panels can be determined by:
0.16 × 𝑈
=𝑓
𝑑 × sin 𝛼
Suppose a 25m/s wind gust is maintained during a storm event for a 20 second gust duration, and the
cord length of the solar panel array is 4m as suggested by Soltec data sheets of their trackers range
compatibility. With a tilt of 300 during the day when the tracker is in use, the estimated shedding
frequency is 2 Hz. In the case of where the SAT structure has a natural frequency of 2Hz, the wind
event will be tuned for dynamic excitation known as the lock-in phenomenon.
With most SAT structures having a low ground clearance ranging from 1m to 3m, the turbulence
intensity becomes higher meaning that the ratio of fluctuation wind speed to the mean wind speed is
greater. Therefore, the range of gusty wind speeds can fluctuate within the arrays enabling a large
range of vortex shedding frequencies within the
From section 6.2 of AS/NZ1170.2 (2021), it was explicitly stated that ground mount solar panels with
natural frequencies greater than 5 Hz does not require any forms of dynamic analysis. Designers can
use Finite element analysis software packages to complete a modal analysis to find the critical mode
shapes and its associated natural frequency. There are also cases where free vibration tests are
conducted on site to measure the logarithmic decrement to determine the damping and natural
frequency of the system. Due to the nature of the SAT structural system being slender, (Gomez et al
2018) , (Valentín et al., 2022) completed a modal analysis on selected make of tracker structure and
identified that critical mode where of 1.1 Hz and 2.17 Hz respectively and the remaining modes to be
under of the 5 Hz threshold. A free vibration test conducted by PVH consultants on site also
determined its first critical mode corresponds to 1.1 Hz.
The mode shape of the modal analysis completed are shown in Figure 2.9 and 2.10 via (MartínezGarcía et al., 2021) and (Gomez et al 2018) modal analysis results.
Figure 2.9: An finite element analysis program producing its mode shape results via (MartínezGarcía et al., 2021)
Figure 2.10: Another mode shape results via (Martínez-García et al., 2021)
(Cain et al., 2015) suggests that modal analysis via finite element analysis model is highly dependent
on the support conditions and fixity of the steel pile. Since soil type surrounding the piles and
embedment length can induce a high level of variance of damping properties. Different makes and
models of the SAT systems can also affect the model results. The most preferred method of obtaining
the structures critical mode and frequency is to conduct a field vibration test.
Designers uses the results of dynamic analysis to develop an amplification factor to be integrated into
the wind loading equation to account for the possibility of structural excitation. There are currently no
dedicated sections of AS/NZ 1170.2 (2021) to determine the dynamic response factor for ground
mounted solar panel arrays, but the standard acknowledges that solar arrays have failed to due
dynamic effects and the current standard refers designers for specialist advice.
(Valentín et al., 2022) performed a thoroughly ground mounted solar array structural failure
investigation. Valentin discusses the realisation of the risk highlighted by (Strobel & Banks, 2014),
(Browne et al., 2020) and(Young et al., 2020) of dynamic excitation in the form of torsional
galloping.
Torsional galloping is flutter in 1 degree of freedom where the mounted solar arrays on the SAT
systems undergoes angular oscillations in the manner like Figure 2.11 and the flutter increases in
amplitude. The galloping causes can be due to vortex shedding, wind buffeting and sudden gust
created by the upwind panels that can coincide with the natural frequency of the structural system.
(Young et al., 2020) suggests that these galloping failures occurs more frequently when the SAT
system orientates its panels at 00 in stowing mode at night. Figure 2.11 shows the tracker has
completed a full lateral rotation about its torque tube with some solar arrays snapped in half.
Figure 2.11 (Valentín et al., 2022) failure analysis collection site photos of a solar farm in Spain
On closer inspection, the torque tube at the shaft joint has experienced complete plastic deformation
due to a high torsional stress. (Valentín et al., 2022) proposes that the trackers in failure caused by a
dynamic phenomenon due to the records of the solar farm indicating the panels where in stowing
position at night implying there should be minimum static wind loads acting on the panel. The
deformations being of torsional natura implies that torsional galloping is a reasonable cause of failure.
Once the natural frequencies have lock in with the surrounding winds, the amplitude of the flutter is
amplified until the torque failures by plastic deformation.
