Experimental and numerical assessment of photovoltaic collectors performance dependence on frame size and installation technique

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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, Universita` 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

Communicated by: Associate Editor Brian Norton

Abstract The performance of a solar photovoltaic silicon panel is inversely proportional to its operating temperature. Therefore the overheating 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 temperature 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 performance 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 The ever growing energy demand and environmental pollution level has pushed research interest toward more efficient conversion of solar to electric energy (Sun and Sariciftci, 2005; Bube, 1998; Yin et al., 2013; Dovic´ Damir, 2012). In this context, photovoltaic (PV) panels represent a potentially clean and renewable energy production technique, that can reduce the dependence on traditional energy sources. In the recent years a significant ⇑ Corresponding author.

E-mail address: [email protected] (F. Arpino). http://dx.doi.org/10.1016/j.solener.2015.05.006 0038-092X/Ó 2015 Elsevier Ltd. All rights reserved.

amount of research has been conducted to increase PV collectors efficiency, and new designs have been proposed for building applications, based on PV modules optical, thermal and electrical generation characteristics (Buonanno et al., 2005; Himanshu, 2009; Arcuri and Reda, 2014). From the optical point of view, modules efficiency can be increased by using non-reflective coatings that enhance optical transmission. Besides, a better efficiency can be obtained by ensuring operating conditions that avoid collectors overheating and the consequent loss of their electric efficiency (inversely proportional to their operating temperature). A typical efficiency value for crystalline Si-based cells is 14–17% and the non converted solar radiation

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Nomenclature G g k kf Px Pk Pe R T Ta ui Yk xi

solar radiation acceleration due to gravity turbulent kinetic energy coverage factor source terms for x source term for k source term for e additional RNG k–e term temperature ambient temperature velocity components sink terms for x coordinate axes

energy, released as thermal energy, may cause PV modules to overheat (Tripanagnostopoulos et al., 2002). PV cells will also exhibit long-term degradation if the temperature exceeds 80–85 °C (Brinkworth et al., 1997; Gra¨tzel, 2004). Therefore effective PV module cooling must be ensured by acting on the Convective Heat Transfer Coefficient (CHTC), that depends on different geometrical and thermodynamics parameters as: wind speed, wind direction, tilt angle of the panel, installation height (distance support-frame), size of the exposed surface and its roughness, air temperature. Various experimental studies on solar collectors flush mounted on the inclined roof of a building were performed. Kind et al. (1983) carried out a wind tunnel study on an array of solar collectors mounted on a 60° inclined roof of a 1:32 scale model house, showing a variation of the heat transfer within 30% for the different wind directions investigated. Results also showed that the CHTC is maximum when the wind direction is perpendicular to the panel. Shakerin (1987) also performed a wind tunnel study on a single solar collector flush mounted on the roof of a scale model of a house with different tilt angles. It was claimed that the flow over the collector was turbulent for inclination angles lower than 40° and laminar for inclination angles larger than 40°. Sartori (2006) compared empirical equations of the CHTC for forced air flow over flat plate solar collectors, with the boundary layer correlation for the convective heat transfer over an horizontal flat plate. The comparison showed that the flow over flat plate solar collectors is generally turbulent and the boundary layer correlation for turbulent flow under predicts the CHTC values significantly. In most of the cases of practical interest, correlations available in the scientific literature for the Nusselt number calculation are not accurate (Bejan and Kraus, 2003). Detailed numerical modeling of temperature and velocity fields is then very useful to obtain more accurate results. In fact, Computational Fluid Dynamics (CFD) can

Greek symbols b thermal expansion coefficient c relative thermal coefficient of module efficiency e specific dissipation rate of k in the k–e model er emissivity of the module surface g0 module efficiency at a temperature T 0 ¼ 25  C l dynamic viscosity lt turbulent dynamic viscosity m cinematic viscosity mt turbulent cinematic viscosity q density r Stefan–Boltzmann constant x specific dissipation rate of k in the k–x model

