## Abstract

The present research integrates the concept of double-pass (DP) flows with high-temperature solar receivers to introduce an innovative design aimed at minimizing heat losses and optimizing performance. The new DP system was developed using a tubular absorber derived from billboard solar tower technology and operated with air as the heat transfer medium. Computational fluid dynamic models are developed based on an experimental campaign conducted at a solar furnace facility. The computational analyses indicated that employing the DP design instead of single-pass (SP) absorbers results in an average enhancement of energy and exergy efficiency by 35% and 225%, respectively, across all test conditions. However, this enhancement is accompanied by an average increase in pressure drop of ∼60%. The detailed exergy analysis also revealed the contribution of each term in the exergetic performance, identifying the exergy destruction between the sun and the absorber as the primary source, accounting for an average of ∼65% of the total inlet exergy for both SP and DP absorbers. Consequently, the DP presents itself as a promising alternative design for future solar tower configurations, offering improved Nu numbers up to ∼50% in air-based solar systems.

## 1 Introduction

With the rising human population, there is a significant surge in the demand for energy resources. This surge is contributing to the rapid depletion of Earth's energy resources and is leading to severe environmental crises. To address this pressing issue, the power sector needs to embark on an energy transition. This transition aims not only at increasing the global power supply but also at prioritizing sustainable development through the widespread adoption of renewable energy sources [1].

Apart from hydropower and wind power, solar energy is experiencing significant growth in use, both in terms of direct electricity generation through photovoltaics and the utilization of thermal power. Concentrating solar power (CSP) plants, as a part of solar technology, are increasingly contributing to the advancement of renewable power generation.

In principle, a CSP plant includes an array of reflectors to collect solar energy on a receiver where the heat transfer fluid (HTF) absorbs the solar heat and transfers it to a heat engine (steam or gas turbine) linked to an electric power generator [2]. Having reached a total value of 6.7 GW of power production by 2023, CSP is expected to double its share in the next 5 years among other main renewable technologies such as hydropower, wind, and solar photovoltaic (PV) [3,4].

When it comes to the collection of solar energy, CSP technologies are categorized into two main types: linear systems and point-focusing systems. Linear systems typically feature uniform flux distributions along their longitudinal axis, while point-focusing systems typically utilize flux distributions that follow a Gaussian pattern [5]. According to another classification, CSP systems are defined based on the type of HTF, where heat transfer oils, molten salts, nanofluids, and gaseous are the main categories [6]. Although liquid-based HTFs have a higher capacity to remove the heat from solar absorbers, the employment of gas-based HTF in CSP plants has reduced significantly the operation and maintenance costs [7], which could offset the lower heat absorption potential with an efficient design of the receiver.

In recent years, scientists have proposed various methods to enhance the thermal performance of gaseous CSP receivers. Most of the work is devoted to increasing the absorbing area using mesh or porous structures in volumetric absorbers [8–10], as well as to enhancing the internal heat exchange using flow inserts [11], or turbulators [12] in tubular absorbers. In a previous work published by the authors [13], for instance, it was proved that using a tubular air-based absorber equipped with a porous medium could enhance the thermal performance in point-focusing solar power plants, advancing the current technology.

This study aims to increase the efficiency of a tubular billboard receiver using the double-pass (DP) flow concept. It is worth mentioning that the integration of double-pass with solar receivers is not a new concept, and literature [14] includes a range of works concerning DP solar air heaters for low-temperature applications. Satcunanathan and Deonarine [15] introduced already in the 70ies a two-pass flat plate solar air heater to enhance the thermal performance by 10–15%, suppressing the heat losses that occur in the space between the flat plate receiver and glass covers.

Forson et al. [16] developed a mathematical model to study the thermal behavior of a double-flow single-pass solar air heater in which two rectangular flow channels were formed: one in the space between the top cover and the absorbing plate, and one below the absorber and the bottom wall. Their results showed that air mass flowrate is a critical factor, driving the overall efficiency of the heater. To further increase the thermal efficiency of double-pass flat plate solar air heaters, Naphon [17] found that the employment of a porous medium with such systems could bring a ∼25% increase in thermal efficiency. Sivarathinamoorthy and Sureshkannan [18] explored the influence of internal fins and heat storage materials on a double-pass solar air heater and realized that their design promotes a nearly 100% enhancement in the thermal performance of conventional collectors.

