Volume 17 Number 4
August 2020
Article Contents
Angelica Palacios, Dario Amaya, Olga Ramos. Parabolic Trough Collector and Central Receiver Coupled with Fresnel Lens: Experimental Tests. International Journal of Automation and Computing, 2020, 17(4): 572-587. doi: 10.1007/s11633-019-1220-9
Cite as: Angelica Palacios, Dario Amaya, Olga Ramos. Parabolic Trough Collector and Central Receiver Coupled with Fresnel Lens: Experimental Tests. International Journal of Automation and Computing, 2020, 17(4): 572-587. doi: 10.1007/s11633-019-1220-9

Parabolic Trough Collector and Central Receiver Coupled with Fresnel Lens: Experimental Tests

Author Biography:
  • Angelica Palacios received the B. Sc. degree in mechatronic engineering, and the M. Sc. degree in project management from Military University, Colombia (UMNG) in 2015 and 2019, respectively. Currently, she is a Ph. D. degree candidate in applied science at the Research Group GAV (Virtual Applications Group), Military University, Colombia and she is also working as a research assistant in the field of sustainable energy and renewable energies at GAV, Colombia. Her research interests include renewable energy, optimization systems, thermodynamics, solar collector and solar energy.E-mail: u1801712@unimilitar.edu.coORCID iD: 0000-0003-3698-9466

    Dario Amaya received the B. Sc. degree in electronics engineering from Antonio Narino University, Colombia in 1995, and the M. Sc. degree in teleinformaticin from Faculty of Engineering, District University Francisco Jose de Caldas, Colombia in 2007. He received the Ph. D. degree in mechanical engineering from Campinas State University, Brazil in 2011, working on hybrid control. He has worked as a professor and a researcher at the Military University, Colombia since 2007. He has been involved in robotics, mechatronics and automation areas. His research interests include robotics, mechatronics and industrial automation. E-mail: dario.amaya@unimilitar.edu.co (Corresponding author) ORCID iD: 0000-0002-1490-4970

    Olga Ramos receiving the B. Sc. degree in electronics engineering from Antonio Narino University (UAN), Colombia in 1998. She obtained her specialization certificate in electronic instrumentation at UAN, Colombia in 2000, and received the M. Sc. degree in teleinformatics from Faculty of Engineering, District University Francisco Jose de Caldas (UFJC), Colombia in 2007. She received the Ph. D. degree in engineering at District University Francisco Jose de Caldas, Colombia in 2017. Currently, she is a Ph. D. degree candidate in engineering at UFCJ, Colombia. Right now, she is working as a teacher at UMNG and as researcher in GAV in different mechatronics fields like system control and industrial automation. Her research interests include control systems and industrial automation.E-mail: olga.ramos@unimilitar.edu.co

  • Received: 2019-10-01
  • Accepted: 2019-12-18
  • Published Online: 2020-04-14
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Parabolic Trough Collector and Central Receiver Coupled with Fresnel Lens: Experimental Tests

Abstract: Renewable energies have a high impact on power energy production and reduction of environmental pollution worldwide, so high efforts have been made to improve renewable technologies and research about them. This paper presents the thermal performance results obtained by simulation and experimental tests of a parabolic trough collector with central receiver coupled to Fresnel lens, under different configurations on the pipe. The simulation method was computational fluid dynamics (CFD) analysis in SolidWorks ® software tool, which works with Naiver-Stokes equations to converge on a solution. Experimental tests were formed with all configurations proposed and three observations for each one, a total of 12 observations were performed in all research. As a result, the best thermal performance in simulation was achieved with the Fresnel lens and black pipe collector, with a maximum temperature of 116 °C under 1 000 W/m2 radiation, the same system achieved in experimental tests a maximum temperature of 96 °C with a radiation of 983 W/m2.

Angelica Palacios, Dario Amaya, Olga Ramos. Parabolic Trough Collector and Central Receiver Coupled with Fresnel Lens: Experimental Tests. International Journal of Automation and Computing, 2020, 17(4): 572-587. doi: 10.1007/s11633-019-1220-9
Citation: Angelica Palacios, Dario Amaya, Olga Ramos. Parabolic Trough Collector and Central Receiver Coupled with Fresnel Lens: Experimental Tests. International Journal of Automation and Computing, 2020, 17(4): 572-587. doi: 10.1007/s11633-019-1220-9
    • Some technologies originating from renewable resources have been established as solar power, thermal energy, wind energy, salinity gradients, kinetic energy[1]. The first one uses the sun as resource since the sun is a source of sustainable and abundant energy. Therefore, solar energy within renewable energies is the most promising source to replace highly polluting fossil fuels. The flow of radiation emitted by the sun towards the earth′s surface can be highly exploitable in photovoltaic or concentration technologies to obtain thermal energy[2]. Concentrating technologies as solar collectors have the capacity to generate high temperatures in the range of 100 °C – 400 °C, associated to a high thermal efficiency. Applications of concentrated heat are: chemistry applications, cooling, freezing, desalination, energy production, hydrogen production among others[3].

