An Experimental Investigation and Numerical Simulation of Photovoltaic Cells with Enhanced Surfaces Using the Simcenter STAR-CCM+ Software

Abstract

This article proposes a passive cooling system for photovoltaic (PV) panels to achieve a reduction in their temperature. It is known that the cooling of PV panels allows for an increase in the efficiency of photovoltaic conversion. Furthermore, reducing the high temperature of the surfaces of PV panels is also desirable to ensure their long-lasting operation and high efficiency. Photovoltaic panels were modified by adding copper sheets to the bottom side of the panels. Two types of modification of the outer surface of the sheet were investigated experimentally, which differed in surface roughness. One was characterised by the nominal roughness of the copper sheet according to its manufacturer, while the other was enhanced by a system of pins. Numerical simulations, performed using the Simcenter STAR-CCM+ software, version 2020.2.1 Build 15.04.010, helped to describe the geometry of the pins and their role in the resulting reduction in the temperature of the PV panel surface. As a result, modifying a typical PV panel by adding a copper sheet with pins helps to achieve a higher decrease in the temperature of the PV panel. The addition of a copper sheet with a smooth surface to the bare PV panel improved the operating conditions by lowering its surface temperature by approximately 6.5 K but using an enhanced surface with the highest number of pins distributed uniformly on the copper sheet surface resulted in the highest temperature drop up to 12 K. The highest number of pins distributed uniformly on the copper sheet surface resulted in the highest temperature drop in its bottom surface, that is, on average by more than 12 K compared to the surface temperature of the bare PV panel surface. The validation of the numerical calculations was performed on data from the experiments. An analysis of the quality of the numerical mesh was also performed using a method based on the grid convergence index.

1. Introduction

The trend towards the use of renewable energy sources is still being reinforced. Today, there is a rapidly expanding market for commercial photovoltaic (PV) solar panels that directly convert solar energy to electricity. Although methods for improving heat dissipation from PV modules are widely known, high efficiency, long lifetime, and preferably simple technical solutions are required and sought in the application of photovoltaic panels.

It is commonly known that electricity generation in photovoltaic panels increases as solar radiation increases. However, an undesirable phenomenon consequently occurs: With the increase in the temperature, the efficiency of PV panels decreases. Undoubtedly, the cooling of photovoltaic panels allows for an increase in the efficiency of photovoltaic conversion. Reducing the high temperature of PV panel surfaces is desirable to ensure the long-lasting operation and high efficiency of PV panels. A brief state-of-the-art study on photovoltaic devices was carried out, and the main findings regarding improving their efficiency by using enhanced surfaces, mini-channels, and other systems are presented in this article.

To choose an optimal method for improving the efficiency of the panels (as devices degrade with rising temperature), we performed a literature review on the various approaches to cooling photovoltaic cells and increasing their efficiency. In the literature, two main groups of cooling methods are indicated, namely active methods (e.g., water flow in channels) and passive ones (e.g., utilising heat pipes).

In a rapidly growing number of studies, researchers have tested various technical solutions by performing experiments and have conducted theoretical studies, often with the help of numerical analysis, to propose and verify the solutions to PV panel enhancement to obtain higher efficiency, taking into consideration heat transfer performance and costs. Most of the investigations focused on the cooling of PV panel surfaces. The state of the art, the scope of the studies, and the findings of interest in this subject are presented in this section [1,2,3,4,5,6,7,8,9,10,11,12,13].

A comprehensive review of the effects of cooling on the performance of photovoltaic/thermal solar panels can be found in numerous works, examples of which are [1,2,3].

Maleki et al. in [1] described and analysed the common methods used for the cooling of photovoltaic panels. According to their study, the efficiency of PV cells depends on several features such as operating conditions, solar irradiation, and the cooling method. Selected factors that influence and help to control the performance of photovoltaic panels were indicated specific to their types and materials, conditions of the ambient air, and temperature. The authors suggested that for the cooling of photovoltaic panels, different configurations should be tested to find the most appropriate type. Furthermore, the shape of the channels affects the intensity of heat transfer processes. The review was performed on the basis of previously published studies. The authors underlined that the performance of PV modules is temperature-dependent, and the efficiency of PV modules with different mountings was estimated. One of the main findings was that the highest reduction in the performance of photovoltaic panels occurred when the cells were inside the glass installed on a roof with a slight slope.

In [2], Bilen and Erdoğan reviewed 208 publications concerning solar panels. The authors concluded that solar panels cannot work with high efficiency when the panels operate at high temperatures. According to the authors, cooling the panels improves their efficiency. A variety of techniques related to PV panel cooling were reported, as well as the impact of the cooling method on reducing the operating temperature and increasing the electrical efficiency.

