Numerical and Experimental Study of an Asymmetric CPC-PVT Solar Collector

Article Numerical and Experimental Study of an Asymmetric CPC-PVT Solar Collector

Pouriya Nasseriyan 1, Hossein Afzali Gorouh 1, João Gomes 2,3, Diogo Cabral 2 , Mazyar Salmanzadeh 1,* , Tiﬀany Lehmann 4 and Abolfazl Hayati 2

1 Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman 76169-14111, Iran; [email protected] (P.N.); [email protected] (H.A.G.) 2 Department of Building Engineering, Energy Systems and Sustainability Science, University of Gävle, Kungsbäcksvägen 47, 801 76 Gävle, Sweden; [email protected] (J.G.);[email protected] (D.C.); [email protected] (A.H.) 3 R&D Department, MG Sustainable Engineering AB, Börjegatan 41B, 752 29 Uppsala, Sweden 4 Department of Energetics and Renewable Energies, Polytech de Montpellier, Place Eugène Bataillon, 34095 Montpellier, France; tiﬀ[email protected] * Correspondence: [email protected]; Tel.: +98-913-141-3523

Received: 28 January 2020; Accepted: 12 March 2020; Published: 3 April 2020

Abstract: Photovoltaic (PV) panels and thermal collectors are commonly known as mature technologies to capture solar energy. The efficiency of PV cells decreases as operating cell temperature increases. Photovoltaic Thermal Collectors (PVT) offer a way to mitigate this performance reduction by coupling solar cells with a thermal absorber that can actively remove the excess heat from the solar cells to the Heat Transfer Fluid (HTF). In order for PVT collectors to effectively counter the negative effects of increased operating cell temperature, it is fundamental to have an adequate heat transfer from the cells to the HTF. This paper analyzes the operating temperature of the cells in a low concentrating PVT solar collector, by means of both experimental and Computational Fluid Dynamics (CFD) simulation results on the Solarus asymmetric Compound Parabolic Concentrator (CPC) PowerCollector (PC). The PC solar collector features a Compound Parabolic Concentrator (CPC) reflector geometry called the Maximum Reflector Concentration (MaReCo) geometry. This collector is suited for applications such as Domestic Hot Water (DHW). An experimental setup was installed in the outdoor testing laboratory at Gävle University (Sweden) with the ability to measure ambient, cell and HTF temperature, flow rate and solar radiation. The experimental results were validated by means of an in-house developed CFD model. Based on the validated model, the effect of collector tilt angle, HTF, insulation (on the back side of the reflector), receiver material and front glass on the collector performance were considered. The impact of tilt angle is more pronounced on the thermal production than the electrical one. Furthermore, the HTF recirculation with an average temperature of 35.1 ◦C and 2.2 L/min flow rate showed that the electrical yield can increase by 25%. On the other hand, by using insulation, the thermal yield increases up to 3% when working at a temperature of 23 ◦C above ambient.

Keywords: cell temperature; CPVT; CPC; CFD

1. Introduction Climate change is an undeniable phenomenon. The greenhouse gases emissions caused by human activities are contributing to approximately 1 ◦C of global warming above pre-industrial levels (0.2 ◦C per decade) [1]. Energy production due to burning fossil fuels is the main source for increasing carbon emissions and this segment needs to switch to renewable energy sources, such as solar (both photovoltaic and thermal), water and/or wind, in order to prevent the most disruptive climate change

Energies 2020, 13, 1669; doi:10.3390/en13071669 www.mdpi.com/journal/energies EnergiesEnergies 20202020,, 1313,, 1669x FOR PEER REVIEW 22 ofof 2121