      For electricity production with renewable resources, we found technologies such as a parabolic dish, linear Fresnel collectors, solar tower and parabolic trough collectors[46]. Parabolic trough collector is the most commonly used in energy plants for high production[7, 8]. These systems are composed by a receiver pipe known as absorber, and to improve its absorption, a selective coating. To reduce heat losses in the absorber, a concentric glass cover is used. In addition, to reduce heat losses in the absorber, a concentric glass cover is used, in order to improve energy efficiency which is a fundamental element to optimize several energy systems[9]. According to this, the optical performance depends on two parameters, pipe absorptance and cover transmittance[10]. In some cases, a parabolic trough collector is coupled with a Fresnel lens to improve the concentrating process on the surface. The Fresnel lens consist on lens which focus lights to a point or a line and are distributed on a curve or a plane[11, 12]. The optical phenomenon of the Fresnel lens is based on refraction, in this case, a ray of light crosses a transparent medium with different density than the air, so it deviates from the normal vector, this occurs due to changes in the speed of light[13]. Currently, there are two types of Fresnel lenses: line focus and point focus[14, 15].

      Some works have been developed in the Fresnel solar collector field. In [16], a hybrid solar collector based on a Fresnel 1 090× lens was researched with the purpose of improving the optical performance. The study consists of simulation and an experiment with the Fresnel solar concentrator under outdoor condition. Results obtained in this work indicated that the optical efficiency is in strong agreement with the simulation. In addition, the concentrating process in a solar collector based on a linear Fresnel lens was investigated experimentally in [17]. Through experimental tests, results show in this paper a thermal efficiency of 50% when fluid temperature was 90 °C. Also, energy losses were around 0.578 W/m2K, which means lower energy losses compared to a receiver pipe without concentrating.

      The thermal performance of a linear Fresnel solar collector with different types of cavities has been developed in [18]. The paper presents an optical performance based on the Monte Carlo ray trace method. The cavity with the highest optical efficiency of 81.2% was a triangular cavity receiver. Thermal performance associated was 30% with a maximum temperature of 120 °C. Through this work, it was possible to identify that the Fresnel lens solar collector with triangular cavity receiver boosts a better performance in terms of both optical and thermal characteristics. In [19], a comparative analysis was carried out of the collector performance. This system uses linear Fresnel lens, a cylindrical cavity and a glass cover on pipe, thus it was possible to concentrate most of the rays inside the black body cavity.

      A novel cavity is presented in [20], where a parabolic trough collector is coupled to an arc-shaped linear cavity receiver with a lunate channel based on the black cavity effect principle. In this case, the effects of the inclination angle, collecting temperature, surface emissivity and aperture width on the heat losses were analyzed. Results show that the natural convection heat loss is significantly affected by the inclination angle, while the radiation heat loss is mainly affected by the surface emissivity and the collecting temperature, and the aperture width of the receiver has a great impact on the thermal performance.

      Analysis of a solar collector based on a fixed-focus Fresnel lens solar concentrator/cavity receiver system is presented in [21]. Results show an optical efficiencies average of spherical cavity is 72.23%, cylindrical cavity is 68.37% and conical cavity is 76.40%, the former significantly is increased by 3.74%, 36.46% and 1.79%, respectively. The cavity receiver surface absorptivity and concentrated sunlight incidence angle show the most significant influence on the optical efficiency and flux uniformity in all studies. Finally, a mathematical model including the optical model of the concentrator and the heat transfer model of the receiver pipe was developed in [22]. The experimental test was in Bourne and temperature achieved in the collector varies from 40 °C to 90 °C. The global efficiency of the collector is limited to less than 20%.

      By simulation and experimental tests, this research evaluates the thermal performance of a parabolic trough collector under different configurations in the receiver. For this purpose, a SolidWorks ® simulation tool was used, for its subsequent manufacture, assembly and experimentation under real environments of available solar radiation.

    • The parabolic cylindrical collector components are a concentration surface, receiver or absorber and cover. The first is an optical system where reflection of solar rays occurs, the second is the heat absorber element and the last is the component which decreases heat losses of the receiver within the environment and usually consists of a glass pipe. All the above mentioned elements are shown in Fig. 1.

      Figure 1.  Parabolic through collector

      On a parabolic trough collector with Fresnel lenses, two optical phenomena, reflection and refraction occur. Reflection relates solar rays on the parabolic surface which are addressed to central receiver. Refraction relates between two media with different densities, in this case solar ray in the environment crosses the Fresnel lens, so it is deviated trough an output angle. In both cases, where an angle impinges on the surface this can be reflected as Fig. 2 (a) ray reflection, or refracted as Fig. 2 (b) ray refraction. In the scheme, both phenomena and the direction of output beam are illustrated.

      Figure 2.  Ray optics phenomena: (a) Ray reflection; (b) Ray refraction.

      In reflection, it is assumed that the output angle is equal to the input angle, as defined in (1).

      ${a_{{i}}} = {a_{\rm{o}}}.$


      Furthermore, if the optical phenomenon is refraction, the angle of exit of the ray will depend on the angle of entry and the refractive indexes of the material of the surfaces, as presented in (2)[23].

      $\frac{{\sin \left( {{\beta _i}} \right)}}{{\sin \left( {{\beta _o}} \right)}} = \frac{{n'}}{n}.$


      Reflection and refraction can be calculated in a 2D plane. In the first case, a ray u is reflected as the vector w, with normal v on the surface. Considering that incident angle is equal to the reflected angle, all angles are located in the same plane as (3). When it performs scalar multiplication by u, (4) is obtained[24].

      $w = au + bv$


      $w \times u = a\left( {u \times u} \right) + b\left( {u \times v} \right).$


      With unit vectors, the scalar product between $\left({w \times u} \right)$ relates a and b magnitudes multiplied by inlet angle cosine $\left({x \times y} \right) = |a| |b|\cos \left( {{\alpha _i}} \right) $, as w and u are unit vectors $ |-x| = |y| = 1 $, resultant equation is described by (5). Similarly, angles can be expressed as (6) by definition $\left({u \times u = 1} \right)$.