Sharaf et al. in [3] provided a comprehensive state-of-the-art study covering the different methods used for PV panel cooling, including active and passive ones, and phase-change material (PCM) cooling. According to the main findings of the authors, although passive cooling is low-cost, it often does not ensure a high level of improvement in the performance of photovoltaic panels. The active cooling method is usually effective in improving the performance of PV panels but is dependent on an external power source. Furthermore, PCM cooling usually provides little improvement. However, the thermal conductivity of the PCM should be improved by adding components. Adding nanoparticles to the PCM can greatly improve the performance of the PCM, but this method is costly. The addition of porous metal to the PCM could improve the cooling performance of the PCM, and this method was indicated as an economical method compared to the addition of nanoparticles.

It is well known that photovoltaic panel efficiency is a temperature-dependent function: It decreases with an increase in the temperature of photovoltaic panels, assuming constant solar radiation. According to [4], at high ambient air temperatures, when the panel temperature increased to 85 °C, there was an impact on the power output of the panels, causing a reduction in electricity production of up to 30%. Furthermore, it has been widely stated that the performance of PV panels changes with varying surface temperatures. As an example, the results of the investigations by Tripathi et al., presented in [5], showed that the surface temperature had an inverse effect on the performance of PV panels.

In terms of technological development, numerous researchers have investigated new technologies to increase the efficiency of photovoltaic cells.

Table 1. Characteristics of selected works on increasing the efficiency of PV panels by cooling the panels.

Citation	Characteristics of Investigations with PV Panel Cooling	Main Findings
[6]	Two typical monocrystalline PV panels (25 W); one of them was perforated, containing 9 holes of 1 cm diameter, distributed along its surface (the distance between holes: 85 mm in the horizontal direction, and 61.33 mm in the vertical direction); Experiment and numerical simulations (ANSYS Fluent).	The temperature of perforated PV panels was lower than the temperature of the nonperforated panels, and the temperature difference increased with an increase in the number of holes; using such PV panels can minimise overheating; The temperature of PV panels decreased with an increase in the number of through holes; The authors stated that there is a critical diameter for through holes, at which maximum cooling of the panel occurs, whereas less cooling occurs below and above the critical diameter.
[7]	Two typical PV panels (50 W): poly- and monocrystalline, set at an inclination of 20°; Goal: to identify the effect of the modifications on the temperature of the panel and velocity distribution; Proposed modifications: (i) change in PV panel frame material; (ii) change in PV panel frame geometry—holes produced on the lower and top frame sections; (iii) modification of front panel surface geometry—holes in the front surface of the panel; (ii) and (iii)—specific hole geometry; Experiment and numerical simulations (ANSYS Fluent).	The PV panel that had slits through the front surface resulted in a reduction of 4 °C in the PV panels’ operating temperature; the other variants were found to result in a temperature reduction of less than 1 °C; The modification of the PV panel frame material did not affect the panel temperature significantly; The performed numerical analysis highlighted the importance of the specific PV panel’s frame geometry and its potential influence on the panel’s effectiveness, by affecting the flow conditions; Using perforations on the front panel surface allows for a smaller area for electricity production, and it can result in higher performance of PV panels due to the enhanced passive cooling effect; however, the holes may influence the PV panels’ structural stability.
[8]	Two monocrystalline typical PV panels (80 W); Investigation of the cooling method using a cold plate attached to the PV panel; The cold plate consists of several guided channels or 0.015 m thick ribbed walls to help circulate water flow from the back of the photovoltaic panel; Experiment and numerical simulations (ANSYS Fluent).	An average decrease of 21.2 °C in the surface, as well as an increase of about 2% in electrical efficiency, 8% in thermal efficiency, and 1.6% in panel efficiency, were observed in comparison to the panel without a cooling system; An increase of 17.2% in efficiency was observed for the PV panel with the cooling plate, compared to the PV panel without the cooling system (at 15.6%); Curve-fitting equations were proposed to determine the association between the average surface temperature and the output power of the PV panel with and without the cooling system and the cooling rate of the panel.
[9]	Poly-crystalline silicon PV panel (10 W); A cooling system was proposed using thermoelectric cooling (TEC) and a water block heatsink to improve the PV panel’s performance; Experiments were conducted for PV panels without and with the cooling system.	The temperature of the PV panel was found to decrease by 16.04%, while the average output power of the PV panel increased (from 8.59 to 9.03 W); By developing a hybrid cooling system (TE modules and water), the output power of the PV panel increased by 5.12%, due to the reduction in the operating temperature of the PV panel (from 56.03 °C to 47.04 °C).
[10]	Typical PV panel (276 W); A cooling channel system with a small rectangular cross-section (4 mm × 5 mm), placed in a parallel array (rows connected in serpentine shape); Cooling medium: mixture of water and ethylene glycol; The panel system was connected to a geothermal cooling system (with pipes in the ground).	The difference between the average temperatures of the two panels without and with additional cooling was up to 17 °C with the higher intensity of solar radiation; The maximum electrical power for the cooled panel was 45 W more than the noncooled PV panel; however, the electrical power difference gradually decreased with decreasing solar energy.
[11]	Typical PV panel; Cooling channel system with multiple porous deflectors elliptic in shape; Cooling medium: nanofluids (alumina nanoparticles mixed in water).	The best cooling performance was achieved when five deflectors with an aspect ratio of 1 were mounted, and a nanofluid at a solid volume fraction of 0.03 was used in a cooler. This system provided a 13.7 °C lower temperature and 107.5% higher Nusselt number compared to the reference PV panel.
[12]	Typical polycrystalline silicon PV panels, 280 W electrical power output; Cooling system with various numbers of segments (U-tube) on the panel backside; The cooling medium: a water–glycol mixture; The system was equipped with a dual-axis sun tracking system (allowing for changing the panels’ position within the inclination from 0° to 270° and orientation angle from 0 to 90°).	The use of solar tracking systems and cooling systems increased the gross efficiency of photovoltaic installations: for sunny days, the increase in gross efficiency reached 6.5%, while an additional 1% increase in efficiency was achieved by using a cooling system; The application of a cooling system with six segments proved the efficient cooling of the PV panel, ensuring its maximum temperature at approx. 32 °C in summer.
[13]	Two monocrystalline typical PV panels (50 W), one with PCM and the other without PCM (the reference PV panel); PCM was applied in the aluminium frame at the rear of the PV panel in a semi-solid state; Experimental investigation (voltage, current, thermal performance, power output, and efficiency).	PCM-based PV panel achieved a temperature lowering of 25% compared to the reference one; had higher output power and efficiency; The average atmospheric temperature remained lower than the PCM’s temperature; An increase in temperature reduction and improvement in PV panel efficiency were observed with the increase in heat storage using by PCM; Generally, PCM-based PV panels achieved a lower temperature, boosting electrical efficiency and power output.