provide a flexible and cost-effective tool to select advantageous configurations from alternative design strategies, which can be subsequently tested in detail either in laboratory or on field. Taking advantage of a validated CFD tool (Arpino et al., 2011, 2013), it is possible to predict and improve thermal performance of a specific PV module design, significantly reducing time and cost required by experiments. Velocity and length scales considered require the adoption of a proper turbulence model. Given the complexity of the problem, turbulence is typically described using the Reynolds Averaged Navier Stokes (RANS) approach and the two-equations, typically k–epsilon (k–e) or k–omega (k–x), turbulence closure models, where k is the turbulent kinetic energy while e and x refer to the turbulent dissipation rate. Such turbulence modeling approach is based on the description of time-averaged properties of the flow, allowing significant reduction of required computing resources. Looking at the scientific literature, different heat and mass transfer numerical simulations have been proposed assimilating the PV panel to a wall mounted cube immersed in a turbulent boundary layer. For instance, such an approach has been adopted by Nicˇeno et al. (2002), Ratnam and Vengadesan (2008), Blocken et al. (2009) and Defraeye et al. (2010). Different turbulent models have also been used. A Large Eddy Simulation (LES) with Spalart’s adjustment in the near wall region, referred as Detached Eddy Simulation (DES), was performed by Nicˇeno et al. (2002). Ratnam and Vengadesan (2008) performed unsteady numerical simulations using standard k–e, low-Re k–e, non-linear k–e, standard k–x and improved k–x turbulence models. They evidenced that results obtained from the non-linear k–e, improved k–x and standard k–x turbulence models agreed well with the experimentally measured temperature profiles at the front and back faces of the cube. Besides, Meroney and Neff (2010) studied the wind effects on roof mounted solar photovoltaic arrays employing different

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turbulence models, showing that the RNG k–e and the k–x models produced reasonable agreement with measurements, 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 efficiency, 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 operating indications that allow efficiency optimization. The PV modules were installed and tested on the roof of the DICeM building of the University of Cassino (Italy). A detailed numerical simulation of the actual PV testing configuration has been conducted employing the commercial CFD code Comsol MultiphysicsÒ, validated against the collected experimental data. On the basis of findings in the scientific literature, turbulence was modeled using the RANS approach and the RNG k–e and standard k–x two-equations models. In particular, the work consists of a study of the effects induced by the thickness of the aluminum frame of a PV module and by the installation techniques (distance panel-supporting panel, tilt angle of the module), on its temperature and efficiency. On the basis of the obtained results, indications about PV collectors installation and frame optimal size are obtained in order to optimize operating conditions and efficiency. 2. Experiments Experimental investigations have been conducted on a two commercially available PV modules assembly installed on the roof of the DICeM building of the University of Cassino. A picture of the experimental apparatus is available in Fig. 1. In particular, it consists of a pair of PV panels arranged horizontally and mounted on a frame structure, with the ability to simulate different roof tilt angles, from 0° to 90°. The PV modules are anchored on a panel of insulating material with a thickness of 40 mm, which simulates actual operating condition of PV panels installed on a roof. A diagram of different components of the investigated assembly is available in Fig. 2. Two models of PV module have been experimentally investigated: (i) the model 1, with a size of 1675  1000 mm and an aluminum frame thickness, h, of 30 mm, characterized by a nominal power of 245 W; (ii) the model 2, with a size of 1655  990, and with an aluminum frame thickness, h, of 50 mm, characterized by a nominal power of 260 W. Considering the size of the fixing bar, d = 40 mm (Fig. 2), the thickness of the PV panel

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Fig. 1. PV collectors assembly employed for experimental investigations.

(5 mm) and the gap (2 mm) between the frame and the glass above, it can be observed that: the distance between the lower surface of the PV module with a 30 mm frame and the upper surface of the insulating support is equal to 63 mm; the distance between the lower surface of the PV module with a 50 mm frame and the upper surface of the insulating support is equal to 83 mm. Experiments have been conducted with a tilt angle of 18° (typical inclination of the roofs of the buildings in central and southern Italy) and an azimuth angle equal to zero. The PV modules were mounted according to the installation procedure provided by the manufacturer, using the support bars and the clamping nuts specifically supplied (Fig. 1), resulting in a gap between the two panels of 21 mm. The temperature of the PV panels and supporting plate were constantly monitored through 10 thermocouples positioned on the back surface of the modules. A schematic of the position of different thermocouples on the back surface the PV modules is presented in Fig. 3. Solar radiation was monitored by means of 2 pyranometers which measured the total and diffuse irradiation incident on the PV panel surface. The wind was monitored using an anemometer which measured the wind velocity and direction, located very close to the support, behind the panel under test. All the sensors and meters were connected to a multimeter and collected data was stored in a dedicated PC. The collection interval was 30 s. The numerous data obtained were, therefore, averaged into time intervals corresponding to a variation of solar radiation no greater than 50 W/m2. The panels were electrically connected to a variable resistor with a max power of 1000 W adjustable with steps of 50 W, sufficient to dispose of all the power generated by the system. In Figs. 4 and 5 the experimental results obtained, respectively, for the front and the rear PV panel with frame of 30 mm (model 1) are reported. In particular, the three measurement points correspond to a distance from the leading edge of 150, 485 and 820 mm, respectively. In such figures the temperature profiles are plotted as a function of