Hence, the potential performance benefits derived from the implementation of DP solar receivers offer a promising avenue for enhancing the existing gaseous CSP receiver technology. The only similar concept can be attributed to the application of bayonet tubes for solar central receivers [19,20], where two concentric tubes are used to reabsorb the heat from the second flow, but without any connection between the two tubes. Numerical results proved that this technology reduces the tube wall temperature significantly, reducing the absorber thermal losses and increasing the thermal efficiency up to ∼95%.

In the evaluation of the receiver performance, the application of both energetic and exergetic points of view in the thermal analysis of the solar energy system is a useful method that has been used by many scientists in this context. Abd El-Hamid et al. [21] used this approach to study the different photovoltaic-thermal hybrid configurations through a numerical investigation. In another work [22], researchers compared the energy and exergy performances of a solar PV–thermal (PV/T) air collector and proved the added value of considering both indicators.

Consequently, this study represents a novel contribution examining the impact of DP flow on gaseous CSP receivers through a comparative analysis from both energetic and exergetic perspectives. The low thermal conductivity of air as the HTF is compensated by the double-pass concept. The insertion of fins enhances thermal conduction between the two tubes, improving the design with respect to the previous bayonet tube designs. This work extends what was presented in Ref. [23], offering more in-depth discussions on the technical aspects. Additionally, the application of double-pass receivers for CSP towers with non-uniform heating makes this study a pioneer in the field.

## 2 Solar Absorber

The solar receiver under investigation is designed as a billboard absorber, composed of a panel of identical parallel tubes interconnected in a series arrangement to achieve the desired high-temperature outlet air temperature, typically sought in CSP systems (Fig. 1(a)). Each individual receiver comprises two concentric tubes: an open-ended inner tube and an outer tube with one closed end, featuring a rounded closed section and three connecting fins that bridge these tubes together (see Fig. 1(b)). In this configuration, concentrated heat is applied to the exterior surface of the outer tube and then conducted to the inner tube through the connecting fins (Fig. 1(c)). The air enters through the inlet of the inner tube, gradually gaining heat as it travels along the longitudinal axis of the tube. As the lengths of these tubes are equal, when the fluid exits from the outlet of the inner tube, it reaches the closed end of the outer tube and redirects into the annular space formed between the inner wall of the outer tube and the outer wall of the inner tube. It divides into parallel channels, defined by the ribs (fins), which serve to secure the inner tube in place. During this phase, as the preheated HTF flows through the annular region in the reverse direction, it is subjected to a higher heat flux compared to the initial pass.

The dimension of the absorber was selected based on the experimental work conducted at the Solar Furnace (SF60) located at Plataforma Solar de Almería (PSA), Spain, during the summer of 2022 (see Fig. 2) [24]. According to the optical characteristics of SF60, to absorb the concentrated solar power on the absorber panel, a total area of 12 × 12 cm^{2} is needed. Therefore, the entire receiver was designed with nine individual tubular absorbers having a 26-mm outer diameter and a 235-mm length. These dimensions were selected to model the exact sample tested during the experiments and replicate its performance through computational fluid dynamics (CFD) modeling. While the tube length may not significantly influence the heat flux distribution on the tube, the tube diameter is a crucial factor to optimize for further improvements. This could be the focus of future studies, providing additional details on how different values of the inner and outer diameters will affect the performance of DP absorbers. The analysis, as well as the tests, was conducted considering the tube located at the center of the heat flux, following the procedures addressed in Refs. [12,25] and the obtained results for the smooth pipe design are reported and used for validation of the numerical simulation in Sec. 4.3. Table 1 provides the details of the experimental parameters and test facility.

Specification | Value/Dimension |
---|---|

SP Inner diameter (D)_{i} | 21 mm |

DP Outer tube inner diameter (D)_{i} | 21 mm |

DP Inner tube outer diameter (d)_{o} | 12.5 mm |

DP Inner tube inner diameter (d)_{i} | 8.5 mm |

Fin thickness | 1 mm |

Fin length | 160 mm |

Tube material | 316 L stainless-steel |

Air volume flowrate | 30, 40, and 50 L/min |

Solar peak flux | 50, 100, and 200 kW/m^{2} |

Tube coating | PYROMARK 2500 |

Tube absorptivity [26] | 0.9 |

Reference pressure | 10 bar |

Specification | Value/Dimension |
---|---|

SP Inner diameter (D)_{i} | 21 mm |

DP Outer tube inner diameter (D)_{i} | 21 mm |

DP Inner tube outer diameter (d)_{o} | 12.5 mm |

DP Inner tube inner diameter (d)_{i} | 8.5 mm |

Fin thickness | 1 mm |

Fin length | 160 mm |

Tube material | 316 L stainless-steel |

Air volume flowrate | 30, 40, and 50 L/min |

Solar peak flux | 50, 100, and 200 kW/m^{2} |

Tube coating | PYROMARK 2500 |

Tube absorptivity [26] | 0.9 |

Reference pressure | 10 bar |

## 3 Thermal Model

This section outlines the theoretical foundations and numerical assumptions applied in constructing the thermal model for the CFD simulations. The analyses are conducted using two distinct approaches, encompassing both the first and second laws of thermodynamics.

