Novel Cooling Strategy for a Hybrid Photovoltaic/Parabolic Dish Concentrator

Abstract

In this paper, the thermo-optical performance using novel cooling strategy improvements for a hybrid photovoltaic/parabolic dish concentrator with a conical thermal receiver using a beam splitter filter (PV/PDC-CTR-BSF) is investigated. The study’s main goal is to improve the cooling effectiveness of the serpentine-shaped cooling duct by investigating the effect of the cross-section shape and positioning of the cooling duct under the PV panel. Typical cooling pipes have either a rectangular or circular cross-section and are usually attached to the back sheet of the PV panel using off-the-shelf adhesives that have very low thermal conductivity. With the advent of 3D printing technology, the back sheets could be 3D-printed with integral cooling ducts of different cross-sections at different locations and orientations within the back sheet that allow for increased heat transfer from the back sheet and thus improve PV/PDC-CTR-BSF’s thermos-optical performance. For this purpose, the study investigates and compares the thermal performance of four different cooling duct cross-sections that include: rectangular, semi-circular, semi-elliptical and triangular. For each of the cooling duct cross-sections, several positions and orientations, which include flush below the back sheet layer and embedded inside the back sheet but positioned at the bottom, middle and top of the back sheet, are examined. Numerical simulations using the commercial software ANSYS FLUENT(R2019) are performed to assess the performance of the cooling ducts and, in turn, the thermo-optical performance of the PV/PDC-CTR-BSF system. The semi-elliptical cross-section duct embedded in the middle of the back sheet was found to yield the best cooling performance since its rate of heat removal from the PV back sheet was found to be the highest.

1. Introduction

The conjunction of photovoltaic panels with solar concentrating devices has been widely suggested by the notion of photovoltaic/ thermal (PV/T) solar systems [1,2]. The purpose of this suggestion is to generate both electric and thermal energy output. The PV panel’s ability to produce electricity has been improved by solar concentrating systems [3,4,5], and this process reduces the total number of cells in the panels, which in turn lowers their installation costs. However, the major drawback of the PV/T systems is related to the high temperature values of the PV cells. This issue needs to be resolved by installing a cooling system beneath the PV cells, and the concept has been called the hybrid concentrating photovoltaic/thermal (CPV/T) solar system. In the literature, the inquiry of the CPV/T receiver cooling mechanism has been investigated and reviewed by several researchers [3,4,6,7,8]. In fact, in 1996, Akbarzadeh et al. [9] established a parabolic trough solar concentrator system that focuses sunrays on PV cells under any degrees of concentration via a numerical and experimental approach. The outcomes demonstrate that reflector characteristics and PV cell cooling systems are linked to the performance enhancement of the suggested concentrating solar system. Mittelman et al. [10], in order to generate both electrical power and thermal energy at low or medium temperatures, examined sun cooling with concentrating photovoltaic/thermal (CPV/T) systems by connecting a single effect absorption chiller to the CPV/T system. The results show that the CPV/T cooling system might cost just as much as a conventional cooling system. Furthermore, Mittelman et al. [11] investigated the distillation process using CPV/T devices. The findings show that this technique is competitive with currently available solar-driven desalination devices and even with conventional reverse osmosis (RO) desalination. Posteriorly, Hedayatizadeh et al. [12] studied the energy balance of a hybrid PV/T system based on compound parabolic concentrator via a computational tool. The thermal and electrical outcomes demonstrate a fair match when compared to experimental testing. In addition, He et al. [13] suggested an analytical model to investigate the properties of the CPV/T system. The results proved that the focusing procedures increase the CPV/T system’s effectiveness. In addition, to accomplish a significant amount of energy for the thermal receiver with a uniform distribution for the PV receiver, Meng et al. [14] proposed an innovative solar concentrator for the CPV/T system. The authors recommended using a PV/T exploitation in conjunction with a Cassegrain concentrator configuration. Hence, the results may be used as an inspiration for the PV/T solar system based on the geometric building technique. Further, Koronaki et al. [15] investigated the performance of a flat plate receiver in hybrid solar collectors. In terms of thermal performance and both exergy and electrical productions, the results demonstrate that the proposed solar collectors operated effectively throughout the year. Recently, a low-concentrated parabolic trough PVT (CPV/T) system was the subject of a performance parameter and electro-thermal analysis by Demircan et al. [16]. The results demonstrate that water, owing to its high specific heat, surpasses the other fluids in the assessment of the electrical and thermal efficiency of the CPV/T system.

