**1. Introduction**

Air heating is used for various applications, such as heating and air conditioning of buildings or drying of food and industrial products, among others. Air can be heated with electric heaters or by directly burning fuels such as gas; however, their use implies the emission of greenhouse gases and their consequent contribution to climate change. One way to minimize fossil fuel burning is to use solar collectors to directly heat the air, ranging from flat-plate collectors to solar concentrators.

According to the International Energy Agency, 985 MWth of solar air collectors were installed by the end of 2020, and the global market was around 12 MWth [1]. As of March 2022, 41 solar air collector systems producing solar process heat are registered, with a cumulative capacity of 6 MWth [1]. Thus, the direct application of solar collectors for air heating is low due to the boost that low fossil fuel prices give to using conventional

**Citation:** Chávez-Bermúdez, I.A.; Rodríguez-Muñoz, N.A.; Venegas-Reyes, E.; Valenzuela, L.; Ortega-Avila, N. Thermal Performance Analysis of a Double-Pass Solar Air Collector: A CFD Approach. *Appl. Sci.* **2022**, *12*, 12199. https://doi.org/10.3390/ app122312199

Academic Editors: Luis Hernández-Callejo, Jesús Armando Aguilar Jiménez and Carlos Meza Benavides

Received: 22 September 2022 Accepted: 27 November 2022 Published: 29 November 2022

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technologies [2], so it is essential to develop reliable and economically efficient solar air heating technologies. Flat-plate solar collectors are recommended for temperatures below 70 ◦C because of their ease of manufacture and operation. For higher temperatures, it is necessary to use some solar concentrating technology, such as compound parabolic concentrators (CPCs), which allow fluid heating temperatures up to 120 ◦C, depending on their design, and are easy to operate and maintain.

However, to ensure good efficiency of CPCs, it is necessary to perform an optimal optical design and minimize thermal losses or improve heat transfer. Strategies to reduce convection losses in the receiver of a solar collector include using evacuated tubes or filling the CPC cavity with gases such as Argon and Krypton [3,4], which are denser gases and have lower thermal conductivity than air, or even applying a vacuum throughout the cavity [5]. In contrast, double absorbers have been proposed to reduce conduction losses [6].

In other technologies, such as flat-plate solar air heaters, it has been proposed to increase the heat transfer rate by incorporating multiple passages, including extended surfaces, artificial roughness, and packed mesh [7]. This multi-pass strategy is used in hybrid CPCs (PV/T) to cool the photovoltaic cells on the flat-plate receiver with fins on the back side [8].

In the general design of solar collectors, computational fluid dynamics (CFD) tools can be used to reliably estimate their thermo-hydraulic performance before building them, saving time and resources. Several analyses of solar collectors by computational fluid dynamics (CFD) can be found in the literature, both for liquid and air heating. Table 1 provides an overview of the different solar collector models and assumptions found in the literature review.


**Table 1.** Solar collectors CFD and radiation models in the literature review.


#### **Table 1.** *Cont.*

IR: Internal radiation; ER: External radiation.

Thus, Mekahlia et al. determined the influence of the thickness and number of transparent covers to reduce the heat losses of a flat-plate solar collector [9], and Pawar and Sobhansarbandi modeled an evacuated heat-pipe solar collector with and without integrated phase change materials as a thermal storage medium [10]. In the particular case of solar air collectors, Singla et al. analyzed an evacuated tube collector with ribs of different roughness [11]. At the same time, Ammar et al. performed a three-dimensional CFD model to optimize the design of a solar air collector with an extended surface area by a different number of rectangular fins [12]. In addition, they analyzed the effect of adding a selective surface on the absorber.

Regarding the analysis of CPC collectors, Li et al. analyzed by CFD the thermal behavior of an evacuated tube collector as a receiver of a compound parabolic concentrator, and the simulation was validated with experimental data [13]. Barrón-Díaz et al. performed the numerical simulation of CPCs with tubular receivers, with and without fins, for residential water heating [14]. This study focused on the ray-tracing analysis of radiation and heat transfer by coupled finite element and CFD methods. In addition, Yuan et al. developed two simplified computational fluid dynamics models to determine the temperature and velocity distribution in two almost identical parabolic tube-receiver CPCs [15]. One had a transparent ETFE sheet around the receiver to reduce convective heat losses. The models included the reflector, receiver, cover, and back insulating material and allowed the analysis of both air movement in the cavity and water movement in the absorber tube. Ray tracing was applied to analyze the radiation distribution on the receiver tube at normal incidence, with a correlation of the absorbed solar energy as a function of the angle along the perimeter of the tube. Both models were experimentally validated, and relative errors of less than 3.7% in temperature and 1% in efficiency were obtained.

