Simulation of a parabolic trough solar collector containing hybrid nanofluid and equipped with compound turbulator to evaluate exergy efficacy and thermal‐hydraulic performance

This research is mainly aimed at investigating the numerical modeling of thermal‐hydraulic and exergy efficiencies of parabolic trough solar collectors (P‐SCs) filled with magnetic hybrid nanofluid. The k‐epsilon turbulence, S2S, and mixture models were used to simulate the turbulence equations, radiation, and two‐phase nanofluid, respectively. The experiments were run using magnetic nanofluid in Reynolds numbers of 5000‐20 000, the volume fractions of 1%‐3%, and the ratios of pitch (ROPs) of 1, 2, and 3 of the combined turbulator. According to the results, there is a significant increase in average Nusselt number (Nu) and pressure drop (ΔP) with increasing Reynolds number, nano‐additive concentration, and ROP. Moreover, the use of the hybrid magnetic turbulator and hybrid nanofluid increased the thermal performance of the P‐SC. It was also found that the Reynolds number of 20 000 and volume fraction of 3% of nanoparticles resulted in the optimal exergy efficiency mode in using a hybrid turbulator.


| INTRODUCTION
Given the importance of energy in everyday human life, many researchers have focused on this issue. [1][2][3][4][5] It has been found that renewable energy can properly meet the needs of countries. In this regard, solar energy is among the energy resources available to humans that have received considerable attention. [6][7][8][9][10] Therefore, many studies have been conducted in this field whose results strongly recommend using renewable energy. [11][12][13][14] Recently, increasing the heat transfer rate (HTR) in renewable systems has been of interest to researchers. [15][16][17][18][19] One of these methods is to use nanofluids as an alternative to conventional liquids. [20][21][22][23][24][25][26][27][28] Nanofluids are widely used in micromixers, 29 heat exchangers, 30 and solar systems. 31 As the experimental tests are costly, 32 , a very effective solution to reduce the costs and examine the effects of different parameters is to adopt numerical methods. [33][34][35][36][37][38][39][40] Recently, the use of turbulators in solar collectors (SCs) to create turbulent flow and increase the resulting heat exchange has become very popular among scientists. [41][42][43] Ahmed et al. 44 examined the influence of using a combined generator on HTR and nanofluid flow specification within a symmetrical duct. Their work was both numerical and experimental, using two nanoparticles (Al 2 O 3 and SiO 2 ). According to the results, using a vortex generator and nanofluid increased the HTR and ΔP. Moreover, the experimental results agreed with the numerical ones with high accuracy. Aliakbari et al. 45 investigated the impact of horizontal fibers on the flow field and HTR of aluminawater nanofluid in a microchannel utilizing the finite volume method (FVM). Their data indicated that growing the height of the ribs horizontally caused a noteworthy augmentation in HTR and ΔP. Amirahmadi et al. 46 examined the effect of a turbulator on exergy efficiency and entropy production within a trapezoidal channel using mathematical methods. Their research was conducted for Reynolds numbers of 400-1600. They found that adding the turbulator to the trapezoidal channel reduced entropy production and exergy efficiency. Sheikholeslami and Ganji 47 experimentally studied the influence of turbulators on hydrothermal efficiency of two-pipe heat exchangers for Reynolds numbers of 6000-12 000 and torsion ratios of 0.72 to 1.29. The maximum hydrothermal increase was 19.15%, which occurred at a Reynolds number of 6000 and torsion ratio of 0.72. Sheikholeslami and Ganji 48 also performed experimental and numerical studies on the effect of simple and hollow turbulators on the hydraulic performance of two-pipe converters. They used air and water fluids in the outer and inner tubes of the heat exchanger, respectively. Their findings showed that the use of hollow turbulators increased the HTR by 26.45% compared to simple turbulators. Rashidi et al. 49 numerically investigated twisted turbulators for fluid flow performance and nanofluid entropy production within a square chamber. The study was performed at nanoparticle concentrations of 0 to 0.05, with the step ratio of the twisted turbulators varying from 180° to 540°. They found that the addition of twisted turbulators to the square chamber reduced the output of entropy. Moreover, the rise in the nanoparticles' concentration had a decreasing impact on the entropy production. Eiamsa-ard and Wongcharee 50 experimentally evaluated the impact of nonuniformly twisted tape on the thermal hydraulic output of water-Ag nanofluid in a tube. Their findings revealed that the HTR