### 3.1 Energy Analysis.

*α*), as reported in Eq. (2).

### 3.2 Exergy Analysis.

*o*”) and input (index “

*i*”) values, for a solar air heater can be expressed as in Eq. (8), in which “

*net*” denotes the net exergy rates and $Exl$ the exergy loss.

*T*denotes the surface temperature of the sun and is usually predicated as 5762 K.

_{sun}The exergy rates lost by the flow friction and by the temperature difference between heat source, receiver, and fluid are internal exergy losses (exergy destruction) [34].

### 3.3 Thermal Enhancement Assessment.

*T*is the average wall temperature obtained from the interface between the fluid and solid regions in both models.

_{w}## 4 Numerical Model

### 4.1 Model Setup.

The commercial software Star CCM+ [38] was used to solve the momentum and continuity equations, as well as the conjugate heat transfer problems. In order to compare the hydraulic and thermal performances between the SP and the DP designs, a tube model was also created. For the SP model, the inlet and outlet faces were elongated to simulate the test facility connections and include the location of inlet and outlet temperature sensors for validation against the experiments (Fig. 3(a)). As shown in Fig. 3(b), for the DP model, dimensions were selected respecting those of the SP sample (*L* = 235 mm), and similar boundary conditions were applied to ensure a fair comparison between the two models. The solution domain comprises both solid and fluid regions, with a contact interface between domains. Steady-state, 3D, and conjugate heat transfer models were employed across all regions. The conjugate heat transfer analysis was performed using a segregated flow temperature model, and the following assumptions were made for the simulations:

The solar and fluid properties are temperature dependent.

The heat losses between the inner and outer tubes are neglected as the annular space is filled with running air.

As the fluid temperature is not uniform across the inlet and outlet cross-sectional areas ($Ac$), air temperature values are extracted from the simulations, using $\u222bA\rho vCpTdAcm\u02d9Cp$ report.

The tube emissivity with the applied coating was set as a function of wall temperature as defined in Ref. [26].

The convection heat transfer coefficient for the loss through the absorber to the ambient ($hw$) was set at 10 W/m

^{2}K (this coefficient was verified to have a small impact on the results).The applied heat flux is modeled as a single tube irradiation and without considering the tube-to-tube interaction effects.

As the heat transfer inside the tube is dominated by the forced convection, the surface-to-surface radiation heat transfer between the inner walls is neglected in this study. Thus, the exergy destruction due to the heat loss between the inner and outer tubes is also neglected.

In order to simulate turbulent flow inside the receiver, a two-equation Reynolds-averaged Navier–Stokes (RANS) model, specifically the two-layer realizable $k\u2212\epsilon $ model, was used with a two-layer wall treatment. It is noteworthy that $k\u2212\epsilon $ turbulence model is widely used in the modelling of solar tubular absorbers [39–43], particularly in scenarios where flow obstacles are absent. The two-layer version of the $k\u2212\epsilon $ model adds flexibility in the wall treatment by automatically switching between low-y+ and high-y+ treatments. As highlighted by Dixon et al. [44], the superiority of the realizable $k\u2212\epsilon $ model over the standard $k\u2212\epsilon $ model refers to the incorporation of an enhanced equation for the turbulent energy dissipation rate ε, with a variable viscosity coefficient C* _{µ}* instead of a constant value. Therefore, this model performs reasonably well when considering rotational boundary layers under strong adverse pressure gradients, separation, and recirculation with strong curvature, as observed in Refs. [45,46]. For the boundary conditions, a velocity inlet interface was defined in the internal fluid domain, while a pressure outlet condition (with pressure gauge

*p*= 0 Pa) was applied at the outlet face. The concentrated solar flux was simulated using field functions applied to the irradiated side of the sample. The boundaries of the inlet and outlet sections were considered adiabatic, as conduction plays a negligible role in total heat loss from the receiver [12]. Furthermore, a no-slip boundary condition was applied at the walls, and inlet air temperatures were set according to the experimental observations. The detailed boundary conditions for the turbulence model can also be found in the Appendix.

