Integration of a Linear Cavity Receiver in an Asymmetric Compound Parabolic Collector

Abstract

The objective of this work is the integration of a linear cavity receiver in an asymmetric compound parabolic collector. Two different numerical models were developed; one for the conventional geometry and one for the cavity configuration. Both models were examined for inlet temperatures from 20 °C up to 80 °C, considering water as the operating fluid with a typical volume flow rate of 15 lt/h. Emphasis was given to the comparison of the thermal and optical performance between the designs, as well as in the temperature levels of the fluids and the receiver. The geometry of the integrated cavity receiver was optimized according to two independent parameters and two possible optimum designs were finally revealed. The optimization took place regarding the optical performance of the collector with the cavity receiver. The simulation results indicated that the cavity design leads to enhancements of up to 4.40% and 4.00% in the optical and thermal efficiency respectively, while the minimum possible enhancement was above 2.20%. The mean enhancements in optical and thermal performance were found to be 2.90% and 2.92% respectively. Moreover, an analytical solution was developed for verifying the numerical results and the maximum deviations were found to be less than 5% in all the compared parameters. Especially, in thermal efficiency verification, the maximum deviation took a value of less than 0.5%. The design and the simulations in the present study were conducted with the SolidWorks Flow Simulation tool.

1. Introduction

Concentrating Solar Thermal Collectors (CSTC) are able to serve a great range of solar thermal applications and are able to be integrated into domestic hot water systems, desalination and dehumidification set-ups, absorption chiller set-ups (solar cooling systems), and power production applications [1,2,3,4,5]. There is a wide agenda that has been developed around the optimization of such systems as concerns the optical and thermal efficiency, with a variety of optimization technics. The most well-known performance enhancement methods are related to the improvement of the convective heat transfer from the receiver to the thermal fluid and they are applied to linear concentrators such as Compound Parabolic Collectors (CPCs) and Parabolic Trough Collectors (PTCs). This enhancement could be achieved with the use of special working mediums such as nanofluids, with sophisticated flow tube geometries (ribbed and corrugated tubes), and with the integration of flow inserts (metal foams, twisted tapes, fins, etc.) along the flow of the working fluid.

There are many studies in which such methods have been proposed for CPCs and PTCs. Korres et al. [6] investigated a nanofluid-based compound parabolic collector (CPC) and they compared it with the case where only the base fluid is applied in laminar flow conditions. The results were positive since the thermal efficiency was improved sufficiently with the enhancement reaching 2.8%. Rehan et al. [7] studied two different nanofluids (Fe₂O₃/H₂O and Al₂O₃/H₂O) as working mediums in a PTC at several different concentrations. The efficiency of the collector was increased and the increment was more significant in higher concentrations and especially in the case where Al₂O₃/H₂O is applied.

A PTC with a hybrid nanofluid and a double twisted tape inside the flow tube was examined by Alnaqi et al. [8]. It was found that there was a specific orientation of the swirling direction where the thermal efficiency was maximized. As regards the hybrid nanofluid, a higher concentration leads to lower thermal losses. It is important to mention that many studies have examined nanofluid integrations numerically, with high particle concentrations and important enhancements came out. However, it should be taken into account that in experimental set-ups has been proved that agglomeration problem occurs and it has a negative impact in such enhancement when the concentrations take very high values [6,9,10]. Liu et al. [11] conducted experiments in outdoor conditions regarding a CPC and a significant enhancement was found with the use of water/CuO nanofluid. In another work, Bellos et al. [12] investigated the integration of a wavy-walled flow tube in a PTC, using a nanofluid as the thermal fluid. The simulation indicated a slight enhancement in thermal efficiency compared with a typical flow tube. Lu et al. [13] used a water-based nanofluid with CuO nanoparticles in a CPC by performing indoor experiments and a very good enhancement was revealed with the use of the nanofluid. Mwesigye et al. [14] used perforated plates parallel to each other inside a PTC flow tube receiver. The positioning of the plates was optimized in order to increase the convective heat transfer and thus the thermal efficiency was enhanced sufficiently. Liu et al. [15] inserted two twisted tapes in a PTC and they investigated the flow regime. It was revealed that the swirling of the fluid inside the tube led to the increment of the convective heat transfer coefficient. In the study of Ref. [16], a PTC with a wavy-type metal strip inserted in the flow tube was investigated. The research showed that there is an important drop in the heat losses which was greater than 15% and thus a significant enhancement was achieved in the thermal efficiency. Similar methods have been applied in studies [17,18,19,20].

