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ScienceDirect
Solar Energy 118 (2015) 7–19
www.elsevier.com/locate/solener

Experimental and numerical assessment of photovoltaic

collectors performance dependence on frame size and installation
technique
F. Arpino ⇑, G. Cortellessa, A. Frattolillo
Dipartimento di Ingegneria Civile e Meccanica, Università degli Studi di Cassino e del Lazio Meridionale, Via G. Di Biasio 43, 03043 Cassino (FR), Italy

Received 17 June 2014; received in revised form 23 March 2015; accepted 5 May 2015
Available online 27 May 2015

Communicated by: Associate Editor Brian Norton

Abstract

The performance of a solar photovoltaic silicon panel is inversely proportional to its operating temperature. Therefore the overheat-
ing risk must be avoided in order to improve the cells electric efficiency. The temperature increase in a solar cell also gives rise to thermal
stresses within the module. In this work the authors propose an experimental and numerical investigation of photovoltaic collectors tem-
perature and efficiency dependence on main design parameters (thickness of the aluminum frame), installation technique (distance
between photovoltaic panel and supporting panel, tilt angle of the module), and environmental operating conditions, with particular
reference to the wind velocity. Experimental investigations have been conducted on a two photovoltaic modules assembly composed
by silicon panels. Numerical simulations have been performed employing a two-dimensional finite element numerical model, validated
against experiments carried out by the authors. The validated numerical tool has been applied to evaluate photovoltaic collector perfor-
mance dependence on panel geometrical parameters, installation procedure and operating conditions. The main objective of the present
paper is to provide installation and operating indications in order to maximize efficiency. From the conducted investigations it has been
evidenced that an optimal distance of the panel from the support can be found, corresponding to which the efficiency is maximized.
Ó 2015 Elsevier Ltd. All rights reserved.

Keywords: Photovoltaic collector; Computational fluid dynamics; Experiments; Efficiency; Installation technique

1. Introduction amount of research has been conducted to increase PV col-

lectors efficiency, and new designs have been proposed for
The ever growing energy demand and environmental building applications, based on PV modules optical, ther-
pollution level has pushed research interest toward more mal and electrical generation characteristics (Buonanno
efficient conversion of solar to electric energy (Sun and et al., 2005; Himanshu, 2009; Arcuri and Reda, 2014).
Sariciftci, 2005; Bube, 1998; Yin et al., 2013; Dović From the optical point of view, modules efficiency can be
Damir, 2012). In this context, photovoltaic (PV) panels increased by using non-reflective coatings that enhance
represent a potentially clean and renewable energy produc- optical transmission. Besides, a better efficiency can be
tion technique, that can reduce the dependence on tradi- obtained by ensuring operating conditions that avoid col-
tional energy sources. In the recent years a significant lectors overheating and the consequent loss of their electric
efficiency (inversely proportional to their operating temper-
⇑ Corresponding author. ature). A typical efficiency value for crystalline Si-based
E-mail address: f.arpino@unicas.it (F. Arpino). cells is 14–17% and the non converted solar radiation

http://dx.doi.org/10.1016/j.solener.2015.05.006
0038-092X/Ó 2015 Elsevier Ltd. All rights reserved.
8 F. Arpino et al. / Solar Energy 118 (2015) 7–19

Nomenclature

G solar radiation Greek symbols

g acceleration due to gravity b thermal expansion coefficient
k turbulent kinetic energy c relative thermal coefficient of module efficiency
kf coverage factor e specific dissipation rate of k in the k–e model
Px source terms for x er emissivity of the module surface
Pk source term for k g0 module efficiency at a temperature T 0 ¼ 25  C
Pe source term for e l dynamic viscosity
R additional RNG k–e term lt turbulent dynamic viscosity
T temperature m cinematic viscosity
Ta ambient temperature mt turbulent cinematic viscosity
ui velocity components q density
Yk sink terms for x r Stefan–Boltzmann constant
xi coordinate axes x specific dissipation rate of k in the k–x model