### 4.2 Grid Study.

A polyhedral-based meshing with a prismatic layer for fluid regions was employed to solve the equations. Figure 4 shows the grid developed for both fluid and solid domains. To verify the accuracy of the meshing grid and ensure that results are independent of the number of cells, a sensitivity study to the grid cell size was carried out on the SP simulation. Four different meshes were tested, ranging from a very coarse mesh to the finest mesh, comparing the pressure drop ratio and the maximum surface temperature against those obtained by the finest mesh. Table 2 details the assessment of the numerical uncertainty due to discretization, where the average cell size is computed as $V/Ncell3$, with *V* being the total volume of the model and *N _{cell}* is the number of cells. The grid chosen for both SP and DP simulations is #3, which shows numerical results with <1% error compared to the finest one in terms of surface temperature increase and pressure drop ΔP. Therefore, the chosen grid resolution ensures accuracy in resolving important flow and heat transfer details. As a result, the numerical results obtained in this research exhibit a numerical uncertainty of approximately 1%, which has been used and validated through rigorous validation processes (Fig. 5). It is important to highlight that the total cell numbers used for SP and DP models were 0.93 million and 1.25 million, respectively.

### 4.3 Validation.

To validate the numerical simulations against experimental data, the experimental test conditions from Ref. [24] were applied to the SP model. As outlined in Table 3, various airflow rates and three different peak solar flux levels were tested. These values were directly selected from the experimental conditions, ensuring safe operation of the SP absorber in the test environment to prevent oxidation and avoid reaching its softening point. The analysis focuses on comparing the maximum temperature rise of the tube wall (*T _{s,}*

_{max}), measured by an infrared camera during the experiments, with the maximum temperature recorded on the outer wall of the tube as computed in the CFD simulations. Figure 5 illustrates the comparison between the experimental and numerical results for nine distinct tests. The data in the figure demonstrate that the CFD model accurately replicates the experimental conditions and outcomes, with an average error of approximately 3%. Additionally, to assess the sensitivity of the turbulent models, simulations were re-analyzed using $k\u2212\omega $ SST model, which yielded comparable results under the same boundary conditions. The two-layer realizable $k\u2212\epsilon $ model was then used for further evaluation.

Test ID | Airflow rate (L/min) | Solar peak flux (kW/m^{2}) | Ambient temperature (°C) |
---|---|---|---|

T5030 | 30 | 49.55 | 27.3 |

T5040 | 40 | 48.72 | 28.2 |

T5050 | 50 | 48.17 | 28.5 |

T10030 | 30 | 101.24 | 29.4 |

T10040 | 40 | 98.41 | 30.5 |

T10050 | 50 | 101.10 | 31.6 |

T20030 | 30 | 196.88 | 27.1 |

T20040 | 40 | 199.23 | 32.6 |

T20050 | 50 | 202.41 | 25.7 |

Test ID | Airflow rate (L/min) | Solar peak flux (kW/m^{2}) | Ambient temperature (°C) |
---|---|---|---|

T5030 | 30 | 49.55 | 27.3 |

T5040 | 40 | 48.72 | 28.2 |

T5050 | 50 | 48.17 | 28.5 |

T10030 | 30 | 101.24 | 29.4 |

T10040 | 40 | 98.41 | 30.5 |

T10050 | 50 | 101.10 | 31.6 |

T20030 | 30 | 196.88 | 27.1 |

T20040 | 40 | 199.23 | 32.6 |

T20050 | 50 | 202.41 | 25.7 |

## 5 Results and Discussion

This section presents the numerical results obtained from the developed thermal models, analyzed using various metrics. In the first part (Sec. 5.1), the hydraulic characteristics of the two models are compared and discussed, focusing on the increase in pressure drop and friction factor when using DP instead of SP. In Sec. 5.2, the thermal features are examined by analyzing the temperature fields computed in the fluid and solid domains. Subsequently, energy and exergy efficiencies are utilized to evaluate the overall performance of the proposed models according to the first and second laws of thermodynamics. Finally, the thermal enhancements achieved by DP are assessed by comparing the increase in the Nusselt number Nu over the SP design.

### 5.1 Hydraulic Results.

In this section, the hydraulic performance of the proposed model is explored under different operational scenarios and through a comparative analysis with the SP design. Figure 6 illustrates the pressure drop values, calculated between the inlet and outlet without any heat input for both configurations, for a range of mass flowrates. As anticipated, an increase in the airflow rate leads to a corresponding growth in the pressure drop. Notably, the DP flow exhibits approximately a 50% higher pressure drop compared to the SP flow. This trend follows a quadratic pattern with respect to the flowrate, consistent with our initial expectations.