increased with the Reynolds number and nanoparticle concentration. Moreover, the placement of nonuniformly twisted tape increased the HTR by 36.21% compared to case in which the plain tube was higher. Applying numerical methods, Akbarzadeh et al. 51 assessed the impact of dissimilar rib shapes on the alumina-water nanofluid behavior in a solar heater. They used triangular and semicircular ribs with Reynolds numbers of 5000-15 000 and volume fraction of two-phase nanofluids ranging from 0% to 4%. According to the results, the index of thermalhydraulic output in the solar heater with semicircular ribs was much higher compared to those with triangular ribs. Sharafeldin and Gróf 52 experimentally and numerically studied the impact of water-CeO 2 nanofluid on the thermal efficiency of SCs. In the experimental part of the study, they fabricated water-CeO 2 nanofluids using a two-step method. Their findings indicated that the temperature discrepancy between the inlet and outlet flow significantly increased by adding the nanofluid to the system. Furthermore, the use of water-CeO 2 nanofluid augmented the HTR by 34% in comparison with the base fluid. Bahrami et al. 53 employed Al 2 O 3 to affect thermal behavior. With the rise in the volume fraction of the nanofluid by 4%, there was a significant improvement in the forced convection heat transfer. Applying experimental methods, Subramani et al. 54 examined the effect of water-TiO 2 nanofluid to improve efficiency and HTR in the turbulent flow regime inside the SC. The study was performed for volume fractions of 0.05%-0.5% of nanoparticles and Reynolds numbers of 2950-8142, which led to a turbulent flow regime. They reported that the thermal efficiency inside the SC increased with the Reynolds number and nanoparticle concentration. Bazdidi-Tehrani et al. 55 studied the effect of ribbed fibers on the flow field and HTR of titan-water nanofluid inside a flat plate SC. It was found that the use of ribs intensified the HTR by 10% compared to other cases. Furthermore, increasing the concentration of nanoparticles resulted in an increment in the thermal efficacy of the flat panel SC. Nguyen et al. 56 applied a triangular rib to make turbulence by exerting magnetic particles. They reported that the simultaneous effect of triangular rib and magnetic nanoparticle could boost the heat transfer by 25%. Obaid et al. 57 checked the influence of a new turbulator on the thermal-economic performance of SCs. It was found that by creating a vortex and disrupting the thermal layers, using new turbulators brought about a remarkable increment in the thermal performance of the SC. The new turbulators were also economically viable. Singh et al. 58 examined the impression of different ribs on the outputs of a solar heater applying a kinematic method. They claimed that when using circular and trapezoidal ribs, the thermal output of the solar heater grew by 17% and 16%, respectively. Employing numerical methods, Ekiciler et al. 59 evaluated the influence of hybrid nanofluids on the thermal performance in a P-SC. Their study was performed on Syltherm 800-based hybrid nanofluids at nanoparticle concentrations of 1%-4%. It was found that the thermal output of the P-SC increased with the nanoparticles' concentration. Sheikholeslami and Farshad 60 numerically investigated the impact of innovative turbulators on the thermal performance within a SC. Their findings revealed that the addition of light turbulators enhanced the SC thermal performance by 56.04% in comparison with the case when the SC had no turbulator.
The following is the innovations of the present work: 1. The use of a magnetic hybrid nanofluid 2. The use of innovative hybrid turbulators 3. Exergy study in parabolic solar collectors A review of the literature reveals that the thermalhydraulic performance and exergy efficacy of the parabolic trough solar collectors (P-SC) equipped with new hybrid turbulators filled with a water-Fe 3 O 4 -MWCNT hybrid nanofluid have not been studied so far, considering the two-phase model in a turbulent flow. Accordingly, the present study has investigated the effect of a hybrid turbulator for the pitch ratios (PRs) of 1, 2, and 3 at Reynolds numbers of 5000-20 000 and volume fractions of 1%-3% of two-phase hybrid nanofluid using mathematical methods. Figure 1 demonstrates a schematic of the investigated P-SC. As can be seen, the SC was equipped with a compound turbulator. The length of the solar culture was 700 mm, the length of the hybrid turbulator was 200 mm, and the diameter of the absorber tube was 50 mm. According to the figure, three different torsion ratios of 1, 2, and 3 for the combined turbulator were studied. The inputs of the study were Reynolds numbers of 5000-20 000, with the volume fractions of the two-phase hybrid nanofluid ranging from 1% to 3%.