      $\cos \left( {{\alpha _i}} \right) = { - u \times v} $


      $a - b\cos \left( {{\alpha _i}} \right) = - \cos \left( {2{\alpha _i}} \right).$


      The equation system $2 \times 2$, composed by two equations and two unknowns (6) and (8), is completed doing the symmetric reflection with the unit vectors $\left({w \times v} \right)$ defined in (7), as $\left({v \times v} \right) = 1 $ and $\left({u \times v} \right) = -\cos \left( {{\alpha _i}} \right) $, resultant escalar product in this case is shown in (8).

      $w \times v = a\left( {u \times v} \right) + b\left( {v \times v} \right)$


      $ - a\cos \left( {{\alpha _i}} \right) + b = \cos \left( {{\alpha _i}} \right).$


      The equation system with relations of (6) and (8), is resolved by Cramer law, then factors a and b are presented in (9).

      $a = \frac{{{{\sin }^2}({\alpha _i})}}{{{{\sin }^2}({\alpha _i})}} = 1;\;b = - 2\cos \left( {{\alpha _i}} \right).$


      In the second case, unlike the previous one, the u ray is refracted and the exit angle is not equal to the incident. Therefore, the relationship established between the angles takes into account the refractive indexes, as in (10)[25].

      $n\sin \left( \beta \right) = n'\sin \left( {\beta '} \right).$


      The scalar product of w with u and v to obtain the system of equations composed by two equations and two unknowns, to calculated a and b values, can be represented as equations (11) and (12)[24]. In the first expression, the resultant vector w is multiplied by u, where $\left({u \times u} \right) = 1 $ and $ \left( u \times v \right) = -\cos \left( \beta \right) $, and second expression, the resultant vector w multiplied by v, so $\left({v \times v} \right) = 1 $ and $ \left( u \times v \right) = -\cos \left( \beta \right) $.

      $w \times u = a - b\cos \left( \beta \right) = \cos \left( {\beta - \beta '} \right)$


      $w \times v = - a\cos \left( \beta \right) + b = - \cos \left( {\beta '} \right).$


      The constants a and b for vector w calculation by refraction are presented in (3).

      $b = - \cos \left( {\beta '} \right) + \frac{1}{{n'}}\cos \left( \beta \right).$

    • To cover the receiver tube in this research, a Fresnel lens array was made, with a total of 16 elements, each with a length of 200 mm and a width of 35 mm. The thickness of each lens is 2 mm and its focal length is at 12 mm. The material is Polymethylmethacrylate (PMMA) optical. The Fresnel lens can be seen in Fig. 3.

      Figure 3.  Fresnel lens

      Applying mathematical relation about optics on Fresnel lens is possible to describe a Fresnel lens, as the following equations proposed in (14)[26], (15)[27] and (16)[28]. Where n is refractive index of the lens, $ \alpha $ is the incident angle, $ \beta $ is the refractive output angle and w is angle between output angle and the normal vector of the lens. The distance between ray and the optical coordinates system is represented by R, so the focal length of the lens is f.

      $n\sin \left( \alpha \right) = \sin \left( \beta \right)$


      $\tan \left( w \right) = \frac{R}{f}$


      $\beta = a + w.$


      As presenting in (16), $ \beta $ is determined by the sum of $ \alpha $ and w, so it is possible to obtain a unique equation between inlet angle $ \alpha $ and resultant or output angle w, replacing expression (16) in (14). The sine of the sum of two angles can be expressed as the combined sum of sines and cosines of the angles. The resultant equation is presented in (17). If we wish to obtain the incident angle $\alpha$, the expression in (18)[15] can be used.

      $n\sin \left( \alpha \right) = \sin \left( \alpha \right)\cos \left( w \right) + \cos \left( \alpha \right)\sin \left( w \right)$


      $\tan \left( \alpha \right) = \frac{{\sin \left( w \right)}}{{n - \cos \left( w \right)}}.$


      Also it is possible to find a mathematical expression which relates resultant angle w in terms of sine and cosine functions with parameters as R and f, from (15). So the angle w can be described as (19).

      $\sin \left( w \right) = \frac{R}{f}\cos \left( w \right).$


      According to (19), expression (18) can be described as (20). In this case, incident angle $ \alpha $ is determined by R, f, n and the cosine of w. Cosine of w can be calculated from Pythagorean theorem, between focus length f and distance R, where f is the leg adjacent to angle w and R is leg opposite to angle w, which means that ${\rm{cos}}\left({{w}} \right) = \frac{{{f}}}{{{{\left({{{{R}}^2} + {{{f}}^2}} \right)}^{\frac{1}{2}}}}} $. It is possible to find a mathematical expression between incident angle and the physical parameters of the lens as (n, R and f), this expression can be observed in (21)[16].

      $\tan \left( \alpha \right) = \frac{R}{f}\frac{{\cos \left( w \right)}}{{\left( {n - \cos \left( w \right)} \right)}}$


      $ \tan \left( \alpha \right) = \frac {R} {{n} \times {\left({{R}^2} + {{f}^2} \right)}^{\frac{1}{2}}}- {f}. $

    • Angles involved in linear Fresnel lens as presented in Fig. 4, are described in (22)–(25)[24].