Figure 7 shows the velocity field on an axial cross section for the test conducted at a flowrate of 400 L/min (8.5 g/s), revealing three different regions responsible for the pressure drop. The first zone is the flow inside the internal tube, where the fluid develops as it proceeds, forming normal boundary layers. The second zone is characterized by the bend that occurs after the outlet of the inner tube, primarily due to the shape of the outer tube's rounded end. As depicted in the zoomed section, this region promotes secondary flows, resulting in increased pressure loss. The third zone refers to the development of the flow in the annulus region, which further contributes to the system pressure loss. Analyzing the fraction of the pressure drops in each zone revealed that the round cap, which promotes the U-turn in the fluid flow, has the maximum pressure drop fraction (59% of the total in the DP configuration). The first zone, with a 40% share, has the second highest contribution to pressure losses, while the third zone (flow in the annulus) presents the lowest fraction, with less than 1% of the total pressure drop. In terms of the flow repartitioning caused by the fins, 24% of the total flow runs inside each of the two upper channels (near heat load), while the lower channel accommodates 52% of the total airflow.

### 5.2 Thermal Results

#### 5.2.1 Tube Wall Temperature.

In this section, the thermal analysis in terms of solid temperatures is presented, to provide insights into the interpretation of the thermal losses experienced by the absorbers. Figure 8(a) indicates the temperature profiles on the SP and DP outer walls in the operating conditions T10040, and these profiles are plotted for two axial lines: one on the heated side (Front) and one on the unheated side (Back). The computed results are extracted for the same locations with respect to the fluid flow directions. As shown in Fig. 8(b), both DP profiles start from higher values than SP, which reflects the lower initial temperature gradient in the second flow as the result of the preheating process taking place thanks to the first flow and inside the inner tube. As the second flow reaches a distance of 35 mm, the SP front temperature profile exceeds the DP front values due to the presence of the fins in the latter. The fins are thus effective in transferring a fraction of heat from the outer tube to the inner tube, resulting in a lower outer wall temperature and minimizing the thermal losses to the ambient. For the backside readings, the SP temperature profile exceeds the DP values after reaching 47 mm, due to the lower cooling capability of this configuration. Moreover, in the middle of the tube, where the solar flux peak is applied, the DP absorber shows a hotspot temperature rise reduced by 27% and 30% on the front and back sides of the outer tube, respectively.

To represent the temperature propagation through the two tubes in the DP design, Fig. 9 has been plotted for the test with a 100 kW/m^{2} solar peak flux and an airflow of 40 L/min. As shown, the fins located between the two tubes are confirmed to have a significant contribution in transferring the heat to the inner tube while they also produce two narrow channels on the half-top of the second flow, that enhance the heat transfer between the fluid and solid regions. Moreover, the length of the fins is shown to be effective enough with respect to the applied heat, which reduces as the tube end is approached.

A comparison of the hotspot temperature rise (maximum temperature on the front side offset with the inlet fluid temperature) for both DP and SP designs is presented in Fig. 10, considering various heat fluxes. The DP flow has resulted in a decrease in the hotspot temperature rise (*T _{s,}*

_{max}) in all test conditions by more than 25%. In more detail, when the solar flux increases, the reduction in

*T*

_{s,}_{max}decreases, showing a lower reduction in thermal losses at high heat loads. This is attributed to the limited capacity of fins to transfer the heat to the inner tube. On the other hand, the growth in airflow rate improves the reduction rate in the hotspot formation, demonstrating the role of high turbulence conditions in intensifying the performance enhancement in the DP design. As a result, the maximum

*T*

_{s}_{, max}reduction is achieved in the operating conditions T5050, reaching ∼30%, whereas the minimum of 20% is attained in the operating conditions T20030.

#### 5.2.2 Fluid Temperature.

This section discusses the temperature distribution within the fluid region to analyze the heat transfer process from the absorber to the airflow. In Fig. 11, the fluid temperature development is illustrated for both designs tested in the operating conditions T10040, with respect to the cross sections along the flow direction. In the case of the SP design, as the fluid proceeds, the thermal boundary layer develops which weakens the heat transfer process from the heated wall. On the other hand, the first flow in the DP absorber has thinner viscous layers and a relatively greater heat transfer rate compared to the SP main flow since the inner tube diameter is reduced and the air velocity is higher. As the air gets preheated in the first flow and is mixed at the round end, the second flow develops at the annulus region, splitting into three channels from *Z* = 188–47 mm. The maximum heat load is applied to this region, where the heat transfer area is extended and the fluid core zone is decreased compared to the SP design. As a result, the heat propagation inside the fluid is enhanced, resulting in higher temperature contours on the outlet face for the DP absorber (at Z = 0) compared to that of SP (at *Z* = 235 mm).