The above investigations make use of a typical off-the-shelf circular or rectangular cross-section cooling duct placed under the PV cells or, to be more precise, under the back sheet of the PV panel to remove excess heat from the panel and help increase its performance. Intuition suggests that embedding the cooling pipe within the back sheet may result in an increased heat transfer. With the advent of 3D printing technology, the back sheets could be 3D-printed with embedded cooling ducts of different cross-sections at different locations and orientations that allow for increased heat transfer and thus improve PV/PDC-CTR-BSF’s thermos-optical performance. Thus, the main objective of the current study is to numerically investigate and compare the thermal performance of four different cooling duct cross-sections that include: rectangular, semi-circular, semi-elliptical and triangular. For each of the cooling duct cross-sections, several positions and orientations, which include flush below the back sheet layer and embedded inside the back sheet but positioned at the bottom, middle and top of the back sheet, are examined. Numerical simulations using the commercial software ANSYS FLUENT are performed to assess the performance of the cooling ducts and, in turn, the thermo-optical performance of the PV/PDC-CTR-BSF system.

In the sections that follow, the PV/PDC-CTR-BSF system and approach is first presented along with the typical cooling strategy.

2. PV/PDC-CTR-BSF Approach

2.1. PV/PDC-CTR-BSF Design

The PV/PDC-CTR-BSF system is made up of a parabolic dish collector, conical receiver cavity, PV cell panel and beam splitter filter. The geometry modeling equations for each component are first developed in order to build the complete system. The design of the system under investigation is shown in Figure 1.

One can observe that the BSF is placed between the two receivers (conical receiver cavity and PV cell panel) and above the parabolic dish collector (PDC). The main goal of the BSF placement is to manage the path of the reflected solar rays due to its wide spectral selective coating [17]. This last one allows one to split the concentrated sun rays intercepted by the BSF according to their wavelengths.

2.2. Solar Dish Reflector

The key feature of the parabolic dish concentrator (PDC) is its two-axis solar tracking systems that focus sun rays on a focal point. The geometry design of the PDC is defined by the following equation:

$$z=\frac{x^2+y^2}{4f}$$

(1)

However, the concentrating solar beam methodology can be affected by different optical and geometric factors [18,19,20,21,22]. Actually, the effectiveness of the PDC system is related to the choice of the receiver design and materials, which are selected according to the desired application [22].

2.3. Reflected Solar Rays and Splitter Filter

After their reflection from the PDC, solar rays intercept on the BSF surface, whose design is defined as the following:

$$z=\frac{x^2+y^2}{4f_s}+z_{fs}$$

(2)

where $z_{fs}$ is the height of the BSF above the parabolic reflector and $f_s$ is the BSF focal length. As was already established, the wavelength values determine when the reflected sunlight is discharged. The spectral width’s bandpass area is expressed as the following [23]:

$$\left\{\begin{array}{c}\rho \left(\lambda \right)=1if380\mathrm{nm}<\lambda <1100\mathrm{nm}\\ \rho \left(\lambda \right)=0if1100\mathrm{nm}<\lambda <2500\mathrm{nm}\end{array}\right.$$

(3)

Equation (3) demonstrate that sun rays, having wavelengths values above 1100 nm, will be transmitted by the BSF and absorbed by the conical cavity receiver (CCR), whereas other sun rays are re-reflected and illuminate the solar cells panel.

2.4. Thermal Receiver and Transmitted Solar Rays

Once they are passed through the BSF, the transmitted solar rays are concentrated on a thermal receiver, which is located at the PDC focal plane. Several receiver geometrical shapes are listed and studied in the literature [24,25,26,27,28,29,30,31,32]. Then, the CCR displays an intriguing performance with regard to other shapes [25,26]. In fact, in Cartesian coordinates, the CCR equation is expressed as the following:

$$z=z_{cr}+(r_{max}-({\left(x_{cr}-x\right)}^2+{\left(y_{cr}-y\right)}^2)\cot ({\theta }_{op})$$

(4)

where $x_{cr}, y_{cr} \mathrm{a}\mathrm{n}\mathrm{d} z_{cr}$ are the coordinates of the CCR center, and ${\theta }_{op}$ is the half opening angle of the CCR defined as:

$${\theta }_{op}={\tan }^{-1}\left(\frac{r_{max}-r_{min}}{h_r}\right)$$

(5)

The solar flux density accumulated on the conical cavity receiver is concentrated on a helical tube mounted inside the conical cavity. Throughout the tube, water is flowing as fluid from the bottom to the top by ascending along the conical height.