An equally important role in the thermal output, also, is played by the receiver design and positioning as well as the reflector’s geometry. As far as the enhancement technics in this field several studies have been conducted, especially with linear cavity receivers, to be an alternative solution. Most of these studies are referred to as PTCs. Korres and Tzivanidis [21] are the first who studied the effect of the angular aperture of circular cavity receivers in the absorbed solar irradiation and they developed two semi-empirical relationships in order to calculate the equivalent absorptance of such receivers, considering the entrapment of solar irradiation inside the cavity. In addition, the study of Korres and Tzivanidis [22] examined the operation of a PTC with an integrated single cavity receiver inside an evacuated glass envelope. This proposal, which appears for the first time in scientific literature, was found to ensure a great thermal performance enhancement of about 12.2% compared to a conventional PTC. Moreover, the same authors investigated the optical and thermal performance of a PTC with a double circular cavity receiver in a vacuum environment [23] and the thermal performance was enhanced by approximately 16%. It should be mentioned that in studies [22,23], the cavity receivers were first optimized. A PTC with a partially-evacuated circular cavity receiver was examined by Avargani et al. [24] and higher thermal performances were achieved compared to the conventional design. More proposals regarding cavity receivers and special reflector designs could be found in many literature studies [25,26,27,28,29,30,31,32,33,34,35,36,37].

Considering the lack of literature regarding enhancement methods in CPCs and especially in cavity receivers, the present study is dedicated to this field. In particular, an innovative linear single cavity receiver with a single glass evacuated tube is integrated into a novel asymmetric compound parabolic collector (ACPC) design which has been developed by the authors in a previous study [25]. The solar collector that appears in the study [25] has a maximum optical efficiency of 77.68% and it was found to exceed by much, three other similar geometries from literature as far as optical efficiency is concerned. In this study, two different numerical models were developed; one for the conventional geometry of study [25] and one for the cavity configuration. Both models were examined for inlet temperatures from 20 °C up to 80 °C as in studies [3,25], considering water as the working fluid with a typical volume flow rate of 15 lt/h [3]. Emphasis was given to the comparison of the thermal and optical performance as well as in the fluid’s outlet and the absorber mean temperature. The geometry of the integrated cavity receiver was optimized according to two independent parameters and two possible optimum designs were revealed. The optimization aims to the maximization of the collector’s optical performance. The global simulation results indicated an enhancement of up to 4.4% and 4% in the optical and thermal efficiency respectively. An analytical solution was developed for verifying the numerical results and the maximum deviations were found to be less than 1% in all the compared parameters. The design and the simulations were performed with SolidWorks which is a proper tool for performing both optical and thermal studies. To our knowledge, there is no other study in literature where such receiver designs have been proposed for CPCs. Hence, the proposed solar collector appears for the first time in the international scientific literature. In particular, it combines a linear cavity receiver, enclosed in a single glass evacuated tube, with an asymmetrical concentrator and it comes to substitute conventional systems, providing higher optical and thermal efficiency. This combination is originally unique and its investigation constitutes a significant contribution to global research on the solar thermal systems field.

2. Material and Methods

2.1. Examined Collectors

An innovative CPC with an asymmetric reflector and a single cavity receiver (SC-ACPC) is examined in the present study and compared with a similar geometry taken from literature with a conventional receiver (CNV-ACPC) [25]. The geometry of each collector is depicted in Figure 1. According to this Figure, the only difference between the two collectors is the receiver geometry and the evacuated tube type. More particularly, in the SC-ACPC there is a single cavity receiver with an integrated flow tube placed at the interior of a single glass evacuated tube. In the case of the CNV-ACPC, a typical double glass evacuated tube with a U-pipe hydroskeleton is applied. The reflector obtains the same design as in Ref. [25], while the placement of the glass tube with respect to the reflector is identical to the one that was followed in the study of Ref. [25]. The dimensions of the collectors can be found in

Table 1. Dimensions of the examined CPCs.