      Figure 4.  Ray lineal Fresnel lens angles

      ${\theta _1} = {\theta _{in}}$


      $\theta _1^{'} = {\sin ^{ - 1}}\left( {\frac{{\sin {\theta _1}}}{{n'}}} \right)$


      $\theta _2^{'} = \theta _1^{'} - {\varphi _r}$


      ${\theta _2} = {\sin ^{ - 1}}\left( {\sin {\theta _2}' \times n'} \right).$

    • The simulation parameters as mass flow was defined to be 0.001 6 kg/s, inlet and environmental temperature was selected in 22 °C and 20 °C respectively, the pressure in the outlet was defined to be 101 325 Pa, finally solar radiation was established as 250 W/m2, 800 W/m2 and 1 000 W/m2. In addition, the system computational domain is defined by coordinates (X, Y, Z) with the maximum and minimum value. The work cell dimensions are presented in Table 1.

      Xmin – 0.243 m
      Xmax0.262 m
      Ymin– 0.057 m
      Ymax0.165 m
      Zmin– 0.550 m
      Zmax0.534 m

      Table 1.  Computational domain

      As part of the simulation process, a mesh was generated for each structure studied. The information about this mesh, as number of cells of solid and fluid are related in Table 2.

      Number of cells in X10
      Number of cells in Y7
      Number of cells in Z18
      Cells27 278
      Fluid cells20 535
      Solid cells6 743

      Table 2.  Basic mesh dimensions

    • The instrumentation equipment implemented in the parabolic trough collector to sense temperature in fluid, receiver surface and air between cover and receiver, consist of four thermocouple type K and one Arduino Mega 2 560 as a data acquisition system. Furthermore, a radiometer was used to obtain solar irradiation in the study place. A technical reference for each equipment is described down below in Table 3.

      Max6675 – Serial peripheral interface (SPI)
      Measurement range–180 °C to 1 372 °C
      Reading error±2.5 °C
      Resolution0.1 °C
      Thermocouple type K
      Inlet voltage3.0 V5.0 V
      Inlet current40 mA
      Resolution12 bits, 0.25 °C
      Measurement range–20 °C to + 85 °C
      Arduino Mega 2 560
      Inlet voltage5.0 V
      Inlet current0.7 mA1.5 mA
      Resolution10 bits
      Photo-radiometer HD2102.1
      Measurement rang(0 – 1 999.9)W/m2
      Reading error(0 – 0.1)W/m2
      Resolution±1 digit

      Table 3.  Experimental equipment

      The system is defined by two variables, pipe type and optical status. The first is composed with 2 conditions, brass without paint and black brass, which consists in a brass pipe painted with black acrylic paint. The second variable is related to the system with and without the Fresnel lens over the pipe. Considering the number of elements, the possible combinations in experimental test are 4, the number of observations defined in each combination is 3, that means a total of 12 observations. In Table 4, we present the variable elements and their combinations.

      Variable AVariable BExperiment
      BrassA0FresnelB0A0B0 (Fig. 5)A0B1 (Fig. 6)
      Black brassA1No fresnelB1A1B0 (Fig. 7)A1B1 (Fig. 8)

      Table 4.  Experimental combinations

      Each experiment model is presented down below. As a simulation, experimental test models were analyzed under real weather conditions.

      Figure 5.  A0B0 model of Experiment 1

      Figure 6.  A0B1 model of Experiment 2

      Figure 7.  A1B0 model of Experiment 3

      Figure 8.  A1B1 model of Experiment 4

    • The energy radiated from concentrator to receiver and cover (Sc), relates optical parameters as specular reflectance in the parabolic surface (ρ), interception factor (γ), incident radiation (Gr) and effective aperture area (Aae). Radiated energy in cover is presented in (26).

      ${S_c} = \rho \gamma {G_r}{A_{ae}}.$


      Radiated energy which reaches receiver pipe (S) in (27), relies on transmittance (τα) and energy radiated from concentrator to receiver and cover (Sc).

      $S = \left( {\tau \alpha } \right){S_c} = \left( {\tau \alpha } \right)\rho \gamma {G_r}{A_{ae}}.$


      For each proposed radiation, Solar heat in the lens and receiver were calculated. Results are enlisted down below in Table 5.

      Radiation250 W/m2800 W/m21 000 W/m2
      Sc89.994 5 W287.982 5 W359.978 2 W
      S86.947 8 W278.232 9 W347.791 1 W

      Table 5.  Radiation in Fresnel lens and pipe

    • Initially, simulation results are presented in this section. In this case, the collector′s experiments were analyzed with 3 observations, which consists in different values of radiation, with the purpose of studying multiple daily changes in the weather.

    • The results resumed in Table 6 show the maximum, minimum and mean temperature in the solid and the fluid. Observation 1 with a total radiation of 250 W/m2, showed a mean solid temperature of 22.25 °C and a mean fluid temperature of 22.83 °C. For Observation 2, the mean temperature was 24.81 °C and 23.81 °C, solid and fluid respectively. The maximum radiation analyzed in Observation 3, presented a mean temperature of 24.2 °C in the pipe and 25.5 °C in fluid.

      solid (°C)
      fluid (°C)
      OBS 1 250 W/m2Max37.96437.964
      OBS 2 800 W/m2Max42.19542.195
      OBS 3 1 000 W/m2Max46.97846.978

      Table 6.  Simulation results – experiment A0B0

      The different results obtained throughout the observations in Experiment 1, are presented in Fig. 9. Through the image, it is possible to visualize the different temperature profiles in the space between the Fresnel lenses and pipe, where the maximum temperature was reached in the central receiver. In Fig. 9 (a), the results of Observation 1 are presented, while Observation 2 is related in Fig. 9 (b), and finally temperature profile related to Observation 3 is defined in Fig. 9 (c).

      Figure 9.  Temperature profile – experiment A0B0: (a) Observation 1 results; (b) Observation 2 results; (c) Observation 3 results; (d) Key points along the pipe

      To show the temperature distribution inside the receiver, Fig. 9 (d) presents the key points along the pipe. It is evident that temperature increases from inlet to outlet. The maximum temperature obtained in the pipe during Experiment A0B0 in simulation analysis was 46.98 °C with Observation 3.

    • For a regular parabolic through collector without Fresnel lens, just a parabolic surface and a central receptor as pipe, the results present a temperature decrease with regard to A0B0 system. The results are related in Table 7. In Observation 1, the mean temperature was 21.57 °C in solid and 21.92 °C in fluid. The maximum average temperature was obtained with the maximum radiation of 1 000 W/m2, a total of 23.65 °C was reached in pipe.

      solid (°C)
      fluid (°C)
      OBS 1 250 W/m2Max22.57622.576
      OBS 2 800 W/m2Max23.37923.379
      OBS 3 1 000 W/m2Max23.91923.919

      Table 7.  Simulation results – experiment A0B1

      Each observation developed for experiment A0B1 is presented in the scheme down below, Observation 1 results are presented in Fig. 10 (a), where it is possible to visualize the lowest temperatures in A0B1 simulations. Similarly, Observation 2 can be observed in Fig. 10 (b), Observation 3 result is related in Fig. 10 (c), with the maximum values.

      Figure 10.  Temperature profile – experiment A0B1: (a) Observation 1 results; (b) Observation 2 results; (c) Observation 3 results

    • System A1B0 results are presented in Table 8, with the minimum radiation, a mean temperature of 28 °C in solid and 26.9 °C in fluid were reached. Furthermore, a mean value of 33 °C and 28.6 °C, in solid and fluid respectively were obtained in Observation 2. Finally, average temperatures of the pipe and fluid inside the pipe for a maximum radiation were 35.5 °C and 30 °C.

      solid (°C)
      fluid (°C)
      OBS 1 250 W/m2Max75.83875.838
      OBS 2 800 W/m2Max98.85298.852
      OBS 3 1 000 W/m2Max116.303116.302

      Table 8.  Simulation results – experiment A1B0

      Temperature profiles of experiment A1B0 in each observation are presented in Fig. 11. As shown in Fig. 11 (c), the maximum temperature in the pipe was 116 °C for the system subjected to 1 000 W/m2 of radiation. Conversely, the minimum temperature was 75.8 °C in Observation 1, as show in Fig. 11 (a). It is evident that there is difference between Experiments A0B0 and A1B0, where an increase of 66 °C was obtained with a black pipe.

      Figure 11.  Temperature profile – experiment A1B0: (a) Observation 1 results; (b) Observation 2 results; (c) Observation 3 results; (d) Key points along the pipe

    • Finally, the last experiment was simulated under different radiation conditions. The results are related in Table 9, mean temperature in solid and fluid can be observed. For a low radiation system, A1B1 achieved a solid temperature of 21.58 °C, whereas for a high radiation, the mean temperature increases to 51.3 °C, and for a very high radiation, the average is incremented to 57.7 °C.

      solid (°C)
      fluid (°C)
      OBS 1 250 W/m2Max23.41723.417
      OBS 2 800 W/m2Max51.94351.941
      OBS 3 1 000 W/m2Max58.47758.476

      Table 9.  Simulation results – experiment A1B1

      The last experiment results in the simulation are visualized in Fig. 12. The maximum temperature in the fluid and the solid for observation is evident in the temperature profiles. Observation 1 in Fig. 12 (a) achieved a maximum temperature of 23.4 °C, the higher temperature were obtained in Observation 2 as show in Figs. 12 (b) and 12 (c), where temperatures upper of 50 °C were achieved.

      Figure 12.  Temperature profile – experiment A1B1: (a) Observation 1 results; (b) Observation 2 results; (c) Observation 3 results

      A summary of the results in the simulation study are presented in Table 10. All temperatures in each observation and each experiment proposed in this research can be visualized. These data will be compared to experimental tests results in real conditions.

      Simulation thermal performanceTemperature solid (°C)Temperature fluid (°C)
      A0B0OBS 1
      250 W/m2
      OBS 2
      800 W/m2
      OBS 3
      1 000 W/m2
      A0B1OBS 1
      250 W/m2
      OBS 2
      800 W/m2
      OBS 3
      1 000 W/m2
      A1B0OBS 1
      250 W/m2
      OBS 2
      800 W/m2
      OBS 3
      1 000 W/m2
      A1B1OBS 1
      250 W/m2
      OBS 2
      800 W/m2
      OBS 3
      1 000 W/m2

      Table 10.  Simulation summary

      As the second part of this research, experimental test results are presented in Section 5.3. In this case, each observation consisted in a different day of data acquisition, so some radiation results were variable between observations for the same system.

    • The A0B0 experiment was conformed by parabolic surface, receiver pipe and Fresnel lens array, as shown in Fig. 13. Each observation was developed in a consecutive day, time acquisition varies between 20 m and 30 m, and the samples for all observations was 800. The test considered 4 temperatures, where Temperature 1 relates to collector inlet, Temperature 2 refers to the pipe surface, Temperature 3 refers to the air around pipe and Temperature 4 refers to the collector outlet.

      Figure 13.  A0B0 system

      Radiation results of observations in the A0B0 experimental test are listed in Table 11. The maximum radiation obtained was 919 W/m2 in Observation 3, the mean radiation in A0B0 test was 298.53 W/m2.

      Radiation (W/m2)Observation 1Observation 2Observation 3

      Table 11.  Radiation – A0B0 test

    • The collector inlet sustained a temperature between 21 °C and 25 °C, collector outlet varied from 22 °C to 27.2 °C, while the environment around pipe achieved a maximum temperature of 31.5 °C and the pipe surface 42.25 °C. That means an increase of 69% between inlet to middle pipe, and an increase of 9% between inlet and outlet. A0B0 temperature results in Observation 1 are presented in Table 12.

      Temperatures (°C)MaxMinMean
      Temperature 125.0021.0022.79
      Temperature 242.2529.2537.77
      Temperature 331.5023.5027.07
      Temperature 427.2022.0024.60

      Table 12.  A0B0 temperatures Observation 1

      Both radiation and temperature graphs in Observation 1 test are illustrated in Fig. 14. Thermal performance in the first observation was consistent with a mean radiation of 300 W/m2, and regular during sample acquisition. Near to completion of the data acquisition, radiation decreased quickly so temperature also decreased gradually.

      Figure 14.  A0B0 thermal performance of Observation 1

    • Minimum, mean and maximum temperatures achieved in Observation 2 are registered in Table 13. All temperatures were increased with regard to temperatures in Observation 1. The maximum temperature was in a pipe surface with a total of 60.74 °C, the environmental temperature was 40.5 °C, which means 20 °C less than the value obtained in the receiver. Temperature $ \Delta $ between inlet and outlet was 1.2 °C.

      Temperatures (°C)MaxMinMean
      Temperature 128.5018.5022.40
      Temperature 260.7525.2540.90
      Temperature 340.5020.7528.57
      Temperature 429.7018.5023.05

      Table 13.  A0B0 temperatures of Observation 2

      The thermal performance in the collector under 30 m of radiation in Observation 2 is presented in Fig. 15. The mean radiation in this case was 200 W/m2, however more peaks of high radiation were constant for 10 m, after this time radiation decreases to a greater extent as, temperature drop was 35.5 °C in 20 m.

      Figure 15.  A0B0 thermal performance of Observation 2

    • The different temperature points in Observation 3 show the best results in the A0B0 experimental test. The pipe surface achieved 49 °C, near air temperature achieved 39.75 °C, around 10 °C less, between inlet and outlet, the difference was 3.25 °C as shown in Table 14.

      Temperatures (°C)MaxMinMean
      Temperature 134.7521.5027.41
      Temperature 249.0031.2540.80
      Temperature 339.7525.7532.14
      Temperature 438.0023.7030.05

      Table 14.  A0B0 temperatures of Observation 3

      Thermal performance in Observation 3 as temperatures and radiation is presented in Fig. 16. It is possible to observe the increase of temperature after radiation as high radiation changed after 15 m since data acquisition begins.

      Figure 16.  A0B0 thermal performance of Observation 3

    • The parabolic through collector without Fresnel lens is shown in Fig. 17. The same parabolic surface and pipe were used in this system. Unlike with A0B0, this experiment did not have a pipe cover. Also, inlet, outlet and surface temperature sensors were kept in system, air temperature was positioned near the pipe but without contact.

      Figure 17.  A0B1 system

      Radiation results obtained in all observations of A0B1 experimental test show a mean radiation of 255.43 W/m2. The maximum radiation observed in this test was 999.6 W/m2 in Observation 2 as shown in Table 15. Despite the maximum radiation being higher than the maximum radiation in the A0B0 test, the average value is lower in this case, due to radiation in Observations 1 and 2, where values of 559 W/m2 and 441 W/m2 were achieved in the second day.

      Radiation (W/m2)Observation 1Observation 2Observation 3

      Table 15.  Radiation – A0B1 test

    • A maximum temperature of 51 °C was achieved in the pipe with the maximum radiation. Also, the flow outside the pipe had a temperature around to 32 °C, as inlet temperature varies from 20 °C to 28.5 °C, and outlet varies from 20 °C to 31 °C. These results can be visualized in the data structure in Table 16.

      Temperatures (°C)MaxMinMean
      Temperature 128.5020.5024.08
      Temperature 251.2521.0033.94
      Temperature 332.0020.7525.74
      Temperature 430.7020.5025.54

      Table 16.  A0B1 temperatures of Observation 1

      As Fig. 18 shows, the temperature performance was variable in function of radiation, so a direct relation between radiation and temperature in the system was found. When solar radiation was higher, the temperature was increased rapidly, otherwise temperature was decreased in time

      Figure 18.  A0B1 thermal performance of Observation 1

    • This observation shows a maximum temperature in pipe of 39.75 °C, similarly air temperature was 1 °C less than pipe temperature. Inlet temperature range varies from 23 °C to 35 °C, and outlet temperature range varies from 22 °C to 34.5 °C. Results can be observed in Table 17.

      Temperatures (°C)MaxMinMean
      Temperature 135.0023.2528.01
      Temperature 239.7524.2530.71
      Temperature 338.7523.2529.07
      Temperature 434.5022.2026.59

      Table 17.  A0B1 temperatures of Observation 2

      Temperature performance in Observation 2 were similar to each other. The variation was proportional in each sensor of the collector. Radiation average during the experiment was 262 W/m2, despite that the highest peak was 900 W/m2, pipe temperature did not exceed 40 °C, as shown in Fig. 19.

      Figure 19.  A0B1 thermal performance of Observation 2

    • In the last observation of A0B1 system, similar temperatures to those in Observation 2 were obtained. However, in this case, the pipe temperature was lower than Temperature 3. The reasons is focal distance location in Observation 3 was modified due to weather conditions. Table 18 presents observation results, as is evident the maximum temperature was 40 °C and minimum 24.75 °C, meaning non-uniform radiation and peaks less than 200 W/m2, in most of the tests.

      Temperatures (°C)MaxMinMean
      Temperature 124.7519.0021.54
      Temperature 233.5019.5025.16
      Temperature 340.0019.7527.24
      Temperature 426.2019.7022.88

      Table 18.  A0B1 temperatures of Observation 3

      In Fig. 20, it is possible to observe two stages in this test. The first stage is the heating process with radiation over 500 W/m2, the second stage is a cooling process when radiation is decreased to 200 W/m2 and 70 W/m2. Cooling time in this case was near to 400 s or 7 m.

      Figure 20.  A0B1 thermal performance of Observation 3

    • The solar collector with black pipe and Fresnel lens is constituted by the A1B0 system, which is visualized in Fig. 21. For this experiment, the maximum radiation was 983 W/m2, presenting one of the highest recorded radiations. In this case, average value was 367 W/m2 in all the observations. Results are presented down below in Table 19.

      Radiation (W/m2)Observation 1Observation 2Observation 3

      Table 19.  Radiation – A1B0 test

      Figure 21.  A1B0 system

    • As presented in the results of Table 20, pipe temperature achieved a maximum value in 96 °C, the highest temperature in the study. In this observation, the outlet temperature was 35 °C and inlet temperature was 41 °C, also air inside the lens achieved a maximum temperature of 48 °C, meaning 50% less than the surface temperature.

      Temperatures (°C)MaxMinMean
      Temperature 140.7526.7534.86
      Temperature 295.5044.2582.93
      Temperature 347.7530.7542.67
      Temperature 435.0026.0031.33

      Table 20.  A1B0 temperatures of Observation 1

      Thermal performance in different points of the parabolic solar collector with a Fresnel lens and black receiver, on a time of 45 m of data acquisition, is shown in the graphs of Fig. 22. Despite of solar radiation was continuously variable, the pipe temperature does not present high variations and the increase in most cases was constant.

      Figure 22.  A1B0 thermal performance of Observation 1

    • In the second test, receiver temperature was 85 °C in the first 10 m, then radiation descended, and the curve decreased to 60 °C and 40 °C, the mean temperature was 60 °C in this test. Differences between air and pipe remain close to 50%. Furthermore, inlet and outlet temperatures achieved lower values than Observation 1, as shown in Table 21.

      Temperatures (°C)MaxMinMean
      Temperature 133.7519.5024.76
      Temperature 285.0037.5059.80
      Temperature 339.0023.7530.81
      Temperature 430.0021.2025.54

      Table 21.  A1B0 temperatures of Observation 2

      Temperature increase and decrease can be visualized in Fig. 23. There is evidently a difference between air and pipe of 40 °C. In the period when radiation decreases, the pipe temperature decreases 20 °C in 10 m, also the collector increases the same 20 °C in only 4 m.

      Figure 23.  A1B0 thermal performance of Observation 2

    • The last test for the A1B0 system shows the lowest temperatures in this experiment, with a maximum temperature of 58 °C in pipe and a mean temperature of 55 °C. Temperatures results, as maximum, minimum and mean values are registered in Table 22.

      Temperatures (°C)MaxMinMean
      Temperature 129.7525.2527.62
      Temperature 258.2544.7554.48
      Temperature 335.2531.0033.32
      Temperature 423.7022.0023.05

      Table 22.  A1B0 temperatures of Observation 3

      Finally, temperature performance with regard to radiation in Observation 3 is shown in Fig. 24.

      Figure 24.  A1B0 thermal performance of Observation 3

    • The last test was related to A1B1 system. In this case, the collector had a receiver without a lens, just the black pipe. As with the A0B1 system, the sensor for Temperature 3 was located near the pipe but without contact. Fig. 25 presents the collector configured to the A1B1 system, and located in collector focal distance.

      Figure 25.  A1B1 system

      The maximum radiation during the A1B1 test observations was 997 W/m2 and the mean radiation in all observations was 247 W/m2, these results are presented in Table 23.

      Radiation (W/m2)Observation 1Observation 2Observation 3

      Table 23.  Radiation – A1B1 test

    • As is possible to observe in Table 24 pipe temperature varies from 22 °C to 55 °C with the average value of 37 °C. The difference between inlet and outlet was 5 °C, while delta between pipe and air was 19 °C, meaning an increase of 52.7% with regard to fluid and surface.

      Temperatures (°C)MaxMinMean
      Temperature 138.0021.0028.72
      Temperature 255.0022.5036.65
      Temperature 336.0021.0027.87
      Temperature 433.0021.2027.28

      Table 24.  A1B1 temperatures of Observation 1

      The heating of the receiver pipe with regard to the available radiation is shown in Fig. 26, with respect to the increase of radiation, the temperature increases, however with variations in the radiation, the temperature is affected decreasing rapidly, therefore the A1B1 system presents continuous variations against changes in solar intensity.

      Figure 26.  A1B1 thermal performance of Observation 1

    • In Observation 2, maximum temperature was near 43 °C, that means 22% lower than that obtained in the first test. Inlet, outlet and air temperatures obtained were similar, near 30 °C, the maximum difference between them was one degree centigrade. The second test results of the A1B1 system are presented in Table 25.

      Temperatures (°C)MaxMinMean
      Temperature 130.2520.2525.45
      Temperature 242.2521.5032.49
      Temperature 330.2521.0025.32
      Temperature 431.7020.5026.07

      Table 25.  A1B1 temperatures of Observation 2

      Graphs in Fig. 27 presents thermal performance in the collector A1B1 in the second test. It can be observed that pipe temperature increases during time, however, temperatures are constantly varying with respect to variations in radiation.

      Figure 27.  A1B1 thermal performance of Observation 2

    • Finally, the last test with collector A1B1 led to the following results in Table 26. Observation 3 presents the lowest radiation in the experimentation. Therefore, collector temperatures did not exceed 30 °C, most of them were close to 27 °C. Therefore, collector temperatures did not exceed 30 °C, most of them were close to 27 °C. It means a temperature increase of 7 °C regard to minimum temperature obtained in Observation 3 for each sensor.

      Temperatures (°C)MaxMinMean
      Temperature 126.5020.7522.80
      Temperature 231.0022.2525.15
      Temperature 326.7521.5023.54
      Temperature 426.7021.2023.64

      Table 26.  A1B1 temperatures of Observation 3

      Radiation and temperature performance in Observation 3 are illustrated in the graph of Fig. 28. During 30 m radiation, it achieved an average of 130 W/m2, according to the solar intensity collector increased pipe temperature until 31 °C, then this temperature decreased in time.

      Figure 28.  A1B1 thermal performance of Observation 3

    • The results summary is presented down below in Table 27. As shown the values obtained in each measured sector, maximum inlet temperature achieved in all tests was 41 °C in A1B0 collector. Similarly, A1B0 system achieves the highest temperatures in pipe surface and air regard all the experiments. However, outlet temperature was highest in A0B0 system. Finally, the maximum radiation was 1 000 W/m2 in Observation 2 of A0B1 collector.

      Experimentation testT 1 °CT 2 °CT 3 °CT 4 °CRadExperimentation testT 1 °CT 2 °CT 3 °CT 4 °CRad
      A0B0OBS 1Max25.0042.2531.5027.20601.10A1B0OBS 1Max40.7595.5047.7535.00983.90
      OBS 2Max28.5060.7540.5029.70656.30OBS 2Max33.7585.0039.0030.00934.70
      OBS 3Max34.7549.0039.7538.00919.60OBS 3Max29.7558.2535.2523.70824.8
      A0B1OBS 1Max28.5051.2532.0030.70559.40A1B1OBS 1Max38.0055.0036.0033.00996.60
      OBS 2Max35.0039.7538.7534.50999.60OBS 2Max30.2542.2530.2531.70558.00
      OBS 3Max24.7533.5040.0026.20441.50OBS 3Max26.5031.0026.7526.70362.90

      Table 27.  Experimentation results summary

      Finally, experimental results and simulation results are related in Table 28.

      A0B047 °C61 °C
      A0B124 °C51 °C
      A1B0116 °C96 °C
      A1B159 °C55 °C

      Table 28.  Results summary

      The best collector was the A1B0 system which achieved in simulation a maximum temperature in pipe of 116 °C, and in experimental test of 96 °C, difference between these studies was 20 °C. Furthermore, collector A0B1, presents the lowest results in all experiments. Through these results, it was possible to identify the importance of a cover in receiver and the influence of a black absorber in heat transfer.

    • From the simulation study developed for each of the proposed collectors, it was possible to identify that the system with the best thermal behavior was the A1B0 system, which consisted of parabolic collector coupled with Fresnel lenses and black receiver. The maximum temperature reached by simulation was 116 °C with a radiation of 1 000 W/m2, while the system A0B1 reached the lowest temperature of the entire study with a maximum value of 24 °C, this system consisted of parabolic collector and brass gold color receiver.

      As a result of experimentation, the systems that did not have Fresnel lenses reached similar temperatures close to 50 °C, the traditional brass system obtained 51 °C, while the system with painted brass reached 5 °C more than the last one. Furthermore, the systems with lenses obtained the highest temperatures, where the collector with golden brass obtained 61 °C and the collector with black brass obtained 96 °C with a maximum radiation in the time of the test of 983 W/m2.

      Comparing results obtained during the simulation and the experimental tests, a temperature delta was found for the A0B0 system of 14 °C, while for the A0B1 system, it was 27 °C. The smallest difference was found in the A1B1 system where the difference was only 4 °C. Likewise, the temperature delta for the system with the best thermal behavior was a total of 20 °C. These differences were due to the fact that in simulation the radiation applied to the system is constant, whereas under experimental tests the radiation varies continuously and does not remain at a high value for a prolonged period of time.

      Within future work, we expect to continue with research in the area of solar collectors, seeking the improvement of thermal behavior through the increase in the transfer area in the receiving tube. Similarly, it is desired to take the research to experimental stages with which theoretical simulation developments can be validated.

    • This paper supported by Research Vice Rectory of Universidad Militar Nueva Granada-validity, Colombia in 2019 (No. IMP-ING-2656).

Reference (28)



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