CFD model of acceleration of thermal-hydrodynamic processes in solar air collectors

. Recent studies on increasing the thermal-hydrodynamic efficiency of solar air collectors have been carried out on the installation of barriers of various shapes on the surface of the absorber, and this method ensures a significant increase in the energy efficiency of the collector. The transfer of the air flow washing the surface of the absorber from a laminar flow state to an accelerated lumped air flow is carried out by installing obstacles. Installation of barriers is the main factor in increasing the heat transfer in solar air collectors and prolongs the time of air flow in the collector. The barrier solar air collector has a high local heat transfer coefficient, and the Nusselt number value is up to 3.5 times higher than that of the flat plate solar air collector. Also, this article presents the results of CFD modeling of the air flow in the solar air collector, the results of which can be used in the theoretical research of the solar air collector.


Introduction
As the main device for collecting solar energy and converting it into useful heat, many researchers have proposed the use of solar air collector (SAC) and several ways to improve heat exchange [1][2][3]. As noted by Arunkumar et al. [4], extensive research has been carried out on improving convective heat transfer in SACs by changing the flow path. Satcunanathan et al [5] first introduced the concept of double transition. Performance is reported to be 10-15% better than a single-use SAC. Ho et al. [6] confirmed that efficiency was achieved due to increased heat transfer area and air residence time. The introduction of obstructions in the air passage increases the heating time (residence time) between the air and the absorber and improves heat transfer in the SAC, creates turbulence for rapid mixing and prevents "hot spots" that reduce heat loss [7] . However, the installation of obstacles in the air passage increases the pressure drop.
Hu et al. [8] studied the pressure drop in an air duct with obstacles perpendicular to the air direction. It was found that the change in pressure drop across the passage decreases with the increase in the number of barriers. A further study by Hu et al [9] shows that reducing the width of the air channel in the first chamber significantly improves the thermal efficiency and reduces the pressure drop. Moummi et al. [10] developed a CW with baffles perpendicular to the flow to create a high turbulence flow. This device was highly effective compared to the unobstructed one. Bensaci et al. [11] conducted experimental tests to investigate the effect of transversal barrier placement on the heat transfer coefficient and thermal efficiency of the SAC.
From the literature analysis of the researches in the field of improving the thermal performance of the air conditioners by changing the flow structure, it can be seen that there are not enough studies on the air conditioners with barriers located parallel and perpendicular to the air direction. Potgieter et al. [12] that the counter/parallel flow created by the optimal selection of the barrier improves the high turbulence and convective heat transfer in the collector also confirmed it. In this thesis, the comparative studies of the cross-barriers of the HFK were carried out using the Computational Fluid Dynamics (CFD) software tool.