shows the characteristics of the selected works that focused on increasing the efficiency of PV panels by cooling the panels. The main topic of these articles was investigating the influence of the temperature of PV panels, by using additional cooling systems and/or modifications in PV panel construction, as a way to improve their efficiency.

According to state-of-the-art research, several cooling techniques have been studied and implemented to reduce the temperature of the bottom surface of photovoltaic panels, which include the following methods:

• Modifications to the surface of photovoltaic panels, for instance, due to their perforation [6,7];
• Attaching a PV panel cooling system with channels of different geometries [8,9,10,11,12];
• Using various improvements in the cooling channel system, such as porous deflectors [11];
• Adding nanofluids to a typical cooling medium [11];
• Using an additional system to change the position of the cooled photovoltaic panels, such as a sun tracking system [12];
• Adding a PCM-based system [13].

It is worth mentioning that thermal management approaches are more useful for hot climate conditions because of the corresponding high working temperatures of PV cells, which reduces their power generation capabilities. Although in recent years, the range of technological solutions for the cooling of photovoltaic cells has considerably broadened, the results are inconsistent. Studies focussing on systems with an enhanced structure have highlighted their potential to serve as cooling systems. It should be noted that innovative methods are still being sought to improve the effectiveness of photovoltaic panel cooling.

This article proposes a passive and environmentally friendly cooling system for photovoltaic panels. A photovoltaic panel with additional copper sheets (with a smooth surface and pins) was tested to investigate whether this structure would improve the cooling of the surface of the photovoltaic panel. This proposal was tested experimentally and numerically. Numerical simulation was performed using the Simcenter STAR-CCM+ software.

Despite the fact that methods for improving heat dissipation from PV modules are widely known, efficient, environmentally friendly, and preferably simple technical solutions are still needed. The proposed solution does not require power and is environmentally safe, fully recyclable, and maintenance-free. It also ensures the safe operation of the PV panels. Moreover, it does not require any modification of the common photovoltaic panels available in the world market. In zones with the highest degree of sunlight and, consequently, with the highest risk of overheating in PV panels, cooling their bottom surface intensifies the dissipation of excessive heat, which has a positive impact on protecting devices against potential failures. Furthermore, by additional cooling, the period of the use of these products, that is, the lifetime of photovoltaic panels, would be extended.

The novelties of this work are as follows: (i) the modification of a typical photovoltaic panel by adding a copper sheet with pins and testing whether this helps to achieve a better effect in terms of the decrease in the temperature of the PV panel; (ii) a numerical analysis of pins with various geometric dimensions installed on the outer surface of the copper sheet; (iii) the validation of numerical calculations, based on data from experiments; and (iv) an analysis of the quality of the numerical mesh using a method based on the grid convergence index.

2. Experiment

2.1. Experimental Stand

The experimental stand consisted of a photovoltaic (PV) panel, a charging regulator, and a gel battery (Figure 1).

The essential element of the setup was a monocrystalline PV panel, model MP-30WP, which was chosen as a typical photovoltaic device (Figure 2). The PV panel was tested during an imposed heat flux to determine the effect of solar exposure on its top side (Figure 2a). To realise enhanced cooling through natural convection, a metal sheet made of copper, considered a highly conductive material, was used, which is a common and popular solution. The bottom side of the panel was equipped with two additional copper sheets, which are illustrated in Figure 2b. The dimensions of each copper sheet were 2 mm in thickness, 120 mm in width, and 500 mm in length.

