Effect of the Number of Nozzles of Swirl Flow Generator Utilized in Flat Plate Solar Collector: An Entropic Analysis

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Introduction
In order to meet the growing energy, it needs different sources of energies that has been considered [1,2]. To this end, various technologies have been developed [3,4]. The heat is a more accessible and transformable types of energy [5,6]. Solar thermal is a new and renewable thermal source that recently lots of systems have been designed and developed for attaining its efficient utilization [7,8]. This clean energy source even can be used for running power plants [9,10]. To this end, the improvement of solar thermal systems has been done from both microscopic [11] and macroscopic viewpoints and in combination with other systems [12,13]. One of the main irreversibility sources [14,15] is the thermal factor; so, the heat transfer quality of the any of thermal systems can be assessed by the entropy concept [16,17]. Pourhedayat et al. [18] studied the effect of using triangular vortex generators inside the pipe on thermal performance and exergy destruction. Different geometrical and structural characteristics of vinglets including winglet plate angle and latitudinal pitch were changed. Results showed that when the pitch equals 20 mm, the highest heat transfer can be achieved. Jalili et al. [19] studied environmental economic analysis of a geothermal-based power plant by the energy concept which is a function of exergetic characteristics of the system. In this study, flash and the binary geothermal system were integrated with each other as a hybrid heat and power generation cycle. They found that the energetic efficiency of the system is 54% while the highest achieved exergetic efficiency is 64%. Al-Turki et al. [20] proposed various parallel/nonparallel plate heat exchangers and numerically investigated the thermal, frictional, and the exergetic characteristics of each of them. It was inferred that different arrangements of flow direction and plates' configurations caused distinct entropy generation. Furthermore, the maximum Nu was achieved when hot and cold streams passed through convergent and divergent channels. Cao et al. [21] conducted a numerical simulation to analyze the effect of making annular depressions on the inner and outer wall of the tube-in-tube helical heat exchanger on the entropy generation. Different configurations and locations of annular depression were tested. Reported results demonstrated that although the case "d" makes the highest heat transfer, it generates the greatest entropy. In another work, Cao et al. [22] selected a helically coiled double tube heat exchanger to investigate R134a flow condensation by entropy generation study as well as sensitivity analysis. Different geometrical and flow conditions were taken into account. It was found that considered flow conditions are sensitive to alteration when mass velocity is considerable (G ≥ 300 kg:m −2 :s −1 ), and the vapor quality at the inlet section is x ≥ 0:5 also for Tsat≤46°C. Li et al. [23] performed thermal analysis on the channel with solid bodies for making swirl flow structure in this study, and different Re numbers and swirl chamber heights were considered. The highest heat transfer and lowest pressure drop achieved when channel height was 19 mm.
There are two major distinctive aspects of the present work with the others that make this study to be novel: (i) using nozzles for inducing swirl flow inside FPSCs and (ii) embedding pipes inside the phase change material (PCM) instead of having contact with absorber plate. No study has explored the effect of equipping the pipes of FPSC with the swirl generator to understand the performance of it based on the first and second laws of thermodynamics. Moreover, in the new design of FPSC, the pipes are embedded inside the PCM so that all area of pipes is subjected to the uniform temperature, while in the conventional type of FPSC, top semiwall of pipes is in contact to the absorber plate, and only this section receives heat. In fact, in this new design absorber plate transfer, the receiver heat to a media like PCM and this media acts as both energy storage and provides uniform heat flux to all part of the pipes. In this study, by considering the multiple-nozzle swirl generator new method that has been introduced for improving the efficiency of FPSC, number of the nozzles of swirl generator was varied from one to four nozzles; also, the sum of mass flow rate of all nozzles varied from 0.2 kg/s to 2 kg/s. The performance of the system was analyzed based on the second law of thermodynamics.