45 climate change scenarios. In 2015, over 190 countries signed a legal agreement at the 21st yearly 46 scenarios.session of the In Conference 2015, over 190of the countries Parties (COP21), signed a legalto keep agreement global warming at the 21stbelow yearly 2 °C session(Paris Climate of the 47 ConferenceConference of[2]). the Global Parties (COP21),warming towill keep reach global 1.5 warming °C between below 2030 2 ◦C and (Paris 2052 Climate if greenhouse Conference gases [2]). 48 Globalemissions warming continue will at reach today’s 1.5 rate◦C between[1]. Technologies 2030 and based 2052 if on greenhouse renewable gases energies emissions are thecontinue solution atin 49 today’sorder to rate prevent [1]. Technologiesthis issue. The based sun is on free renewable and available energies everywhere. are the solution The active in order applications to prevent of solar this 50 issue.energy The technologies sun is free andare availablethe photovoltaic everywhere. panels The (PV) active to applications generate electricity of solar energy and solar technologies thermal 51 arecollectors the photovoltaic to generate panels heat. (PV)The low to generate surface electricitypower and and energy solar density thermal of collectors PV cells, toplus generate the limited heat. 52 Theavailable low surface ground power area, andcan energybe solved density by using of PV a cells, solar plus photovoltaic-thermal the limited available (PVT) ground system area, or, can if 53 becoupled solved with by using reflective a solar materials, photovoltaic-thermal composing a concentrated (PVT) system photovoltaic-thermal or, if coupled with reflective collector materials, (CPVT). 54 composingA PVT collector a concentrated produces both photovoltaic-thermal electrical and thermal collector power (CPVT). from Athe PVT same collector area. The produces conversion both 55 electricalefficiency andof solar thermal radiation power into from electricity the same for area.a commercial The conversion monocrystalline efficiency PV of cell solar is, radiationtoday, at 20%, into 56 electricitywith the forShockley–Queisser a commercial monocrystalline limit defining PV a cellmaxi is,mal today, theoretical at 20%, with efficiency the Shockley–Queisser of 33.7% for single limit 57 definingjunction cells a maximal [3]. The theoretical remaining e ffisolarciency radiation of 33.7% is converted for single to junction heat and cells wasted [3]. The (if no remaining Heat Transfer solar 58 radiationFluid (HTF) is convertedis used). The to heatefficiency and wasted of PV cells (if no decr Heateases Transfer by increasing Fluid (HTF) their is temperature used). The e[4].fficiency In a PVT of 59 PVsystem, cells decreasesHTF (air, bywater increasing or water their with temperature a percentage [4]. of In an a PVT anti-freeze system, fluid HTF (air,in case water of ora closed-loop water with 60 asystem) percentage is used of anto carry anti-freeze the excess fluid heat in case from of athe closed-loop PV cells to system) the thermal is used solar to carrysystem. the This excess method heat 61 fromaims theat increasing PV cells to the the overal thermall efficiency solar system. of PV This cells. method aims at increasing the overall efficiency of 62 PV cells.In a CPVT, the concentration factor defines the working temperature. Low concentration PVT 63 collectorsIn a CPVT, are typically the concentration limited to low factor working defines temp theeratures working (30–80 temperature. °C), which Low makes concentration them ideal PVT for 64 collectorsDomestic areHot typically Water limited(DHW) toapplications low working [5]. temperatures PVT collectors (30–80 are◦C), classified which makes according them idealto their for 65 Domesticoperating Hottemperature Water (DHW) range, applications system layout, [5]. PVT design collectors (glazed, are classifiedunglazed accordingand/or concentrating) to their operating and 66 temperaturetheir HTF (air range, and water) system [6]. layout, design (glazed, unglazed and/or concentrating) and their HTF (air 67 and water)Table [16 ].shows a brief combination of the components of solar energy technologies. These 68 combinationsTable1 shows consist a brief of combinationConcentrated-Photovolt of the componentsaics (CPV), of solarConcentrated-Thermal energy technologies. (CT) These and 69 combinationsPhotovoltaic-Thermal consist (PVT of Concentrated-Photovoltaics) systems. The combination of (CPV), all the Concentrated-Thermal above is called the Concentrated (CT) and 70 Photovoltaic-ThermalPhotovoltaic-Thermal (CPVT) (PVT) systems. collector. The combination of all the above is called the Concentrated Photovoltaic-Thermal (CPVT) collector. 71 Table 1. Combination of individual solar energy technologies. Table 1. Combination of individual solar energy technologies. Solar Photovoltaics Concentration PhotovoltaicsThermal Solar Thermal Concentration CPV CPV ☑ ☑ CT CT ☑ ☑ PVT ☑ ☑ PVT CPV CPVT ☑ ☑ ☑ T

72 WhenWhen comparedcompared toto thermal and PV systems individually,individually, PVTPVT collectors reach higher eefficiencyfficiency 73 byby reducingreducing thethe PVPV cellcell temperaturetemperature andand byby havinghaving fewerfewer rawraw materialsmaterials thanthan anan equivalentequivalent area ofof 74 thermalthermal andand PVPV andand useuse lessless installationinstallation area.area. TheThe mainmain disadvantagedisadvantage forfor PVTPVT collectorscollectors isis thethe highhigh 75 complexitycomplexity forfor collectorcollector productionproduction andand systemsystem installation.installation. 76 TheThe concentratingconcentrating collector is a practicalpractical approachapproach to focusfocus thethe solarsolar incidentincident radiationradiation onon aa 77 smallersmaller areaarea (receiver)(receiver) and and to to produce produce thermal thermal power power at higherat higher temperatures. temperatures. Concentration Concentration ratio ratio (the 78 ratio(the ratio between between aperture aperture area area of the of reflector the reflector and theand receiver the receiver/absorber/absorber area) area) can becan classified be classified as low as 79 concentrationlow concentration ratio ratio (between (between 2 and 2 10, and no 10, tracking no tracki system),ng system), medium medium concentration concentration ratio (between ratio (between 10 and 80 60,10 and with 60, one-axis with one-axis tracking tracking system) system) and high and concentration high concentration ratio (from ratio 60 (from to 1500, 60 requiringto 1500, requiring a two-axis a 81 trackingtwo-axis system)tracking [7 ].system) Concentration [7]. Concentration reduces the redu amountces the of PV amount cells, thermalof PV cells, absorber thermal materials absorber and 82 heatmaterials losses, and and heat accordingly, losses, and increases accordingly, the operating increases temperature. the operating One temperature. disadvantage One of concentrationdisadvantage 83 isof thatconcentration the components is that become the components more expensive become due more to the expensive increase indue operating to the increase temperature. in operating 84 temperature.In the 1970s, theoretical and experimental studies have been reported on PVT technologies [8]. 85 MbeweIn the et al. 1970s, [9] developed theoretical a conversionand experimental efficiency studies model have for concentrating been reported systems on PVT and technologies validated that [8]. 86 withMbewe experimental et al. [9] developed results. Garg a conversion and Adhikari efficiency [10] worked model onfor air-cooled concentrating PVT andsystems on the and eff validatedect of the 87 that with experimental results. Garg and Adhikari [10] worked on air-cooled PVT and on the effect

Energies 2020, 13, 1669 3 of 21 front cover on heat losses. They showed that the collector with a single glass is better. The heat loss reduction with a second cover did not justify the transmission losses. Zondag et al. [11] developed three steady-state models in one-dimensional (1D), 2D, 3D and 3D dynamical, and validated them with an experimental model. Coventry [12] developed a high concentrator and showed a decrease in electrical efficiency due to higher working temperatures. The results showed a decrease in electrical efficiency from 20% at Standard Test Conditions (STC, Solar cell temperature of 25 ◦C and Solar irradiation of 1000 W/m2 with solar spectrum air mass of 1.5) to 11% and thermal efficiency of 58%. Chow [8] compared air-cooled and water-cooled PVTs, and their overall thermal efficiencies were in the range of 45% to 70% for water-cooled and 55% for air-cooled collector. Reichl et al. [13] developed a CFD model for a CPC collector and compared the model with experimental results. The results showed that a steady 2D model matched well with experimental results. It also showed that the heat loss through the covering glass is 73%. Buonomano et al. [14] designed and developed experimental analyses on a PVT collector. The collector thermal and electrical efficiencies were 13% and 15%, respectively. Stylianou [7] developed a CFD model for a CPVT collector. The obtained results showed that the thermal efficiency varied from 45% to 55% and electrical efficiency varied from 8% to 11%. Tyto [15] worked on a numerical model to evaluate the performance of the Solarus PowerCollector under indoor and outdoor conditions and compared it numerically with experimental results. Li et al. [16] worked on a CFD simulation of a CCPC (crossed compound parabolic concentrator) to estimate natural heat transfer behavior and optical performance. Yi [17] performed a Computational Fluid Dynamics (CFD) simulation and determined the effects of natural convection, radiation and conduction heat transfer on the thermal performance of the Solarus PowerCollector. Campos et al. [18] studied the effects of HTF on the efficiency of a CPVT collector. Tiemessen [19] developed a CFD simulation model for the Solarus PowerCollector and compared with experimental results and modified the model to reduce the heat losses. The results showed that the most heat losses are by convection (78%) and the rest (22%) is by radiation. The Solarus PowerCollector is characterized by the electrical power of 270W and thermal power of around 1350W [20]. A CPC collector is a linear two-dimensional and non-imaging concentrator and it has the ability to reflect all of the incident radiation to the receiver within wide limits. In order to better understand the collector’s behavior, experimental tests were conducted. Several measurements under different conditions allowed a better understanding of the heat transfers inside the receiver. The present work reports a two-dimension CFD simulation on the Solarus PowerCollector to analyze and improve its thermal and electrical production. A CFD simulation model can predict the airflow, temperature gradient and thermal performance inside the collector. In previous works about this specific collector, Monte Carlo Ray Tracing (MCRT) was used to find the solar radiation distribution on the receiver, and this distribution was set as a boundary condition on the CFD model. In this paper, to the best of the authors’ knowledge, the Discrete Ordinate Method (DOM) was used for the first time to solve the radiation field, for this specific collector type. This model can find the entire solar radiation boundary conditions inside the domain, therefore there is no need to define them on the receiver. The CFD results were compared to the experimental results and have been successfully validated. This paper also evaluated the potential of the CPVT collector and measured its electrical and thermal generation. Different CFD simulations were done to find the optimum tilt angle for a specific location (Gävle, Sweden) in order to achieve the best energy yield. The effect of HTF on the collector yield was considered and several modifications were made on the collector based on the CFD results.

2. Materials and Methods

2.1. Description of the Collector and the Properties of its Components Figure1 shows the Solarus’s CPVT, which is called the PowerCollector. In Figure1, it is possible to see the PV cell string layout on both sides (top side (facing the sky) and bottom side (facing the reﬂective material)) of the bifacial PVT receiver. Energies 2020, 13, 1669 4 of 21 Energies 2020, 13, x FOR PEER REVIEW 4 of 21

Energies 2020, 13, x FOR PEER REVIEW 4 of 21

Figure 1. Solarus Power Collector. Figure 1. Solarus Power Collector. Figure 1. Solarus Power Collector. Figure 2 shows a schematic of the same collector from a top view [20]. The collector is 2.2 m2 and Figure2 shows a schematic of the same collector from a top view [ 20]. The collector is 2.2 m2 it is divided into two troughs, each one with one receiver with 2.29 m of length and 0.158 m2 of width. and it isFigure divided 2 shows into a twoschematic troughs, of the each same one collector with onefrom receiver a top view with [20]. 2.29 The mcollector of length is 2.2 and m and 0.158 m of It is characterized by an overall thermal efficiency of around 52% and the linear loss coefficient is width.it is divided It is characterized into two troughs, by an each overall one with thermal one re eﬃceiverciency with of 2.29 around m of 52%length and and the 0.158 linear m of loss width. coe ﬃcient 3.47W/(mIt is characterized2 K) [21]. by an overall thermal efficiency of around 52% and the linear loss coefficient is is 3.47W/(m2 K) [21]. 3.47W/(m2 K) [21].

FigureFigure 2. 2.Top Top view view of of the the concentrated concentrated photovoltaic-thermalphotovoltaic-thermal collector collector (CPVT) (CPVT) collector. collector. The The water water Figure 2. Top view of the concentrated photovoltaic-thermal collector (CPVT) collector. The water connectionsconnections are are marked marked in in blue blue and and the the electrical electrical connectionsconnections in in red red [20]. [20]. connections are marked in blue and the electrical connections in red [20]. Reflector: Vattenfall AB has developed the reflector geometry of the collector, called Maximum Reflector: Vattenfall Vattenfall AB AB has has developed developed the the reflec reflectortor geometry geometry of the of thecollector, collector, called called Maximum Maximum ReflectorReflector Concentration ConcentrationConcentration (MaReCo). (MaReCo).(MaReCo). The The The reflector reflector reflector is is a combinationisa combinationa combination of of a parabolicaof parabolic a parabolic and and circular andcircular circular reflective surfacereflective (commonly surfacesurface (commonly (commonly known as known CPCknown reflectors)as as CPC CPC reflector reflector thats) concentrate thats) that concentrate concentrate the solarthe solarthe radiation solar radiation radiation onto onto the ontothe receiver. the Thereceiver. details TheThe of the details details full of geometryof the the full full geometry aregeometry described are are described described by Adsten by byAdsten et Adsten al. [et22 al. ,et23 [22,23]. al.]. The[22,23]. The reflective Thereflective reflective material material material has been selectedhas been from selectedselected Almeco from from (VEGA125), Almeco Almeco (VEGA125), (VEGA125), with a total with with solara to atal to reflectance talsolar solar reflectance reflectance of around of around of 96%around 96% for 96% thefor the full for full spectrumthe full andspectrum 92% for andand the 92% visible92% for for the spectrum.the visible visible spectrum. Thespectrum. equation The The equati of equati theon parabolic onof theof theparabolic parabolic part of part the part of reflector the of reflector the reflector is (x is2 =(x2 y is=/ 0.0017), (x2 = thereforey/0.0017), the thereforetherefore focal length the the focal focal is 144.86 length length mmis is144.86 144.86 (and mm circlemm (and (and radius). circle circle radius). The radius). focal The The pointfocal focal point of thepoint of parabolicthe of parabolic the parabolic is located rightisis located on the centerrightright on on of the the the center center circle of (Figureof the the circle circle3). Figure(Figure (Figure4 3). shows 3).Figure Figure how 4 shows 4 solar shows how radiation how solar solar radiation is reflected radiation is reflected to is the reflected receiver andto PVthe cells. receiverreceiver and and PV PV cells. cells. Receiver: The receiver core is an aluminum extrusion with 8 elliptic channels. The PV cells are Receiver:Receiver: The The receiver receiver core core isis anan aluminumaluminum extrusionextrusion with with 8 8 elliptic elliptic channels. channels. The The PV PV cells cells are are encapsulated with silicone on both sides of the receiver core. encapsulatedencapsulated with with silicone silicone on on both both sides sidesof of thethe receiverreceiver core. Cell encapsulationencapsulation and and silicone: silicone: The The PV PV cell cell encapsulation encapsulation is done is done with with two twolayers layers of silicone of silicone Cell encapsulation and silicone: The PV cell encapsulation is done with two layers of silicone produced byby Wacker. Wacker. The The encapsulation encapsulation is isdone done by bypouring pouring a bottom a bottom layer layer of 1 ofmm 1 mmof silicone of silicone under under producedthe PV cells by Wacker.and a top The layer encapsulation of around 1 mm is doneover the by PV pouring cells. a bottom layer of 1 mm of silicone under the PV cells and a top layer of around 1 mm over the PV cells. the PV cells and a top layer of around 1 mm over the PV cells.