In Figure 3, two views of the opposite sides of the PV panel with the arrangement of copper sheets are shown: one from the top side (Figure 3a) and the other from the bottom side (Figure 3b).

Two types of modifications of the outer surface using copper sheets (in contact with ambient air) were simultaneously investigated, which differed in surface roughness. One was characterised by the nominal roughness of the copper sheet according to its manufacturer. This copper sheet was named ‘smooth’. The other copper sheet, named ‘with pins’, was characterised by a mechanically modified outer surface due to milling. The pins were manufactured with a CNC machine to achieve a depth of 0.5 mm and a width of 4 mm, spaced every 5 mm. Both copper sheets were connected to the bottom part of the PV panel using a thermal paste with a conductivity coefficient equal to 0.78 W/(mK) [14]. Figure 4 illustrates the components of the PV panel according to its manufacturer [15]. The milled pins formed squares with a side length of 4 mm. Figure 4 shows a cross-section diagram, in addition to the typical elements (a protective glass panel; EVA (ethylene–vinyl acetate) foil layers provided by the manufacturer; a silicon layer; and a thermal paste layer). The arrangement of pins in the copper sheet is also shown, with the dimensions of the pins set as A = 4 mm, H = 0.5 mm, W = 1 mm, and P = 5 mm.

2.2. Experimental Procedure

The surfaces of the bare PV panel and both copper sheets of the modified part of the panel on the bottom side and the corresponding fragments of the top side surface were covered with sprayable black backing paint. This black paint (its manufacturer is LCR Hallcrest, LLC, Glenview, IL, USA) is characterised by an emissivity of 0.98. To conduct an experiment under real operating conditions, the PV panel was set at an angle of 45 degrees to the horizontal plane. It was connected to a charging regulator and a gel battery. The outer surface of the panel was exposed to sunlight at 10 GMT (local time—Poland, 12:00) to consider incident solar irradiance. A distance of 1 m was set between the camera lens and the top side of the PV panel, and then its bottom side. After a period of 1 h, the temperature measurement was recorded. During the experiment, thermograms were taken on both outer surfaces of the photovoltaic panel (the top and the bottom sides) after 1 h of exposure to stabilise the thermal conditions. Temperature measurement was performed on both sides of the PV panel using a pistol-grip infrared camera. Depending on the area of the panel, the temperature distribution was recorded directly on the surface of the PV panel and the surfaces of each copper sheet (smooth and with pins) using infrared thermography (FLIR E96 infrared camera, FLIR Systems Inc., Wilsonville, OR, USA).

The time interval between the measurements of both surfaces of the PV panel did not exceed 1 min. The surfaces under investigation coated with black paint had a known emissivity of 0.98. The values of the main physical conditions of ambient air, namely temperature, atmospheric pressure, and air humidity readings, were also determined using a LAB-EL meter, model LB-532TWPL.

2.3. Experimental Data and Uncertainties

An E96 FLIR infrared camera was used for temperature measurements. The camera is characterised by a temperature measurement accuracy of ±2 °C or ±2% a measured temperature range according to its manufacturer [16]. Furthermore, the proposed method for the estimation of temperature uncertainty measurements based on the Monte Carlo method was described in detail in [17]. In this method, experimental data were collected with the use of a FLIR A655SC infrared camera.

Thermograms recorded with the infrared camera were used to generate the temperature field using FLIR ResearchIR Max software version 4.40. The selected data covered six parallel lines (their location is shown in Figure 3).

The base experimental data collected during the experiments and used in further calculations are shown in

Table 2. The base experimental data used in further calculations.

Parameter	Value
Average temperature on the outer surface of the PV panel from the top side, K	325.60
Temperature of the ambient air, K	295.15
Atmospheric pressure, Pa	101,325
Relative humidity, %	41.2

. The temperature on the outer surface of the PV panel was calculated as the average of the measured temperature on the panel surface, based on the infrared camera measurement.

Furthermore, in

Table 3. Measurement ranges and uncertainties of relative humidity, temperature, and air pressure.

Parameter	Measurement Range	Measurement Uncertainty
Relative humidity, %	0–100	±2.0
Temperature, °C	0–+40	0.11
Pressure, hPa	700–1100	1.0

, the measurement uncertainties of relative humidity, temperature, and air pressure are indicated, based on information from the catalogue cards of the LAB-EL meter, model LB-532TWPL [18]. These uncertainties were considered when measuring the basic parameters of ambient air, i.e., the relative humidity, temperature, and absolute pressure.

Figure 5 shows the experimental data for temperature measurement using infrared thermography. The local temperatures recorded on the top and bottom sides of the PV panel are provided at the central line of each area chosen for the analysis (for a bare panel surface, a panel with a copper sheet with a smooth surface, and a panel with a copper sheet with pins).