Model Description and Calculation Method
A new design has been proposed for FPSC in which the pipes of FPSC have been equipped with the swirl generator. In this study, the swirl flow is induced inside the piping system of FPSC by designed nozzles as shown in Figure 1. The number of employed nozzles is a key parameter; so, in this study, swirl generators with "single," "dual," "triple," and "quad" nozzles were tested to understand the effect of each of them on the entropic behavior of the system. According to Figure 1, except inlet and outlet sections, all of the surfaces have been defined as a wall. Only the peripheral surface of the cylindrical tube was subjected to the constant temperature (to simulate the working condition of FPSC) while the rest of the walls was assumed to be adiabatic. The overall mass flow rate was varied from 0.2 kg/s to 2 kg/s that this flow rate was divided among nozzles proportional to the number of them. Unlike other dimensions of the tube, its length had a constant size (700 mm). This study eliminates the need for using advanced technologies for enhancing performance of the system [24,25].
To analyze the system based on the obtained data from numerical calculations following calculation method was adopted, the formulation of the total entropy balance for an open thermodynamic system is [7] 〠 Q Based on mass balance [26], For "single-nozzle" swirl generator, mass balance can be expressed as [26] m : When this generalized for swirl generator with "n" nozzles [26], By substituting Eq. (6) in Eq. (3) [7], International Journal of Photoenergy The involved irreversibility sources in this system are thermal and frictional sources; hence. entropy generation can be expressed as [20,21] For S : gen, Thermal , For S : gen,Frictional , Replacing Eq. (8) and Eq. (9) into Eq. (10), the total equation of entropy generation can be achieved [7]: Dimensionless form of Eq. (11) can be calculated as follows [20]: To find the ratio of entropy generation number of modified (N s,m ) to unmodified system (N s,um ), the nondimensional parameter N E has defined as follows [20]: Similarly, Nu * is the ratio of Nu of the modified (Nu m ) to the unmodified ðNu um Þ system that can be obtained by [20,27]

International Journal of Photoenergy
To obtain the ratio of Nu * to N E , the following parameter was considered [7,8]: Also, Witte-Shamsundar efficiency (η W−S ) can be calculated by [7,8]  (i) Continuity equation: (ii) Momentum equation: θ-component: z-component: (iii) Energy equation: Made assumptions and defined boundary conditions are (i) Side wall of cylindrical pipe was under constant wall temperature of 360°C (ii) Inlet temperature was 300°C (iii) Except inlet, outlet, and peripheral wall of pipe the rest of walls had no heat and mass flux (iv) Inlet boundary condition was selected as "mass flow rate" (v) Outlet boundary condition was "pressure-outlet" (vi) All walls were smooth with "no-slip" boundary condition (vii) It was considered that the temperature changes have no effect on the properties of materials

Numerical Scheme, Validation, and Grid Independency.
This simulation was done based on the finite volume method (FVM). ANSYS CFX 15 was used for simulating the 3D model of problem. Swirl flow is a turbulent flow; so, k-omega SST model was adopted for modeling swirl flow accurately. This turbulent model (k-omega SST) provides more accurate results since it blends k-epsilon and k-omega models to take near wall and far wall regions into account. In the real conditions due to the swirl nature of flow, the hydraulic conditions in the core of pipe are very different than near-wall regions. High-resolution scheme and fourth-order pressure velocity coupling algorithm were employed. The calculation process stopped when the residuals of continuity, momentum, and energy were less than 10 -5 , 10 -5 , and 10 -8 , respectively. Four different mesh structures with the number of elements of 822436, 1356287, 1808762, and 2209345 were used for testing the grid independency [28]. As presented in Figure 2(a), total pressure changes are not meaningful after 1356287; so, this was selected as the grid structure of the computational domain. Figure 2(c) shows the validation results based on U /U ave . Result accuracy verification was checked by the results provided by Chan and Dahir [29]. The considered conditions were Re = 12500, the ratio of nozzle momentum flux to tube momentum flux ðM t /M T Þ, and ration of tube length to tube diameter of 10 (x/D = 10). These applied conditions were exactly taken by Chan and Dahir [29]. According to this comparison, obtained results have an excellent agreement, and numerical settings can be used for intended simulations. The CFD process flowchart of numerical scheme has been provided in Figure 2(c).     Figure 3. It is clear that the "single-nozzle" swirl generator has the highest entropy generation also as the number of nozzles increases entropy generations decreases. Moreover, the mass flow rate and the inclination angle of nozzles grow entropy generation increases. However, the effect of mass flow on the entropy generation augmentation is much more considerable than the injection angle of nozzles. Maximum amount of entropy generation is 428 J/K which is achieved by the case with a single nozzle and geometrical hydraulic specifications of "A60-D50-N12.5-M2." Conversely, the minimum entropy generation is 25 J/K which belongs to the case with four nozzles and specifications of "A30-D50-N12.5-M0.2." Figure 4 shows the entropy generation caused by a frictional source. According to the results, as the angle of nozzles grow from 30°to 90°, the entropy generation increases. In fact, the growth of nozzles' angle pressure drop goes up where this causes augmentation in the entropy generation. In addition to the growth of injection angle, the increment of mass flow rate increases entropy generation. Moreover, increasing the number of nozzles declines the entropy generation. Based on the said definitions, maximum and minimum frictional entropy generation is 0.72 J/K and 0:011 × 10 −3 J/K, respectively, caused by "single-nozzle; A90-D50-N12.5-M2" and "quad-nozzle; A30-D50-N12.5-M0.2." Figure 5 presents the values of dimensionless entropy generation (Ns) for each of the cases. The behavior of dimensionless entropy generation is similar to total entropy generation with different values. In other words, the magnitude order of cases and parameters is same under all of the studied conditions. Only, there is a big difference, when mass flow rate increases entropy generation grows as well, while dimensionless entropy generation reduces. According to the presented results in Figure 5, the highest and the lowest dimensionless entropy generation is 0.065 and 0.0178, respectively, which are related to "single-nozzle; A90-D50-N12.5-M0.2 " and "quad-nozzle; A30-D50-N12.5-M2."