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

Fig. 3. Layout of the thermocouples installed on the PV collectors.

the distance from PV panel leading edge, obtained for a radiation, G, between 700 W/m2 and 1000 W/m2, a wind

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 temperature 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 difference 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 surrounding air are slightly higher. In fact, an average temperature 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 velocity 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 rear PV one, where a temperature drop of 5 °C has been observed. For a better understanding of the reported measurements, it must be pointed out that the experimental set 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).

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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 present at a distance of approximately 6 m upstream the wind direction, with an height of approximately 2 m. In Figs. 6 and 7 the experimental results obtained, respectively, for the front and the rear PV panels with a frame of 50 mm (model 2) are reported. The temperature profiles in the figures are plotted as a function of the distance from the PV panel leading edge for a radiation, G, between 350 W/m2 and 950 W/m2, a wind speed, u, ranging from 0.6 m/s to 1.8 m/s and an air temperature, Ta, between 30 °C and 38 °C. The three thermocouples are placed at a distance from the PV modules leading edge of 270, 420 and 750 mm. From the measurements it can be observed that, as expected, the PV panels average temperature increases as the solar radiation, G, increases. The temperature difference between the leading and the trailing edges of each PV panel, seems less pronounced if compared to the panel with a frame of 30 mm thick. The measured temperature was in fact lower than 10 °C when the solar radiation, G, was comprised between 900 W/m2 and 1000 W/m2. In particular, for the analyzed frame size, the ratio between the difference maximum–minimum of the

two panels averaged temperature and the difference maximum–minimum of the solar radiation is equal to 5.5  102 °C m2 W1 when the wind velocity, u, is 0.8 m/s; such ratio decreases to 3.9  102 °C m2 W1 for a wind velocity, u, equal to 1.6 m/s. 3. Uncertainty analysis In order to carry out the temperature profile on the test panels, 6 thermocouples (Tc1–Tc6), type K, vertically arranged, according to the scheme of Fig. 3, have been used. The four thermocouples located near the lateral edges (Tc7–Tc10) have been used only with the purpose to evaluate the non-uniformity of the temperature profile over the entire surface. The uncertainty associated with the temperature measurement was estimated on the basis of UNI CEI ISO 13005 (2000) with the following parameters: – calibration, ucal; – accuracy, uacc; – 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).

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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; – standard deviation of the mean, rm. As regard the first two parameters, all thermocouples 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 uncertainty is 0.5 °C (kf = 2), including the resolution of the sensor. The maximum error found in calibration was not greater than 0.4 °C, in the range explored. The verification of calibration carried out at the end of the test showed a negligible drift. As regards the contact error, the sensitive element of each thermocouple have the exposed junction, with spherical shape of diameter approximately equal to 1.5 mm. During the installation, particular attention has been paid to ensure intimate contact between the bulb and the measurement surface, binding the same bulb with a thermal paste having a thermal conductivity of 9 W/m/K. No signs of detachment was detected during the test campaign. The use of the thermal paste with type K thermocouples has also been tested in the Laboratory of Industrial Measurements (LaMI) of the University of Cassino, generally ensuring a contact error less than 0.8 °C in the temperature range explored. The difference between the readings of the sensors placed on the median and the ones positioned near the lateral edges showed a deviation generally increasing with the irradiation and always less than 0.1 °C/cm. The uncertainty of positioning the sensors on the panel is estimated to be 0.6 cm, therefore the non-uniformity contribution is equal to 0.06 °C. The acquisition device has been programmed to acquire and store data from sensors at intervals of 30 s for the entire day. For purposes related to this research, only the data captured during stable boundary conditions (±50 W/m2 for solar radiation and ±0.5 m/s for wind) have been used, by calculating the average of at least 15 consecutive readings. The standard deviation was always better than 1.6 °C.