2.5. PV Panel and the Conventional Cooling System

As previously mentioned, the re-reflected solar rays from the BSF are projected to the PV panel. Figure 1 shows the different layers in a typical PV panel with a cooling pipe attached to the back sheet. A view of the serpentine-shaped cooling pipe from the back of the panel is shown in Figure 1.

3. Novel Cooling Strategy

Although the use of cooling ducts for heat dissipation from the back side of the PV panel back sheet has been in use for some time, the optimum cross-section geometry and location of the pipes in effectively dissipating heat have not been studied to date. In this regard, a 1.4 m × 1.4 m mono-crystalline silicon-based module PV panel back sheet, see Figure 1, along with 16 different configurations, shown in Figure 2[1(a)–4(d)], representing four different cross-sections (rectangle, semicircle, semi-ellipse and triangle) and four different locations (below the back sheet, embedded and flush with bottom surface of back sheet, embedded in the middle of back sheet and embedded and flush with top surface of back sheet) was modeled and subjected to steady-state coupled flow and thermal analysis using the commercial computational fluid dynamics code ANSYS FLUENT.

Table 1. Geometric characteristics of the different cooling duct cross-sections considered in this study.

No	Geometry	Dimensions	Width w (mm)	Perimeter * p (mm)	Depth d (mm)	Hydraulic Diameter Dh (mm)
1.			50.00	132.0	16.00	24.2
2.			45.14	141.8	22.57	22.6
3.			63.66	158.3	16.00	20.2
4.			80.00	169.4	20.00	18.9

* Perimeter p is the sum of length of the sides of the channel minus the top side or width w.

lists the geometric characteristics of the pipe cross-sections.

3.1. Computational Modeling

The computational domain consisting of the PV panel back sheet and the cooling duct geometry were numerically modeled and discretized using a mesh composed of tetrahedral cells. To guarantee that the non-dimensional height at the wall is y+ < 1, a number of mesh layers were employed for effectively resolving the velocity boundary layer. In this regard, the first cell height, rate of growth and total number of layers were chosen as 5 × 10⁻⁵ m, 1.15 and 25, respectively.

For the numerical solution, the Reynolds-averaged Navier–Stokes (RANS) equations for the energy, momentum and mass were solved using the pressure-based model. The Spalart–Allmaras turbulence model was used for the closure of the numerical model. The mass, momentum, energy and turbulence model equations were discretized using a second-order upwind scheme. The pressure–velocity interaction strategy was subsequently employed. Effective convergence of the solutions is noted when all of the discretized equations have under-relaxation parameter equal to 0.5. The solution is considered to be converged when the residuals are less than 1 × 10⁻⁵ and both the mass flow and net heat transfer rates are less than 1 × 10⁻². Typical plots of the wall y+, residuals, net heat transfer and mass flow rates are shown in Figure 3a–d.

3.2. Input and Boundary Conditions

In this study, water was used as the cooling fluid. For consistency, all cross-section areas (0.0008 m²), the shape (serpentine), the total length of the ducts (12.637 m) and the cooling fluid inlet conditions, i.e., temperature ($T_{\mathrm{i}\mathrm{n}}=298\mathrm{K}$) and mass flow rate ${\dot{m}}_{in}\cong$0.1 kg/s of the fluid through the duct, were kept constant in all simulation cases. The back sheet was subjected to a heat flux $q″=6400$ W/m² from the top. The surrounding temperature and emissivity of the back sheet were assumed as $T_{\mathrm{s}\mathrm{u}\mathrm{r}}=298\mathrm{K}$ and $\epsilon =0.9.$