Dimension	SC-ACPC	CNV-ACPC
Mirror length	1440 mm	1440 mm
Mirror width	153 mm	153 mm
Cover outer diameter	47 mm	47 mm
Cover thickness	1.5 mm	1.5 mm
Copper fin outer diameter	-	30 mm
Copper fin thickness	-	0.6 mm
Receiver outer diameter	33 mm	33 mm
Receiver thickness	0.6 mm	1.5 mm
Flow pipe external diameter	10 mm	9.52 mm
Flow pipe thickness	1 mm	0.65 mm

. It should be mentioned that in the double glass case, the inner glass cover plays the role of the receiver. Hence, in this case, the copper fin’s outer diameter is identical to the inner diameter of the receiver.

The flow pipes and the fins were considered to be made of copper. The same was assumed for the receiver in the SC-ACPC case. All the considered materials of each component are given in

Table 2. CPCs components materials.

Object	Material
	SC-ACPC and CNV-ACPC
Flow tube	Copper
Receiver/Fins	Copper
Evacuated tube	Borosilicate glass
Concentrator	Stainless Steel with mirror finish

, while the respective thermal and optical characteristics are provided in

Table 3. Optical and thermal properties [3,25].

Parameter	Symbol	Value
Absorbance	α	0.92
Receiver emittance	εr	0.08
Transmittance	τ	0.915
Glass emittance	εg	0.88
Reflectance	ρ	0.902

. The values in Table 3 are typical ones and were taken from studies [3,25]. It should be mentioned that the material of all the components in SC-ACPC was considered to be the same as the respective of the CNV-ACPC and thus with the experimental set-up in the study [25]. In addition, all the properties were taken according to the same study.

2.2. Methodology and Implementation

2.2.1. Optical Optimization of the Cavity Receiver

The cavity receiver in the SC-ACPC geometry was optimized aiming to achieve maximum optical efficiency. It is essential to state that in the SC-ACPC case both the inner and the outer surfaces were considered to be coated with the same selective film of 0.92 absorptance and 0.08 emittance, as in the CNV-ACPC configuration. The optimization was conducted by modifying two independent parameters. More specifically, the cavity’s angular aperture (φ) and the cavity rotation angle (ω) were taken to several different values (see Figure 2) and the optical performance of the collector was found each time.

For the ray tracing process, solar rays were considered to be parallel to the collector’s width, while several different transversal angles of incidence (θ_tr) were examined. The details of the ray tracing parameters are available in

Table 4. Optical simulation parameters.

Parameter	Value
Effective solar irradiation intensity (Geff,n)	800 W/m2
Simulated solar rays	106
Transversal incident angle (θT)	0°–60°
Cavity’s angular aperture (φ)	40°–140° per 10°
Cavity’s rotation angle (ω)	20°–80° per 10°

. There were 16 incident angles, 7 cavity rotation angles, and 11 angular apertures which were combined with each other with 1232 total simulation scenarios conducted.

2.2.2. Operating Conditions in Thermal Analysis

In this section, a detailed thermal analysis is put forward for the calculation of the thermal efficiency, the thermal losses, and the temperature regime in both collectors. The analysis was conducted for a volume flow rate of 15 lt/h, which is a typical one in such applications [3], while the inlet temperature took values in the range of 20 °C up to 80 °C, as in other studies [3,25]. Water was assumed to be the working medium of the analysis. The ambient temperature was considered to be 20 °C and the heat transfer coefficient took the value of 10 W/m²/K. The effective solar irradiation for the thermal analysis part was considered to be 800 W/m², while the simulations were conducted for a transversal incident angle of 10° and the consideration that the solar rays are falling parallel to the width of the collector. The operating conditions are given in

Table 5. Thermal analysis operating conditions.

Parameter	Value
Effective solar irradiation intensity	800 W/m2
Simulated rays	106
Transversal incident angle	10°
Environment temperature	20 °C
Wind heat transfer coefficient	10 W/m2/K
Inlet temperature range	20 °C–80 °C
Volume flow rate	15 lt/h

.

2.2.3. Numerical Simulation

The software of the present simulation study is SolidWorks Flow Simulation [38]. A wide range of solar thermal systems have been examined with the particular software and the results have been verified via analytical and experimental results. It is critical to note that with the use of specific software, fluid dynamics, thermal simulation, and ray tracing can be conducted at the same time. More details regarding the present simulation tool and the assumptions which are adopted could be found in previous literature studies [3,6,19,21,22,23,25,26,39,40,41,42].

As regards the boundary conditions, several different conditions were introduced in the program. The inlet temperature and the inlet volume flow rate were the first two parameters that were defined at the inlets of the collectors. The ambient temperature and the wind heat transfer coefficient were defined later at the outer glass surfaces for simulating the convective thermal losses from the cover to the environment. The sky temperature was considered to be equal to the ambient one as in studies [22,43] since the glass envelope is very close to the asymmetric reflector in both cases. The radiative surface conditions were defined according to Table 3, for the proper simulation of the thermal radiation exchange between the components and losses to the ambient. The ray tracing was conducted by assuming a real concentrating consideration, where the reflector acts as a real mirror. Thus, the concentration on the receiver is not considered uniform but is dependent on according to the reflector’s shape and the incident angle.

As far as the mesh grid is concerned, great emphasis was given to the fluid regions and the fluid-to-solid interfaces. More specifically, several different refinements were conducted in fluid and partial cells by developing local grids inside the U-pipes and on the interface between the tube walls and the fluid. Great attention was paid to the formation of the receiver mesh with several refinements applied on the body and its absorbing surfaces of it. This was performed for ensuring that the conduction heat transfer at the interior of the receiver’s body is being performed well and for achieving a proper ray tracing in order to take into consideration all the incident solar irradiation on the receiver. Another important factor for obtaining an accurate ray tracing is the reflector’s surface the grid of which was, also, refined enough.

2.3. Mathematical Formulation

The equations which were used for the analysis of the present models are given in the specific part of the manuscript. Equation (1) is referred to the thermal performance calculation using the useful thermal output and the available solar power, while Equation (2) corresponds to the optical efficiency calculation dividing the absorbed solar power by the available one.

$${\eta }_{th}=\frac{Q_u}{Q_s}=\frac{Q_u}{A_a{G}_{eff,T}}$$

(1)

$${\eta }_{opt}=\frac{Q_{abs}}{Q_s}$$

(2)

The useful thermal output is given by Equation (3) and it can be calculated with two different expressions. Equation (4) gives the mean temperature of the working fluid.

$$Q_u=\dot{V}\cdot \rho \cdot C_p\cdot \left(T_o-T_i\right)=h_f\cdot A_s\cdot \left(T_s-T_{f,m}\right)$$

(3)

$$T_{f,m}=\frac{T_o+T_i}{2}$$

(4)

The overall thermal losses are provided via Equation (5) with three different expressions to be available. The first consideration regards the heat exchange between the outer cover surface and the ambient while the second one calculates the losses considering the heat transfer between the cover and the receiver.

$$Q_L=\left[h_w\cdot \left(T_g-T_{\alpha }\right)+{\epsilon }_g\cdot \sigma \cdot \left(T_g^4-T_{\alpha }^4\right)\right]\cdot A_{g,o}=\frac{A_{p,o}\cdot \sigma \cdot \left(T_p^4-T_g^4\right)}{\left(\frac{1}{{\epsilon }_p}+\frac{1-{\epsilon }_g}{{\epsilon }_g}\cdot \frac{D_{p,o}}{D_{g,i}}\right)}=Q_{abs}-Q_u$$

(5)

Regarding the flow regime in the water tube, Equation (6) gives the Darcy friction factor, and Equation (7) provides the Reynolds number. Equation (8) calculates the critical values of the Reynolds number and enables the characterization of the flow as turbulent when the Reynolds number exceeds the respective critical limit and as laminar in the opposite case.

$${\lambda }_t=2\cdot \frac{D_{t,i}}{L_t}\cdot \frac{\mathrm{\Delta }{p}_t}{u_t{}^2\cdot {\rho }_f}$$

(6)

$$R{e}_{D,t}=\frac{u_t\cdot D_{t,i}}{\nu }$$

(7)

$$R{e}_{cr,t}=140\cdot \sqrt{8/{\lambda }_t}$$

(8)

As far as the heat transfer equations from the flow tube to the fluid are concerned, Equation (9) provides us with the heat transfer coefficient expression arising by solving Equation (3) for (h_f).

$$h_f=\frac{Q_u}{A_s\cdot \left(T_s-T_{f,m}\right)}$$

(9)

Through the heat transfer coefficient, it is possible to calculate the Nusselt number as Equation (10) suggests.

$$Nu=\frac{h_f\cdot D_{t,i}}{k_f}$$

(10)

For the development of the analytical model, which will be introduced later in the manuscript, it is essential to use the theoretical approaches of the Nusselt number as these are described in Equations (11) and (12) for turbulent and laminar flow regimes [6,7,44,45,46,47].

$$N{u}_{lam}=\frac{3.66+0.0668\cdot R{e}_{D_t}\cdot Pr\cdot D_t/L_t}{\left(1+0.04\cdot {\left(R{e}_{D_t}\cdot Pr\cdot D_t/L_t\right)}^{2/3}\right)}$$

(11)

$$N{u}_{tur}=0.023\cdot R{e}_{D_{1,\mathit{i}}}{}^{0.8}\cdot P{r}^{0.4}$$

(12)

Thus, the theoretical value for the heat transfer coefficient in the water tube could be calculated by solving Equation (10) as Equation (13) shows.

$$h_f=\frac{Nu\cdot k_f}{D_{t,i}}$$

(13)

2.4. Analytical Approach

In this part of the manuscript, the method around the analytical approach which was developed is described and the main assumptions are provided.

The main assumptions regarding the analytical solution are listed down:

• The solar energy which is absorbed from the receiver (Q_abs) in every case is available through ray tracing simulation.
• The solar energy which is available on the aperture of the collector (Q_s) was calculated as the product between the aperture area of the collector and the effective solar irradiation (see Table 5).
• The mean temperature of the working medium was defined as the average value between the inlet and the outlet temperature.
• The temperature of the flow tube walls was considered to be equal to the respective of the receiver.

The last assumption appears, also in studies [3,22], in which similar methods were developed. A flow chart of the analytical method is given in Figure 3 and the steps that were followed are presented clearly. First of all, a random value was given for the outlet temperature and the useful power was calculated according to the first part of Equation (3). Then the mean fluid temperature was calculated via Equation (4) and the thermal losses were defined through the third part of Equation (5). By using the first part of Equation (5) it was possible to calculate the glass temperature iterationally. More specifically, several (T_g) values were given until the first and the last part of Equation (5) come to a convergence. After that, the receiver temperature was found with the contribution of the second part of Equation (5). Given the mean fluid temperature, it was feasible to calculate the theoretical values of the Nusselt number (Equations (11) and (12)) and thus the theoretical heat convection coefficient can be calculated (Equation (13)). By having calculated all the above, the next step is the calculation of the new useful power value through the second part of Equation (3). Last but not least, a new value for the outlet temperature was calculated by solving properly the first part of Equation (3). The described procedure was applied in all the operating points and it was repeated, each time, until the old and the new outlet temperature value converge with each other with an absolute error lower than 10⁻⁴.

3. Results

The optical and thermal analysis results arising from the simulation are available in the present part of the manuscript. The comparison between the numerical and the analytical results is, also, presented for ensuring the reliability of the present simulation.

3.1. Verification of the Numerical Model

The verification of the simulation results is presented in this particular section. This verification was conducted as regards conventional design for the thermal efficiency, the thermal losses, and the temperature deviation between the receiver and the inlet of the fluid and between the glass and the ambient respectively. The particular deviation was calculated as $\left|\frac{\mathrm{numerical} \mathrm{result}}{\mathrm{analytical} \mathrm{result}}-1\right|$. The temperature differences were selected in order to evaluate in a proper manner the results. Figure 4, Figure 5, Figure 6 and Figure 7 present the results of the verification procedure and it can be said that there is a satisfying agreement between the numerical and the analytical results

More specifically, Figure 4 declares that the maximum deviation in the thermal efficiency comparison was found to be less than 0.5% which is a relatively low value that indicates the high accuracy of the model. Figure 5 shows that the maximum deviation of the thermal losses is up to 5% which is an acceptable limit. Figure 6 indicates that the maximum deviation regarding the receiver-to-inlet fluid temperature difference does not exceed 1.0%, while Figure 7 shows that the glass-to-ambient temperature difference has a maximum deviation of up to 5%. The aforementioned values prove that the present model is a verified one and so it can further be used in the present study.

3.2. Ray Tracing Results

In this section, the SC-ACPC configuration is set under a detailed optical optimization procedure according to the details referred to previously in the manuscript (see Section 2.2.1).

At this point, it is important to provide some extra information regarding the ray tracing tool and the method that was followed. SolidWorks software has been successfully applied as a ray tracing tool in numerous other studies where solar collectors have been investigated. Indicatively, studies [19,22,23] use SolidWorks software for ray tracing, while study [39] verifies it with TracePro software. It is, also, significant to state that the used simulation tool adopts the Monte-Carlo ray tracing model as far as the optical analysis is concerned. For the present ray tracing analysis, the number of solar rays was selected after a detailed independency procedure and took the optimum value of 10⁶. Another significant point that should be re-mentioned is that during the ray tracing process the longitudinal incident angle was considered to be zero.

Via the optimization process, two different cavity geometries SC-ACPC 1 (ω = 50°, φ = 90°) and SC-ACPC 2 (ω = 40°, φ = 70°) were picked out for being compared with the CNV-ACPC. These geometries were selected since they ensure maximum optical performances in wide incident angle ranges of (2°…25°) and (2°…15°) respectively. Figure 8 illustrates the ray tracing results. More specifically, Figure 8a shows that the proposed designs ensure greater optical efficiency than the conventional ACPC in wide ranges of solar incident angles. Figure 8b shows clearly the enhancement percentage in the range from 2° to 25°.

In particular, SC-ACPC 1 ensures a mean enhancement of 2.90% for an incident angle range of 23°, with the maximum possible enhancement reaching approximately 3.90%. SC-ACPC 2 configuration seems not to contribute significantly to an incident angle greater than 15°. However, it provides greater enhancements than the SC-ACPC 1 for incident angles lower than 15°, with the maximum value being 4.35% at 10°. The mean enhancement, in this case, corresponds to 3.48% for the range of (2°…15°). The operation of the proposed geometries seems not to diversify significantly from the previous study model for incident angles greater than 30°.

For the determination of the optimum geometry between the two proposals, an efficiency index (EI) should be introduced. The product between the incident angle range and the mean optical efficiency enhancement in the respective range is a proper EI that could be used for comparing the two proposed geometries. The main criterion is the maximization of the mean optical efficiency enhancement in combination with the maximization, as much as possible, of the incident angle range. Hence, the EI could take the following form:

$$EI=en{h}_{opt,m}\left(\mathrm{\Delta }{\theta }_T\right)\cdot \frac{\mathrm{\Delta }{\theta }_T}{1^o}$$

(14)

where enh_opt,m (Δθ_Τ) is the mean optical efficiency enhancement in Δθ_Τ range and Δθ_Τ is the transversal incident angle range.

Table 6. Efficiency Index values for SC-ACPC 1 and SC-ACPC 2.

Geometry	SC-ACPC 1	SC-ACPC 2
enhopt,m (ΔθΤ)	2.90%	3.48%
ΔθΤ	23°	13°
EI	0.667	0.452

gives EI values for the two cases. More specifically, Table 6 indicates that although the mean optical efficiency is greater in the case of SC-ACPC 2, the EI is higher in the case of SC-ACPC 1. This happens because the incident angle range is much wider in this case. Hence, SC-ACPC 1 geometry seems to be more efficient for a wide range of incident angles.

3.3. Thermal Efficiency and Losses

In the present section, the thermal performance results will be presented. The thermal efficiency is depicted in Figure 9 for each one of the examined models. According to Figure 9a, the two proposed designs seem to exceed in thermal performance of the CNV-ACPC geometry. Particularly, the cavity configurations SC-ACPC 1 and SC-ACPC 2 appear sufficiently greater thermal efficiency in the whole operating range, with SC-ACPC 2 being the leader of this prevalence. The mean enhancement for the SC-ACPC 1 is equal to 2.92% with a maximum value of 3.70%, while in the case of the SC-ACPC 2 the maximum enhancement reaches 4.00% and the mean one is 3.20%. It is remarkable to mention that the minimum enhancement remains greater than 2.20% in both cases and appears in T_i = 80 °C. As regards the thermal losses in Figure 9b, there is a significant difference between the SC-ACPC geometries and the CNV-ACPC one. This difference exists due to the reason that the SC-ACPCs absorb more solar energy than the CNV-ACPC. Another reason for this deviation is that the flow tube in the SC-ACPCs is far from the edge points of the receiver compared to the CNV-ACPC since in the last one there are two straight parts of the U-pipe that are sharing the receiver’s body in terms of heat transfer.

3.4. Allocations of the Temperature

In this section, various allocations of the SC-ACPC and the CNV-ACPC collectors for the simulation point with T_i = 60 °C are available for evaluation. Figure 10 gives the temperature distribution at a transversal section in the middle of each collector. The surface temperature distribution around the whole receiver in each collector is illustrated in Figure 11.

As is seen in Figure 10, the temperature regime differentiates among the APCs. In particular, the temperature fields seem to take their highest values in the SC-ACPC 2 case and the lowest ones in the CNV-ACPC geometry. This is reasonable since the SC-ACPC 2 absorbs the greatest amount of solar power in contradiction with the CNV-ACPC which absorbs the lowest one of all cases. It is, also, remarkable to notice the high-temperature areas in each collector. These areas represent the regions where most of the solar irradiation is being concentrated in each receiver. Figure 11 indicates one more solar irradiation concentration region and it declares that the SC-ACPC 2 configuration appears the highest temperatures on average compared to the other two collectors. It is, also, important to see that in all cases the temperature is reasonably becoming reduced going from the outlet to the inlet.

4. Conclusions

In this work, the integration of a linear cavity receiver in an ACPC, developed by the authors in a previous study, was investigated. This is the first time in literature that such integration is being proposed. Two different cavity receiver designs (SC-ACPC 1 and SC-ACPC 2) were proposed and compared with the previous study’s design (CNV-ACPC). Next, the most important concluding remarks are listed.

• The numerical results were verified through an analytical solution developed by the authors with a sufficient agreement to be achieved (deviations less than 0.5% in thermal performance and 5.0% in thermal losses).
• Two new geometries were revealed from the optical optimization process.
• The proposed designs came out from a detailed optical performance optimization conducted through ray tracing.
• The cavity configurations lead to a significant enhancement of the optical performance of the CNV-ACPC geometry up to 4.4% for θ_Τ range of 23°.
• SC-ACPC 1 seems to be more suitable for wide incident angle range applications since it ensures a greater mean enhancement for θ_Τ in the range of 2° to 25° in contrast to SC-ACPC 2 which is better for θ_Τ in the range of 2° to 15°.
• SC-ACPC 1 was found to be the best solution between the two suggestions according to an evaluation process with an Efficiency Index (EI), having as the main criterion the balance between the maximization of the mean optical efficiency enhancement and the wider possible incident angle range.
• The mean enhancement with the use of SC-ACPC 2 for θ_Τ in the range of 2° to 20° is slightly greater than the respective of SC-ACPC 1 considering the same θ_Τ range (3.15% against 3.05%).
• SC-ACPC 2 ensures 3.2% mean thermal efficiency enhancement against CNV-ACPC. The maximum possible thermal efficiency enhancement, in this case, reaches 4.0% and it appears for T_i = 20 °C.
• SC-ACPC 1 configuration appears slightly lower mean and maximum enhancements than the SC-ACPC 2 geometry (2.92% and 3.70% respectively).

In general, the proposed designs ensure sufficient enhancements both in thermal and optical performance. These enhancements could be even greater when low-absorbing coatings with an absorptance of around 80% are applied, as in various studies [23,48].

Future work could be conducted for a deeper investigation of the proposed systems. It would be useful for the proposed configurations to be tested in terms of the convective regime inside the flow pipe and for possible enhancements in the field using flow inserts, nanofluids, or even a combination of them. Another interesting aspect would be the investigation of non-cylindrical cavities applied to the receiver geometry and the comparison of them with the cylindrical ones. This is recommended, to determine how the cavity’s design affects the collector’s performance.