energy, released as thermal energy, may cause PV modules provide a flexible and cost-effective tool to select advanta-
to overheat (Tripanagnostopoulos et al., 2002). PV cells geous configurations from alternative design strategies,
will also exhibit long-term degradation if the temperature which can be subsequently tested in detail either in labora-
exceeds 80–85 °C (Brinkworth et al., 1997; Grätzel, 2004). tory or on field. Taking advantage of a validated CFD tool
Therefore effective PV module cooling must be ensured (Arpino et al., 2011, 2013), it is possible to predict and
by acting on the Convective Heat Transfer Coefficient improve thermal performance of a specific PV module
(CHTC), that depends on different geometrical and ther- design, significantly reducing time and cost required by
modynamics parameters as: wind speed, wind direction, tilt experiments. Velocity and length scales considered require
angle of the panel, installation height (distance the adoption of a proper turbulence model. Given the com-
support-frame), size of the exposed surface and its rough- plexity of the problem, turbulence is typically described
ness, air temperature. Various experimental studies on using the Reynolds Averaged Navier Stokes (RANS)
solar collectors flush mounted on the inclined roof of a approach and the two-equations, typically k–epsilon (k–e)
building were performed. Kind et al. (1983) carried out a or k–omega (k–x), turbulence closure models, where k is
wind tunnel study on an array of solar collectors mounted the turbulent kinetic energy while e and x refer to the tur-
on a 60° inclined roof of a 1:32 scale model house, showing bulent dissipation rate. Such turbulence modeling
a variation of the heat transfer within 30% for the different approach is based on the description of time-averaged
wind directions investigated. Results also showed that the properties of the flow, allowing significant reduction of
CHTC is maximum when the wind direction is perpendic- required computing resources. Looking at the scientific lit-
ular to the panel. Shakerin (1987) also performed a wind erature, different heat and mass transfer numerical simula-
tunnel study on a single solar collector flush mounted on tions have been proposed assimilating the PV panel to a
the roof of a scale model of a house with different tilt wall mounted cube immersed in a turbulent boundary
angles. It was claimed that the flow over the collector layer. For instance, such an approach has been adopted
was turbulent for inclination angles lower than 40° and by Ničeno et al. (2002), Ratnam and Vengadesan (2008),
laminar for inclination angles larger than 40°. Sartori Blocken et al. (2009) and Defraeye et al. (2010). Different
(2006) compared empirical equations of the CHTC for turbulent models have also been used. A Large Eddy
forced air flow over flat plate solar collectors, with the Simulation (LES) with Spalart’s adjustment in the near
boundary layer correlation for the convective heat transfer wall region, referred as Detached Eddy Simulation
over an horizontal flat plate. The comparison showed that (DES), was performed by Ničeno et al. (2002). Ratnam
the flow over flat plate solar collectors is generally turbu- and Vengadesan (2008) performed unsteady numerical sim-
lent and the boundary layer correlation for turbulent flow ulations using standard k–e, low-Re k–e, non-linear k–e,
under predicts the CHTC values significantly. standard k–x and improved k–x turbulence models.
In most of the cases of practical interest, correlations They evidenced that results obtained from the non-linear
available in the scientific literature for the Nusselt number k–e, improved k–x and standard k–x turbulence models
calculation are not accurate (Bejan and Kraus, 2003). agreed well with the experimentally measured temperature
Detailed numerical modeling of temperature and velocity profiles at the front and back faces of the cube. Besides,
fields is then very useful to obtain more accurate results. Meroney and Neff (2010) studied the wind effects on roof
In fact, Computational Fluid Dynamics (CFD) can mounted solar photovoltaic arrays employing different
 F. Arpino et al. / Solar Energy 118 (2015) 7–19 9