Failures of this nature is at the forefront of the discussion within the large-scale solar industry, with
certain farms adopting real time wind speed monitoring system and installations of hydraulic dampers
on at risk arrays.
3 Methodology
3.1 Wind Tunnel
The wind tunnel is a 2.5m wide x 2m tall x 22 m long Boundary Layer wind tunnel at James Cook
university in Townsville, Australia. The suction type wind tunnel can generate a mean wind velocity
of roughly 10m/s. To generate the turbulence approach for the representative boundary layer, a
250mm high trip board with foam blocks is to be placed at the upwind end of the wind tunnel to
create the needed turbulence on the approach to the model. The mean velocity, gust and turbulence
intensity profiles generated at a reference height are to be measured. This would need to be matched
or within tolerated similarity defined by AS/NZ1170.2 Terrain Category 2 in Clause 4.2.1
3.2 Ground Mounted Solar panel array structure
Consider a ground mounted array system consists of 32 solar panels of the dimensions 2.5m x 1.2m
forming a 19.2 m long (b) x 5m wide (d) solar array system. The naming conventions of the array
shall be A, B, C and D with the wind approach direction angle 𝜃 show in Figure 3.1. The pressure
distribution resolution required 64 pressured taps per side of panels. Each pressure tap is numbered
from 1 to 64 from array A to D in the manner shown in Figure 3.1.
𝜃0
ℎ𝑚
𝛼
Figure 3.1 Experimental solar panel array schematic with proposed dimension
Consider the table 3.1 for the proposed testing configuration. It should be noted that the only variation
of the configuration is the panel tilt angle, the array height and array row spacing are to remind the
same.
Table 3.1: Testing configuration proposed for the wind tunnel study
Configuration
Inclination angle: 𝛼 (0)
Height: hm
(m)
Spacing:
s(m)
Array
Length b
(m)
Array
width d
(m)
Aspect ratio
b/d
1
0
2
7
19.2
5
3.84
2
17
2
7
19.2
5
3.84
3
20
2
7
19.2
5
3.84
4
40
2
7
19.2
5
3.84
The simulated length scale chosen for the proposed study is 1/20 (𝐿𝑟 =
𝐿𝑚𝑜𝑑𝑒𝑙
𝐿𝑓𝑢𝑙𝑙−𝑠𝑐𝑎𝑙𝑒
= 1⁄20). The wind
tunnel model is 960mm x 250mm with 7mm thickness to install pressure taps on the top and
𝐿
underside of the panels. The velocity scale of the wind tunnel will be calculated (𝑈𝑟 = 𝑇𝑟 ) and used to
𝑟
determine the time scale (𝑇𝑟 = 𝑇
𝑇𝑚𝑜𝑑𝑒𝑙
𝑓𝑢𝑙𝑙−𝑠𝑐𝑎𝑙𝑒
) of the wind tunnel and will indicate the testing duration of
1
the model. The scale frequency (𝑓𝑟 ) the pressure taps is dependent on the time scale ( 𝑓𝑟 = 𝑇 ) where
𝑟
the data measuring frequency is to be twice the value of the measure full scale frequency of the
model.
The model will be installed on the turntable of the wind tunnel. The turntable will be used to rotate the
model in 100 increments to record surface pressure data of the model for 36 wind approaches. The
data are to be recorded for 3 repetitions per wind approach at a sample rate and time. This procedure
is to be repeated for all 36 wind approaches per model configuration.
Since the time series pressures are recorded on the top and bottom taps of same location of the array.
They can be summed relatively to their direction of action to derive the net pressure acting on the
array at the tap location.
𝑝(𝑡)𝑛𝑒𝑡 = 𝑝(𝑡)𝑡𝑜𝑝 − 𝑝(𝑡)𝑏𝑜𝑡𝑡𝑜𝑚
The pressure time series data pnet(t) recorded from the wind tunnel can be represented as the pressure
coefficient 𝐶𝑝𝑛𝑒𝑡 (𝑡) in reference to a height. The net coefficient is ratio between the net pressure and
dynamic pressure at the reference height (hm) expressed as:
𝐶𝑝𝑛𝑒𝑡 (𝑡) =
𝑝𝑛𝑒𝑡 (𝑡)
1 ̅̅̅2
2 𝜌𝑣 ℎ𝑚
̅
The (𝐶𝑝𝑛𝑒𝑡
), maximum (𝐶̂𝑝𝑛𝑒𝑡 ), and minimum (𝐶̌𝑝𝑛𝑒𝑡 ) for the wind directions of 𝜃 =
0 , 90, 180 𝑎𝑛𝑑 270 0 for all the proposed configuration listed in table 3.1 are to be obtained in the
wind tunnel experiment.