Figure 12 displays a comparison of the fluid temperature difference $(To\u2212Ti)$ obtained using SP and DP absorbers for the same test conditions. As expected, for the two absorber designs, the solar flux has a positive impact, and the airflow rate has a negative impact, on the fluid temperature difference. The utilization of DP design instead of SP leads to an average improvement of 35% in the air temperature difference. Moreover, at a given solar flux, as the airflow rate increases the improvement effect is decreased. Adversely, at a given airflow rate, the increase in solar flux enhances the improvement effect on the fluid temperature difference as more heat is transferred to the inner tube. Thus, the maximum temperature difference increase is ∼50% for the test carried out at a peak solar flux of 200 kW/m^{2} and an airflow rate of 30 L/min, while the minimum augmentation is achieved in the operating conditions T5050, with only a ∼23% higher ΔT for the DP design, with respect to the SP one.

### 5.3 Energy Efficiency.

In this section, the overall thermal performance in terms of energy efficiency is presented to finalize the comparison between the DP and SP absorbers. Figure 13(a) presents the variations in the total heat loss computed for both absorbers under various test conditions. As observed, the increase in the airflow rate decreases the total heat lost from the absorbers at each solar heat flux, resulting in higher useful heat gain as well as increased turbulence in the heat transfer coefficient from both absorbers to the running air. However, increasing the solar flux increases the total heat loss from the absorber due to the higher temperature levels on the absorber surface. As a result, the maximum heat loss for the SP and DP absorbers is 178 W and 135 W, respectively, for the test with the lower airflow rate of 30 L/min, and the highest flux of 200 kW/m^{2}.

Figure 13(b) shows the variations in the energy efficiency based on the test modes and for the two samples. In the case of the SP absorber, the maximum and minimum energy efficiencies are achieved as 51% and 32% for the operating conditions T5050, and T20030, respectively. Similarly, the maximum and minimum energy efficiencies for the DP absorber were obtained for the operating conditions T5050 and T20030, respectively, with values of 65% and 49%. Analyzing the improvement effects of the DP flow over the single-pass flow, it was found that a ∼35% higher efficiency can be achieved as an average among all the studied cases. Furthermore, increasing the solar flux from low to medium and high levels for constant airflow maximizes the positive effects of DP, reaching the highest value of 51% in the operating conditions T20030. The average growth at each heat flux proved that increasing the solar peak flux from 50 to 100 kW/m^{2} improves the energy efficiency enhancement by an additional 5%, while increasing the flux from 100 to 200 kW/m^{2} brings 12% higher enhancement effects. This suggests that DP is a favorable candidate for operations under high solar flux levels.

### 5.4 Exergy Efficiency.

In order to perform the exergy analysis on the two investigated absorbers, it is crucial to present the variation of different exergy loss terms versus the testing conditions to find the most and the least significant terms. For better comparison, their values are normalized by that of the net inlet exergy of the sun. Figure 14 shows the computed terms for the case of the SP. Analyzing the loss exergy terms revealed that the term based on the temperature difference between the absorber surface and the sun ($Exdes,Tsun\u2212Tp$) is the major source of exergy loss, accounting for an average value of 63%. In more detail, the maximum (75%) was achieved in the operating conditions T5050, whereas the minimum (51%) was computed in the operating conditions T20030. This can be explained by considering that operating the solar absorber at the higher flux levels reduces the ($Exdes,Tp\u2212Tsky/Exi,net$) fraction by reaching a lower temperature difference between the two sources. In addition, the effect of the mass flowrate at each heat flux shows that the absorber temperature decreases as the heat dissipation is enhanced with the rise in the flowrate, and the exergy destruction increases.