turbulence models, showing that the RNG k–e and the k–x
models produced reasonable agreement with measure-
ments, whereas the standard k–e model failed to replicate
experiments.
In the author’s opinion, even though significant research
activity is currently conducted to improve PV panels effi-
ciency, there is a lack of information about collectors design
optimization and installation procedures. In fact, a detailed
understanding of temperature and velocity fields in relation
to the panel could give important information in order to
avoid over-heating and improve efficiency. To this aim,
numerical modeling represents a powerful tool to support
experiments, saving time and costs. Nevertheless, CFD
effectiveness depends on its ability to reproduce in detail
real PV modules in actual operating conditions.
In this paper the authors propose an experimental and
numerical investigation of two commercially available PV
modules assemblies aimed at providing installation and Fig. 1. PV collectors assembly employed for experimental investigations.
operating indications that allow efficiency optimization.
The PV modules were installed and tested on the roof of (5 mm) and the gap (2 mm) between the frame and the glass
the DICeM building of the University of Cassino (Italy). above, it can be observed that: the distance between the
A detailed numerical simulation of the actual PV testing lower surface of the PV module with a 30 mm frame and
configuration has been conducted employing the commer- the upper surface of the insulating support is equal to
cial CFD code Comsol MultiphysicsÒ, validated against 63 mm; the distance between the lower surface of the PV
the collected experimental data. On the basis of findings module with a 50 mm frame and the upper surface of the
in the scientific literature, turbulence was modeled using insulating support is equal to 83 mm.
the RANS approach and the RNG k–e and standard k–x Experiments have been conducted with a tilt angle of 18°
two-equations models. In particular, the work consists of (typical inclination of the roofs of the buildings in central
a study of the effects induced by the thickness of the alu- and southern Italy) and an azimuth angle equal to zero.
minum frame of a PV module and by the installation tech- The PV modules were mounted according to the installation
niques (distance panel-supporting panel, tilt angle of the procedure provided by the manufacturer, using the support
module), on its temperature and efficiency. On the basis bars and the clamping nuts specifically supplied (Fig. 1),
of the obtained results, indications about PV collectors resulting in a gap between the two panels of 21 mm.
installation and frame optimal size are obtained in order The temperature of the PV panels and supporting plate
to optimize operating conditions and efficiency. were constantly monitored through 10 thermocouples posi-
tioned on the back surface of the modules. A schematic of
2. Experiments the position of different thermocouples on the back surface
the PV modules is presented in Fig. 3. Solar radiation was
Experimental investigations have been conducted on a monitored by means of 2 pyranometers which measured
two commercially available PV modules assembly installed the total and diffuse irradiation incident on the PV panel
on the roof of the DICeM building of the University of surface. The wind was monitored using an anemometer
Cassino. A picture of the experimental apparatus is avail- which measured the wind velocity and direction, located
able in Fig. 1. In particular, it consists of a pair of PV panels very close to the support, behind the panel under test. All
arranged horizontally and mounted on a frame structure, the sensors and meters were connected to a multimeter
with the ability to simulate different roof tilt angles, from and collected data was stored in a dedicated PC. The collec-
0° to 90°. The PV modules are anchored on a panel of insu- tion interval was 30 s. The numerous data obtained were,
lating material with a thickness of 40 mm, which simulates therefore, averaged into time intervals corresponding to a
actual operating condition of PV panels installed on a roof. variation of solar radiation no greater than 50 W/m2. The
A diagram of different components of the investigated panels were electrically connected to a variable resistor with
assembly is available in Fig. 2. Two models of PV module a max power of 1000 W adjustable with steps of 50 W, suf-
have been experimentally investigated: (i) the model 1, with ficient to dispose of all the power generated by the system.
a size of 1675  1000 mm and an aluminum frame thick- In Figs. 4 and 5 the experimental results obtained,
ness, h, of 30 mm, characterized by a nominal power of respectively, for the front and the rear PV panel with frame
245 W; (ii) the model 2, with a size of 1655  990, and with of 30 mm (model 1) are reported. In particular, the three
an aluminum frame thickness, h, of 50 mm, characterized measurement points correspond to a distance from the
by a nominal power of 260 W. Considering the size of the leading edge of 150, 485 and 820 mm, respectively. In such
fixing bar, d = 40 mm (Fig. 2), the thickness of the PV panel figures the temperature profiles are plotted as a function of
10 F. Arpino et al. / Solar Energy 118 (2015) 7–19

Fig. 2. Sketch of the PV collector position with respect to fixing bar and supporting plate.

speed, u, ranging from 0.2 m/s to 2.9 m/s and for an air
temperature, Ta, between 17 °C and 26 °C. Looking at
the reported data, it can be observed that a significant tem-
perature difference is present between the leading edge and
the center of the PV panel, probably due to the buoyancy
effect in correspondence of the gap between the module
and the supporting insulating panel. Such effect is more
pronounced for the front panel, where a temperature differ-
ence of 25 °C was measured in a distance of 335 mm.
During experiments, the front panel presented an average
temperature more than 30 °C larger than the surrounding
atmospheric air temperature (i.e. Tpan  Ta > 30 °C). Such
temperature difference reaches 46 °C in the proximity of
the PV panel trailing edge. As regards the rear PV panel
the measured temperature differences with respect to sur-
rounding air are slightly higher. In fact, an average temper-
ature of 32 °C larger than the temperature of the
surrounding air has been registered during experiments.
Looking at the collected data, it seems that the wind veloc-
ity does not significantly affect the PV panels temperature if
it is below 2 m/s. When the wind speed increases to 3 m/s
a temperature drop of 10 °C has been registered in nearby
of the trailing edge of the front PV panel and the leading
edge of the rear PV panel. Such effect is less pronounced
at the inlet of the front PV panel and at the outlet of the
Fig. 3. Layout of the thermocouples installed on the PV collectors.
rear PV one, where a temperature drop of 5 °C has been
observed. For a better understanding of the reported mea-
the distance from PV panel leading edge, obtained for a surements, it must be pointed out that the experimental set
radiation, G, between 700 W/m2 and 1000 W/m2, a wind up was not placed at the highest level of the building roof,