References
1. Browne, M. T. L., Taylor, Z. J., Li, S., & Gamble, S. (2020). A wind load design method for
ground-mounted multi-row solar arrays based on a compilation of wind tunnel experiments.
Journal of Wind Engineering and Industrial Aerodynamics, 205, 104294.
https://doi.org/https://doi.org/10.1016/j.jweia.2020.104294
2. Cain, J. H., Banks, D., Principal, & Petersen, C. P. (2015). Wind Loads on Utility Scale Solar
PV Power Plants. SEAOC Convention Proceedings, Seattle.
3. Chen, J. M., & Fang, Y.-C. (1996). Strouhal numbers of inclined flat plates. Journal of Wind
Engineering and Industrial Aerodynamics, 61(2), 99-112.
https://doi.org/https://doi.org/10.1016/0167-6105(96)00044-X
4. Fage, A., & Johansen, F. (1927). On the flow of air behind an inclined flat plate of infinite
span. Proceedings of the Royal Society of London. Series A, Containing Papers of a
Mathematical and Physical Character, 116(773), 170-197.
5. Mackenzie, W. (2019). The global PV tracker landscape 2019 [Market report](The global
solar PV tracker landscape, Issue. https://www.woodmac.com/our-expertise/focus/Power-Renewables/the-global-pv-tracker-landscape-2019/
6. Martínez-García, E., Blanco-Marigorta, E., Parrondo Gayo, J., & Navarro-Manso, A. (2021).
Influence of inertia and aspect ratio on the torsional galloping of single-axis solar trackers.
Engineering Structures, 243, 112682.
https://doi.org/https://doi.org/10.1016/j.engstruct.2021.112682
7. Matty, R. R. (1979). Vortex Shedding From Square Plates Near a Gound plane: An
Experimental Study [Graduate Thesis, Texas Tech University]. Texas. https://ttuir.tdl.org/bitstream/handle/2346/12675/31295005927990.pdf?sequence=1
8. Pfahl, A., Buselmeier, M., & Zaschke, M. (2011). Wind loads on heliostats and photovoltaic
trackers of various aspect ratios. Solar Energy, 85(9), 2185-2201.
https://doi.org/https://doi.org/10.1016/j.solener.2011.06.006
9. Strobel, K., & Banks, D. (2014). Effects of vortex shedding in arrays of long inclined flat
plates and ramifications for ground-mounted photovoltaic arrays. Journal of Wind
Engineering and Industrial Aerodynamics, 133, 146-149.
https://doi.org/https://doi.org/10.1016/j.jweia.2014.06.013
10. Valentín, D., Valero, C., Egusquiza, M., & Presas, A. (2022). Failure investigation of a solar
tracker due to wind-induced torsional galloping. Engineering Failure Analysis, 135, 106137.
https://doi.org/https://doi.org/10.1016/j.engfailanal.2022.106137
11. Warsido, W. P., Bitsuamlak, G. T., Barata, J., & Gan Chowdhury, A. (2014). Influence of
spacing parameters on the wind loading of solar array. Journal of Fluids and Structures, 48,
295-315. https://doi.org/https://doi.org/10.1016/j.jfluidstructs.2014.03.005
12. Yemenici, O., & Aksoy, M. O. (2021). An experimental and numerical study of wind effects
on a ground-mounted solar panel at different panel tilt angles and wind directions. Journal of
Wind Engineering and Industrial Aerodynamics, 213, 104630.
https://doi.org/https://doi.org/10.1016/j.jweia.2021.104630
13. Young, E., he, X., King, R., & Corbus, D. (2020). A fluid-structure interaction solver for
investigating torsional galloping in solar-tracking photovoltaic panel arrays. Journal of
Renewable and Sustainable Energy, 12, 063503. https://doi.org/10.1063/5.0023757
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