The temperature measurement uncertainty (kf = 2) has been estimated equal to: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ut ¼ 2 u2cal þ u2acc þ u2con þ u2uni þ r2m ¼ 1:4  C ð1Þ

4. Mathematical model, computational domain and boundary conditions Experiments were accompanied by numerical investigations that allowed a better understanding of temperature and velocity fields in correspondence of the two PV panels. Since measurements showed that the wind blew mainly from south to north, the experimental apparatus has been numerically reproduced by means of two-dimensional steady-state simulations. The computational domain and the boundary conditions employed are available in Fig. 8, where the fluid domain is represented in blue1, the PV modules are painted in red, while the aluminum frame together with the supporting insulating plate are green. Simulations have been conducted using the finite element based commercial software Comsol MultiphysicsÒ. The air has been assumed incompressible and ideal. The fluid velocity, pressure and temperature fields have been obtained by solving the well known mass, momentum and energy conservation equations (Lewis et al., 2004), not reported here for brevity. The buoyant forces have been taken into account invoking the Boussinnesq approximation, while turbulence was modeled using the Reynolds Averaged Navier Stokes (RANS) approach. In particular, numerical investigations have been performed by employing the following two RANS based turbulence models: (i) the Re-Normalization Group (RNG) k–e; (ii) and the standard k–x turbulence model (Wilcox, 2006). In fact, the RNG k–e model allows to account for the effects of smaller scales of motion, while the k–x one allows an accurate prediction 1 For interpretation of color in Fig. 8, the reader is referred to the web version of this article.

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

of velocity field in the proximity of solid walls (Zaı¨di et al., 2010; Versteeg and Malalasekera, 1995). Additional terms have been considered in the turbulence models to take into account buoyant effects (Braga and Lemos, 2008, 2009). Results obtained by employing the two turbulence models have been compared to experiments in order to identify the most appropriate model for the description of the problem under investigation. In the following, the Partial Differential Equations (PDEs) solved for the RNG k–e and standard k–x turbulence models are briefly reported. RNG k–e model Turbulent kinetic energy k:      @ðui kÞ @ mT @k q mþ ¼q @xi @xi rk @xi   @ui @uj @ui mT þ qe þ qb g  rT þ lT @xj @xi @xj rT |fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

ð2Þ

Turbulent dissipation e:      @ðui eÞ @ mT @e q mþ ¼q @xi @xi re @xi   e @ui @uj @ui e2 þ q ðC e2 þ C e1 lT k @xj @xi @xj k |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} ð3Þ

The additional term R is obtained from the following equations:  R¼

C l g3 1gg

0

ð1þb g3 Þ

0 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi pffiffiffiffiffi @uj @ui @ui k g¼e þ @xi @xj ¼ ke P t @xj

rk ¼ 1

C e2 ¼ 1:92

ð4Þ

where Pk and Pe are the source terms for the turbulent kinetic energy, k, and turbulent dissipation, e, respectively

re ¼ 1:3

b0 ¼ 0:012

C e1 ¼ 1:44

g0 ¼ 4:377

ð5Þ

k–x model The equation related to the turbulent kinetic energy k is the same to that reported above for the RNG k–e model. Specific dissipation rate x:    @ @ lt @x ðqxui Þ ¼ lþ @xi @xi rx @xi x mT ð6Þ þ a P k  b0 qx2 þqb g  rT |fflffl{zfflffl} k r T |fflffl{zfflffl} Yx

where Px and Yx are, respectively, the source and sink terms for k and x (Versteeg and Malalasekera, 1995; Hirsch, 1989). The constants values used into the model are: b0 ¼ 0:072

P e ¼C e1 ke lT P t

mT g  rT rT

C l ¼ 0:0845

Px

P k ¼lT P t

þ RÞ þ qb

(Versteeg and Malalasekera, 1995; Hirsch, 1989). The constants used into the model are:

a ¼ 0:52

rx ¼ 0:5

rt ¼ 0:85

ð7Þ

In order to solve the above mathematical model, an appropriate set of boundary conditions (BCs) has been imposed. With reference to Fig. 8, in order to accurately reproduce experiments, a uniform horizontal velocity has been imposed in correspondence of the BG side of the domain, while a no-slip condition has been adopted for the AG side. In fact, the AG side represents a step that delimitates the roof level at which experiments were carried out from an upper level of the building. A symmetry BC was imposed in correspondence of the side BC of the domain, whereas a zero-pressure boundary condition was considered at the outlet section (side CD). As regards BCs used for the resolution of the energy conservation equation, a constant and uniform temperature (environmental temperature) was imposed at the DE, BG and AG sides. The incoming solar radiation was simulated imposing the following heat flux to the upper surface of the PV modules:

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 qirr ¼ er Gf1  g0 ½1  cðT  T 0 Þg  rer T 4  T 4a