4. Numerical Results

The main goal of this paper is to determine which of the combinations of the cooling duct cross-section geometry and position, shown in Figure 2, is able to remove heat the most. This was achieved by examining the heat flux density and heat transfer distributions for all proposed cooling duct geometries and positions. As mentioned earlier, the simulation and boundary conditions were kept the same for all configurations as listed in Table 1 except for the cross-section shape and position of the cooling duct. In this regard, Figure 4a,b show the contour plots of the static pressure and velocity magnitude, respectively, along the length of the cooling duct for all configurations. The cooling fluid (water) enters the inlet of the cooling duct located at the top-left corner and exits the cooling duct outlet at the bottom-right corner in each case. Inlet and boundary conditions for all cases were fixed as stated earlier. Figure 4b shows that the cooling pipe curvature imparts a slight fluctuation in the flow velocity after each bend due to the serpentine shape of the duct. This fact is also observed in flow simulations of all the configurations.

4.1. Area-Weighted Temperatures and Heat Transfer Rates

Table 2. Summary of area-weighted temperatures and heat transfer rates from the top and sides of the channel/pipe and the back sheet.

No.	Geometry	${\mathit{T}}_{\mathit{o}\mathit{u}\mathit{t}}$ (K)	$∆\mathit{T}$ $(\mathit{℃}$)	${\mathit{T}}_{\mathit{p}\mathit{i}\mathit{p}\mathit{e}}$ (K)	${\mathit{T}}_{\mathit{b}\mathit{a}\mathit{c}\mathit{k}}$ (K)	${\dot{\mathit{q}}}_{\mathit{o}\mathit{u}\mathit{t}}$ (kW)	${\dot{\mathit{q}}}_{\mathit{p}\mathit{i}\mathit{p}\mathit{e}}$ (W)	${\dot{\mathit{q}}}_{\mathit{b}\mathit{a}\mathit{c}\mathit{k}}$ (W)
1(a)		326.6	28.6	311.72	342.70	11.548	154	779
1(b)		327.1	29.1	312.38	333.12	11.786	98	597
1(c)		328.1	30.1	–	325.48	12.197	–	289
1(d)		327.3	29.3	–	325.64	11.826	–	656
2(a)		326.2	28.2	311.93	344.76	11.491	136	854
2(b)		327.0	29.0	312.90	334.90	11.734	92	656
2(c)		327.1	29.1	–	326.60	11.800	–	681
2(d)		327.1	29.1	–	328.20	11.761	–	721
3(a)		327.9	29.9	312.1	337.60	11.730	149	603
3(b)		331.4	33.4	315.2	335.80	11.765	151	573
3(c)		328.4	30.4	–	324.50	12.203	–	278
3(d)		327.7	29.7	–	324.50	11.855	–	626
4(a)		328.3	30.3	313.82	333.10	11.834	195	446
4(b)		327.5	29.5	314.80	333.10	11.876	185	420
4(c)		327.9	29.9	–	322.35	11.978	–	574
4(d)		328.0	30.0	–	321.89	11.920	–	562

summarizes the area-weighted temperatures and heat transfer rates as predicted by the numerical simulation runs for all of the configurations investigated in this study as shown in Figure 2. In Table 2, $T_{out}$ is the exit cross-section area-weighted static temperature of the cooling fluid as it exits the duct, $∆T$ is the difference in cooling fluid temperature between exit and inlet, $T_{pipe}$ is the area-weighted average static temperature of the whole duct (fluid + conduit), $T_{back}$ is the area-weighted temperature of the back sheet, ${\dot{q}}_{out}$ is the thermal power of the fluid flowing out the cooling duct and ${\dot{q}}_{pipe}$ and ${\dot{q}}_{back}$ are the thermal power lost to the surrounding from the cooling duct surface and the back sheet, respectively.

Amongst all of the configurations investigated, the semi-ellipse cross-section configuration, case 3(b) in Table 2, yields the maximum increase in the cooling fluid temperature at the duct exit. However, if the objective is to achieve the lowest possible back sheet temperature, then the triangular duct placed flush with the back sheet top, i.e., case 4(d) in Table 2, is seen to be the best candidate, and may enhance the electric output power of the mono-crystalline PV module by at least 8% since most of the solar PV modules have a power–temperature coefficient of around −0.4%/°C.

It is also interesting to note that placing the duct at the mid-height location within the back sheet results in the maximum heat transfer rate leaving the system through the fluid flowing out of the duct for each of the duct cross-sections. And, amongst these four duct cross-sections, the semi-elliptical duct placed in the middle of the back sheet is found to dissipate heat the most within a given time.