On the other hand, Antonelli et al. analyzed the air heat transfer inside the cavity of a collector with a tubular receiver and with a flat-plate receiver and developed some correlations to express the Nusselt over the receiver [16]. Subsequently, Francesconi and Antonelli performed the numerical analysis of a panel with several tubular receiver CPCs to determine the influence on the thermal efficiency of the number and position of the CPCs along the panel, the use of a second transparent cover, the spacing between collectors, and the truncation of the reflectors [17]. For their part, Reddy et al. performed threedimensional modeling of a flat-plate receiver CPC to determine the thermal losses in the cavity as a function of its aspect ratio and tilt, the optical properties of the materials, and the absorber and ambient temperatures [18]. To model the internal radiative heat transfer, they used a discrete ordinary radiation model, and for the external one, they established the thermal boundary conditions and emissivity.

As mentioned above, another strategy to improve the efficiency of solar air heating collectors is to increase the number of passes. Thus, Al-Damook et al. analyzed the effect of double-pass configuration in a solar air heater when operating in concurrent parallel flow, parallel in counterflow, and double U-pass [19]; the latter presented the best thermal performance. Tuncer et al. analyzed, through CFD simulation, two flat-plate solar collectors for air heating with three and four passes and determined which one had the best performance to evaluate it experimentally [20]. In both solar collectors analyzed, air enters through the lower pass and exits through the upper pass, which has the radiant heat gain. They found that the four-pass collector has a heat gain 3 ◦C higher than that obtained with the three-pass collector and that the maximum deviation between the CFD model and the experimental results was 10%. In addition, Mutabilwa and Nwaigwe performed a CFD analysis of a two-covers, double-pass flat-plate solar collector for air heating, which was validated with experimental results [21]. The air enters through the space between the two covers and returns between the second cover and the absorber plate. The temperatures on the absorber plate obtained with the model had a standard deviation from experimental results between 1.05 K and 4.65 K, while for the cover, it was between 0.1 K and 0.45 K.

Likewise, improved surfaces or novel geometries have been incorporated in multipasses solar collectors, such as the work of Desisa and Shekata [22]; they analyzed the impact of using smooth, rough, and corrugated surfaces in a double-pass flat-plate air solar collector and obtained average thermal efficiencies of 78%, 62%, and 90%, respectively. On the other hand, Singh determined the performance of double-pass flat-plate air solar collectors with different fin configurations [23]. They varied in size, angle, arrangements (in-line, staggered, and hybrid), and hydraulic diameter. Finally, Kumar et al. proposed a curved air heater with asymmetric double-pass counterflow turbulators, whose design was determined from CFD analysis by comparing various flow configurations and geometric parameters [24].

Two or more pass technologies have been applied in flat-plate solar collectors to improve their efficiency; however, this strategy has not been applied in CPCs for air heating. This study proposes the CFD analysis of a CPC-type solar air heater with U-shape double-pass airflow. The air first circulates through the trapezoidal cavity contained in the volume formed by the cover, the reflecting walls of the CPC, and the flat-plate receiver and then circulates in counterflow through the receiver's duct interior. The objective of the numerical analysis presented is to test different inlet and outlet configurations in the CPC array to determine how these configurations influence the velocity distribution, outlet temperature, and instantaneous efficiency of the U-shape double-pass CPC solar heater.

Section 2 of this manuscript describes the main characteristics of the U-shape doublepass CPC and the four air inlet/outlet configurations considered in its design. It also defines the mesh design to perform the CFD simulation, the mathematical model for such simulation, the boundary conditions applied in the study, and the methodology followed

to estimate the thermal efficiency of the U-shape double-pass CPC. Section 3 includes a summary of the simulation results obtained and their discussion and concludes with a summary of the efficiencies calculated for each of the four configurations analyzed.
