1. Introduction
To effectively deal with environmental concerns, global warming, and increasing demand for energy, using renewable and sustainable energy resources instead of fossil fuels is widely considered. Solar energy has attracted more attention among different renewable energy sources due to its accessibility worldwide and abundant energy [
1]. Different systems are introduced to use the unlimited power of the sun, e.g., solar collectors [
2], photovoltaic cells [
3], photovoltaic thermal modules [
4], etc. A direct absorption parabolic trough collector (DAPTC), as a linear concentrating solar collector, concentrates the solar irradiation in an absorber tube via a reflector, where a heat transfer fluid (HTF) absorbs the thermal energy. The solar radiation is absorbed volumetrically in HTF in a DAPTC. Therefore, they have higher thermal performance [
5,
6] because of the lower convective losses compared to indirect absorption parabolic trough collectors, of which the sun’s radiation first hits the surface of the absorber tube and then is transferred to the HTF through conduction and convection. Increasing the temperature of the surface of the absorber tube in an indirect absorption parabolic trough collector causes more heat loss to the environment. However, the important challenge in direct absorption collectors is the low radiation absorption coefficient of heat transfer fluids, such as water. To resolve this issue, researchers have proposed various methods such as adding nanoparticles to the base heat transfer fluid [
7], utilizing metal porous foams [
8], or a combination of metal foam with nanofluids [
9] to improve the absorption of radiation and the thermal efficiency of direct absorption solar systems. In general, the use of metal foam in improving the efficiency and heat transfer in indirect and direct absorption solar collectors has been of interest to researchers.
Conducting both experimental and numerical studies, Saedodin et al. [
10] evaluated flat-plate solar collector efficiency using metal foam and showed that the thermal efficiency was improved by 18.5%. Jamal-Abad et al. [
11] employed copper foam inside a copper absorber tube to inspect the efficiency of a parabolic trough collector (PTC) experimentally. They showed that using foam slightly improved the PTC performance, resulting in an increment in the friction factor. These studies clearly show the effective role of using metal foam to increase heat transfer through the different types of solar collectors. In addition to improving the heat transfer through the HTF flow due to fluid mixing as well as thermal dispersion, applying metal foam in direct absorption solar systems augments the solar absorption. The received rays of the sun enter the pores, and during several collisions with the surface of the pores, the radiant energy is absorbed volumetrically in the porous medium. Then, the working fluid receives the absorbed heat. Therefore, the thermal efficiency of such direct absorption solar systems can improve by utilizing metal foam, although the pressure drop also increases.
The effects of using ceramic foam with single and multiple layers as solar radiation absorbers for heat generation were investigated by Zaversky et al. [
12], experimentally and numerically. They revealed that to achieve higher efficiency, the highest possible porosity should be chosen. Furthermore, while the thermal performance depended on the single layer, the second layer had to be applied to satisfy the mechanical stability. Valizade et al. [
8] experimentally inspected the effect of employing copper foam on the thermal performance of a DAPTC. Their outcomes revealed that filling the whole absorber tube with the foam (fully porous) could increase the HTF temperature difference to 12.2 °C, which was 270% higher than that without foam, leading to an improvement of thermal efficiency by 171.2%. However, applying metallic foam increased the friction factor substantially. They also illustrated that the maximum thermal efficiency can be achieved by raising the flow rate and declining the HTF inlet temperature.
Heyhat et al. [
9] experimentally examined the hydrothermal performance of a DAPTC integrated with semi-porous foam with 95% porosity and 100 mm spacing between pieces of the metal foam and CuO/water nanofluids with different volume fractions. Their results showed that using metal foam significantly augmented the friction factor up to 80 times compared to the pure water. However, it made a maximum temperature difference of 8.8 °C. Moreover, they concluded that combining the metal foam and nanofluid with a volume fraction of 0.1% could improve the thermal efficiency by 79.3%. A similar idea was numerically checked by Esmaeili et al. [
13] using copper oxide as the porous foam, as well as nanoparticles. They studied the effects of flow rate, foam pore sizes, layer thicknesses in the channel, and foam positions on the upper and lower sides of the channel. They showed that the maximum thermal efficiency could be achieved once the channel was completely filled with foam. Hooshmand et al. [
14] deliberated the effects of applying a combination of nanofluid (SiC/water) and porous foam (SiC ceramic) in a direct absorption solar collector experimentally. The maximum thermal efficiency of the system with porous foam was reported to be equal to 37%. Moreover, they showed that higher porosity and pore size led to higher system thermal performance.
The previously mentioned studies have investigated the use of porous foams from the aspect of energy efficiency. However, consideration of exergy, environmental and economic aspects is also very important for the appraisal of a direct absorption solar energy conversion system. Therefore, some studies have been dedicated to investigating these aspects.
Ehyaei et al. [
15] inspected a PTC based on energy, exergy, and economic analysis in Tehran. They applied nanofluids containing CuO and Al
2O
3 nanoparticles with base fluids of water and thermal oil VP-1. Their numerical outcomes indicated that applying water base fluid resulted in higher exergy and energy efficiencies than thermal oil. Moreover, the addition of nanoparticles to both base fluids generally did not significantly affect the performance of the solar collector.
Moosavian et al. [
16] assayed the effects of different climates on the exergy, energy, environmental and economic aspects of a PTC. Their results showed that the highest thermal energy belonged to the Mediterranean Climate, while the Humid Continental Climate had the maximum exergy efficiency.
Mashhadian and Heyhat [
17] examined the exergy and energy efficiencies as well as the environmental aspects of a DAPTC in transient behavior mode. They used CuO–water nanofluids as the heat transfer fluid. The results indicated that the thermal efficiency was reduced with the increase in mass flow and inlet temperature of the working fluid.
Jafari et al. [
18] explored an optimal location for installing domestic flat-plate solar thermal collectors in Iran based on the energy, economic, and environmental aspects. They applied an analytical hierarchy process and found that Yazd in the center of Iran was the best location to install the solar collector.
Exploring the literature, it turns out that the use of metal foam has been introduced as an effective method to ameliorate the efficiency of the direct absorption solar collectors. However, these studies are very limited, and thus far, no study has been reported on the exergy, environmental and economic analysis of different schemes of a metal foam insertion into the absorber tube of a DAPTC. Therefore, this paper aims to analyze a DAPTC filled with various arrangements of metal porous foams based on exergy, environmental and economic aspects. In this regard, the experimental data were collected for various flow rates and inlet temperatures of HTF at ten distinct schemes of porous metal foams. The exergy efficiency, entropy generation ratio, embodied water, embodied energy, Bejan number, and levelized cost of energy (LCE) were obtained and compared for different placements of porous foams as volumetric absorbers of the DAPTC.
In
Section 2, the experimental setup is described. Measurement instruments, specifications and patterns of the applied metal foams, and uncertainty analysis are given in this section. The exergy analysis method and pumping power calculation are presented in
Section 3 and
Section 4, respectively. Then, in
Section 5, the results are reported and discussed. In this section, the results of exergy analysis, pumping power, analysis of environmental effects in the form of embodied water and embodied energy, and economic analysis are explained. Finally, in
Section 6, the results are summarized.
3. Exergy Analysis
Different parameters including thermal efficiency, pumping power, entropy generation, and exergy are deliberated to compare the applying the various layouts of copper foams. The thermal efficiency of the DAPTC can be calculated as follows [
22]:
where
(kg/s),
(J/kg·°C),
(°C), and
(°C) are HTF mass flow rate, specific heat capacity, outlet, and inlet temperatures, respectively. Moreover, I (W/m
2) and
(m
2) refer to the solar irradiation and collector aperture area. The exergy balance for the DAPTC is as follows [
23]:
In this equation,
is the solar irradiation exergy received by the system, which can be defined by the following equation [
23]:
Herein, T
amb and T
sun represent the ambient and sun (≈5800 K) temperatures, respectively. The difference between output and input exergies is useful exergy, which can be calculated by [
24]:
T
m is the average of the HTF inlet and outlet temperatures. The exergy efficiency of the DAPTC can be determined as follows:
To evaluate the entropy generation through the system, the losses (
) due to both thermal and frictional generation should be taken into account. The entropy generation owing to the HTF friction can be calculated as follows [
25,
26]:
Eventually, the total entropy generation can be calculated as follows [
26,
27]:
To better evaluate the metal foam insertion on the entropy generation, the entropy generation ratio as the ratio of the entropy generation of a system with metal foams to the entropy generation of the base case is defined [
28]:
Moreover, to consider the contribution of the pressure drop and heat transfer in the total entropy generation, the Bejan number (Be) is used [
28], as follows:
6. Conclusions
Exergy, economic and environmental analysis of a direct absorption parabolic trough collector filled with various configurations of porous metal foam were investigated. Different parameters, including exergy efficiency, entropy generation, Bejan number, and pumping power at various HTF flow rates (40–120 L/h) and inlet temperatures (20–40 °C) were evaluated. Moreover, different configurations were compared from environmental, size reduction, and economic viewpoints. The key findings are summarized as follows:
Based on the exergy analysis, the maximum useful exergy ratio is provided by Case 1 in all flow rates, where the exergy efficiency reached a high value of 20.4% at 120 L/h.
Using metal foam resulted in either increasing or decreasing entropy generation, depending on flow rate and foam arrangement. Furthermore, the Bejan number is reduced at higher flow rates and larger porous configurations due to the higher pressure drop and frictional entropy generation. The worst case regarding the Bejan number was Case 1, leading to a significant rise in pumping power.
In terms of the pressure drop, using foam dramatically increased the pumping power. The required pumping powers for Case 1 and Case 2 were about 153.4 and 92.8 times higher than the base case, i.e., pure water, respectively.
The environmental and size reduction analyses demonstrated that using Case 1 has a maximum size reduction of 50%, embodied energy of 559.5 MJ, reduction in water consumption of 1520.8 kL, and reduction in CO2 by 339.62 kg compared to the base case.
Investigating the LCE showed that increasing the mass flow rate and adding metal foam reduced the heat production cost, e.g., Case 1 at highest mass flow rate is 50% lower than the base case.
Consequently, although employing porous foam in the form of Case 1 reflected the best performance in terms of exergy, economic and environmental aspects, the required pumping power for this case showed a huge difference from other cases. Therefore, the designer should consider all these positive and negative effects simultaneously.