Based on the analysis of the temperature data shown in Figure 5, the bare surface had the highest temperatures both on the top side and bottom side of the tested photovoltaic panel (the PV panel with only the original surface). A lower temperature was recorded for PV panels with copper sheets, but when its surface had pins, the lowest temperature was observed. It can be stated that the highest rate of heat transfer occurred in the case where the PV panel was equipped with a copper sheet with pins compared to other cases, i.e., the panel with the addition of a copper sheet with a smooth surface and the bare PV panel. The lowest temperature difference was observed for the bare PV panel. The pins installed on the outer bottom surface of the PV panel play a role in achieving the highest temperature difference between the layers of the panel, in comparison to other cases.

As is clear from the graph shown in Figure 5, the highest rate of heat transfer occurred in the case where the PV panel was equipped with a special pin pattern (named PV 4-1-0.5), compared to other cases, that is, the panel with the additional copper sheet with a smooth surface and the bare PV panel. This resulted from a continuous heat transfer process. It is obvious that the bare PV panel had the lowest temperature difference. The pins installed on the outer bottom surface of the PV panel play a role in achieving the highest temperature difference between the layers of the panel, compared to other cases. The reason is that the surface with pins improves heat dissipation from PV modules, which is widely known.

Regarding the heat transfer across the ‘sandwiched’ structure of the panel layers, two mechanisms of heat transfer were considered: free convection (which occurs on the outer surfaces of the panel) and heat conduction across the layers of the photovoltaic panel (solids), with or without copper sheet (with an outer surface that is smooth or enhanced with pins). Significant heat transfer occurs on the copper sheet–ambient air contact surface, while the temperature difference between the glass panel and ambient air contact surface is very slight (a good thermal isolator). Therefore, the most significant factor to consider in heat transfer is the heat exchange in the contact surface between the copper sheet and the air via free convection and heat conduction through the copper sheet. The increase in heat transfer as a result of convection is reflected in the value of the heat transfer coefficient, dependent on various factors. The most important factors are the geometry of the surface of heat transfer exchange (that is, whether it is a smooth or enhanced surface, which is the metal sheet with pins constituting fins) and the temperature of the air. The heat transfer coefficient for convection when the surface with fins is considered the heat transfer surface is usually higher than the heat transfer coefficient when considering the copper sheet with a smooth surface. Heat transfer via conduction mainly depends on the thickness of the wall and the temperatures on each surface of the wall.

3. Numerical Simulation with Mesh Validation

3.1. CAD Model of the PV Panel

A CAD model of the modified PV panel and the ambient air area was generated in the SOLIDWORKS programme 2023 SP3.0 and then adopted for numerical simulations. The main elements of the test taken into account are presented in Figure 4, in the form of a cross-section of the model of the PV panel equipped with an additional copper sheet, in which pins were installed. The important dimensions of the copper sheets and pins are marked in this figure. In the numerical simulations, a fragment of the PV panel with dimensions of 80 mm × 80 mm was used. It was approximately one-fourth of the entire PV panel area and was treated as a model area. It was assumed that the PV panel was uniformly heated due to sunlight. Figure 6 shows the location of the selected area of the PV panel in relation to its entire surface.

The numerical calculations were performed using the Simcenter STAR-CCM+ programme, version 2020.2.1 Build 15.04.010. The Simcenter STAR-CCM+ programme is a CFD tool that allows for the creation of geometry, meshes, and boundary conditions, helping to enter physical assumptions and mathematical models and obtain simulation results from one integrated interface. According to the authors, the main advantages of this software are clarity for users and the possibility of conducting calculations in a fully coupled way in a highly consolidated environment. It increases the accuracy of the results and eliminates problems with the lack of integration between each step in the CFD simulation. However, the programme may be limited when solving complicated computational problems such as heat transfer with phase change during fluid flow. It should be emphasised that these types of computational problems are also always very difficult to model and calculate with the help of all sophisticated commercial programmes.

The computations with the aid of the Simcenter STAR-CCM+ programme were conducted on a PC with the following main specifications: Intel Core i9-10920X CPU processor (24 cores), 256 GB of RAM, and 3.50 GHz of clock speed, LGA2066 19.25 MB, similar to that indicated in [19]. Numerical calculations took about 6–10 h of CPU time.

To perform a numerical simulation, nine geometrical values were used in testing the models of the photovoltaic panels (the bare PV panel and the panels with copper sheets of various levels of roughness). The main differences between the variants were in the arrangements of the pins installed on the copper sheet and their dimensions. The most important dimensions of the copper sheets and pins are listed in

Table 4. Geometric parameters of the bottom surfaces of the PV panels.