The second largest source is the exergy loss based on heat losses ($Exl,th$), that uses 10–30% of the total inlet exergy depending on the operating conditions. As shown, the rise in the heat flux is detrimental and brings higher ($Exl,th/Exi,net$), while the growth in airflow rate reduces the overall heat loss coefficient. As a result, the maximum loss is computed in the operating conditions T20030, while the minimum occurs in the case T5050. The optical-related loss ($Exl,opt/Exi,net$) is the third major source of the exergy loss and comes regardless of the operating conditions, with a constant value of 0.1. The fraction of the exergy destructed in the heat flow from the absorber to the fluid was also obtained with respect to that of inlet exergy ($Exdes,Tp\u2212Ta/Exi,net$) and shows an average of 0.075, based on the simulation conditions. At the peak flux of 50 kW/m^{2}, the rise in the airflow rate from 40 to 50 L/min shows a smooth descending trend with a 3% reduction, revealing that the improvement in convective heat transfer has resulted in lowering the exergy destruction at this heat flux level. However, for the 100 and 200 kW/m^{2} simulations, the airflow of 50 L/min has the maximum exergy destruction share and the thermal enhancement is not enough to increase the quality of energy delivered by the air absorber. Finally, the effects of the friction factor are also presented showing an almost negligible contribution to total exergy loss. As shown, the rise in the airflow rate has a detrimental effect on the energy quality, increasing the destructed exergy due to higher friction losses at each heat flux level. Moreover, as the values of $Exdes,fr$ at the same flowrate remain independent from the heat flux, the ratio of $Exdes,fr/Exi,net$ decreases as the heat flux increases, and the total solar input exergy rises. In the case of exergy efficiency, the effects of airflow rate are ascending for the two peak flux levels of 100 and 200 kW/m^{2}, while at the peak flux of 50 kW/m^{2}, the exergy efficiency reaches the peak at the flowrate of 40 L/min and then descends by the airflow rate of 50 L/min. The reason for such a behavior can be attributed to the role of airflow rate in enhancing $Exl,th$ (the second major source of exergy loss), where these effects are more pronounced at the heat flux levels of 100 and 20 kW/m^{2} and less in the 50 kW/m^{2} case. Note that the changes in $Exdes,Tsun\u2212Tp$, depending on the airflow rate are slight and show a small influence. Moreover, the rise in the peak flux improves the exergy efficiency, as the maximum was achieved as ∼3% at a flowrate of 50 L/min and a peak flux of 200 kW/m^{2}. At that value of heat flux, the rate of the exergy destructed for the energy flow from the sun to the absorber is the lowest, having the highest surface temperature.

Figure 15 shows the exergy terms computed for the DP absorber with respect to the various test conditions. As expected, the optical exergy loss remains the same and constant with the change of the sample. The comparison of $Exl,th/Exi,net$ between the DP and SP absorbers shows a reduction in the exergy loss fraction by 30% on average using the DP absorber, which demonstrates the effective thermal enhancement inside the DP absorber in view of the lower thermal losses. The maximum reduction is 37% for the case T5050, while the minimum difference is 22% at the peak flux of 200 kW/m^{2} and an airflow of 30 L/min. This suggests that the enhancement effect of the DP flow in the exergy loss to the ambient is more significant at lower values of the heat flux and increases with the rise in the fluid flowrate.

Comparing the exergy loss share based on the exergy destructed for the temperature difference between the sun and the absorber ($Exdes,Tsun\u2212Tp/Exi,net$), it can be concluded that DP has a nearly similar behavior with respect to the SP absorber. This confirms that DP flow alongside the internal thermal enhancement does not provide a significant sacrifice in the major source of exergy destruction and this will allow higher exergy efficiency. However, considering the exergy destructed in the heat flow from the absorber to the fluid, the working conditions play an important role. In other words, for the peak flux of 50 kW/m^{2}, DP shows an enhancing role in reducing the destructed exergy fraction by 5–15% based on the airflow rate. At the peak flux of 100 kW/m^{2}, DP results in a higher exergy destruction ratio by 2% more at the flowrate of 30 L/min, and then provides 3 and 8% less values for the flow rates of 40 and 50 L/min. Increasing the peak flux to 200 kW/m^{2}, DP has detrimental effects on the exergy at all flowrates which ranges from 3 to 12%, respectively, for the higher to lower flowrate. Finally, comparing the exergy destruction based on the air friction inside the samples reveals that DP increases the destructed exergy in all the simulated conditions by an average value of 155%. However, note that although when the DP absorber is used a higher amount of exergy is destructed by the higher pressure drop, this growth is negligible compared to total input exergy. The cumulative effects of all the exergy terms can be evaluated by the total exergy efficiency as shown in Fig. 15. According to the graph, the DP configuration enhances $\eta ex$ by an average of 225% compared to the SP absorber, where the rise in the heat flux has a positive effect of this augmentation and the increase in the airflow rate decreases it. This reflects the fact that, although DP has some negative effects on the exergy based on the friction and energy flow from the absorber to the fluid, its boosting effects on $Exl,th$ and keeping $Exdes,Tsun\u2212Tp$ at a stable level, compared to SP, led overall to total higher exergy efficiencies. The maximum computed enhancement is >350% in the case T20030, which indicates the ability of the DP absorber to improve the thermal performance of the absorber under the worst operating conditions (the highest peak flux and the lowest airflow rate). Studying the pure behavior of $\eta ex$ by the DP absorber shows that the airflow rate of 40 L/min has the maximum efficiency at each heat flux level compared to the other flowrates. As a result, the maximum exergy efficiency of 8.5% using the DP absorber is achieved by operating at an airflow rate of 40 L/min and a peak flux of 200 kW/m^{2}.

