Thermal Performance Enhancement Using Absorber Tube with Inner Helical Axial Fins in a Parabolic Trough Solar Collector

Abstract

In the present work, a parabolic trough solar (PTC) collector with inner helical axial fins as swirl generator or turbulator is considered and analyzed numerically. The three-dimensional numerical simulations have been done by finite volume method (FVM) using a commercial CFD code, ANSYS FLUENT 18.2. The spatial discretization of mass, momentum, energy equations, and turbulence kinetic energy has been obtained by a second-order upwind scheme. To compute gradients, Green-Gauss cell-based method has been employed. This work consists of two sections where, first, four various geometries are appraised, and in the following, the selected schematic of the collector from the previous part is selected, and four various pitches of inner helical fins including 250, 500, 750 and 1000 mm are studied. All the numerical results are obtained by utilizing the FVM. Results show that the thermal performance improvement by 23.1% could be achieved by using one of the proposed innovative parabolic trough solar collectors compare to the simple one. Additionally, the minimum and maximum thermal performance improvement (compare to the case without fins) belong to the case with P = 250 mm by 14.1% and, to the case with P = 1000 mm by 21.53%, respectively.

1. Introduction

Heat exchangers, which transfer thermal energy through direct and indirect contact between fluids, are considered an indispensable part of several industries, from pharmaceutical to petrochemicals. Indirect contact heat exchangers are extensively used in solar systems. Due to the increasing importance of solar energy, nowadays, improving the performance of solar systems is one of the most important challenges for human beings and researchers. One of the most efficient types of solar collectors is a parabolic trough solar collector (PTSC), which is employed in both domestic and power plant applications. Recently, many efforts have been made by scientists to increase the efficiency of this type of collector. Actually, the PTSC component is a heat exchanger in which heat transfer fluid (HTF) flows in the receiver tube and absorbs the radiated solar energy.

In order to improve the thermal performance of this type of heat exchanger, various methods have been proposed and studied by researchers. Berger et al. [1] categorized heat exchangers’ augmentation procedures into passive and active subdivisions. One of two categories of ameliorating heat exchange methods is passive procedures [2]. It means that there is no requirement for any type of additional force. This method includes techniques such as nano particle [3], helical tubes [4], treated area [5], vortex generator [6], displaced increase devices [7], extended surfaces [8], and jagged surfaces [9].

Tang et al. [10] checked the heat transfer in the heat exchanger. According to their results, an increase of length enhances the performance of the vortex-generator fin. Azari et al. [11] checked the heat exchange in a heterogeneous circular microchannel, the results show the maximum heat exchange rates are got when the boundary conditions are symmetrical. Darzi et al. [12] have performed an experimental probing in a corrugated tube with nanofluid, they deduced that nanofluid with corrugated tubing could increase heat exchange by 330% compared to net liquid. Du et al. [13] numerically have worked on tube layouts, they demonstrated that the comprehensive efficiency of the optimized heat transfer device is ameliorated by about 50%. Bahiraei et al. [14] have checked on a triple-tube that their outcomes show that, based on heat exchange efficiency, an increase in height and reduced pitch are suggested. Abolarin et al. [15] have checked the impact of various geometries in twisted tapes, and the results pointed out that connection angle increases heat transfer. They found that when the wavelength is smaller, the temperatures near the walls increased. Zhang et al. [16] checked the thermal performance in corrugated pipes. According to the outcomes, the corrugated pipe ameliorated the heat transfer rate. Therefore, the other passive methods containing turbulator, etc., are usually better in the turbulent flow [17]. Several of the new works related to the utilization of inserts and the other passive methods to improve the thermal performance of the heat exchangers are displayed and listed in

Table 1. Overview of articles to improve the heat transfer.