Designation of PV Panel: PV A-W-H	A, mm	G, mm	W, mm	P, mm	H, mm
PV bare (used in the experiment and simulation)	-	-	-	-	-
PV with a cooper sheet with a smooth outer surface (used in the experiment and simulation)	-	2	-	-	-
PV 1-0.5-1	1	2	0.5	1.5	1
PV 2-0.5-1	2	2	0.5	2.5	1
PV 2-1-1	2	2	1	3	1
PV 2-1.5-1	2	2	1.5	3.5	1
PV 4-1-0.5 (used in the experiment and simulation)	4	2	1	5	0.5
PV 4-1-1	4	2	1	5	1
PV 6-1-1	6	2	1	7	1

, and the type of PV panel designation used in the subsequent analysis is also presented. The thickness of the glass plate was 3 mm, the thickness of the silicon layer was 0.2 mm, and the thickness of the EVA element was 0.5 mm (see Figure 4).

The views of four selected PV panels equipped with copper sheets containing pins on the outer surfaces are shown in Figure 7, while their geometric parameters are listed in Table 4.

3.2. Characteristics of Numerical Calculations

The following assumptions were made:

• A steady-state condition was assumed for the experiment.
• The ambient air temperature was assumed to be similar to that measured in the experiment.
• The temperature of the panel from the sunlight side corresponded to the average temperature based on the infrared measurements on the outer PV surface according to the data collected in the experiment.
• The K-epsilon turbulence and Reynolds-averaged Navier–Stokes (RANS) computational models were adopted for the volume corresponding to the air surrounding the PV panel. The main physical parameters of the air were described using the real gas and equilibrium air modules.
• The properties of the PV panel materials were independent in terms of temperature.

The main models that were selected for the numerical calculations of the fluid material (ambient air) using the Simcenter STAR-CCM+ programme are indicated in

Table 5. Models used for the numerical calculations of the fluid (ambient air).

Models Used for the Fluid
K-epsilon turbulence
Segregated fluid temperature
Reynolds-averaged Navier–Stokes
Steady
Constant density
Segregated flow
Three-dimensional model

. The main properties of the air were the typical values used in this programme.

The temperature data of the outer surface of the PV panel from the top side, based on the experimental data (see Table 2), were used in the numerical calculations. The temperature of the ambient air was considered to be 295.15 K, while the atmospheric pressure was equal to 101,325 Pa. The physical properties of the PV panel materials used in the numerical computations are listed in

Table 6. Main physical properties of the PV panel materials [20].

Material of the PV Panel Components	Density $\mathit{\rho },\frac{\mathbf{k}\mathbf{g}}{{\mathbf{m}}^3}$	Thermal Conductivity $\mathit{\lambda },\frac{\mathbf{W}}{\mathbf{m}·\mathbf{K}}$	Specific Heat ${\mathit{c}}_{\mathit{p}},\frac{\mathbf{J}}{\mathbf{k}\mathbf{g}·\mathbf{K}}$
EVA	960	0.311	2090
Silicon	2330	130	677
Glass pane	3000	2	500

.

3.3. Mesh Validation Analysis Based on the Grid Convergence Index (GCI)

To ensure the convergence stability of the numerical calculations, a mesh dependency analysis was carried out based on the grid convergence index (GCI). This method is based on the idea of Richardson extrapolation. It is recommended by ASME, that is, the Fluids Engineering Division of the American Society of Mechanical Engineers [21,22]. Mesh dependency studies based on the GCI were carried out similarly to the authors’ previous work [19]. The model was meshed with a 20 mm base grid size (minimum surface size 0.05 mm, prism layer total thickness 0.2, and maximum tet size 30 mm) for defining the discretisation error. The base grid size was increased by 50% and 105% to obtain a grid refinement ratio greater than 1.1. The number of cells, faces, and vertices for the default mesh (fine), increased by 50% (medium) and by 105% (coarse), are listed in

Table 7. Number of elements in meshes with three values of base size.

	Element	Air	Copper Sheet	Glass	EVA (Top Side)	Silicon	EVA (Bottom Side)
Fine Mesh	Cells	637,219	730,292	769,735	3,260,947	3,927,365	3,260,134
	Faces	4,497,251	3,371,534	4,178,783	14,431,146	17,089,479	14,427,322
	Vertices	3,9464,12	2,317,029	3,172,407	9,648,596	11,870,043	9,645,604
Medium Mesh	Cells	629,440	663,401	604,430	2,365,707	2,502,711	2,377,716
	Faces	4,446,619	2,907,102	2,996,423	10,741,002	11,323,517	10,826,120
	Vertices	3,901,707	1,924,429	2,160,637	7,616,690	8,820,739	7,726,620
Coarse Mesh	Cells	512,583	646,805	574,856	1,684,657	871,050	1,676,866
	Faces	3,601,988	2,811,248	2,794,824	7,616,690	4,397,346	7,544,567
	Vertices	3,166,144	1,849,253	1,991,685	9,643,857	4,351,275	5,344,702

. This table contains data for two EVA layers, i.e., between the glass pane and silicon, named ‘EVA (top side)’, and the other layer, named ‘EVA (bottom side)’.

The GCI calculation was presented in detail in [21]. First, the representative cell h was determined based on the total number of cells (N) in the CFD model. To calculate the order of convergence p, it was necessary to obtain the grid refinement factor r. The mean temperature $\varphi$ of the surface in the indicated section in Figure 6 was determined considering the contact surface between air and the copper sheet, to compute the approximate relative errors ($e_a$). Finally, to obtain the GCI, a safety factor equal to 1.1. for three meshes in CFD simulations was used. The complete results of the calculations performed are shown in

Table 8. Results of calculations of grid convergence index (GCI).

Mesh	$\mathit{h}$ (−)	$\mathit{N}$ (−)	$\mathit{\varphi }$ (K)	$\mathit{r}$ (−)	$\mathit{e}$ (K)	$\mathit{p}$ (−)	${\mathit{e}}_{\mathit{a}}$ (%)	$\mathit{G}\mathit{C}\mathit{I}$ (%)
Fine	5.22 × 10−4	12,585,692	318.49	1.112	0.283	1.714	0.09	0.55
Medium	5.80 × 10−4	9,143,405	318.78
				1.153	0.928		0.29	1.32
Coarse	6.69 × 10−4	5,966,817	319.70

.

After analysing the results from the GCI calculation procedure, considering the selected three base sizes of the mesh, it was found that with the fine and coarse values of the meshes, the GCIs were 0.55% and 1.32%, respectively. With the assumed variables, the fine grid resulted in a significantly reduced GCI value, compared with the coarse grid. Therefore, in further calculations, the mesh with the fine grid was chosen.

4. Results from Numerical Simulations

Nine series of simulations were selected for analysing the material characteristics of the outer bottom surfaces of the PV panels. The base characteristics of the selected series are given in Table 4 (describing the geometric parameters of the bottom surfaces of the PV panels) and Table 6 (showing the physical properties of the materials of the PV panel components), while the necessary information regarding the calculation models used for ambient air is listed in Table 5. The raw data from the experiment (the average temperature based on measurements of the outer top surfaces of the photovoltaic panels) were input into the numerical programme. In Figure 8, the temperature distribution is presented versus the length of the selected lines, obtained as a result of numerical simulations. The location of the lines is illustrated in Figure 3.

According to the temperature results shown in Figure 8, it can be observed that applying an additional copper sheet with a smooth surface to the bare PV panel improved the operating conditions by lowering its surface temperature by approximately 6.5 K. The highest number of pins distributed uniformly on the copper sheet surface, the 1-0.5-1 variant of the PV panel, resulted in the highest drop in the temperature of its bottom surface, that is, on average by more than 12 K compared to the temperature of the bare PV panel surface. This variant of the PV panel can be considered to have the highest surface development compared to other surfaces with pins. Based on the analysis of the results of using the 2-0.5-1 PV variant, it also resulted in a significant decrease in surface temperature—over 10 K—compared to the temperature of the bare PV panel surface. It should be noted that all other surfaces with pins and the smooth copper sheet surface led to a reduction of approximately 7 K in temperature compared with the bare PV panel surface, and the temperature difference between them was not greater than 1 K. Therefore, it was concluded that all copper sheets helped to improve the thermal operating conditions of the photovoltaic panel. The smallest pins installed on the bottom copper sheet (variants PV 1-0.5-1 and PV 2-0.5-1) significantly increased the heat transfer process in terms of the efficiency of heat dissipation to the environment.

Regarding the results of other researchers on the additional cooling of PV panels by modifying their overall structure (according to Table 1), their main findings can be summarised as follows:

• With drilled holes on the surface of the free spaces between the PV panel [6], the temperature difference was up to 19 °C (depending on the number of holes);
• Using perforations on the surface of the front panel [7] helped to reduce the temperature by 4 °C;
• The application of water to the bottom surface of the photovoltaic panel for cooling (a cold plate attached to the PV panel consisting of several channels) [8] led to a temperature reduction of up to 23.5 °C;
• Using a hybrid cooling system (thermoelectric modules and water) [9] resulted in a reduction in operating temperature by 9 °C;
• Considering the effect of composite phase-change materials (paraffin jelly–expanded perlite) [13] led to a reduction of 5.1 °C in the average temperature difference.

All the results are reported in comparison to the data collected for a bare PV panel.

Figure 9 and Figure 10 illustrate examples of the results of numerical computations, namely the temperature distributions in the layers of the PV panel with the copper sheet with pins (Figure 8), shown in the longitudinal section. The presented results were obtained for PV 1-0.5-1, with the fine mesh size used in the numerical computation.