### 5.5 Thermal Enhancement Assessment.

Figure 16 shows the relations between the *Nu* and *Re* numbers for the two absorbers, (note that the *Re* number is not the same for a given airflow rate). Since the fluid passage in the DP flow configuration is reduced, the *Re* number increases for the same flowrate compared to SP flow. Moreover, concentrating on the 2500 < Re < 3500, in the range that is shared between the two designs, the DP configuration shows an improvement in the *Nu* number by more than 50% compared to the SP design. This indicates that the thermal enhancement achieved by the DP is not only due to the higher heat transfer area but also comes from the improvement in fluid flow conditions. In more detail, the proposed design helps in reducing thermal losses. The inner fluid is insulated by the outer fluid, minimizing heat loss to the surroundings, which is a common issue in conventional SP systems.

## 6 Conclusion

A numerical investigation was conducted to assess the performance of an innovative double-pass tubular receiver when used in point-focusing solar systems, with air as the heat transfer medium.

The CFD analysis is rooted in a robust validation exercise conducted on a single-pass absorber, giving very good agreement with experimental data obtained during a test campaign at the Plataforma Solar de Almeria.

The numerical results indicate that the DP design presents an increased pressure drop compared to the SP design, primarily due to the flow within the inner tube and the flow redirection caused by the rounded cap. Additionally, the presence of fins plays a notable role in reducing surface temperature profiles, suggesting lower thermal losses and reduced thermal stress in the DP design. A detailed exergetic analysis reveals that a significant portion of exergy destruction occurs in the energy transfer from the sun to the absorber, accounting for an average of more than 60% of the total input exergy for both SP and DP absorbers, respectively. Furthermore, the exergy efficiency is shown to have a more substantial improvement compared to energy efficiency, with solar flux contributing to the increase in the DP performance. As a next step, an optimization study should be pursued for the proposed design to provide an alternative solution for future solar tower configurations. Furthermore, future studies could incorporate the radiation heat transfer between the two tubes, by possibly using surface-to-surface radiation models, thereby exploring an additional source of exergy destruction in the exergy analyses.

## Acknowledgment

We acknowledge the use of the computational resources provided by hpc@polito, which is a project of Academic Computing within the Department of Control and Computer Engineering at the Politecnico di Torino. This work has been supported by the Italian Super Computing Resource Allocation (ISCRA-CINECA) within the Application ID: GRECIAN—HP10C6U7V4. The experimental tests have been also financed by the European Union's Horizon 2020 research and innovation program: Solar Facilities for the European Research Area—Third Phase (SFERA III) under grant agreement N. 823802.

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

## Nomenclature

*h*=heat transfer coefficient

*v*=fluid

*A*=area

*E*=thermal energy

*L*=tube length

*N*=cell number

*T*=temperature

*V*=total volume of the model

- $m\u02d9$ =
mass flowrate

*Cp*=specific heat capacity

*C*=_{µ}viscosity coefficient

*C*_{1ε}=constant

*C*_{2ε}=constant

*C*_{3ε}=constant

*G*=_{b}generation of turbulence kinetic energy due to buoyancy

*G*=_{k}generation of turbulence kinetic energy due to the mean velocity gradients

*S*=_{ε}source term

*S*=_{κ}source term

- CSP =
concentrating solar power

- DP =
double-pass

- HTF =
heat transfer fluid

- Nu =
Nusselt number

- RANS =
Reynolds-averaged Navier–Stokes

- Re =
Reynolds number

- SP =
single-pass

- YM =
dilatation dissipation

### Greek Symbols

### Subscripts

## Appendix

*k*and for its dissipation rate $\epsilon $ are expressed as follows: