Renewable Energy 93 (2016) 125e141
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Renewable Energy
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Parabolic trough solar collector for low enthalpy processes: An analysis of the efficiency enhancement by using twisted tape inserts
* O.A. Jaramillo a, ,Monica Borunda b, c, K.M. Velazquez-Lucho d, M. Robles a a Instituto de Energías Renovables, Universidad Nacional Autonoma de M exico, Priv. Xochicalco s/n, Temixco, Morelos, 62580, Mexico b CONACYT Research Fellow e IIE, Consejo Nacional de Ciencia y Tecnología, Av. Insurgentes Sur 1582, Col. Cr edito Constructor, Del. Benito Juarez, D.F., 03940, Mexico c Instituto de Investigaciones El ectricas, Reforma 113, Col. Palmira, Morelos, 62490, Mexico d Universidad Veracruzana, Campus Xalapa, Lomas del Estadio s/n, Col. Zona Universitaria, Xalapa, Veracruz, 91090, Mexico article info abstract
Article history: Concentrated solar energy is a promising source of energy which is currently attracting many efforts to Received 15 October 2015 enhance its exploitation. In particular, parabolic trough collectors for low enthalpy processes is an Received in revised form emerging technology. Lately, many work is done focused on the improvement of these devices. One 9 February 2016 technique to achieve this is by augmenting the heat transfer in the receiver tube by inserting a twisted Accepted 17 February 2016 tape in the tube. In this work, we develop a thermodynamic model framework to analyse the perfor- Available online 1 March 2016 mance of a parabolic trough collector with a twisted tape insert. We find the set of conditions under which a twisted tape insert is useful to boost the performance of a parabolic trough collector. This set of Keywords: Concentrated solar energy conditions corresponds to devices with low twisted ratios operating at low Reynolds numbers. The Parabolic trough collector proposed model is supported with experimental data. Second law analysis © 2016 Elsevier Ltd. All rights reserved. Low enthalpy processes Twisted-tape elements Exergy efficiency
1. Introduction Rankine Cycle (ORC) with potential applications to industrial pro- cesses [2]. A parabolic trough concentrator (PTC) is a promising solar On the other hand, the generation of thermal energy for some concentration technology to integrate solar energy into the primary industrial processes requires temperatures between 85 and 250 C energy sources. This technology converts the solar beam radiation [1]. These applications are cleaning, drying, evaporation, distilla- into thermal energy in its linear focus receiver. PTC applications can tion, pasteurization, sterilization and cooking, among others, as be divided into two main groups: a) for electricity generation and b) well as applications with low-temperature heat demand and high for thermal applications in solar heating for industrial processes. consumption rates (domestic hot water, space heating and swim- Concentrated Solar Power (CSP) Plants is one of the main ming pool heating), and heat-driven refrigeration and cooling [3] renewable energy technologies for the production of electricity by [4], and [5]. It is common that these kind of concentrators are means of the Rankine cycle. This is a common technology employed modular devices with solar collector areas in the range of for commercial projects in the capacity range from 10 MWe to 90 2.5e5.0 m2 and they are used to generate hot water and low MWe, and the operating temperature is in the range from 300 to enthalpy steam. Table 1 shows some efficiency curves that have 400 C. CSP projects have recently become more economically been reported in the literature for this type of PTCs. appealing due to the improvements in concentrated solar power The efficiency equations shown in Table 1 are established on the technology and cost [1]. It is important to point out that in recent basis of the First Law of Thermodynamics. years, a way to harness the solar energy is to co-generate through Recently, one of the aims of solar-thermal engineering is to Concentrated Solar Power (CSP) technology coupled to an Organic enhance parabolic trough concentrators for industrial processes. Some research reported in literature is addressed to the develop- ment of new devices, new applications, control methodologies,
* thermodynamic and technical-economic analysis, as well as the Corresponding author. fl E-mail address: [email protected] (O.A. Jaramillo). development of components, support structures, re ective http://dx.doi.org/10.1016/j.renene.2016.02.046 0960-1481/© 2016 Elsevier Ltd. All rights reserved. 126 O.A. Jaramillo et al. / Renewable Energy 93 (2016) 125e141
Nomenclature Ts ¼ 4500 K Apparent temperature of the Sun [K] 2 UL Global loss coefficient [W/m K] V Velocity [m/s] Symbols , V Volumetric flow rate [l/min] A Aperture area [m2] a W Aperture width [m] A Receiver area [m2] a r w Tape width [m] C ¼ A /A Concentration ratio [ ] o a r y Tape pitch length [m] Cp Specific heat at constant pressure [kJ/kgK] D Internal diameter [m] i Greek letters Do External diameter [m] , a Absorptivity [ ] 2 ED Exergy destruction [W] a¼k/rCp Thermal diffusivity [m /s] , DFR Enhancement factor for the heat removal factor [ ] EU Exergy useful [W] , Df Change in the friction factor [ ] 2 ES Exergy supplied via solar energy [W] DP Pressure drop [kgm/s ] F'Efficiency factor [ ] DNu Enhancement factor for the Nusselt number [ ] FR Heat removal factor [ ] DhI Enhancement factor by First Law [ ] f Focal length [m], Friction factor [ ] DhII Enhancement factor by Second Law 2 GB Direct solar radiation [W/m ] ε Emissivity [ ] 2 h Heat transfer coefficient [W/m K] g Intercept factor [ ]
I Irreversibility ho Optical efficiency [ ] l Length [m] k Thermal conductivity [W/mK] , m_ Mass flow rate [kg/s], ðm_ ¼ rVÞ m Dynamic viscosity [kg/ms] n Kinematic viscosity [m2/s] NS,a Augmentation entropy generation number [ ] r Density [kg/m3], Reflectivity [ ] Nu, Nu Nusselt number (internal and external flow) [ ] h Thermal efficiency [ ] P Pressure [kgm/s2] I h Exergy efficiency [ ] fl II Pr, Pr Prandtl number (internal and external ow)[ ] e , s Stefan Boltzmann constant 8 2 4 Q loss Heat loss [W] [5.67051 10 Wm K ] , f Rim angle []+ Q u Heat useful [W] , Q Solar beam radiation collected by the PTC [W] Subscripts Re, Re Reynolds number (internal and external flow) [ ] air air , D Circular tube S Entropy generation rate [W/K] gen E Empty tube T Ambient temperature [K] a TT Twisted tape inserts T Temperature at the input of the receiver tube [K] in r Receptor T Temperature at the output of the receiver tube [K] out v wind T Temperature of the receptor [K] r w water TR ¼ y/w Twist ratio [ ]
materials, materials for the receiver, and absorber surfaces. One general purpose in heat exchangers. In the literature the applica- way to enhance the efficiency of a solar collector is to produce a tions of twisted-tape inserts in tubular heat exchangers, as a pas- high convection heat transfer coefficient in order to increase the sive technique for heat transfer enhancement, have been widely heat exchange between the solar energy arriving into the surface of studied. Various designs of twisted tapes have been tested in many the absorber and the thermal fluid. Heat transfer enhancement devices for heat transfer augmentation [15e34]. techniques can be classified into active and passive techniques, the In particular, the use of twisted tapes could play a significant former needs an external power source and the later dispenses it. role to improve the performance of solar water heating systems Both techniques have been applied to improve heat transfer in [35], since twisted tapes can be inserted inside the flow tubes in several areas such as nuclear reactors, chemical reactors and for solar water heating systems to enhance the heat transfer rate, however the pumping power may increase significantly and its cost becomes significant during the operation. A brief review of the Table 1 literature in this topic is presented below. Thermal efficiency for different low-medium-temperature parabolic trough concentrators. In 2000, Kumar and Prasad [36] studied the heat transfer and the pressure drop in a solar water heater with twisted tapes inserts. Equation Reference Their experimental investigations showed that the heat transfer
hI ¼ 0.66 0.233(DT/GB) [6] increased by 18e70%, whereas the pressure drop increased by ¼ D hI 0.65 0.382( T/GB) [7] 87e132%, as compared to plane collectors. They observed that heat h ¼ 0.642 0.44(DT/G ) [8] I B losses were reduced (due to the lower value of the plate temper- hI ¼ 0.638 0.387(DT/GB) [9] ature) consequently increasing the thermal performance by about hI ¼ 0.69 0.39(DT/GB) [11] and [10] hI ¼ 0.0543 0.1889(DT/GB) [12] 30% over the plane solar water heaters under the same operating ¼ D hI 0.5608 2.468( T/GB) [13] conditions. The effect of twisted-tape geometry, flow Reynolds ¼ D hI 0.5523 2.0099( T/GB) [14] number, and intensity of solar radiation on the thermal O.A. Jaramillo et al. / Renewable Energy 93 (2016) 125e141 127 performance of the solar water heater were reported. They re- with spacer. They showed that the decrease in friction factor is ported that the twisted tape collectors perform remarkably better maximum in twist fitted with spacer compared to twist fitted with in the lower range of flow Reynolds number (Re z 12,000), beyond rod and described that the over all performance for twist fitted with this regime the increase in thermal performance is monotonous. rod is better than twist fitted with spacer. In the work [42], Jai- They showed that such collectors might perform even better at sankar et al. carried out an experimental investigation of heat higher values of intensity of solar radiation. transfer, friction factor and thermal performance of thermosyphon In 2008, Jaisankar et al. [37] conducted an experimental inves- solar water heater system fitted with helical twisted tape of various tigation of heat transfer, friction factor and thermal performance of twist ratios. They developed empirical correlations for Nusselt left-right twisted tape solar water heater with various twist ratios. number and friction factor with various twist ratios 3, 4, 5, and 6. They compared their results with a plain tube collector at the same They compared their results with a plain tube collector at the same operating conditions. They developed empirical correlations for operating conditions. They concluded that heat transfer enhance- Nusselt number and friction factor with various left-right twist ment in twisted tape collector is higher than the plain tube col- ratio. They confirmed that the heat transfer augmentation in left- lector with minimum twist ratio and gradually decreases with right twisted tape collector was better than plain tube collector. increase in twist ratio. They showed that thermal performance of They reported that the heat enhancement and pressure drop were twisted tape collector increase with the solar intensity. higher with minimum twist ratios. In 2013, Bhattacharyya et al. [43] reported an experimental In 2009, Hobbi and Siddiqui [38] reported an experimental investigation about the friction factor and the Nusselt number for study conducted to investigate the impact of heat enhancement laminar flow through a circular duct having integral transverse ribs devices on the thermal performance of a flat-plate solar collector. and fitted with centre-cleared twisted-tape. They found that the They studied different passive heat enhancement devices that centre-cleared twisted tapes in combination with transverse ribs include twisted strip, coil-spring wire and conical ridges. Their perform significantly better than the individual enhancement study showed no appreciable difference in the heat flux to the technique acting alone for laminar flow through a circular duct up collector fluid. They found significantly high values of Grashof, to a certain amount of centre-clearance. In the same year, Sekhar Richardson and Rayleigh numbers indicating that the heat transfer et al. [44] carried out an experimental simulation using flat plate mode in the solar collector is of mixed convection type with free collectors under constant heat flux boundary condition. In their convection as the predominant mode. They concluded that due to study, convective heat transfer analysis for a horizontal circular the significant damping of shear-produced turbulence by buoyancy pipe with fluid in mixed laminar flow range was performed forces, the applied passive methods based on the enhancement of considering passive augmentation techniques such as twisted tapes shear-produced turbulence are ineffective in augmenting heat and swirl generators in the fluid flow path. They studied the vari- transfer to the collector fluid in flat-plate solar collectors. In the ation of heat transfer coefficient and pressure drop in the pipe flow same year, Kumar and Prasad [39] developed and tested solar water for water and water based Al2 O3 nanofluids at different volume heater having twisted tape inserted inside the tubes. Their exper- concentrations and twisted tapes. imental evaluation was carried out under solar radiation covering In 2014, Chang et al. [45] presented numerical studies of the the Reynolds number from 4000 to 20,000, and twist pitch ratio enhanced turbulent heat transfer of molten salt in solar thermal from 3 to 12. They showed that in the range of parameters inves- absorber tubes. They reported that the insert twisted tape can tigated, thermal enhancement factor varied between 1.18 and 2.7 significantly improve the uniformity of temperature distribution of and the maximum value of collector efficiency increased by about tube wall and molten salt. They found that the decrease of clearance 30% compared to that of plain ones at same operational condition. rate and twisted rate can enhance the heat transfer effectively. They They developed empirical equations for such type of solar water showed that in the case when clearance rate C ¼ 0, heat transfer heater. Other work reported in this year is developed by Hasan and enhancement effect with tight-fit twisted tape is the most signifi- Sumathy [40]. They carried out an experimental investigation about cant, but at the same time, the decrease of clearance rate and the thermal performance of a solar air heater with helical tape twisted rate also lead to the increase of the friction factor. In the inserts of two different twist ratios (23 and 11). They studied the same year, Sandhu et al. [46] Reported an experimental study about friction factor and heat transfer coefficient for a flow in a circular the thermal performance of a flat-plate solar collector using insert tube maintained at uniform heat flux conditions. The tested was devices, over a Reynolds number range 200e8000 and a Prandtl carried out at low Reynolds numbers, well in the turbulent region, number range 5e8, using water as the working fluid. They for a wide range, 8.05 103e1.36 104. Their results proved that considered a variety of conventional and novel insert configura- this system with helical tape inserts could enhance heat transfer by tions which include, twisted-tape inserts, wire coil inserts, and wire about 1.15e1.7 times compared to that of plain tube. Also, their mesh insert. Their results showed that the enhancement of the study demonstrated that higher heat transfer rates were recorded Nusselt number by all insert devices. Comparison of the best inserts for lower twist ratios. from different insert families showed that in the laminar flow Also in 2009, Jaisankar et al. published two papers about the regime, the mesh insert performed the best whereas, the concen- heat transfer and the pressure drop in a solar water heater with tric coils achieved the highest Nusselt number augmentation in the twisted tape inserts. In the paper [41] they reported an experi- turbulent regime, relative to the smooth pipe with no inserts. They mental investigation of heat transfer and friction factor character- reported that the concentric coils were the best insert among those istics of thermosyphon solar water heater system with full-length tested. Their experimental results showed an overall Nusselt twist, twist fitted with rod and spacer fitted at the trailing edge for number enhancement of 110% in the low Reynolds number range lengths of 100, 200 and 300 mm for twist ratio 3 and 5. They and 460% in the high Reynolds number range. They also investi- compared their results with plain tube collector for the same gated the impact of collector inclination of the performance of operating conditions. They verified with fundamental equations those insert devices and their results showed that the channel the experimental data for Nusselt number and friction factor for inclination does not have a significant impact on the Nusselt plain tube collector. They developed empirical correlations for number enhancement. Nusselt number and friction factor. They concluded that the In 2015, Chang et al. [47] carried out a numerical study per- decrease in Nusselt number for full length helical twist compared to formed with FLUENT 6.3.2 code for investigating the heat transfer twist fitted with rod is minimum and is quite significant for twist enhancement in a molten salt solar receiver tube with the twisted 128 O.A. Jaramillo et al. / Renewable Energy 93 (2016) 125e141 tapes. They compared their previous correlation of the Nusselt solar thermal parabolic trough concentrator system by enhance- number and friction factor of twisted tape in order to evaluate the ment of heat transfer rate using a nanofluid, plain twisted tape and turbulence models used. They examined the effects of the clearance nail twisted tape inserts. Their results were obtained by simulation ratios (C ¼ 0 (tight fit), 0.2, 0.5, 0.7 and 1) and twist ratios (y ¼ 2.5, modelling. 5.0, 12.5, 15.6, 25, 41.7) on heat transfer rate (Nu), friction factor (f) The main objective of this work is to analyse the thermal- under non-uniform heat flux using molten salt as the testing fluid in hydraulic performance of a PTC with twisted tape inserts for low the range of Reynolds number 7485e30,553. They reported the enthalpy processes by considering the First and the Second Law of influence of grid generation on prediction results Their results Thermodynamics. In order to estimate the behaviour of the PTC showed that the insert twisted tape can significantly improve the when twisted tape insert is used, we develop a thermodynamic uniformity of temperature distribution of tube wall and molten salt. model framework based on empirical correlations to calculate the In the same year, Pavendan et al. [48] developed experimental heat transfer rate and pressure drop for fully developed condition. studies on solar water heater system fitted with seven type of in- The thermodynamic model framework includes an exergetic serts cross type insert; twisted tape insert (i) with three different analysis to provide useful information for the exergy efficiency of pitch ratio; (ii) with perforation; (iii) with fins; and (iv) alternative the PTC. It is important to notice that the thermodynamic model axis with fin. They carried out the experiments both in modified framework is conducted to study low-temperature parabolic solar water heater and conventional solar water heater for the same trough concentrators similar in size to smaller-scale commercial operating conditions with Reynolds number ranging from 3000 to solar collector considering that the temperature range in which the 9000. They showed that plain twisted tape with PR ¼ 3 gives better PTC operates is in the range between 70 and 110 C, without phase performance than cross type insert and other type of twisted tape change in the working fluid and unshielded receiver. Nevertheless, due to high whirling effect. They reported that the Nusselt number, if a concentric glass tube is considered around the receiver to friction factor, and thermal performance factor of solar water heater reduce the heat losses or different configurations for the twisted fitted with alternative axis of finned twisted tape insert for PR ¼ 3 tape inserts are proposed, we include the necessary modification of are respectively 1.43e1.2, 1.43e1.32, 1.27e1.11 times superior than the thermodynamic model at the end of Section 3. plain twisted tape of PR ¼ 3 due to better mixing flow with fin effect. The paper is organized as follows: In Section 2 we present the Nevertheless, it is important to point out that the use of twisted background related to the present work. We describe the previous tape inserts in the absorber tube of a PTC has not been investigated PTCs developed by the group which are the fundamentals of our in depth. Only a few studies have been reported in the literature. new PTC and are used to compare the results obtained in this work. In 2013, Ghadirijafarbeigloo et al. [49] studied the enhancement In Section 3 we describe the thermodynamic model of the PTC with of convection coefficient in the receiver tube of a PTC. They re- twisted tape insert, the thermal efficiency using the First Law of ported a simulation study where they analysed the use of a new Thermodynamics is calculated in Subsection 3.1 and the exergy perforated louvered twisted tape in the absorber tube of the PTC. In efficiency using the Second Law of Thermodynamics is calculated in their study they described numerical simulations and an experi- Subsection 3.2. The modification of the thermodynamic model mental validation for three different twist ratios, TR ¼ y/w ¼ 2.67, 4, when glass shielded receiver is used or different configurations of 5.33. They assumed that the flow is turbulent due to the louvered the twisted tape inserts are considered is reported in Subsection perforated surface and the rotational shape of the tape. The heat 3.3. Results and discussion are presented in Section 4. In Subsection transfer rate and pressure drop were determined for fully devel- 4.1 we validate the theoretical model with experimental data and in oped condition at several Reynolds numbers. They reported that addition, in Subsection 4.2 we carry out numerical simulations to the heat transfer coefficient and the pressure drop increase compare the behaviour of the PTC with twisted tape insert with the significantly in comparison with a typical plain twisted-tape. behaviour of the PTC without insert. Finally we present our con- In 2014, Jafar and Sivaraman [50] carried out an experimental clusions at the last section. investigation about the heat transfer and friction factor of a solar parabolic trough collector. They studied the impact of absorber 2. Background device with nail twisted tape of two different twist ratios of y ¼ 2.0, and 3.0 and using Al2O3/water nanofluid as the working fluid at In 2012, five parabolic trough collectors were constructed in the 0.1%, and 0.3% particle volume concentration. The tests were per- Institute of Renewable Energy (Instituto de Energías Renovables, formed in the laminar range 710e2130 using indoor simulation IER [54]) in Temixco, Morelos, Mexico, from which two of them under constant heat flux conditions. They observed that the nail were designed with a 45 rim angle, ”PTC-45-I”, and the remaining twisted tape absorber with nanofluids can significantly improve three with a 90 rim angle, ”PTC-90-I” [53]. These collectors were the heat transfer performance of PTC. They concluded that the experimentally evaluated finding out maximum efficiency values of friction factor increases with twisted tape absorber due to swirl 56% for the 90 PTCs and 35% for the 45 PTCs [53]. The PTC-45-I flow and over particle volume concentration and this is due to the collectors show less efficiency since some of the radiation is not increased nanofluid viscosity while increasing particle volume intercepted on the receiver tube and therefore they have less low concentration. optical efficiency. In 2015, Jafar and Sivaraman [51] carried out an experimental In order to improve the PTC we constructed a new PCT, ”PTC-45- study of an absorber with twisted tape in a PTC. They reported, with II”, with 45 rim angle and twice as long as the previous PTC-45-I. statistical tools, the optimum parameters such as Reynolds number We decided to double the PTC length to elongate the focal length and twist ratio in order to optimize the performance of the device and hence, reduce the edge effects [13]. We achieved a 20% increase taking into account the heat transfer and friction factor. They in the efficiency in the new PTC-45-II compared to the PTC-45-I. concluded that a significant augmentation in the Nusselt number In this work we present a new 90 PTC, namely ”PTC-90-II”. The and a considerable friction factor can be obtained at high Reynolds new PTC-90-II is twice longer than PTC-90-I, and its construction number and low twist ratios parameters. Finally, from the experi- was similar to the one reported in Ref. [13]. One of the main mental design and the analysis of variance (ANOVA), using Design components of the PTC-90-II is its ribs shaping the reflective sheet Expert software, they found that the twist ratio is the parameter to its parabolic shape. The PTC-90-II has 6 ribs made of a 10 mm that most influences the performance of the PTC absorber. In the thick aluminium plate. They were assembled with five 1” schedule same year, Nayak et al. [52] studied the performance prediction of a 40 aluminium pipes in 5 m long sections with 5/16” 1/2” O.A. Jaramillo et al. / Renewable Energy 93 (2016) 125e141 129 setscrews. Once we attached the tubes to the ribs, we proceeded to Table 2 place a 1 1/2” 4” rectangular hollow section (RHS) 5 m long to The specifications of PTC-90-II. support the PTC as a vertebral column. Six aluminium angles of 6” Feature Value Feature Value were used to fixed the (RHS). 2 Aperture area, Aa 5.187 m Reflectivity, r 0.92 2 Fig. 1 shows the PTC-90-II and Table 2 shows its main Receiver area, Ar 0.389 m Absorptivity, ar 0.96 parameters. Aperture width, Wa 1.063 m Emissivity, εr 0.96 fi The thermal performance of the PTCs was experimentally Length, l 4.88 m Optical ef ciency, ho 0.70 External diameter, D 2.54 cm Intercept factor, g 0.85 evaluated according to the ASHRAE 93-1986 (RA 91) standard [55]. o Internal diameter, Di. 2.32 cm Concentration ratio, Co 13.33 The purpose of this standard is to provide test methods for deter- Focal length, f 0.266 m Rim angle, f 90 mining the thermal performance of solar energy collectors that use Material of the tube Copper Working fluid Water ¼ D ¼ 2 single-phase fluids and have no significant internal energy storage. hI 0.6224 2.368( T/GB) at 4 l/min at GB 865W/m In section 8.2.1.1 of the ASHRAE 93 1986 (RA 91) standard a test method for determining the thermal efficiency of a concentrating collector is described. This method is widely used to obtain the et al. [33] in order to establish the enhancement of convection thermal efficiency and to compare it with thermal efficiencies of coefficient in the receiver tube of PTC when a twisted tape insert is similar solar collectors. In Refs. [13] and [53] we reported a com- placed. A schematic representation of the twisted tape insert is plete description of the system for the characterization of the PTCs. depicted in Fig. 2. Table 3 shows the efficiency curves for the different developed The thermal analysis at low temperature PTC with a twisted fl prototypes. tape insert is very similar to the analysis performed, for the at- In the next section we describe a theoretical model to estimate plate collector [56]. The actual useful heat gain Q u ,ofa the thermal behaviour of the PTC-90-II based on the First and concentrating solar collector system is based on the so-called Second Law of Thermodynamics. conceptual energy balance equation and it is given by Ref. [56],
3. Thermodynamic model framework ¼ ð Þ ð Þ εs 4 4 : A passive way to augment the heat transfer in the receiver tube Qu AaGB 1 ho AaGB Arhv Tr Ta Ar Tr Ta of a PTC is by inserting a twisted tape insert such that the flow (1) rotates in the axial direction modifying the Reynolds and the Nusselt numbers [33]. In this section we develop a thermodynamic As for the flat-plate collector, the temperature of the receptor, Tr model framework for estimating the behaviour of the PTC, when in Eq. (1), can be replaced by the fluid temperature at the input of the empty tube is considered and when a twisted tape insert is the receiver tube Tin through the use of the heat removal factor [56]. used. The theoretical framework is based on empirical correlations Therefore, Eq. (1) can be written as to calculate the heat transfer rate and pressure drop for fully developed condition. We include an exergetic analysis to provide useful information for the exergy efficiency of the PTC. It is important to notice that the thermodynamic model , Q ¼ F ðh A G A U ðT T ÞÞ; (2) framework developed in this section is conducted to study low- u R o a B r L in a temperature parabolic trough concentrators similar in size to where F is the heat removal factor, h is the optical efficiency, A is smaller-scale commercial solar collector considering that the R o a the aperture area of the concentrator, G is the direct solar radia- temperature range in which the PTC operates is in the range be- B tion, A is the receiver area, U is the global loss coefficient, and T is tween 70 and 110 C, without phase change in the working fluid. r L a the ambient temperature. Notice that Eq. (2) is usually a second order equation for concentrated solar collectors, however since we 3.1. Modelling the PTC based on the First Law Thermodynamics are dealing with low temperature ranges we neglect the second order term and it is well justify to approximate it with a linear In this subsection, we analyse the thermal efficiency of the equation. collector by using the First Law of Thermodynamics. The model On the other hand, the efficiency hI by First Law of Thermody- takes into account empirical correlations described by Eiamsa-ard namics of the PTC is given by
Fig. 1. Parabolic trough concentrator PTC-90-II. 130 O.A. Jaramillo et al. / Renewable Energy 93 (2016) 125e141
Table 3 Table 4 Thermal efficiencies for previous prototypes of PTCs. Constant values for the Zhukauskas relation.
fi Ef ciency equation (at 4 l/min) Reference ReD Bm
PTC 45 hI ¼ 0.3513 2.117(DT/GB) [53] 0.4e4 0.989 0.330 ¼ D PTC 45-II hI 0.5608 2.468( T/GB) [13] 4e40 0.911 0.385 ¼ D PTC 90 hI 0.5586 2.227( T/GB) [53] 40e4000 0.683 0.466 ¼ D PTC 90-II hI 0.6224 2.368( T/GB) This Work 4000e40,000 0.193 0.618 40,000e400,000 0.027 0.805
, Q F U T T h ¼ u ¼ h R L in a ; I , FR o (3) VvDo Co GB Re ¼ ; (8) Q D n , ¼ where C0 Aa/Ar is the concentration ratio, and Q is the solar where Vv is the velocity of the wind, and Do is the external diameter beam radiation collected by the aperture area of the PTC, of the receiver tube. The variables in Eq. (7) are evaluated at a surrounding temper- , ature which can be considered to be the ambient temperature Ta. Q ¼ AaG : (4) B However it is important to mention that the value of Prr depends on It is important to point out that thermal losses from the receiver the receiver temperature Tr. The values of B and m are listed 2 in Table 4. If the Prandtl number is Pr 10 then n ¼ 0.37, and on the are usually estimated in terms of the loss coefficient, UL½W=m K , contrary, if. Pr>10,n ¼ 0.36. which is based on the area of the receiver, Ar. For a bare tube Therefore, the calculation of the wind loss coefficient, h , is given receiver the loss coefficient UL, considering both convection and v radiation from the surface, and neglecting conduction through the by the following relation [63], support structure since it is isolated, is given by Ref. [56], kv hv ¼ NuD ; (9) Do UL ¼ hr þ hv; (5)
where kv is the thermal conductivity of the air. where hr is the linearized radiation coefficient, and hv is the heat To calculate the coefficients hr and hv it is needed to estimate the transfer coefficient due to wind. receiver temperature Tr.Afirst approximation to calculate the The values of hr can be estimated as [56]. receiver temperature is through an energy balance in the receiver tube neglecting the heat losses in order to estimate the maximum ¼ sε 3; value of Tr. We consider that the receiver tube has a high thermal hr 4 rTr (6) diffusivity and thin walls (the receiver tube is made of copper, ¼ 6 2 where s is the StefaneBoltzmann constant, εr is the emissivity of a 117 10 [m /s]), i.e. we suppose the same temperature at the the surface receptor and Tr is the temperature in the surface of the inner wall and the external surface, such that, receiver. If a single value of hr is not acceptable due to large tem- ð Þ¼ ; perature variations along the flow direction, the collector can be hw Tr Tout hoCoGB (10) divided into small segments, each with a constant hr [56]. where T is the average fluid temperature at the outlet of the To estimate the wind loss coefficient, hv, the Zhukauskas relation out is proposed because a cross-flow over the receiver is considered receiver tube. Therefore, the estimated value of Tr is, [63], hoCoGB Tr ¼ þ Tout; (11) hw m 1=4 n Pr NuD ¼ðBÞ ReD ðPrÞ ; (7) Prr where hw is the convection heat transfer to the interior of the receiver given by Eq. (14). Note that we consider the temperature 6 where the Reynolds number has to satisfy 1 Fig. 2. Schematic representation of the twisted tape insert. O.A. Jaramillo et al. / Renewable Energy 93 (2016) 125e141 131 the Reynolds number Re is estimated when the tube is empty [33], , ¼ ð Þ; hoCoGBAr mCp Tout Tin (12) , ¼ 4m ; fl Re (18) where Tin is the average uid temperature at the inlet of the pDimw receiver tube. Finally, the outlet temperature, T , can be written in out , ¼ terms of the receiver area, Ar piDoL as follows where m and mw are the mass flow and dynamic viscosity of the fluid. h C G ðpD LÞ ¼ o o B o þ : Finally, the value of FR is calculated by Ref. [56], Tout , Tin (13) mCp , " !# 0 mCp U F Ar fi F ¼ 1 exp L ; (19) The coef cient hw can be calculated by means of the Nusselt R A U , r L mCp number NuD, which is defined as: _ fl fl k Nu where m is the heat transfer uid ow and Cp is the heat h ¼ w D : (14) fl fi fi w D transfer uid speci c heat at constant pressure, and the ef ciency i factor F' of the collector is given by Refs [56, 58]. where the value of kw can be obtained from the thermodynamic 1 0 tables reported in the literature [63], and Di is the internal diameter F ¼ U L ; (20) of the receiver tube. 1 þ Do þ Do ln Do The thermodynamic framework for the modelling of PTCs is UL hwDi 2k Di addressed to consider two study cases: a) an empty receiver tube and, b) a receiver tube with a twisted tape insert. where Do and Di are the external and internal diameters of the In the first case, when an empty tube is considered, the receiver tube, respectively, and k is the thermal conductivity of the convective heat transfer coefficient, hw (Eq. (14)), can be obtained tube. from the standard pipe flow equation [56]: It is important to note that the thermodynamic framework developed in this section allows us to calculate the heat removal : : ¼ : ð Þ0 8ð Þ0 4; factor FR and the global loss coefficient UL either for the empty tube NuDE 0 023 Re Pr (15) or when twisted tape inserts are used. It is clear that Eq. (3) corresponds to a linear equation with the where the empirical correlation for the Nusselt number, NuD , is the E ¼ þ well-known the DittuseBoelter equation for heating of the fluid, Re form of y b mx, where FRho is the y-intercept and FRUL/Co is the is the Reynolds number, and Pr is the Prandtl number. slope. Note that the linear fit instead of a 2nd degree fit is accept- Whereas in the particular case of a swirl flow due to the twisted- able in the present case since we are dealing with solar concen- tape insert, the coefficient hw (Eq. (14)) can be calculated by using trators for low temperature [56]. In the literature, linear models of the equation, thermal efficiency for solar concentrators for low temperature have been reported by Rabl [57], Duffie and Beckman [58], Stine and : : : y 0 6 Harrigan [59], and Kalogirou [56]. Nu ¼ 0:224ðReÞ0 66ðPrÞ0 4 ; (16) DTT w 3.2. Analysis of the PTC based on the Second Law of where NuDTT is the empirical correlation from the experimental results reported in Ref. [33], and the relation TR ¼ y/w is twist ratio, Thermodynamics where y is the tape pitch length, and w is the tape width. This empirical correlation was obtained by using twisted tape insert In this subsection we developed a model for estimating the fi fi with four different twist ratios (y/w ¼ 2.5, 3.0, 3.5 and 4.0) for Second Law ef ciency of the PTC. The set up is de ned by the Reynolds numbers range between 2700 and 21,000 under uniform receiver tube, where different heat transfers occur across the wall- fl fl fl heat flux conditions. The test tube was made of copper, the twisted uid, and the uid ow. The system comprises dissipative phe- tapes were made of aluminium strips, and the tests was developed nomena (or spontaneous non-equilibrium processes) since the in a uniform heat flux tube with water as working fluid. The twisted natural tendency of system is to achieve equilibrium with their tapes are considered to be inserted at the core tube along the tube surroundings, and therefore the irreversibilities always occur in the providing sufficient contact surface between the tapes and tube actual process. , wall for the firm attachment of the tapes to the tube without the The overall entropy generation rate Sgen of the PTC can be need of any extra fitting. During the test reported in Ref. [33], the assessed by considering the simpler form [60,61], fl 0 1 tube was heated by continually winding exible electrical wire , , , , ! fl , D providing a uniform heat ux condition and the average Nusselt ¼ @Q loss þ Q u Q A þ m P ; fl Sgen r (21) numbers were calculated by considering all uid properties at the Ta Tin Ts Ta overall bulk mean values. Note that variation of heat transfer is described by means of Nusselt number Nu because it is the ratio DTT where the first term in parenthesis is due to the heat transfer rate, and of convective to conductive heat transfer across the boundary. In the secondterm isdue to the irreversibilitycaused by the fluid friction. this context, convection includes both advection and diffusion as a In Eq. (21), Ta is the ambient temperature and Ts is the apparent fin effect due to the twisted tape. temperature of the Sun as an exergy source which is of the order of In both study case, the empirical correlations for the Nusselt 4500 K [62]. The pressure difference is defined as DP>0 since there is numbers, Eqs. (15) and (16), the Prandtl number, Pr, is defined by, a pressure drop between the inlet and outlet of the absorber tube. The n PTC has an aperture area, Aa, that receives direct solar radiation, GB,at Pr ¼ ; (17) _ a an energy rate from the sun Q as it, is shown in Eq. (4) In Eq. (21), the, useful heat gain Q u , is established by Eq. (2), where n is the kinematic viscosity and a is the thermal diffusivity, and the heat transfer Q loss represents the heat loss to the ambient 132 O.A. Jaramillo et al. / Renewable Energy 93 (2016) 125e141 established by, , , 3 , , , Ta ð Þ 32 m l Q u 1 f 2 r2 5 ¼ ; Tin p D Q loss Q Q u (22) ¼ ED ¼ i : hII 1 , , (30) T Es Q 1 a and the pressure drop DP can be calculated by, Ts r 2 Note that if the friction factor, f, is neglected, it is possible to 4l Vw DP ¼ f ; recover the Second Law Efficiency of a solar thermal collector, Di 2 where l is the length of the absorber tube, Di is the internal diam- , Ta 1 T eter of the tube, r is the density of the fluid, f is the friction factor ¼ Qu in ; , hII , (31) and V ¼ m=rA is the velocity of the fluid. T w , Q 1 a Ts Rearranging Eq. (21), the entropy generation rate, Sgen ,of the PTC can be written as, where hII establishes the rate of exergy associated with the solar , 3 ! , , , radiation incident on the collector surface, that has been converted 1 Ta Ta 32 m l into the delivered exergy by the collector. Sgen ¼ Q 1 Q u 1 þðf Þ : T T T p2 r2 5 fi a s in Di Rearranging, Eq., (30), and considering the thermal ef ciency (Eq. ¼ = (23) (3)), as hI Q u Q , we can write , 0 1 , 3 0 1 note that there is a contribution from the useful heat gain, Q , T T u 1 a ðf Þ 32 m l 1 a and the friction factor, f, either in the presence or absence of the B Tin p2 r2 D5 C F U Tin h ¼ @F h i A @ R L A twisted tape insert. II R o Ta Ta Co Ta 1 AaGB 1 1 The correlation of the friction factor for the empty tube can be Ts Ts Ts expressed as [33]. Tin Ta : : GB f ¼ 0:376Re 0 259; (24) E (32) and, on the other hand, the friction factor when the twisted tape is It is important to note that Eq. (32) also corresponds to a linear used is calculated by Ref. [33]. equation with the form of y ¼ bþmx, where 1:31 0 1 0:52 y , 3 ¼ : : Ta fTT 65 4Re (25) 1 ðf Þ 32 m l w B Tin p2 r2 D5 C i ; @FRho A (33) On one hand, the exergy supplied via solar energy to the PTC is Ta Ta 1 AaGB 1 calculated by Ref. [60], Ts Ts , , Ta corresponds to the y-intercept and the slope is given by, Es ¼ Q 1 ; (26) Ts 0 1 1 Ta some of this exergy is destroyed due to irreversible processes. F U Tin @ R L A: (34) It is important to point out that the exergy EU delivered by a PTC Co 1 Ta system is given by, Ts , , ¼ ðð Þ ð ÞÞ; EU m ho Taso hi Tasi (27) , where m is the mass flow rate, ho and hi are the specific enthalpies, at the outlet and the inlet of the PTC, respectively, and so and si are 3.3. Glass-shielded receiver and other configurations for the twisted fi the speci c entropies, at the outlet and the inlet, respectively., tape inserts However, it is possible to calculate, the exergy delivered EU by considering the useful energy, Q u at the temperature Tin. The overall heat loss coefficient could be improved by using a Therefore PTC delivers exergy EU at a rate: glass-shielded receiver. If a concentric glass tube is considered , , around the receiver to reduce the heat losses where the space be- Ta tween the receiver and the glass is usually evacuated and therefore EU ¼ Q u 1 : (28) Tin the convection losses are negligible, in this case, the global loss coefficient, UL based on the receiver area Ar, is given by Ref. [56]. The exergy destruction ED of the system is calculated by considering its irreversibility I, established by the Gouy-Stodola " # 1 theorem, Ar 1 UL ¼ þ ; (35) þ ; , hw hr;c a Ac hr r c ED ¼ TaSgen ¼ I; (29) instead of the previously proposed by Eq. (5), where hr,c a is the and refers to the degraded useful energy when real processes are linearized radiation coefficient from cover to ambient estimated by carried out. Eq. (6), Ac is the external area of glass cover, and hr,r c is the line- On the other hand, the exergy efficiency hII is defined by arized radiation coefficient from receiver to cover, given by Ref. [56], O.A. Jaramillo et al. / Renewable Energy 93 (2016) 125e141 133 removal factor, the thermal efficiency calculated by using the First 2 2 s T þ T ðTr þ TcÞ and the Second Law of Thermodynamics, the friction factor, and the r c hr;r c ¼ ; (36) entropy generation number. 1 þ Ar 1 1 εr Ac εc 4.1. Experimental validation where εr and εc are the emissivities of the receptor and the glass cover, respectively, and Tr and Tc are the temperatures of the re- In this subsection we validate the theoretical model with ceptor and the glass cover, respectively. experimental data. We consider the empty tube and a twisted tape fi To estimate hr,r c it is necessary calculate the temperature of the insert in order to evaluate the ef ciency of the PTC. We experi- glass cover, Tc. This temperature is closer to the ambient tempera- mentally evaluated the thermal performance of PTC at low- ture than the receiver temperature.Tr. The estimation of the tem- temperature testing according to the ASHRAE 93-1986 (RA 91) perature Tr can be carried out by considering Eq. (11) and the values standard [55]. This standard is widely known and provides test fi of Tc be obtained from Ref. [56], methods for determining the thermal ef ciency of a concentrating collector (section 8.2.1.1).The experimental procedure imple- þ þ Arhr;r cTr Ac hr;c a hw Ta mented in this work is the same as the one reported in Ref. [13]. Tc ¼ : (37) Arhr;r c þ Ac hr;c a þ hw The experimental evaluation of PTC was carried out in Temixco, Morelos, Mexico (18 50021.8200N, 99 14007.5900W, 1254 m.a.s.l.) by fi The procedure to nd Tc is by iteration, i.e., estimate UL from Eq. using outdoor experimental measurements where the solar beam (35) by considering an arbitrary value of T (close to T ). Then, if T 2 c a c radiation at noon was GB ¼ 865 W/m , the ambient temperature obtained from Eq. (37) differs from original value, iterate. Usually, was Ta ¼ 20C+, and the wind velocity was Vv ¼ 2.3 m/s. It is no more than two iterations are required [56]. important to point out that during the evaluation process of the PTC, The theoretical framework developed in this section is based on it was rotated about a horizontal eastewest axis with an adjustment empirical correlations for the Nusselt number, NuD, (Eqs. (15) and in the northesouth plane in order to minimize the angle incidence. (16)), and for the friction factor, f (Eqs. (24) and (25)), either in Additionally, the PTC was evaluated under steady irradiation and the presence or absence of the twisted tape insert. If other con- steady state fluid flow rate during the experiment procedure. fi gurations are considered for the twisted tape inserts, Eqs. (16) and Fig. 3 shows the thermal efficiency and the enhancement factor fi (25) can be modi ed by the most suitable empirical correlations. for the thermal efficiency, defined as For example: if the tube is fitted with the counter-swirl flow gen- h erators [33], the Nusselt number is established by, D ¼ I;TT ; hI (42) hI;E 0:9 ¼ : ð Þ0:66ð Þ0:4 y ; NuDCT 0 473 Re Pr (38) w where hI,TT is the thermal efficiency of the receiver tube with twisted tape insert and h is the thermal efficiency of the empty fi I,E and the friction factor is de ned by, tube. The points show the instantaneous measured thermal effi- 1:01 ciency of the PTC with twisted tape insert (purple points) and of the 0:53 y fi fCT ¼ 72:29Re : (39) empty PTC (green points). On the other hand, the thermal ef - w ciencies calculated from the theoretical model are shown with the or in the case where the tube is fitted with the co-swirl flow gen- straight lines for both cases. Additionally, as the green line shows, D erators [33], the Nusselt number is defined by, the enhancement factor increases as T/GB increases. In order to implement the theoretical model we consider two 0:61 0:66 0:4 y study cases: a) an empty receiver tube and, b) a receiver tube with a NuD ¼ 0:264ðReÞ ðPrÞ ; (40) ¼ CoT w twisted tape insert y/w 2. It is important to point out that the tube of PTC was made of copper and the twisted tapes were made of and the fiction factor is calculated as, aluminium strip in order to validate the experimental results re- ported in Ref. [33]. The twisted tapes were inserted at the core tube 0:84 0:52 y along the tube providing sufficient contact surface between the fCoT ¼ 41:7Re : (41) w tapes and tube wall for the firm attachment of the tapes to the tube fi In the next section we show our results and a discussion about without the need of any extra tting. the using of twisted tape insert in a parabolic trough concentrator In Table 5 we describe the main key features in the imple- that operates a low temperature range and without the use of a mentation of the theoretical model, corresponding to the thermo- glass shielded receiver. physical properties of saturated water at a pressure of 1.21 atm (absolute pressure) and air at 20 C and an pressure of 1 atm. These values were taken from Ref. [63] for averaged properties at the 4. Results and discussion operating range of 25e90 C. In Table 6 we report the values of the theoretical thermal effi- In this section we present the experimental validation and the ciency, hI in (Eq. (3)), the heat removal factor, FR, in Eq. (19) and the numerical simulation of important thermodynamical quantities. In overall heat loss coefficient, UL, in Eq. (5), for both two study cases. As particular, we perform an experimental validation of the PTC with it is shown in the results, the heat removal factor, FR, increase close to twisted tape insert in Subsection 4.1. We report the instantaneous 3% while the overall heat loss coefficient, UL, decrease in about 1.5% measured thermal efficiency and compared it with the efficiency when the twisted tape insert is placed in the receiver tube. calculated from the theoretical model. Additionally we compared The results show that it is possible to enhance the efficiency the theoretical efficiency of the PTC with the twisted tape insert close to 3.5% when a twisted tape insert is used. Note that the with the efficiency of an empty PTC. In Subsection 4.2 we present twisted tape insert inherently affects the performance of the heat numerical simulations to show the behaviour of the most impor- transfer in the absorber tube. If the heat removal rate is increased, tant quantities of the system such as the Nusselt number, the the average absorber temperature decreases and more useful heat 134 O.A. Jaramillo et al. / Renewable Energy 93 (2016) 125e141 Fig. 3. Comparisons of experimental data and predicted values from the theoretical model. Table 5 Relevant values used into the modeling process. Property Value Property Value 3 Density, rw 992.23kg/m Twist ratio, y/w 2 3 Dynamic viscosity, mw 0.653 10 kg/ms Tape width, w 0.023 m , , Heat capacity, Cp,w 4.1785 kJ/kg K Mass flow rate, m 0.0331 kg/s 2 , Kinematic viscosity, nw : 6m 2.0l/min 0 659 10 s Volumetric flow rate, V 2 Kinematic viscosity, nair : 6m Ambient temperature, Ta 20 C 0 153 10 s 2 Thermal diffusivity, aw : 7m Wind velocity, Vv 2.3 m/s 1 522 10 s Thermal conductivity, k 380.5 W/m,K B 0.683 Thermal conductivity, kair 0.0263 W/m,K n 0.37 Thermal conductivity, kw 0.631 W/m,K mm 0.466 Values used in the modelling process. is delivered. since it describes the ratio of convective to conductive heat transfer across the receiver tube. We define the enhancement factor for the Nusselt number DNuD, which describes the activity when a twisted 4.2. Numerical simulations tape insert is used, as Once the theoretical model is validated based on experimental : data, we carry out different simulations in order to compare the Nu : y 0 6 DNu ¼ DTT ¼ 9:739ðReÞ 0 14 ; (43) behaviour of PTC when twisted tapes inserts are used with respect D NuDE w to the empty tube. For the numerical simulations we consider five ¼ ¼ different twist ratios (TR y/w 1,2,3,4,, and 5), that operate under where NuDTT corresponds to the Nusselt number when twisted tape fl ¼ : six different volumetric ow rates (V 1 0, 2.0, 3.0, 4.0, 5.0 and inserts are used and NuDE is the Nusselt number for the empty tube. 6.0 l/min). During the simulation the heat transfer rate and pres- Note that DNuD does not dependent on the Prandtl number because sure drop are determined for fully developed conditions for the kinematic viscosity n and the thermal diffusivity a remain different Reynolds numbers based on the tube diameter and mean practically constant in the presence of an empty tube or when the flow velocity. twisted tape is inserted. We begin by studying the behaviour of the Nusselt number, Fig. 4 shows the dependence of DNuD on the Reynolds number Table 6 Theoretical values of the thermal efficiency. , ¼ : kg Empty tube y/w ¼ 2 Variation m 0 0331 s hI[ ] 0.592009 2.33235DT/GB 0.610655 2.37068DT/GB þ3.5% þ FR[ ] 0.8457 0.8723 3.1% W 36.76 36.22 1.5% UL m2 K O.A. Jaramillo et al. / Renewable Energy 93 (2016) 125e141 135 Fig. 4. Enhancement factor for the Nusselt number, DNuD. (Re), in the range of 1350e8350, and on the twist ratio (TR), in the Fig. 5 shows the behaviour of both the variation factor for the range of 1e5. global loss coefficient, DUL, and the removal factor, DFR, as a func- As it is shown in Fig. 4, the values of DNuD increase as the tion of the Reynolds number (Re), in the range of 1350e8350, and Reynolds number and the twist ratio decrease. The results show the twist ratio (TR), in the range of 1e5. that the highest value of DNuD is around 3.5 corresponding to a As it is shown in Fig. 5, the variation factor for the global loss Reynolds number (Re) of 1350 and at a twist ratio equal to 1. Note as coefficient is diminished as the Reynolds number and the twist the twist ratio increases, the increment of DNuD is neglected and ratio decrease, therefore the energy losses to the ambient are indeed, it tends to 1. diminished by the using of the twisted tape inserts operating at low On the other hand, the variation factor for the global loss coef- volumetric flow rate. The results show that the minimum value for ficient, DUL, calculated using twisted tape inserts with respect to the DUL is close to 0.96 and the variation of the values of DUL are the empty tube, is defined by neglected for high twist ratios and high Reynolds numbers. U ; In the same Fig. 5, the removal factor exhibits a similar to the D ¼ L TT UL (44) one of the Nusselt number. The values of DFR increase as the Rey- UL:E nolds number and the twist ratio decrease. By comparing the D D D and the enhancement factor for the removal factor DF defines the behaviour between FR and NuD, it can be seen that FR decreases R D ratio of useful energy calculated using twisted tape inserts with faster than NuD at the same Reynolds numbers and its behaviour D respect to the empty tube, is not linear. The results show that the highest value of FR is close D ! to 1.077 and the values of FR are neglected for high twist ratios in 0 0 1 the same way that DNu . U ; F A D L TT TT r 1 exp , The enhancement factor of the thermal efficiency Dh , which B mCp C I FR;TT UL:E B ! C fi DFR ¼ ¼ @ A; (45) accounts for the increase in thermal ef ciency when the twisted F ; U ; 0 R E L TT ; fi UL EFEAr tape is placed in the receiver tube of the PTC, is de ned by, 1 exp , mCp where FR,TT is the heat removal factor when twisted tape inserts are used and FR,E is the heat removal factor for the empty tube. Fig. 5. Variation factor for the global loss coefficient, UL, and enhancement factor for the removal factor, DFR. 136 O.A. Jaramillo et al. / Renewable Energy 93 (2016) 125e141 Fig. 6. Thermal efficiency, hI, and enhancement factor, DhI. D fi and includes the enhancement factor hI for each thermal, ef - ciency. We consider 6 different volumetric flow rates (V ¼ 1:0, 2.0, U ; L TT Tin Ta 3.0, 4.0, 5.0 and 6.0 l/min), and 5 different twist ratios (TR ¼ y/ FR;TT ho h Co GB D ¼ I;TT ¼ : w ¼ 1,2,3,4, and 5). hI (46) h ; U ; fi I E L E Tin Ta As it is shown in Fig. 6, the thermal ef ciency, hI, is higher as the FR;E ho Co GB twisted ratio gets closer to 1, regardless of the volumetric flow. On the contrary, as the twisted ratio increases, the thermal efficiency Fig. 6 shows the thermal efficiency, Eq. (3), for 30 study cases O.A. Jaramillo et al. / Renewable Energy 93 (2016) 125e141 137 Fig. 7. Change in the friction factor, Df. , decreases. Additionally, as the flow rate increases the efficiency cases corresponding to 6 different volumetric flow rates (V ¼ 1:0, increases, and at high flow rates the efficiency becomes indepen- 2.0, 3.0, 4.0, 5.0 and 6.0 l/min), and 5 different twist ratios (TR ¼ y/ dent of the twisted ratio. On the other hand, as it can be seen in w ¼ 1,2,3,4, and 5). This figure shows the augmentation of DhII for D fl Fig. 6, the enhancement, factor, hI, is close to 9% in the case of a different volumetric ow rates and different twist ratios as function volumetric flow rate V ¼ 1:0l=min and twist ratio y/w ¼ 1. The use of the three parameters defining the operating conditions: the solar fl fl of twisted, tape inserts when the PTC operates at volumetric ow irradiance GB, i.e. (Tin Ta)/GB, the uid inlet temperature Tin, and the rate V ¼ 1:0l=min shows an enhancement factor, DhI in the range of ambient air temperature Ta. It is possible to consider two cases for 9e4%. In the cases when the volumetric flow rate is in the range of the values of DhII, one corresponding to values less than unity and 2e3 lpm, and taking into account twist ratios between 1 and 2, the the other one corresponding to values greater than unity. For low values of DhI are in the range of 5e3%. Moreover, as it is shown, in volumetric flow rates DhII is greater than one regardless of the twist _ the case of high volumetric flow rates and high twist ratios the ratio. However for flow rates m 3 the behaviour of DhII depends values of DhI are close to 1%, and therefore, in such conditions, there on the twist ratio. are no advantages to using twisted tape inserts in order to enhance As it is shown in Figure 8, there are some values of the the performance of the PTC. enhancement factor, DhII, greater than unity, therefore there are It is important to point out that when a twisted tape insert is some advantages in the use of twisted tape inserts in order to used in the PTC, we must consider the change in the friction factor, enhance the performance of the PTC. This behaviour is basically Df, which is defined by, established for small volumetric flow rates between 1 and 2 lpm. Other combination of volumetric flow rates and twisted tape in- 1:31 serts that exhibit a Dh bigger than unity is for example by using fTT 0:261 y II Df ¼ ¼ 173:936 Re : (47) twist ratios between 1 and 2 at different flow rates. However, in fE w general, for cases where the Reynolds number is high combined D The change in the friction factor, f, as a function of the Reynolds with high twist ratios the values of DhII are less than the unity, and number and the twisted ratio is shown in Fig. 7. Once again, we therefore there are no advantages to using the twisted tape inserts encounter the same behaviour, the friction factor increases as the in order to enhance the performance of the PTC. Reynolds number and twisted ratio decreases. Indeed, the pressure On the other hand, the effect of the augmentation entropy on drop increases significantly when a twisted tape insert is consid- the thermodynamic performance is evaluated by comparing the ered at both low Reynolds numbers and low twisted ratios. Note for entropy generation rate before and after implementing the twisted example that the value of fTT is close, to 26 times the value of fE in tape inserts. The augmentation entropy generation number, NS,a,is the case of a volumetric flow rate of V ¼ 1:0l=min, corresponding to defined as [60], a Reynolds number of 1389.67, and a twist ratio of y/w ¼ 1. However , , , 3 the values of Df drastically decrease for high twist ratios. , Ta Ta þð Þ 32 m l Q 1 Q ; 1 f 2 2 5 D Ts u TT Tin TT p r D The enhancement factor, hII, established by considering the Sgen;TT i N ; ¼ , ¼ : Second Law of Thermodynamics as follows, S a , , , 3 Ta Ta þð Þ 32 m l Sgen;E Q 1 Q ; 1 f 2 2 5 Ts u E Tin E p r D i , , 3 Ta ð Þ 32 m l (49) Qu;TT 1 fTT 2 r2 5 h Tin p D D ¼ II;TT ¼ i ; hII , (48) _ h ; , 3 where S ; is the generation rate when twisted tape insert is used II E Ta ð Þ 32 m l gen TT Q ; 1 f 2 2 5 _ u E Tin E p r D i and Sgen;E corresponds to the entropy generation rate for the empty absorber tube. As the entropy generation number gets smaller, the takes into account the exergetic behaviour of the PTC when a heat exchange process exhibits a better performance. Therefore, the twisted tape is used in the receiver tube. entropy generation analysis due to fluid flow and heat transfer Fig. 8 shows the efficiency calculated by the Second Law of evaluates the effectiveness of different configurations. Indeed, the Thermodynamics, hII, and the enhancement factor, DhII for 30 study augmentation techniques yielding NS,a less than unity are 138 O.A. Jaramillo et al. / Renewable Energy 93 (2016) 125e141 Fig. 8. Second Law efficiency, hII, and enhancement factor, DhII. thermodynamically better since they enhance heat transfer and other one corresponding to values greater than unity. reduce the irreversibility of the apparatus [60]. As Fig. 9a shows, a volumetric flow rate between 1 and 2 liter per Fig. 9 shows the augmentation entropy generation numbers for minute, regardless of the twist ratio, allows to obtain a NS,a less than different volumetric flow rates and different twist ratios as function unity. This region describes an enhancement in heat transfer and a of the three parameters defining the operating conditions: the solar reduction in the irreversibility of the PTC. Note that the best con- fl ¼ irradiance GB, i.e. (Tin Ta)/GB, the uid inlet temperature Tin, and the dition occurs, when the twist ratio is y/w 1 and the volumetric ambient air temperature Ta. It is possible to consider two regions for flow rate is V ¼ 1:0 lpm. Note that Fig. 9b shows other combina- NS,a, one region corresponding to values less than unity and the tions of volumetric flow rates and twisted tape inserts that describe O.A. Jaramillo et al. / Renewable Energy 93 (2016) 125e141 139 Fig. 9. Augmentation entropy generation number, NS,a. a NS,a less than the unity, for example, twist ratios between 1 and 2 by using a glass-shielded receiver. However, considering the tem- and volumetric flow rates between 3 and 4 lpm. perature range in which the PTC operates (between 70 and 110 C), On the other hand, as it can be seen in Fig. 9b, there is a region we consider that augmenting the thermal availability by adding a with values of NS,a greater than unity, therefore there are no ad- glass tube is not necessary. Reference [14] reports that the instan- vantages to using twisted tape inserts in order to enhance the taneous thermal efficiency for low temperature PTC's. As can be performance of the PTC. This region is located for example at seen in Fig. 10, the use of a glass shield does not translate into a volumetric flow rates between 4 and 6 lpm combined with twist significant increase in the efficiency for temperatures under 100 C. ratios between 4 and 5. It should also be mentioned that the use of glass-shielded receivers In Table 7 we summarize the behaviour of the augmentation in developing countries represents an increase in the associated entropy generation number, NS,a for the different study cases. costs given that such tubes are not fabricated locally and must be It is clear that the overall heat loss coefficient could be improved imported. The use of twisted tape to enhance the thermal 140 O.A. Jaramillo et al. / Renewable Energy 93 (2016) 125e141 Table 7 Values of augmentation entropy generation number. Twist ratio TR / y/w ¼ 1 y/w ¼ 2 y/w ¼ 3 y/w ¼ 4 y/w ¼ 5 , , Re[ ] V½l=min m½kg=s 1.0 0.0165 1389.67 NS,a<1NS,a<1NS,a<1NS,a<1NS,a<1 2.0 0.0331 2779.34 NS,a<1NS,a<1NS,a<1NS,a<1NS,a<1 3.0 0.0496 4169.02 NS,a<1NS,a<1NS,a<1NS,a<1 NS,a>1 4.0 0.0661 5538.69 NS,a<1NS,a<1NS,a<1 NS,a>1 NS,a>1 5.0 0.0827 6948.36 NS,a<1NS,a<1 NS,a>1 NS,a>1 NS,a>1 6.0 0.0992 8338.03 NS,a<1 NS,a>1 NS,a>1 NS,a>1 NS,a>1 The bold values highlight the numbers bigger than unity. performance of low-temperature PTCs can be a solution with a low the pressure drop through the tube length. The analysis based on cost associated instead of using a glass-shielded receiver. the Second Law of Thermodynamics shows that the enhancement In the next section we present our main findings about the use of the exergy efficiency takes place only under certain conditions of twisted tape inserts in order to enhance the efficiency of a where the augmentation entropy generation number NS,a is less parabolic trough solar collector for low enthalpy processes. than one. On the contrary, if NS,a is bigger than one it is not worth to use the twisted tape insert. On the other hand, from our results, it is clear that the thermal efficiency increases as the volumetric flow 5. Conclusions increases. Additionally, our results suggest that a minimum irre- versibility rate may exist for a particular combinations of the twist The thermodynamic model framework presented here allows to ratio y/w and the Reynolds number. describe a detailed simulation of a parabolic trough solar collector It is worth to keep shedding more light in these passive tech- for low enthalpy processes without changes of phase in the thermal niques for heat transfer enhancement. For instance, in future work fluid. The model allows to predict the thermal efficiency and the it will be worth to perform a similar analysis with other kind of exergy efficiency of a PTC when a twisted tape insert is used in inserts and study their effect in PTCs. order to increase its performance. The simulation results show that in the presence of a twisted Acknowledgements tape insert, the Nusselt number, the removal factor, the friction factor and the thermal efficiency increase with respect to the ones The authors wish to thank Ing. Jose de Jesús Quinones~ Aguilar associated to an empty tube, as both the twist ratio (y/w) and the for his technical assistance in the development of the experimental Reynolds number decrease. On the contrary, the results show these device and evaluation. We thank also Dr. Maximiliano Valdez quantities does not present an enhancement when the twist ratio Gonzalez for their technical support in the network management. (y/w) increases. Monica Borunda wish to thank Consejo Nacional de Ciencia y Tec- From this work we can conclude that a twisted tape insert is a nología, CONACYT, support for her Cathedra Research Position with good passive way to augment the heat transfer in a PTC only under ID 71557, and to Instituto de Investigaciones Electricas, IIE, for its certain conditions. These optimal conditions to enhance the heat hospitality. This work was supported by PAPIIT-UNAM under the transfer of the system correspond to a system with twist ratio close project IT100514. to 1, and low Reynolds number corresponding to small flow rates of the order of 1lpm. It is clear that typical twisted tape inserts enhance heat exchange between the absorber tube surface and the References thermal fluid by generating a swirling flow, but they also increase [1] A. Fernandez-García, E. Zarza, L. Valenzuela, M. Perez, Parabolic-trough solar collectors and their applications, Renew. Sustain. Energy Rev. 14 (2010) 1695e1721. [2] M. 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