ð8Þ

where er represents the emissivity of the module surfaces, experimentally estimated to be equal to 0.95; G is the solar radiation; g0 represents the module efficiency at a temperature T0 = 25 °C; c is the relative thermal coefficient of module efficiency; r = 5.67  108 W m2 K4 is the Stefan– Boltzmann constant; T and Ta are, respectively, the local temperature and the ambient temperature. The bottom sides of the PV panels, the frame surfaces and the upper side of the insulating panel exchange heat with the air by convection and with the surroundings and the other surfaces by radiation. To this aim, the surfaces are considered to behave as a gray body. The remaining domain sides have been assumed to be adiabatic. 5. Model validation Results from numerical investigations have been firstly validated against data collected during experiments. On the basis of available measurements, the main input parameters reported in Table 1 were used for numerical simulations. Since it has been experimentally observed that the wind direction was from south to north when measurements reported in Figs. 4 and 5 have been conducted, comparisons between simulations and experiments were carried out referring to PV module with frame size of 30 mm. The employed computational grid is available in Fig. 9. It is composed by 418,818 triangular elements, chosen on the basis of a proper grid sensitivity analysis. The mesh is significantly refined in correspondence of the solid walls and in the proximity of the PV modules in order to properly

capture the gradients of the quantities of interest in correspondence of the boundary layers. The temperature contours obtained in correspondence of the rear and the front PV panels are available in Fig. 10, while in Fig. 11 are reported the velocity field and the streamlines computed in the whole domain, together with a view of detail in correspondence of the leading edge of both PV modules. From the analysis of such figures it can be clearly evidenced a recirculation zone in correspondence of the PV panels leading edge, that is responsible for a significant variation of heat transferred from the module to the surrounding air. As expected the presence of the step upstream the wind direction generates a large recirculation zone, that behaves in practice as a wind screen at low wind speeds. The comparison between numerical and experimental data is available in Fig. 12. Error bars in Fig. 12 represent the measurement uncertainty associated to experiments. In particular, Fig. 12a shows the temperature profile numerically obtained in correspondence of the front PV module as a function of the distance from the panel trailing edge, while Fig. 12b refers to the rear PV module. Numerical results have been obtained employing both RNG k–e and standard k–x turbulence models. From the analysis of Fig. 12 it is possible to observe that the maximum temperature difference between simulations and experiments is equal to 5 °C for the front PV module, while it is lower than 3 °C for the rear PV module. Even though the two employed turbulence models produced basically the same results for the rear PV module, larger differences have been found between the results obtained from the RNG k–e and the standard 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 Wind velocity, u Ambient temperature, Ta Ambient pressure, p Solar irradiance, G Module emissivity, e Module frame emissivity, ec Module efficiency at 25 °C, g0 Relative temperature coefficient, c Gap between modules, dL Frame length Frame height Installation height, d

18° 0.5 m/s 23.5 °C 101,325 Pa 980.7 W/m2 0.95 0.07 14.6% 0.48%/K 0.021 m 0.015 m 0.03 m 0.04 m

Fig. 9. Computational grid composed by 418,818 quadratic triangular elements.

Fig. 10. Zoom of the temperature contours obtained in correspondence of: (a) the rear PV panel and; (b) the front one.

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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.

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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 simulations from the RNG k–e model and measurements is equal to 5 °C in correspondence of the center of the module, and 2 °C at the two panel ends. The deviation between experiments and simulations using the standard k–x turbulence are equal to 5 °C in correspondence of the first half of the PV front module, and 2 °C in the second half. The discrepancy between numerical results and experiments is comparable with the expected uncertainty affecting the temperature measurements, that depends not only on the sensor metrological performance, but also on the significant variability of the environmental conditions, hardly reproducible in numerical investigations. It must also be pointed out that the proposed numerical results have been obtained from a two-dimensional model. As a consequence, the validation proposed in Fig. 12 is considered acceptable within the present work. Since the RNG k–e model showed a better agreement with experiments, it has been selected for the parametric numerical analysis reported in the next section.

6. Numerical results In this section a parametric analysis was carried out in order to analyze the effects of same geometrical and fluid-dynamics parameters on PV modules performance. In particular, with reference to the base case discussed in Section 4, a sensitivity analysis was performed as a function of the following influence factors: the modules installation tilt angle, installation height, frame size and the wind velocity. Since the main aim of this paper consists of the investigation of PV modules performance dependence on installation, frame size and fluid-dynamic field, in the present analysis solar radiation that reaches PV modules is kept constant. 6.1. PV modules installation tilt angle The PV modules average temperature and efficiency (evaluated on the basis of the temperature coefficient)

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numerically estimated as a function of the installation tilt angle is available in Fig. 13 and in Fig. 14, for a frame height of 30 mm and 50 mm, respectively. The installation tilt angle considered is in the range between 15° and 30°. The difference of the average temperature was, for both the considered frame sizes, of 4 °C on the front panel and 6 °C on the rear panel, when the installation tilt angle ranges from 15° to 30°. In fact, even though the optimal tilt angle depends on the site latitude, it is common to observe different installation angles. From the analysis of the obtained results it is possible to observe that the modules averaged temperature decreases as the tilt angle increases. In the same way, the mean efficiency value increases as the angle of installation increases. The lowest average temperature (56 °C) was found in correspondence of the front module for a frame height of 30 mm and a tilt angle of 30°; the correspondence maximum value of the efficiency was found equal to 0.124.

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6.2. PV modules installation height In this subsection PV modules performance is discussed for different installation heights. Results in Fig. 15 have been obtained for the PV module with a frame size of 30 mm and with an installation height ranging from 0 mm (distance panel-support equal to 23 mm) to 80 mm (distance panel-support equal to 103 mm). In the case of total absence of the fixing bar (panels directly mounted on the support: d = 0), the averaged temperatures is 90 °C. Increasing the installation height from 0 mm to 40 mm and then to 60 mm, a significant temperature drop is evidenced for both PV models considered. In particular, the averaged temperature of the front PV panel drops from 90.1 °C to 59.1 °C when the installation height increases from 0 mm to 40 mm. In the same conditions, the averaged temperature of the rear PV panel decreases from 88.5 °C to 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.

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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 front PV panel and of 3.5 °C for the rear PV panel. Such temperature difference produces an efficiency variation of 0.2%. Results obtained for an installation height d = 80 mm are very similar to that produced for d = 60 mm. Numerical results in Fig. 16 have been obtained for the PV module with a frame of 50 mm. Even though results are very similar to that in Fig. 15, it can be noticed that the averaged temperature is generally smaller, for both front and rear PV modules, with respect to the model with a frame of 30 mm. When the installation height, d, is supposed to be 0 mm, the averaged temperature resulted to be 2 °C larger with respect to the model 1 case. Increasing the installation height, such temperature difference also increases reaching a value of 5 °C, suggesting that a frame size of 50 mm is advantageous in terms of PV module performance. 6.3. Wind velocity Figs. 17 and 18 show the PV modules averaged temperature and efficiency as a function of the wind velocity. Simulations have been performed ranging such parameter from 0.1 m/s to 0.6 m/s. The maximum averaged temperature variation for both PV models was 1 °C in the considered wind velocity range. The low dependence of PV modules temperature on wind velocity is due to the step that is present upstream the wind velocity direction, modeled trough the wall AG in Fig. 8. This aspect was also evidenced by experiments. 7. Conclusions In this paper the authors investigated experimentally and numerically a two PV modules assembly aimed at providing installation and operating indications that allow

efficiency optimization. In particular, temperature and efficiency dependence on the aluminum frame size, distance between photovoltaic panel and supporting panel, tilt angle of the module, and environmental operating conditions, with particular reference to the wind velocity, was analyzed. Experiments were conducted on a pair of solar panels arranged horizontally and mounted on a frame structure, able to reproduce different tilt angles of installation, from 0° to 90°. Experiments were accompanied by numerical investigations that allowed a better understanding of temperature and velocity fields in correspondence of the two PV modules. Since measurements showed that the wind blew mainly from south to north, the experimental apparatus has been numerically reproduced by means of two-dimensional steady-state simulations. A detailed numerical simulation of the actual PV testing configuration has been conducted employing the commercial CFD code 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 good agreement was obtained between numerical and experimental data. In particular, the RNG k–e model better reproduced experiments. The validated numerical tool has been employed to perform a parametric analysis in order to analyze the effects of same geometrical and fluid-dynamics parameters on PV modules performance. Keeping constant the solar radiation that reaches the PV panels, it has been observed that the efficiency increases as the tilt angle and the installation height increase. Furthermore from the conducted investigations it has been evidenced that installing the PV modules directly on the roof the averaged temperature reaches 90 °C and the efficiency significantly drops. At the same time, an installation of the PV modules at a height larger than 60 mm does not produce a significant efficiency improvement. Finally, numerical analysis evidenced that a frame size of 50 mm generally allows better performance with respect to the PV modules with a frame size of 30 mm.

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