5. Validation of the Calculation Results with Experimental Data

The results of the temperature distribution based on the numerical simulations were compared with the corresponding results obtained from the experiment. Figure 10 shows the temperature distributions for the bottom surfaces of two PV panels, i.e., the bare PV panel and the PV panel using a copper sheet with a smooth surface. The temperature distribution obtained for the PV panel with pins based on experimental data exhibited a significant scatter compared to the results from the numerical simulations. This may be attributed to a less precise measurement of the temperature field on the surface with pins using infrared thermography as a result of heat reflection on the pin surface, which influences the change in its emissivity factor. That is the reason why the PV surface that had a copper sheet with pins was not used in validation.

Based on the results of the comparison of the numerical simulations with the experimental data illustrated in Figure 10, similar temperatures were generally obtained. In both cases, that is, taking into account the results obtained for the bare PV panel surface (Figure 10a) and the PV panel using a copper sheet with a smooth surface (Figure 10b), the maximum differences between the temperature results did not exceed 1.45 K (Figure 10c). Less difference was observed in the temperature values between the data recorded during the experiment and those obtained from the numerical simulation for the bare PV panel surface. Its average value was close to 0.16 K (minimum 0.01 K and maximum 0.63 K). Considering the PV panel equipped with a copper sheet with a smooth surface, the temperature was higher, close to the maximum of 1.45 K (minimum 0.69 K and arithmetic mean 1.05 K). This may be due to the assumption that the copper plate was affixed to the panel using a perfect joining mechanism. However, there was a thin layer of thermal paste between the PV plate and the copper plate. Considering the bare panel–copper plate contact surface, in numerical calculations, lower values of the temperature surface were achieved in comparison to the data obtained from the experiment (measured with an infrared camera).

It is worth mentioning that the temperature measurement accuracy using the infrared camera was 2 K (or 2% in the measurement temperature range). This means that the resultant temperature difference in both cases was within the uncertainty threshold of the infrared camera’s temperature measurement.

6. Conclusions

The main objective of this article was to propose a passive cooling system for photovoltaic (PV) panels to achieve a reduction in their temperature, resulting in an increase in the efficiency of photovoltaic conversion. Reducing the PV panels’ temperature ensures their long-lasting operation.

Two types of modification of photovoltaic panels by adding copper sheets to the bottom panel side were proposed: smooth and enhanced with a system of pins. Numerical simulations, performed using the Simcenter STAR-CCM+ software, helped to analyse the effects of the geometry of the pins and their placement on the resulting reduction in the temperature of the PV panel surface.

According to the experimental results, using a copper sheet with pins of specific geometrical dimensions led to a higher reduction in the temperature of the PV panel compared to the PV panel with a smooth copper sheet and the bare PV panel. The addition of the copper sheet with a smooth surface to the bare PV panel improved the operating conditions by lowering its surface temperature by approximately 6.5 K. Furthermore, the highest number of pins distributed uniformly on the copper sheet surface resulted in the highest drop in the temperature of its bottom surface, that is, on average by more than 12 K compared to the surface temperature of the bare PV panel surface.

The commercial software Simcenter STAR-CCM+ was used to perform numerical simulations to determine the specific geometry of the pins. The PV panel with the copper sheet with pins of specified dimensions exhibited the highest reduction in the temperature compared to those using copper sheets with other geometric dimensions of the pins, the PV panel with a smooth copper sheet, and the bare PV panel. The validation of the numerical calculations was performed on data from the experiments. An analysis of the quality of the numerical mesh was also carried out using the method based on the grid convergence index.

The novelties of this work include the modification of a typical photovoltaic panel by adding a copper sheet with pins and evaluating different options to achieve a better effect in decreasing the temperature of the PV panels; performing a numerical analysis of various geometric dimensions of the pins installed on the outer surface of the copper sheet; carrying out the validation of numerical calculations (based on data from experiments); and conducting an analysis of the quality of the numerical mesh using the method based on the grid convergence index.

In summary, technical solutions to ensure high efficiency in electricity production using photovoltaic panels, as well as simple, easy, and ecological solutions to achieve this goal, are of great interest to scientists. The modification of the structure of photovoltaic panels by adding metal sheets enhanced with the application of pins helps to decrease the bottom panel surface’s temperature by improving heat dissipation from PV modules. The results of the studies carried out in both experimental and numerical investigations showed that the use of an enhanced PV panel helps the panel cooling process. It is worth mentioning that the proposed method does not require any modification of the common photovoltaic panels available in the world market. Furthermore, by additional cooling, the period of the use of these products, that is, the lifetime of the PV panels, would be extended.

The authors plan to conduct future experimental studies using this method. Investigations will cover testing various materials that can be used in the bottom sheets of PV panels (such as aluminium PA4, PA6, PA9, PA13, PA38, and brass instead of copper). Furthermore, numerical simulations will be carried out, considering the pin size and regularity of the pin distribution to find pin dimensions and patterns that help to achieve more effective PV panel cooling. A technologically easy solution for areas with the greatest solar exposure and the highest air temperature could help reduce the risk of overheating photovoltaic panels. After conducting the appropriate economic analyses, an improved PV panel can be developed that contributes to advancements in the photovoltaic industry.