Materials and methods
Currently, a large number of different models have been created for the calculation of hydrodynamics and heat exchange, one of which is the COMSOL Multiphysics software tool [13]. The choice of this program is based on its ease of use, accuracy of the experiment, and unlimited opportunities in scientific research. COMSOL Multiphysics is an interactive software tool designed for modeling scientific and engineering problems based on solving partial differential equations with the finite element method. This software is designed for modeling hydrodynamics, heat transfer, mass transfer and other processes.
The following equations and models are considered in the COMSOL Multiphysics software tool to solve various hydrodynamics and heat transfer problems:  The vector form of the Nave-Stokes equation: ; (1)  Energy equation: (2)  Equation of motion:  Continuity equation:  k-ε model of turbulence:  k-ω model of turbulence: Where -density; -vector field of velocities; -pressure; -vector specific force field; -time; -temperature conductivity coefficient; -temperature; -capacity of internal sources of heat; -isobaric heat capacity; -kinetic energy of turbulence; -turbulent viscosity coefficient; -turbulence dissipation; -the rate of turbulent energy dissipation.
The finite element method allows the designer to calculate difficult details by dividing them into many small parts -finite elements [14]. Post-partitioning calculations are performed for each finite element. Triangular and rectangular elements are often used for 2d areas.
This study aims to evaluate the thermal efficiency improvement in a CHP with different obstacles, i.e., longitudinal obstacles in the direction of air flow, using the COMSOL Multiphysics software tool. The computational modeling adopted in this study was developed based on the following assumptions:  Fluid flow and heat transfer are three-dimensional.  The state is steady state and incompressible flow state.  The heat loss from the bottom and side walls of the QHK frame is not taken into account.  The heat loss at the inlet and outlet of the heat exchanger is very small.  The thermal-physical properties of air, aluminum frame and barrier plate remain unchanged throughout the process.
First, the computational model adopted in this study is derived from previous works to investigate the performance of a UMS Eco-Solar combined heat exchanger, and the model results have been validated with experimental results [15]. In previous experimental tests, the absorber of the SAC consisted of a recycled aluminum box, the frame of which was covered with plywood and the top part was covered with acrylic. In this study, the absorber baffles of the recycled aluminum cans were replaced by baffle plates placed in the transverse direction. The computational model was developed based on the same geometry and measurements as in the previous work. The quality of the resulting mesh was then analyzed by examining mesh independence. After the validation of the developed CFD model, it was adopted to study the influence of the location of the obstacles on the performance of the SAC.
The mechanism of increasing the air temperature in SAC was evaluated based on the increase of air temperature and velocity vector and pressure decrease in the collector. Parameters such as Nusselt number, local heat transfer coefficient, and friction coefficient along the air passage were calculated to analyze the overall performance of the SAC and to determine the thermal-hydraulic performance of the SAC. For comparison, a simulation of the air duct without obstructions was also developed. Each process of modeling was carried out according to the boundary condition, according to which the air speed in natural convection is 0.12 m/s. Then the obtained results were compared in terms of heat transfer characteristics, fluid flow conditions, thermal efficiency and thermal-hydraulic parameters.
Physical model of SAC. The 3D geometry of the SAC considered in this study is shown in Figure 1. QHK consists of five main parts: transparent cover, absorber plate, baffles, collector frame, and the air passage channel between the transparent cover and the lower absorber plate where the heated air moves. The dimensions of SAC are as follows: length 2112 mm, width 910 mm and thickness 100 mm. The coating is transparent acrylic with a thickness of 5 mm. A 3 mm thick aluminum absorber plate is installed under the cover to absorb sunlight. The frame is well insulated to minimize heat loss through the aluminum collector frame. In order to achieve maximum heat transfer between the air and the absorber surface, baffles covering 80% of the total height of the air passage are installed on the lower absorber plate of the collector. Barriers occupying 80% of the total width of the KHK were installed perpendicularly to create a serpentine passage of air along the collector in the KHK. The width of the air channel between the barriers is 182 mm, which is equal to the width of the air inlet.
Calculation model. The CFD model of the SAC used in this study consists of a rectangular solid geometry and includes seven main areas: top wall (cover), side wall (collector frame), absorber wall, baffles, top wall and absorber the area of liquid flow passing through the air channel between the wall, the area of liquid flow passing through the air channel between the absorber and the lower wall, the air channel and the air outlet hole. There is one input and one output channel at each end of the SAC. Modeling was done using the ANSYS 2021 R1 Fluent package. The flow in the SAC is assumed to be steady, three-dimensional and incompressible. In addition, this research is aimed at studying the performance of SAC under natural convection conditions, gravity is also taken into account. During the entire process, all properties of air and solid material remain constant at the average air temperature of 300.15 K. Boundary conditions. The irradiance model used in this study is the Roseland model, which is combined with a solar tracking algorithm. The turbulence k-e model with improved wall processing was used to calculate the turbulent flow that occurs in the air channel due to obstacles. All interfaces of the wall are determined by the no-slip condition. The top wall (cover) is a semi-transparent acrylic with a transmittance of 0.8 and is involved in tracking sunlight. The side wall (collector frame) is an adiabatic wall (heat flow=0) that does not participate in solar tracking, and it is made of aluminum material. The absorber plate under the cover is made of aluminum and placed under the influence of solar radiation. The inlet is assigned a mass flow rate condition, while the outlet is modeled as a pressure drop. All other boundary conditions are listed in Table 1.
Modeling. The operating parameters used to evaluate the improvement mechanism in SAC are outlet air temperature, air velocity and pressure drop in the air channel, the contour plot is obtained from the CFD software. The Nusselt number, Nu and the friction coefficient, f dimensionless parameters that determine the thermal-hydraulic performance of SAC are estimated by the following equations [16]: Where -heat transfer coefficient ( ); -thermal conductivity of air ( ).
Model validation. Validation of the computational model proposed in the Computational Model section was carried out in terms of grid independence and analysis of experimental results. In this case, it was found that the calculation model corresponds to the measured value for the air flow with a single pass with a deviation of 1.76% [15]. The basic structure of the SAC discussed in this study is very similar to the model presented in the previous work [15], which used recycled aluminum cans to change the airflow configuration in the air passage. Thus, it can be assumed that the presented empirical investigation can be applied to this study.
Calculation mesh. The computational mesh for the domains was developed using an irregular mesh with a uniform growth rate of 1.2. During mesh development, it is very important to determine the number of nodes generated in the domain in order to achieve an accurate numerical result [18]. Thus, a mesh independence test should be performed to evaluate the quality of the mesh at different sizes. Five different mesh sizes were used in this study -0.014, 0.015, 0.018, 0.020 and 0.025 mm. The number of cells was increased from 101991 to 443928 using the mesh software installed in ANSYS Fluent. Each case was performed under turbulent flow conditions with Re=7580 (velocity 2 m/s). The mesh quality was evaluated based on the temperature of the hot air at the outlet, as this operating parameter has been widely defined in the literature to study the performance of the SAC. The results of the grid independence test for SAC are presented in Table 2, respectively. Based on the results presented, the error of the coarse mesh method is large and gives a less accurate solution. Therefore, for a smaller deviation percentage (less than 1%), a very small element size is chosen.

Results and Discussion
Temperature distribution and thermal efficiency. The temperature change along the length of the HSC with barriers is shown in Figure 2. The results were obtained with an input velocity of 0.12 m/s and a solar irradiance of 438.578 W/m 2 . The results modeled in CFD and based on the graph in Figure 2 show that the temperature of the air flowing through the HF increases significantly as it approaches the outlet. It can be seen from Figure 2 that the barriers provide an even distribution of air temperature along the length of the air duct, which indicates a reduction in the dead zone due to the presence of barriers in the cross section of the air passage. In addition, the performance of the SAC is significantly improved in terms of outlet temperature compared to the flat-plate SAC, because the maximum temperature of the air at the outlet of the flatplate SAC is 319 K. The highest predicted outlet temperature for the barrier SAC is 331.26 K and 331.26 K, respectively.
It can be seen from Figure 3 that the temperature is uniform for SAC. The temperature contour has a large temperature gradient compared to the flat-plate SAC, which is justified by the formation of a lump in the barrier SAC, especially where the highest temperature was observed at the outlet section ( Figure 3). In this area, the heat exchange between the air and the absorber is improved due to the separation and recombination of the air flow, this process is formed after the barrier, which ensures the gradual heating of the air and leads to the maximum temperature at the outlet. Hu et al. [8] reported a similar achievement in a four-barrier HCC. The study shows that the air temperature achieved along the air channel in the serpentine flow channel is fully consistent with the flow pattern. Figure 4 shows the variation of temperature along the length of the pipe at different relative pitches of the barrier. As can be seen from Figure 4, the temperature of the heat carrier is much higher in the rough heat exchangers compared to the smooth heat exchangers. It also shows that the change in the relative pitch of the barriers has a different effect on the temperature of the heat carrier. As the relative pitch of the barriers decreases, the temperature of the heat carrier increases and vice versa. The reason for this is the sharp decrease in the thickness of the laminar boundary layer in the pre-wall zones on the surface where the barriers are installed, and the effect of the heat transfer of the layer on the transfer of heat from the absorber to the heat carrier is small.
The estimated thermal efficiency for flat-plate and barrier-type SACs is 26.6% and 43.4%, respectively. It can be concluded that the installation of barriers in SAC significantly increases efficiency. Despite the fact that the accumulation zone formed in the cross-section of the air passage accelerates the heat exchange between the liquid and the absorber, the flow configuration in the SAC also increases the residence time of the air in the air passage. As a result, due to long-term heating of the air in the collector, the heat on the absorber plate is completely absorbed by the air, and the efficiency of the SAC increases.
Heat transfer properties. The heat transfer characteristics between the air and the absorber plate in the air channel were studied based on the local convection heat transfer coefficient obtained directly from Fluent and the Nusselt number calculated according to equation (7). The variation of the estimated local convective heat transfer coefficient of the air flow along the length of the air duct for each air duct is presented in Figure 5. As shown in the graph, the heat transfer in the barrier heat exchanger is higher than the flat plate heat exchanger, and the maximum value of the heat transfer in the flat plate heat exchanger is 4.15 W/m 2 K. For comparison, the highest heat transfer coefficient recorded in the barrier SAC is 18.81 W/m 2 K. As can be seen from the results, the use of barriers in the SAC increases the heat transfer by approximately 3.5 times. In their study, Mahanand and Senapati [19] pointed out that the convective heat transfer in the finned SAC is improved due to the disruption of the boundary layer in the air duct, resulting in the acceleration of the heat transfer between the air and the absorber plate.
The effect of the location of barriers on the local convective heat transfer coefficient can also be seen in Figure 5. It can be seen that the barrier heat exchanger has a very high heat transfer coefficient, which is due to the fact that a large turbulence is created with the help of barriers. Because the baffles are placed transversely across the passage, the air flow is continuously blocked by the baffle as it approaches the outlet. This distortion created in the air passage leads to rapid air mixing, which leads to improved convective heat transfer. The value of the Nusselt number is 27.63 and 125.12 for the flat-plate and barrier-type SAC, respectively. As expected, the baffled HSC has the highest Nusselt number value and shows the least dead zones among the tested HSCs. Ozgen et al. [20] and Abdullah et al. [21] also confirmed the reduction of the dead zone corresponding to the turbulence regime. It is worth noting that the increase in thermal conductivity in the cross-barred HCV is a result of the improvement of convective heat transfer, which corresponds to the strong cumulative flow generated in the air passage.

Conclusion
The effect of different locations of barriers on heat transfer characteristics, fluid flow characteristics, and pressure drop was studied when barriers were installed in the air passage section of air ducts. The main results of the conducted research are as follows:  Due to the long time of air residence in the air channel, the blocked SAC has a higher thermal efficiency than the flat-plate SAC. Due to this, when the air passes through the barrier KHK, due to the energy absorbed by the absorber and the barrier, the air heats up for a longer time and has a higher temperature when leaving the collector.  The local heat transfer coefficient is high in the barrier heat exchanger and is 18.81 W/m 2 K. The value of Nusselt number is equal to 125.12, which is up to 3.5 times higher than that of flat-plate heat exchanger.  The velocity profile obtained from the CFD shows that the air is mixed more intensively in the obstructed SAC, as a result, the convective heat transfer dominates the heat transfer process in the collector and minimizes the heat loss.