Fig. 4. Temperature measured and relative uncertainty in correspondence of the surface of the front PV panel with a 30 mm frame (model 1).
 F. Arpino et al. / Solar Energy 118 (2015) 7–19 11

Fig. 5. Temperature measured and relative uncertainty in correspondence of the surface of the rear PV panel with a 30 mm frame (model 1).

and a stepping-up wall delimitating a higher level roof was two panels averaged temperature and the difference maxi-
present at a distance of approximately 6 m upstream the mum–minimum of the solar radiation is equal to
wind direction, with an height of approximately 2 m. 5.5  102 °C m2 W1 when the wind velocity, u, is
In Figs. 6 and 7 the experimental results obtained, 0.8 m/s; such ratio decreases to 3.9  102 °C m2 W1 for
respectively, for the front and the rear PV panels with a a wind velocity, u, equal to 1.6 m/s.
frame of 50 mm (model 2) are reported. The temperature
profiles in the figures are plotted as a function of the dis- 3. Uncertainty analysis
tance from the PV panel leading edge for a radiation, G,
between 350 W/m2 and 950 W/m2, a wind speed, u, ranging In order to carry out the temperature profile on the test
from 0.6 m/s to 1.8 m/s and an air temperature, Ta, panels, 6 thermocouples (Tc1–Tc6), type K, vertically
between 30 °C and 38 °C. The three thermocouples are arranged, according to the scheme of Fig. 3, have been
placed at a distance from the PV modules leading edge of used. The four thermocouples located near the lateral edges
270, 420 and 750 mm. From the measurements it can be (Tc7–Tc10) have been used only with the purpose to evalu-
observed that, as expected, the PV panels average temper- ate the non-uniformity of the temperature profile over the
ature increases as the solar radiation, G, increases. The entire surface.
temperature difference between the leading and the trailing The uncertainty associated with the temperature mea-
edges of each PV panel, seems less pronounced if compared surement was estimated on the basis of UNI CEI ISO
to the panel with a frame of 30 mm thick. The measured 13005 (2000) with the following parameters:
temperature was in fact lower than 10 °C when the solar
radiation, G, was comprised between 900 W/m2 and – calibration, ucal;
1000 W/m2. In particular, for the analyzed frame size, the – accuracy, uacc;
ratio between the difference maximum–minimum of the – uncertainty of contact, ucon;

Fig. 6. Temperature measured and relative uncertainty in correspondence of the surface of the front PV panel with a 50 mm frame (model 2).
12 F. Arpino et al. / Solar Energy 118 (2015) 7–19

Fig. 7. Temperature measured and relative uncertainty in correspondence of the surface of the rear PV panel with a 50 mm frame (model 2).

– uniformity of the surface, uuni; The temperature measurement uncertainty (kf = 2) has
– standard deviation of the mean, rm. been estimated equal to:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
As regard the first two parameters, all thermocouples ut ¼ 2 u2cal þ u2acc þ u2con þ u2uni þ r2m ¼ 1:4  C ð1Þ
used were previously calibrated in a thermostatic bath in
the range 10 °C to 120 °C, using a PT25 standard directly
traceable to the national standards. The calibration uncer- 4. Mathematical model, computational domain and boundary
tainty is 0.5 °C (kf = 2), including the resolution of the sen- conditions
sor. The maximum error found in calibration was not
greater than 0.4 °C, in the range explored. The verification Experiments were accompanied by numerical investiga-
of calibration carried out at the end of the test showed a tions that allowed a better understanding of temperature
negligible drift. and velocity fields in correspondence of the two PV panels.
As regards the contact error, the sensitive element of Since measurements showed that the wind blew mainly
each thermocouple have the exposed junction, with spher- from south to north, the experimental apparatus has been
ical shape of diameter approximately equal to 1.5 mm. numerically reproduced by means of two-dimensional
During the installation, particular attention has been paid steady-state simulations. The computational domain and
to ensure intimate contact between the bulb and the mea- the boundary conditions employed are available in Fig. 8,
surement surface, binding the same bulb with a thermal where the fluid domain is represented in blue1, the PV
paste having a thermal conductivity of 9 W/m/K. No modules are painted in red, while the aluminum frame
signs of detachment was detected during the test campaign. together with the supporting insulating plate are green.
The use of the thermal paste with type K thermocouples Simulations have been conducted using the finite element
has also been tested in the Laboratory of Industrial based commercial software Comsol MultiphysicsÒ.
Measurements (LaMI) of the University of Cassino, gener- The air has been assumed incompressible and ideal. The
ally ensuring a contact error less than 0.8 °C in the temper- fluid velocity, pressure and temperature fields have been
ature range explored. obtained by solving the well known mass, momentum and
The difference between the readings of the sensors placed energy conservation equations (Lewis et al., 2004), not
on the median and the ones positioned near the lateral edges reported here for brevity. The buoyant forces have been
showed a deviation generally increasing with the irradiation taken into account invoking the Boussinnesq approxima-
and always less than 0.1 °C/cm. The uncertainty of position- tion, while turbulence was modeled using the Reynolds
ing the sensors on the panel is estimated to be 0.6 cm, there- Averaged Navier Stokes (RANS) approach. In particular,
fore the non-uniformity contribution is equal to 0.06 °C. numerical investigations have been performed by employing
The acquisition device has been programmed to acquire the following two RANS based turbulence models: (i) the
and store data from sensors at intervals of 30 s for the Re-Normalization Group (RNG) k–e; (ii) and the standard
entire day. For purposes related to this research, only the k–x turbulence model (Wilcox, 2006). In fact, the RNG k–e
data captured during stable boundary conditions model allows to account for the effects of smaller scales of
(±50 W/m2 for solar radiation and ±0.5 m/s for wind) motion, while the k–x one allows an accurate prediction
have been used, by calculating the average of at least 15
consecutive readings. The standard deviation was always 1
For interpretation of color in Fig. 8, the reader is referred to the web
better than 1.6 °C. version of this article.
 F. Arpino et al. / Solar Energy 118 (2015) 7–19 13

Fig. 8. Numerical modeling of photovoltaic panels: computational domain and employed boundary conditions.

of velocity field in the proximity of solid walls (Zaı̈di et al., (Versteeg and Malalasekera, 1995; Hirsch, 1989). The con-
2010; Versteeg and Malalasekera, 1995). Additional terms stants used into the model are:
have been considered in the turbulence models to take into
C l ¼ 0:0845 rk ¼ 1 re ¼ 1:3 C e1 ¼ 1:44
account buoyant effects (Braga and Lemos, 2008, 2009). ð5Þ
Results obtained by employing the two turbulence models C e2 ¼ 1:92 b0 ¼ 0:012 g0 ¼ 4:377
have been compared to experiments in order to identify
the most appropriate model for the description of the prob- k–x model
lem under investigation. In the following, the Partial
Differential Equations (PDEs) solved for the RNG k–e The equation related to the turbulent kinetic energy k is
and standard k–x turbulence models are briefly reported. the same to that reported above for the RNG k–e model.
Specific dissipation rate x:
RNG k–e model   
@ @ lt @x
ðqxui Þ ¼ lþ
Turbulent kinetic energy k: @xi @xi rx @xi
     x mT
@ðui kÞ @ mT @k þ a P k  b0 qx2 þqb g  rT ð6Þ
q ¼q mþ k |fflffl{zfflffl} r
@xi @xi rk @xi |fflffl{zfflffl} Yx
T
  Px
@ui @uj @ui mT
þ lT þ qe þ qb g  rT ð2Þ where Px and Yx are, respectively, the source and sink
@xj @xi @xj rT
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} terms for k and x (Versteeg and Malalasekera, 1995;
P k ¼lT P t
Hirsch, 1989). The constants values used into the model are:
Turbulent dissipation e: b0 ¼ 0:072 a ¼ 0:52 rx ¼ 0:5 rt ¼ 0:85 ð7Þ
    
@ðui eÞ @ mT @e
q ¼q mþ In order to solve the above mathematical model, an
@xi @xi re @xi
  appropriate set of boundary conditions (BCs) has been
e @ui @uj @ui e2 imposed. With reference to Fig. 8, in order to accurately
þ C e1 lT þ q ðC e2
k @xj @xi @xj k reproduce experiments, a uniform horizontal velocity has
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
P e ¼C e1 ke lT P t been imposed in correspondence of the BG side of the
mT domain, while a no-slip condition has been adopted for
þ RÞ þ qb g  rT ð3Þ the AG side. In fact, the AG side represents a step that delim-
rT
itates the roof level at which experiments were carried out
The additional term R is obtained from the following from an upper level of the building. A symmetry BC was
equations: imposed in correspondence of the side BC of the domain,

C l g3 1gg
whereas a zero-pressure boundary condition was consid-
0
R¼ ð1þb g3 Þ
ered at the outlet section (side CD). As regards BCs used

0
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi ð4Þ for the resolution of the energy conservation equation, a
k @ui @uj @ui pffiffiffiffiffi
g¼e @xj
þ @xi @xj ¼ ke P t constant and uniform temperature (environmental temper-
ature) was imposed at the DE, BG and AG sides. The incom-
where Pk and Pe are the source terms for the turbulent ing solar radiation was simulated imposing the following
kinetic energy, k, and turbulent dissipation, e, respectively heat flux to the upper surface of the PV modules:
14 F. Arpino et al. / Solar Energy 118 (2015) 7–19


qirr ¼ er Gf1  g0 ½1  cðT  T 0 Þg  rer T 4  T 4a ð8Þ capture the gradients of the quantities of interest in corre-
spondence of the boundary layers.
where er represents the emissivity of the module surfaces, The temperature contours obtained in correspondence
experimentally estimated to be equal to 0.95; G is the solar of the rear and the front PV panels are available in
radiation; g0 represents the module efficiency at a tempera- Fig. 10, while in Fig. 11 are reported the velocity field
ture T0 = 25 °C; c is the relative thermal coefficient of mod- and the streamlines computed in the whole domain,
ule efficiency; r = 5.67  108 W m2 K4 is the Stefan– together with a view of detail in correspondence of the
Boltzmann constant; T and Ta are, respectively, the local leading edge of both PV modules. From the analysis of
temperature and the ambient temperature. The bottom such figures it can be clearly evidenced a recirculation zone
sides of the PV panels, the frame surfaces and the upper in correspondence of the PV panels leading edge, that is
side of the insulating panel exchange heat with the air by responsible for a significant variation of heat transferred
convection and with the surroundings and the other sur- from the module to the surrounding air. As expected the
faces by radiation. To this aim, the surfaces are considered presence of the step upstream the wind direction generates
to behave as a gray body. The remaining domain sides have a large recirculation zone, that behaves in practice as a
been assumed to be adiabatic. wind screen at low wind speeds. The comparison between
numerical and experimental data is available in Fig. 12.
5. Model validation Error bars in Fig. 12 represent the measurement uncer-
tainty associated to experiments. In particular, Fig. 12a
Results from numerical investigations have been firstly shows the temperature profile numerically obtained in cor-
validated against data collected during experiments. On respondence of the front PV module as a function of the
the basis of available measurements, the main input param- distance from the panel trailing edge, while Fig. 12b refers
eters reported in Table 1 were used for numerical simula- to the rear PV module. Numerical results have been
tions. Since it has been experimentally observed that the obtained employing both RNG k–e and standard k–x tur-
wind direction was from south to north when measure- bulence models. From the analysis of Fig. 12 it is possible
ments reported in Figs. 4 and 5 have been conducted, com- to observe that the maximum temperature difference
parisons between simulations and experiments were carried between simulations and experiments is equal to 5 °C for
out referring to PV module with frame size of 30 mm. The the front PV module, while it is lower than 3 °C for the rear
employed computational grid is available in Fig. 9. It is PV module. Even though the two employed turbulence
composed by 418,818 triangular elements, chosen on the models produced basically the same results for the rear
basis of a proper grid sensitivity analysis. The mesh is sig- PV module, larger differences have been found between
nificantly refined in correspondence of the solid walls and the results obtained from the RNG k–e and the standard
in the proximity of the PV modules in order to properly k–x turbulence model in correspondence of the front PV

Table 1
Main input parameters used in the numerical investigations.
Parameter Value
Module installation angle, a 18°
Wind velocity, u 0.5 m/s
Ambient temperature, Ta 23.5 °C
Ambient pressure, p 101,325 Pa
Solar irradiance, G 980.7 W/m2
Module emissivity, e 0.95
Module frame emissivity, ec 0.07
Module efficiency at 25 °C, g0 14.6%
Relative temperature coefficient, c 0.48%/K
Gap between modules, dL 0.021 m
Frame length 0.015 m
Frame height 0.03 m
Installation height, d 0.04 m

Fig. 9. Computational grid composed by 418,818 quadratic triangular Fig. 10. Zoom of the temperature contours obtained in correspondence
elements. of: (a) the rear PV panel and; (b) the front one.
 F. Arpino et al. / Solar Energy 118 (2015) 7–19 15

Fig. 11. u-velocity contour and streamlines (a) together with their enlargements obtained in correspondence of the front PV panel (b) and the rear one (c).

Fig. 12. Temperature profile on the upper surface of the front PV module (a) and the rear one (b), obtained for G = 980.7 W/m2, Ta = 23.5 °C and
u = 0.5 m/s.

Fig. 13. Average temperature variation with the tilt angle on the upper surface of the front PV module (a) and the rear one (b), obtained with the frame
height of 3 cm.
16 F. Arpino et al. / Solar Energy 118 (2015) 7–19

Fig. 14. Average temperature variation with the tilt angle on the upper surface of the front PV module (a) and the rear one (b), obtained with the frame
height of 5 cm.

Fig. 15. Average temperature variation with the installation height on the upper surface of the front PV module (a) and the rear one (b), obtained with the
frame height of 3 cm.

module. In fact, the temperature difference between simula- 6. Numerical results

tions from the RNG k–e model and measurements is equal
to 5 °C in correspondence of the center of the module, and In this section a parametric analysis was carried out in
2 °C at the two panel ends. The deviation between exper- order to analyze the effects of same geometrical and
iments and simulations using the standard k–x turbulence fluid-dynamics parameters on PV modules performance.
are equal to 5 °C in correspondence of the first half of the In particular, with reference to the base case discussed in
PV front module, and 2 °C in the second half. Section 4, a sensitivity analysis was performed as a function
The discrepancy between numerical results and experi- of the following influence factors: the modules installation
ments is comparable with the expected uncertainty affect- tilt angle, installation height, frame size and the wind
ing the temperature measurements, that depends not only velocity.
on the sensor metrological performance, but also on the Since the main aim of this paper consists of the investi-
significant variability of the environmental conditions, gation of PV modules performance dependence on installa-
hardly reproducible in numerical investigations. It must tion, frame size and fluid-dynamic field, in the present
also be pointed out that the proposed numerical results analysis solar radiation that reaches PV modules is kept
have been obtained from a two-dimensional model. As a constant.
consequence, the validation proposed in Fig. 12 is consid-
ered acceptable within the present work. 6.1. PV modules installation tilt angle
Since the RNG k–e model showed a better agreement
with experiments, it has been selected for the parametric The PV modules average temperature and efficiency
numerical analysis reported in the next section. (evaluated on the basis of the temperature coefficient)
 F. Arpino et al. / Solar Energy 118 (2015) 7–19 17

numerically estimated as a function of the installation tilt 6.2. PV modules installation height
angle is available in Fig. 13 and in Fig. 14, for a frame
height of 30 mm and 50 mm, respectively. The installation In this subsection PV modules performance is discussed
tilt angle considered is in the range between 15° and 30°. for different installation heights. Results in Fig. 15 have
The difference of the average temperature was, for both been obtained for the PV module with a frame size of
the considered frame sizes, of 4 °C on the front panel 30 mm and with an installation height ranging from
and 6 °C on the rear panel, when the installation tilt angle 0 mm (distance panel-support equal to 23 mm) to 80 mm
ranges from 15° to 30°. In fact, even though the optimal tilt (distance panel-support equal to 103 mm). In the case of
angle depends on the site latitude, it is common to observe total absence of the fixing bar (panels directly mounted
different installation angles. on the support: d = 0), the averaged temperatures is
From the analysis of the obtained results it is possible to 90 °C. Increasing the installation height from 0 mm to
observe that the modules averaged temperature decreases 40 mm and then to 60 mm, a significant temperature drop
as the tilt angle increases. In the same way, the mean effi- is evidenced for both PV models considered. In particular,
ciency value increases as the angle of installation increases. the averaged temperature of the front PV panel drops from
The lowest average temperature (56 °C) was found in cor- 90.1 °C to 59.1 °C when the installation height increases
respondence of the front module for a frame height of from 0 mm to 40 mm. In the same conditions, the averaged
30 mm and a tilt angle of 30°; the correspondence maxi- temperature of the rear PV panel decreases from 88.5 °C to
mum value of the efficiency was found equal to 0.124. 66.0 °C. A further increment of d from 40 mm to 60 mm