4.2. Surface Heat Flux Distribution

Figure 5, Figure 6, Figure 7 and Figure 8 present contour plots of surface heat flux entering the ducts from the topside representing the back sheet of the PV module. The results have been plotted using an identical scale to distinguish the amount of heat flux through visual reference, i.e., colors on the lower end of the legend represent lower heat transfer to the back sheet leading to cooler back sheet temperatures and greater heat transfer to the cooling fluid. However, these contour plots must be viewed with the fact in mind that, except for the case of the duct flush with the bottom side of the back sheet, i.e., case (a) in Figure 5, Figure 6, Figure 7 and Figure 8, all other cases also allow for heat transfer throughout the perimeter or other sides of the duct, which is not obvious from these contour plots. The case that allows for maximum heat transfer to the cooling fluid can be gleaned from Table 2, which lists the summary of area-weighted temperatures and heat transfer rates at the outlet of the cooling ducts. Table 2 indicates that the case (c), representing the duct embedded in the middle of the back sheet in all the cases, results in the highest heat transfer rate ${\dot{q}}_{out}$ as well as the highest cooling fluid temperature $T_{out}$ at the exit while case (a), representing the duct flush with the bottom side of the back sheet in all the cases, results in the lowest heat transfer rate ${\dot{q}}_{out}$ as well as the lowest cooling fluid temperature $T_{out}$ at the exit. Therefore, results shown in Figure 5, Figure 6, Figure 7 and Figure 8 should be viewed together with the results summary in Table 2 to determine which of the cases result in enhanced heat transfer to the cooling fluid and lowest back sheet temperatures. Hence, for the case of the rectangular duct, Figure 5a–d, case (c) of the duct embedded in the middle of the back sheet represents the case that results in the highest heat transfer rate ${\dot{q}}_{out}$ as well as the highest cooling fluid temperature $T_{out}$ at the exit while case (a), representing the duct flush with the bottom side of the back sheet, results in the lowest heat transfer rate ${\dot{q}}_{out}$ as well as the lowest cooling fluid temperature $T_{out}$ at the exit of the duct. Similar results were obtained for all four different cooling duct cross-sections (shown in Figure 6, Figure 7 and Figure 8), where case (c) of the embedded duct in all cases resulted in the highest heat transfer rate ${\dot{q}}_{out}$ as well as the highest cooling fluid temperature $T_{out}$ at the exit while case (a) of the duct flush at the bottom of back sheet in all cases resulted in the lowest heat transfer rate ${\dot{q}}_{out}$ as well as the lowest cooling fluid temperature $T_{out}$ at the exit of the duct. Ducts located flush on the bottom or top inside the side of the back sheet, cases (b) and (d) in Figure 5, Figure 6, Figure 7 and Figure 8, exhibit similar performance, with the duct flush on the top inside of the back sheet being slightly superior regarding cooling performance compared to the duct flush on the bottom inside of the back sheet.

4.3. Back Sheet and Cooling Fluid Temperatures

Figure 9, Figure 10, Figure 11 and Figure 12 present the contour plots of the back sheet bottom-side and cooling duct mid-plane temperature distributions for the four different cross-section geometries at the four different positions and orientations of the cooling duct. For all the different cross-sections investigated in this study, numerical simulation results indicate that the lowest back sheet bottom-side temperatures and highest cooling fluid temperatures result when the ducts are placed in the middle of the back sheet, i.e., case (c) of the embedded duct in Figure 9, Figure 10, Figure 11 and Figure 12. As the ducts are raised from the bottom to the middle of the back sheet, there is a decrease in the back sheet temperatures and, at the same time, an increase in the cooling fluid temperatures. Placing the duct flush with the topside of the back sheet, i.e., case (d) in Figure 9, Figure 10, Figure 11 and Figure 12, results in an increase in the back sheet bottom-side temperatures and a decrease in the cooling fluid temperatures. This interesting finding suggests that there is an optimum location within the back sheet for placing the cooling duct. In addition, the triangular duct, when placed in the middle of the back sheet, i.e., case (c) of the embedded duct in Figure 9, Figure 10, Figure 11 and Figure 12, yields the lowest back sheet temperatures; see Figure 12c.

5. Validation

Table 3. Comparison with previous studies.

Investigators	Type of Study	Type of CS System	Type of Cooling System	Optical CR	Cooling Fluid	ΔT (°C)
Akbarzadeh et al. [9]	Numerical and experimental	One-axis tracked east–west parabolic trough concentrator	Thermosyphon external to the system	20 suns	R-11, R-22 and water	21
Othman et al. [33]	Experimental	Compound parabolic concentrator	Fins external to the system	1.86 suns	air	18
Hedayatizadeh et al. [12]	Numerical	Compound parabolic concentrator	Duct external to the system	2 suns	water	7.7
Han et al. [34]	Numerical	Linear flat mirror concentrator	Channel external to the system	24 suns	liquid	23.9
Present work	Numerical	Hybrid photovoltaic/ parabolic dish concentrator	Channels embedded within the PV back sheet with different cross-sections and locations	6.4 suns	water	29-33

provides a comparison of results with previous studies (numerical and/or experimental) on the active cooling of the CPV/T in terms of thermal and electrical performance enhancement.

6. Conclusions

In this paper, the thermo-optical performance using novel cooling strategy improvements for a hybrid photovoltaic/parabolic dish concentrator with a conical thermal receiver using a beam splitter filter (PV/PDC-CTR-BSF) is investigated. The results show that the PV/PDC-CTR-BSF system performance can be enhanced by improving the effectiveness of the cooling ducts through appropriate selection of the cooling duct cross-section and its placement and orientation with respect to the back sheet of the PV panel. With the advent of 3D printing technology, the back sheets could be 3D-printed with embedded cooling ducts of different cross-sections at different locations and orientations that allow for increased heat transfer and thus improve PV/PDC-CTR-BSF’s thermos-optical performance. Typical cooling ducts are employed for dissipating excess heat from under the PV panels that have either a rectangular or circular cross-section and are usually placed right under the back sheet of the PV panel. The novel aspect of the current study is that, in addition to the typical rectangular cooling ducts, ducts with semi-circular, semi-elliptical and triangular cross-sections were considered. Furthermore, for each of the cooling duct cross-sections, several positions and orientations, which include flush below the back sheet layer and embedded inside the back sheet but positioned at the bottom, middle and top of the back sheet, were examined. The following important conclusions can be gleaned from this study:

• The results prove that the conventional rectangular cross-section cooling duct is the least effective configuration in cooling the PV panel back sheet and removing heat as compared to the other cross-section considered in this study.
• The results show that cooling ducts that are an integral part of the back sheet, i.e., the ducts that are embedded within the back sheet, are more effective in removing the heat from the PV back sheet.
• Amongst the cases studied, case (a), representing ducts flush at the bottom of back sheet, irrespective of the cross-section, resulted in the lowest heat transfer rate ${\dot{q}}_{out}$ as well as the highest cooling fluid temperature $T_{out}$ at the exit of the duct.
• Amongst the cases studied, case (c), representing ducts embedded in the middle of the back sheet, irrespective of the cross-section, resulted in the highest rate of heat removal as suggested by the heat transfer rate flowing out from the duct ${\dot{q}}_{out}$ as well as the cooling fluid temperature $T_{out}$ at the exit of the duct.
• Amongst the four duct cross-sections, the semi-elliptical duct placed in the middle of the back sheet was found to remove the heat the most within a given time.
• Ducts located flush on the bottom or top on the inside of the back sheet exhibit similar cooling or heat transfer performance, with the duct flush on the top inside of the back sheet exhibiting slightly better cooling performance.
• The heat flux distribution and heat transfer rates are directly proportional to the width of the contact area between the back sheet and the cooling pipe.
• Amongst the configurations investigated, the semi-ellipse cross-section, configuration 3(b) in Table 2, yields the maximum increase in the cooling fluid temperature at the duct exit.
• If it is desired to have the lowest possible back sheet temperature, then the triangular duct placed flush with the back sheet top, i.e., case 4(d) in Table 2, is seen to be the best candidate because it can result in an increase in the electric output power of the mono-crystalline PV modules by at least 8%.

In view of the current study, a more detailed study involving the elliptical cross-section is planned that will focus on the eccentricity of the elliptical cross-section.