| Governing equations
In order to simulate the MWCNT-Fe3O4/water magnetic hybrid nanofluid flow through the P-SC, a mixed twophase liquid model was applied, which is more accurate compared with other methods. 61 In all models simulated during the present investigation, the fluid flow inside the P-SC was turbulent because the Reynolds number was over 2300. Due to the simulation of the turbulent flow inside the absorber tube, the equations of the k-ε model F I G U R E 1 A schematic of the studied P-SC with the compound turbulator were used, as well as the equations of continuity, motion, and energy, in the commercial software ANSYS-Fluent. The following provides the equations used 62,63 : Continuity equation: Momentum equations: where r, , and z are the coordinates, and u, v, and w are the velocity components. Energy equation: As noted previously, the Reynolds number is defined as 62 : The average Nu is expressed as 62 : The following equation gives the pressure drop: Further, the friction factor coefficient is computed as 63 : The thermal and hydraulic performance evaluation criterion (PEC) can be defined as the following equation to make a comparison between the hydrothermal performance of simple P-SC and compound turbulator 62 : The exergy efficiency for parabolic collectors is expressed as the net useful exergy divided by the exergy of direct solar radiation entering the collector and is calculated using the following equation: in which, P is the pump power, which was considered equal to 85%.

| Nanofluid
The Newtonian nanofluid, called magnetic hybrid nanofluid, was used in the current study. It was comprised of water, Fe 3 O 4 , and MWCNT, and applied in the two-phase mixture method for simulation. The volume fraction varied from 0.01 to 0.03. Table 1 lists the properties of the thermophysical nanofluid.
As the hybrid nanofluid included various materials, the density of water-Fe 3 O 4 -MWCNT nanofluid ( nf ) could be obtained as follows: 64,65 and the specific heat, c P,nf , of this hybrid nanofluid is obtained from the following equation: Furthermore, the thermal conductivity and dynamic viscosity of the aforementioned nanofluid can be described as conformity relations 64,65 .

| Grid independency testing
In order to obtain a proper grid, the mean Nu was evaluated for various grids in a P-SC with ROP = 3 at Re = 20 000 and ϕ = 3% (see Table 2). According to the values of the mean Nu, it was observed that the grids with a number of 1 391 674 were suitable for simulating the P-SC with ROP = 3

| Numerical procedure validation
The numerical results were validated with the results of a study by He et al. 66 Based on the outputs of Figure 2, the discrepancy of the mean Nu values obtained in the simulations was small compared to that obtained by He et al., 66 and the maximum error rate was 4.78%. As an outcome, the precision of the modeling results was ensured.

| RESULTS AND DISCUSSION
This section provides the outcomes of the numerical simulation. First, the pressure, speed, and temperature of the  P-SC are given. Then, the diagrams of changes in mean Nu, ΔP, PEC index, and exergy efficiency changes are presented. Figure 3 shows the pressure-related contours for Re = 20 000 and in the P-SC for different ROPs. Based on the pressure meters, it is clear that the density of flow lines for a P-SC with ROP = 3 (c) was much higher compared to ROP = 1 (a) and ROP = 2 (b). This can be attributed to the change in torsion ratio, the flow between the blades, and the twists of the compound turbulator, causing the accumulation of lines. The pressure also decreased with the increasing length of the P-SC. In all P-SCs, the pressure was maximum at the inlet of the channel. The inactive flow caused a lot of pressure at the inlet due to the collision with the compound turbulator; and as a result, the whole speed changes to pressure. Figure 4 shows the velocity contours for Re = 20 000 and the P-SC for different ROPs. As can be seen, in the P-SC close to the walls, since there was no slip, it stuck to the collector walls, and its speed was equal to the speed on the wall. Therefore, near the P-SC wall, the velocity had its lowest value. However, by approaching the center of the P-SC, the speed increased over time. Separation occurred when the current struck the hybrid turbulators, which formed the vortices and made them swirl. As can be seen, the size of these vortices in the parabolic collector with ROP = 3 was much larger and more elongated compared to the combined turbulator with ROP = 1 and ROP = 2. Figure 5 shows the pressure contours for Re = 20 000 in the P-SC for different ROPs. The figure for the thermal boundary layer increased with the ROP. The existence of vortices was the reason behind this phenomenon. Figure 6 shows the changes in flow lines for Re = 20 000 = in the P-SC for different ROPs. As can be seen, the density of flow lines increased with the ROP. However, the highest density of flow lines belonged to the P-SC with a hybrid turbulator of ROP = 3. Figure 7 depicts the average Nu changes against the Reynolds number in the P-SC with turbulator in different ROPs and volume fractions. As can be seen, the average Nu grew with the Reynolds number. It can be said that the velocity and density of the flow lines increased with the Reynolds number, resulting in a higher heat transfer coefficient. Furthermore, the rise in the ROP in the P-SC increases the thermal performance, significantly. This can be attributed to the increased mixing and turbulence. For this reason, the average Nu would increase as a representative of this HTR. The rise in the average Nu in SC with ROP = 3 was more than the other two cases, which can be attributed to the presence of more vortices. These vortices, as shown in the contours in the previous section, were longer and longer when the combined turbulator was longer. Therefore, their accumulation between the blades and the twists of the combined turbulator would increase the HTR. The maximum increase in thermal performance belonged to ROP = 3 and a volume fraction of 3% of nanoparticles. At Reynolds numbers of 5000, 10 000, 15 000, and 20 000, it increased by 70.93%, 81.16%, 70.63%, and 56.10%, respectively. Figure 8 demonstrates the variations in ΔP against Reynolds number in a P-SC with turbulator in different ROP ratios and volume fractions. As can be seen, the ΔP was greater when the P-SC with ROP = 3 was larger than the two ROP channels. Therefore, the pressure increased with an increase in the ROP in the hybrid turbulator. The maximum increase in ΔP was associated with ROP = 3 and a volume fraction of 3% of nanoparticles. At Reynolds numbers of 5000, 10 000, 15 000, and 20 000, it increased by 19.53%, 110.28%, 100.22%, and 80.23%, respectively. Figure 9 presents the changes of PEC index to Reynolds number in volume fraction of 1%-3% of nanoparticles in P-SC with combined turbulator for ROP = 1 (a), ROP = 2 (b), and ROP = 3 (c), respectively. As can be seen, the PEC index in the P-SC with hybrid turbulator was higher than 1 for all volume fractions and ROPs. Therefore, these results showed that the use of hybrid state turbulators had an effective role in improving HTR, and its use in a P-SC was appropriate in terms of the PEC index.
Exergy performance discrepancy against Reynolds number in a P-SC with a combined turbulator for ROP = 1, 2, and 3 at various volume fractions is depicted in Figure 10. As it is demonstrated, in all cases, the exergy performance grew with the volume fraction. However, in all cases, exergy efficiency increased with rising Reynolds number until reaching 10 000, and then decreased. Therefore, it can be concluded that the optimal state of exergy occurred in Reynolds number of 10 000 and volume fraction of 0.03% of nanoparticles.

| CONCLUSION
In this study, the effect of a hybrid turbulator with the pitch ratios of 1, 2, and 3, Reynolds numbers of 5000-20 000, and volume fractions of 1%-3% of two-phase hybrid nanofluid was evaluated through mathematical methods. Based on numerical methods, the impact of compound turbulator on thermal-hydraulic performance and exergy efficiency of P-SC filled with magnetic hybrid nanofluid and modeled in two phases was examined. The use of compound turbulators and magnetic hybrid nanofluids boosted the thermal performance of the P-SC. The maximum increase in ΔP belonged to ROP = 3 and volume fraction of 3% of nanoparticles. At Reynolds numbers of 5000, 10 000, 15 000, and 20 000, it increased by 19.53%, 110.28%, 100.22%, and 80.23%, respectively. The use of hybrid turbulators in terms of the PEC index in P-SC was desirable. The optimal mode of using a hybrid turbulator in terms of exergy efficiency belonged to Reynolds number of 20 000 and volume fraction of 3% of nanoparticles.