Analysis of Dimensionless Parameters.
The ratio of modified Nu to unmodified Nu for all types of samples is provided in Figure 6. It can be seen "singlenozzle" case has great potential to improve Nu compared to others. Indeed, as the number of nozzles increases although entropy generation increases, heat transfer potential (Nu) increases as well. At the highest level, the Nu of  International Journal of Photoenergy "single-nozzle" swirl generator (with the specification of "A45-D50-N12.5-M2") is about 5.85 times greater than a pipe with no swirl generator. As the number of nozzles reduces, the effect of mass flow rate on Nu * becomes considerable. Figure 7 shows the ratio of modified dimensionless entropy generation to the unmodified entropy generation (N E ). The magnitude order of samples of N E is like Nu * . Comparing results of Nu * ( Figure 6) and N E (Figure 7) demonstrate that the enhancement of heat transfer of the designed swirl generators is greater than the augmentation of entropy generation. The maximum amount of N E is 4.23 achieved by "single-nozzle; A90-D50-N12.5-M2." Heat transfer improvement index (HTI) equals Nu * /N E . The results of HTI are shown in Figure 8. Based on this parameter, it can be found that whether heat transfer improvement is greater than entropy generation number or not. According to Figure 8, all of the values of HTI are greater than unit where this implies that the ratio of Nu improvement is higher than entropy generation. Results show that the "single-nozzle" swirl generator has a higher HTI compared with others except for the inclination angle of 30°. Generally, the values of HTI are greater at the lower flow rates. Increasing nozzles cause the reduction of HTI. The maximum and minimum HTI is about 1.7 and 1.189   Figure 9 provides the results of Witte-Shamsundar efficiency (η W−S ).
As the values of η W−S get close to unit, it shows that the quality of heat transfer is high, and the amount of generated irreversibility is low. Therefore, according to Figure 9, the highest η W−S can be achieved when the nozzle inclination angle is 30°. Case "quad-nozzle; A30-D50-N12.5-M2" has the maximum η W−S with a value of 0.9, while for the rest of the conditions, "quad-nozzle" swirl generator has the lowest η W−S . When there is merely one nozzle, the value of η W−S remains constant for injection angles of 45°and 60°. Also, the injection angle is 45°and 60°with the addition of nozzles η W−S that comes down.

Conclusion
The second law analysis of a pipe equipped with a swirl generator was done through numerical simulation. Number of nozzles was increased from one to four nozzles, and the inclination angle of them was varied from 30°to 90°. Irreversibility of all of the obtained designs was explored under three different mass flow rates. Results showed that by adding nozzles to the swirl generator, thermal and frictional entropy generation as well as HTI decreased. Furthermore, the increment of mass flow rate and injection angle  International Journal of Photoenergy increased thermal and frictional entropy generation while decreased HTI. Interestingly, HTI values were higher than unit, and its maximum amount was 1.7 when case "singlenozzle; A90-D50-N12.5-M0.2" was tested. The swirl generator "quad-nozzle; A30-D50-N12.5-M2" made the highest η W−S with a value of 0.9.

Data Availability
Data are available on request.

Conflicts of Interest
The authors declare that they have no conflicts of interest.