Author	Year	Method (Exp/Num)	Inserts	Result
Kareem et al. [18]	2015	Experimental and Numerical	Spirally corrugated tube	The tube of higher severity index has the best thermal performance.
Lu et al. [19]	2016	Numerical	Vortex generator	Their results pointed out that holes close to the leading-edge give better efficiency.
Mashoofi et al. [20]	2017	Experimental	Helically coiled	Findings showed that the use of a turbulator increases Nusselt number around 8–32%.
Aghaei et al. [21]	2018	Experimental and Numerical	Horizontal and vertical elliptic baffles	The heat exchange attains the utmost at the arrangement angle of 15°.
Noorbakhsh et al. [22]	2019	Numerical	Twisted-tapes	The enhancement of fin number goes up the heat exchange.
Kwon et al. [23]	2019	Numerical	static mixers	Static mixers registered heat transfer coefficient an increase of about 100%.
Ho et al. [24]	2019	Experimental	Mini-channel	Conforming outcomes, the friction factor reduced as the temperature of the inlet rises.
Liu et al. [25]	2019	Experimental	Heat sinks	Heat exchange had a peak at θ = 20° and β = 0.8.
Ramalingam et al. [26]	2020	Experimental	Automotive radiator	Enhancement heat dissipation was got for nanofluid at 0.8.
Qi et al. [27]	2020	Experimental	Triangle tube	Triangular tubes have the most positive impact on the rate of increase of heat exchange.
Nakhchi et al. [28]	2020	Numerical	Perforated hollow cylinders	Outcomes saw that the resistance of flow can be decreased up to 86.2% with go upping the perforated index.
Rahbarshahln et al. [29]	2020	Numerical	Microchannels	The use of hydrophobic models could decline the required power fluid pump up to 69% and go up heat flux up to 15%.
Jamesahar et al. [30]	2020	Numerical	Flexible fins	Due to the oscillation of the fins, the heat exchange rate goes up.
Benabderrahmane et al. [31]	2020	Numerical	Central corrugated insert	The overall heat transfer performance was achieved in the range of 1.3–2.6.
Akbarzadeh and Valipour [32]	2020	Experimental	Helically corrugated tube	The maximum obtained thermal performance (2.29) belongs to the case with pitch length and roughness height of 3 mm and 1.5 mm, respectively.
Chakraborty et al. [33]	2020	Numerical	Helical absorber tube	Thermal efficiency and exergy rise by 1–10% and 0.2–3.2%, correspondingly.
Amani et al. [34]	2020	Numerical	Conical strip inserts	The overall thermal–hydraulic performance was obtained in the range of 0.679–1.107.
Khan et al. [35]	2020	Numerical	Absorber tube with twisted tape insert and tube with longitudinal fins	Thermal efficiency of the cases with twisted tape insert, tube with internal fins, and plain tube are by 72.26%, 72.10% and 71.09%, respectively.
Saedodin et al. [36]	2021	Numerical	Turbulence-Inducing elements	The maximum achieved thermal efficiency was by 29%.
Vasanthi and Jaya Chandra reddy [37]	2021	Experimental	Angular twisted strip inserts	The obtained enhancement efficiency was in the range of 145–215%.
Chakraborty et al. [38]	2021	Numerical	Helical absorber tube	Thermal efficiency and exergy rises by 4–10%, and 4–5%, correspondingly.
Akbarzadeh and Valipour [39]	2021	Numerical	Helically corrugated tube	The thermal performance shows a growth of 26–176%.
Peng et al. [40]	2021	Experimental and Numerical	Semi-annular and fin shape metal foam hybrid structure	Performance evaluation criteria augmentation, total entropy generation decrease in addition to exergetic efficiency growth maximally reach 360, 93.3 and 10.2%, correspondingly.

.

Solar energy is considered as a heat flux for solar collectors. The survey of a solar heat transfer device is trusted for increasing the thermal performance of the available system to obtain an outcome [41]. Moghaddaszadeh et al. [42] used two passive techniques to ameliorate the efficiency of heat exchangers in solar collectors. The outcomes illustrate that the use of nanofluid went up the Nusselt number up to 4%. Ghasemi and Ranjbar [43] in the numerical verification on solar parabolic collector demonstrated that adding nanoparticles increase thermal performance and using Al₂O₃ or CuO as nanofluid at 3% volume fraction enhances the heat exchange up to 28 and 35 percent, respectively. Reddy et al. [44] investigated the thermal analysis of parabolic trough collectors for various geometrical parameters such as porosity and fin aspect ratio. Their results pointed out that the porosity will increase the heat exchange by about 17%.

According to the presented literature review of previous works (Table 1) related to heat transfer enhancement of the PTSC by various passive methods, it can be concluded that among different kinds of utilized methods, employing helical axial fins has not been considered and analyzed previously. In the present work, one parabolic trough solar collector with inner helical axial fins as swirl generator or turbulator is considered and analyzed. This work consists of two sections. In the first section, four various schematics of the collector are appraised. In the second section, the selected geometry of the collector from the previous part (first section) is selected, and four various pitches of inner helical fins including 250, 500, 750 and 1000 mm are studied.

2. Materials, Methods and Boundary Conditions

Parabolic trough collector systems, as demonstrated in Figure 1a, in the studied geometry, a parabolic concentrator is used, which is due to the reduction of heat loss and increase of the produced temperature. Figure 1 shows the schematic of the checked geometry, and also

Table 2. Physical parameters of the analyzed collector.

Parameters		Value
Diameter of inner the tube	D1	30 mm
Diameter of outer the tube	D2	60 mm
Length of the tube	L	2000 mm
Height of the fins	H	10 mm
Thickness of the fins	th	5 mm
Helix pitch of the fins	P	500 mm
Helical angle of the fins	α	180 °

displays the geometrical constants and parameters. According to the check accomplished, for turbulent flow the entry region length is five times more than the diameter of the inner tube [35]; however, some researchers are of the opinion that it has a slight impact [45,46]. The three-dimensional numerical simulations have been done by finite volume method using commercial CFD code, ANSYS FLUENT 18.2. The geometrical parameters of the considered heat exchanger are illustrated in Figure 1c. The 30 °C inflow enters the tube at different velocities, namely 0.2, 0.24, 0.28 and 0.32 m·s⁻¹. Velocity–inlet and pressure–outlet boundary conditions were considered at the inlet and outlet ports, respectively. A heat flux of 60,000 W·m⁻² (is calculated by dividing the power consumption (6000 W) to the side surface area (0.10 m²) is transferred and applied to the outer part of the geometry made of an internally threaded steel layer. Moreover, the thermos–physical properties of tube material and fluid are noted in

Table 3. The thermos–physical properties of materials [46].

Fluid (Water)	Pipe (Steel)	Property
4182	502	Specific Heat [J/(kg·K)]
0.6	16	Thermal Conductivity [W/(m·K)]
998.2	7881.8	Density [kg/m3]
0.001003	−	Viscosity [kg/m·s]

. The following situations are assumed in simulations:

• The inlet fluid at all velocities is 30 °C.
• The flow is turbulent and in a steady mood.
• The heat flux applied to the surface of the outer tube is 60,000 W·m−2.

The present work includes two sections. In the first part, three geometries with various schematics of the inner helical axial fins are considered and investigated, and the obtained results are compared with the simple collector without any insert (fins). The schematics of the evaluated geometries in the first section of present work are illustrated in Figure 2. In the second section, the selected model according to the first section obtained results is considered with various pitch of the inner helical axial fins (P) including 250, 500, 750 and 1000 mm which the evaluated cases are depicted in Figure 3.

3. Governing Equations and Dimensionless Parameters

The actual system is governed by the continuity, momentum, and energy equations that are defined, respectively, as [47,48]:

$$\frac{\partial \rho }{\partial t}+\nabla \nabla .\left(\rho \overrightarrow{v}\right)=S_m$$

(1)

$$\frac{\partial \left(\rho \overrightarrow{v}\right)}{\partial t}+\nabla .\left(\rho \overrightarrow{v}\overrightarrow{v}\right)=-\nabla p+\nabla \left(\stackrel{=}{\tau }\right)+\rho \overrightarrow{g}+\overrightarrow{F}$$

(2)

$$\frac{\partial \left(\rho E\right)}{\partial t}+\nabla .\left(\overrightarrow{v}\left(\rho E+p\right)\right)=\nabla \left(k_{eff}\nabla T-{{\displaystyle \sum }}_j{h}_j{\overrightarrow{J}}_j+\left({\stackrel{=}{\tau }}_{eff}.\overrightarrow{v}\right)\right)+S_h$$

(3)

The thermal performance coefficient (η) can be exerted to quantify the yield of a heat exchanger that contains the Nusselt number and the friction factor (f), and is defined as [49,50,51,52,53,54,55,56,57,58]:

$$Nu=\frac{h_m{d}_h}{k}$$

(4)

$$f=\frac{2d_h\Delta P}{\rho u^{2}L}$$

(5)

$$\eta =\left(\frac{Nu}{N{u}_0}\right){\left(\frac{f_0}{f}\right)}^{\frac{1}{3}}$$

(6)

The three-dimensional numerical simulations have been done by finite volume method using commercial CFD code, ANSYS FLUENT 18.2. The spatial discretization of the mass, momentum, turbulence kinetic energy, turbulence dissipation rate and energy equations has been achieved by a second-order upwind scheme. The velocity-pressure coupling has been overcome by the SIMPLE algorithm. To calculate the gradients, Green-Gauss cell-based method has been utilized. The convergence criteria were set to 10⁻⁶ for the residuals of all equations except energy equation (10⁻⁸).

4. Results

4.1. Grid Independency Study

The generated grids for the proposed collector geometry is displayed in Figure 4. Four variant grids were checked to certify the accuracy of the numerical outcomes. The analysis outcomes are offered in

Table 4. Outcomes of the grid independence check.

Nusselt Number Error	Grid Number
17.2%	65421
9.04%	121470
2.13%	164957
1.98%	235712

. It is vivid that the two middle mesh sizes do not vary substantially and in the interest of minimizing the computational time whilst attaining trust outcomes, demonstrate that a third option is a good selection.

4.2. Validation Study

The Dittus-Boelter correlation [59] provides the Nusselt number as a function of the Re and Pr according to Equation (7):

Nu = 0.023 Re^0.8 Pr^0.4

(7)

Additionally, the Seban-Shimazaki correlation [59] (Equation (8)) is employed to compare with the simulation outcomes. A high correlation is suggested for Pe_D ≥ 100. The outcomes of the validation study are demonstrated in Figure 5. Therefore, the available work presents good accuracy. Additionally, to validate the present numerical model with the results of the performance of a real PTC system, the experimental results of Zou et al. [60] are used, and the comparison is presented in Figure 6. It can be concluded that present numerical method has good capacity for modeling the fluid and thermal characteristics in a PTC system. The uncertainty in measurement of the experimental parameters of the Zou et al. work [60] was as follows. The uncertainty in HTF velocity measurement was $\pm 0.05\mathrm{m}/\mathrm{s}$ for HTF velocity up to $0.28 \mathrm{m}/\mathrm{s}$ and $\pm 0.2 \mathrm{m}/\mathrm{s}$ for HTF velocity between 0.28 and $0.32 \mathrm{m}/\mathrm{s}$. The uncertainty of HTF temperature was $\pm 0.3°\mathrm{C}$ in this study.

Nu = 5 + 0.025 Pe_D^0.8

(8)

4.3. The Impact of the Schematic of the Proposed Collector’s Fins

In this section, the influence of the collector shape on thermal efficiency is investigated numerically. Three various models are considered, and the obtained results have been compared with the simple shaped collector. The considered models here are shown in Figure 2. The variation of heat transfer coefficient versus different inlet velocity for various models is illustrated in Figure 7. Hence, it can be concluded that firstly, all the proposed models show higher heat transfer coefficient more than the simple collector (Model 1). Secondly, it is depicted that among the studied models, the maximum heat transfer coefficient belongs to Model 2 in all studied inlet velocities. Additionally, the minimum heat transfer coefficient belongs to Model 4 in all considered inlet velocities.

To realize better the effect of geometry on the thermal performance of the proposed system, the streamline with the contour of temperature for all four studied models is shown in Figure 8. Hence, it can result that the schematic of the geometry and also the attendance of the inner axial helical fins have a significant impression on the rotation flow production and finally more heat transfer rate. Furthermore, contours show that Model 4 could enhance the heat transfer rate more than the other models. Additionally, all models depict better thermal performance in comparison with the collector equipped with simple channel (Model 1) because of the presence of swirl flows generated by the helical fins.

The variation of pressure drop and friction factor (f) versus various inlet velocities for various models are illustrated in Figure 9a,b, respectively. Figure 9a depicts that all models have more pressure drop compare to Model 1 (collector with simple channel, without helical fins) obviously because of presence of swirl flows. The maximum pressure drop belongs to Model 2 and the Model 4 shows lowest pressure drop among these four models. Additionally, as the inlet velocities rises, the pressure drop increases due to the effect of forced convection in the channel. This trend is the same for all models. Moreover, by increasing the inlet velocities, the differences between the studied models rises. This point could be important considering the pressure drop factor, as the differences between Model 4 and Model 1 (as base model) are very low.

Figure 9b shows that the trend of variation of fraction factor among the models is the same with pressure drop (Figure 9a). However, it should be focused that the variation of friction factor with inlet velocities is not the same with pressure drop, and they are exactly the opposite. By increasing the inlet velocity, the friction factor declines. According to Equation (5), the friction factor is directly related to the pressure drop; however, the squared velocity is placed at the denominator of the equation.

Contours of temperature at outlet for various models and P = 500 mm are presented in Figure 10. The impact of changing the schematic of the collector on temperature distribution in the outlet port and also the heat transfer rate is presented clearly in this figure. Accordingly, all models show better temperature distribution than the Model 1 (simple one, without fins).

The best parameter to comprehensively study the impact of efficient parameters on the performance of the proposed collector is thermal efficiency (η), which is calculated by Equation (6). In this Equation, the index 0 refers to the base collector (without fins). The variation of this parameter versus various inlet velocity for variant models are presented in Figure 11. Hence, it can be firstly concluded that all the models illustrate higher thermal performance than Model 1 (simple collector without fins), which means that the values of thermal performance are higher than unity. Furthermore, the highest and lowest thermal performance improvements (compared to Model 1) belong to the Model 3 by 23.1% (at V_inlet = 0.2512 m/s) and Model 3 by 20.7% (at V_inlet = 0.1884 m/s), respectively. Contours of velocity magnitude at surface X = 0 for various models at P = 500 mm and V_Inlet = 0.1256 m/s are illustrated in Figure 12. It can be realized that among the considered models in this section, Model 2 depicts higher velocity magnitude and consequently more swirl flows in the proposed collector, which leads to a higher heat transfer rate.

4.4. The Impact of the Inner Helical Fins Pitch (P)

In the second section, according to the obtained numerical results from the last section (Section 4.3), Model 2 (see Figure 2) is considered as the selected model here. Results from the last section showed that Model 2 has the maximum heat transfer coefficient with the highest pressure drop. Therefore, to study the impact of the inner helical fins pitch, this model is used. In this section, the impact of the inner helical fins pitch on the thermal efficiency of the system is evaluated numerically. Four various pitches of the inner helical fins including 250, 500, 750 and 1000 mm are considered, and the obtained outcomes are compared with the simple collector (without fins). The considered models here are shown in Figure 3. The variation of heat transfer coefficient versus different inlet velocity for various models is illustrated in Figure 13.

According to Figure 13, it can be concluded that firstly, all the proposed models show higher heat transfer coefficient more than the simple collector (without fins). Secondly, it is depicted that among the studied models, the unmost heat transfer coefficient belongs to case with P = 250 mm in all studied inlet velocities. Additionally, the least heat transfer coefficient belongs to the case with P = 1000 mm in all considered inlet velocities. To realize better the impact of the pitch of inner helical fins on the thermal performance of the proposed collector, the contour of temperature at outlet and a slice in the middle of the computational domain (X = 0) for all cases are shown in Figure 14. It can be obviously seen that higher temperature in the proposed collector is achieved at lower pitch of the inner helical fins.

The variations of pressure drop and friction factor (f) versus various inlet velocities for various models are illustrated in Figure 15a,b, respectively. Figure 15a depicts that all models have higher pressure drop compared to the case without helical fins obviously because of the presence of swirl flows. The greatest pressure drop belongs to the case with P = 250 mm, and the case with P = 1000 mm shows the lowest pressure drop among the investigated models. Additionally, as the inlet velocities rise, the pressure drop increases due to the effect of forced convection in the channel. This trend is the same for all models. Moreover, by increasing the inlet velocities, the differences between the studied models rise. This point could be important considering the pressure drop factor, as the differences between the cases with P = 500, 750 and 1000 mm are very low.

Figure 15b shows that the trend of variation of fraction factor among the models is the same with pressure drop (Figure 15a). On the other hand, as same as Figure 15a, the highest and lowest friction factor belong to the cases with P = 250 mm and P = 1000 mm, respectively. However, it should be focused that the variation of friction factor with inlet velocities is not the same with pressure drop and they are exactly the opposite. By increasing the inlet velocity, the friction factor declines. According to Equation (5), the friction factor is directly related to pressure drop; however, the squared velocity is placed at the denominator of the equation.

The streamline with the contour of temperature for various models are presented in Figure 16. The impact of changing the schematic of the collector on temperature distribution in the outlet port and also the heat transfer rate is presented clearly in this figure. Accordingly, all models show better temperature distribution than the case without fins.

The best parameter to study comprehensively the impact of efficient parameters on the performance of the proposed collector is thermal efficiency (η), which is calculated by Equation (6). The variation of this parameter is presented in Figure 17. Therefore, it can be concluded firstly that all the models illustrate higher thermal performance than the case without fins, which means that the values of thermal performance are higher than unity. Furthermore, the greatest and smallest thermal performance improvement (compare to the case without fins) belong to the case with P = 1000 mm by 21.53% and the case with P = 250 mm by 14.1% for the latest velocity, respectively.

5. Conclusions and Future Scope

In the present work, a PTC collector with inner helical axial fins as a swirl generator or turbulator is considered and analyzed. This work consists of two parts. In the first part, four various geometries of the collector are appraised. In the second part, the selected schematic of the collector from the first sector is selected and four various pitches of inner helical fins including 250, 500, 750 and 1000 mm are studied. Results presented that the thermal performance improvement by 23.1% could be achieved by using one of the proposed innovative parabolic trough solar collector compare to the simple one. Additionally, the utmost and least thermal performance improvement (compare to the case without fins) belong to the case with P = 1000 mm by 21.53% (at V_inlet = 0.314 m/s) and the case with P = 250 mm by 14.1% (at V_inlet = 0.314 m/s), respectively.

Although present work has presented new insight into the flow and thermal characteristics of a parabolic trough solar collector combining innovative inner helical axial fins as a swirl generator, additional research is required to determine the capability of this design in more realistic engineering situations by the development of an experimental prototype.