Fig. 16. Average temperature variation with the installation height on the upper surface of the front PV module (a) and the rear one (b), obtained with the
frame height of 5 cm.

Fig. 17. Average temperature variation with the u-velocity on the upper surface of the front PV module (a) and the rear one (b), obtained with the frame
height of 3 cm.
18 F. Arpino et al. / Solar Energy 118 (2015) 7–19

Fig. 18. Average temperature variation with the u-velocity on the upper surface of the front PV module (a) and the rear one (b), obtained with the frame
height of 5 cm.

produces a averaged temperature drop of 2.2 °C for the efficiency optimization. In particular, temperature and effi-
front PV panel and of 3.5 °C for the rear PV panel. Such ciency dependence on the aluminum frame size, distance
temperature difference produces an efficiency variation of between photovoltaic panel and supporting panel, tilt angle
0.2%. Results obtained for an installation height of the module, and environmental operating conditions,
d = 80 mm are very similar to that produced for with particular reference to the wind velocity, was ana-
d = 60 mm. lyzed. Experiments were conducted on a pair of solar pan-
Numerical results in Fig. 16 have been obtained for the els arranged horizontally and mounted on a frame
PV module with a frame of 50 mm. Even though results are structure, able to reproduce different tilt angles of installa-
very similar to that in Fig. 15, it can be noticed that the tion, from 0° to 90°. Experiments were accompanied by
averaged temperature is generally smaller, for both front numerical investigations that allowed a better understand-
and rear PV modules, with respect to the model with a ing of temperature and velocity fields in correspondence of
frame of 30 mm. When the installation height, d, is sup- the two PV modules. Since measurements showed that the
posed to be 0 mm, the averaged temperature resulted to wind blew mainly from south to north, the experimental
be 2 °C larger with respect to the model 1 case. apparatus has been numerically reproduced by means of
Increasing the installation height, such temperature differ- two-dimensional steady-state simulations. A detailed
ence also increases reaching a value of 5 °C, suggesting numerical simulation of the actual PV testing configuration
that a frame size of 50 mm is advantageous in terms of has been conducted employing the commercial CFD code
PV module performance. Comsol MultiphysicsÒ. Turbulence has been modeled
using the RANS approach and the RNG k–e and standard
k–x two-equations models. The model was validated and
6.3. Wind velocity
good agreement was obtained between numerical and
experimental data. In particular, the RNG k–e model bet-
Figs. 17 and 18 show the PV modules averaged temper-
ter reproduced experiments. The validated numerical tool
ature and efficiency as a function of the wind velocity.
has been employed to perform a parametric analysis in
Simulations have been performed ranging such parameter
order to analyze the effects of same geometrical and
from 0.1 m/s to 0.6 m/s. The maximum averaged tempera-
fluid-dynamics parameters on PV modules performance.
ture variation for both PV models was 1 °C in the consid-
Keeping constant the solar radiation that reaches the PV
ered wind velocity range. The low dependence of PV
panels, it has been observed that the efficiency increases
modules temperature on wind velocity is due to the step
as the tilt angle and the installation height increase.
that is present upstream the wind velocity direction, mod-
Furthermore from the conducted investigations it has been
eled trough the wall AG in Fig. 8. This aspect was also evi-
evidenced that installing the PV modules directly on the
denced by experiments.
roof the averaged temperature reaches 90 °C and the effi-
ciency significantly drops. At the same time, an installation
7. Conclusions of the PV modules at a height larger than 60 mm does not
produce a significant efficiency improvement. Finally,
In this paper the authors investigated experimentally numerical analysis evidenced that a frame size of 50 mm
and numerically a two PV modules assembly aimed at generally allows better performance with respect to the
providing installation and operating indications that allow PV modules with a frame size of 30 mm.
 F. Arpino et al. / Solar Energy 118 (2015) 7–19 19

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