Energies 2020, 13, x FOR PEER REVIEW 5 of 21 Energies 2020, 13, x FOR PEER REVIEW 5 of 21 Standard Solar Cells: Each receiver side has two strings of 38 PV cells with an efficiency of 18.7% at StandardStandard Test Solar Conditions Cells: Each (STC) receiver and connected side has two in stseries.rings ofThese 38 PV PV cells cell with series an efficiencyon both sides of 18.7% of the receiverat Standard are connected Test Conditions in parallel. (STC) The and PV connected cell temp inerature series. coefficientThese PV cell was series measured on both by sides Bernardo of the et al. receiverand found are toconnected be 0.4%/C in [24].parallel. The The PV PVcells cell have temp beenerature cut, coefficientin order to was be ablemeasured to have by dimensions Bernardo et of al. and found to be 0.4%/C [24]. The PV cells have been cut, in order to be able to have dimensions of 52 by 148 mm. Overall, the collector has a total of 152 PV cells. The goal of cutting the cells is to lower 52 by 148 mm. Overall, the collector has a total of 152 PV cells. The goal of cutting the cells is to lower the current, which is specifically important for concentrating collectors. the current, which is specifically important for concentrating collectors. Glass: The solar glass is made out of low iron with a solar-weighted transmittance of 95% (stated Energies 2020Glass:, 13 ,The 1669 solar glass is made out of low iron with a solar-weighted transmittance of 95% (stated5 of 21 by the producers, SunArc). by the producers, SunArc). TableTable 2 shows2 shows the the features features and and details details ofof thethe collector.

FigureFigure 3. 3. The The detail detail of of geometric geometric concentration concentration (all(all dominations dominations in in mm). mm).

FigureFigure 4. 4.Concertation Concertation of of solar solar radiationradiation on the re receiverceiver and and location location of of the the focal focal point point.. Figure 4. Concertation of solar radiation on the receiver and location of the focal point. Standard Solar Cells: EachTable receiver 2. The side features has two of the strings PowerCollector of 38 PV. cells with an efficiency of 18.7% at Standard Test Conditions (STC)Table and 2. The connected features of in the series. PowerCollector These PV. cell series on both sides of the Features Values/Units receiver are connected in parallel. The PV cell temperature coefficient was measured by Bernardo et al. Collector Featuresproduction (nominal) 1350W thermal,Values/Units 270W electrical and found to be 0.4%/C[24]. The PV cells have been cut, in order to be able to have dimensions of 52 CollectorCollector production total (nominal) area 1350W thermal, 2.2 m 270W2 electrical by 148 mm. Overall, the collector has a total of 152 PV cells. The goal of cutting the cells is to lower the Receiver area 0.362 m2 current,Collector which is specificallytotal area important for concentrating collectors. 2.2 m Concentration ratio 1.52 2 Glass:Receiver The solar area glass is made out of low iron with a solar-weighted 0.362 m transmittance of 95% (stated Reflector reflectivity 96% for the full spectrum and 92% for the visible spectrum by the producers,Concentration SunArc). ratio 1.52 Receiver channel area 8 channels with 154 mm2 (one channel) TableReflector2 shows reflectivity the features and details 96% of for the the collector. full spectrum and 92% for the visible spectrum Silicone thickness 1 mm on both side of PV cells Receiver channel area 8 channels with 154 mm2 (one channel) Solar cell efficiency 18.7% (STC) Silicone thickness Table 2. The features of the 1 PowerCollector. mm on both side of PV cells Solar cell Temperature coefficient 0.4%/C Solar cell efficiency 18.7% (STC) Glass transmittanceFeatures Values 95%/Units Solar cell TemperatureCollector production coefficient (nominal) 1350W thermal, 0.4%/C 270W electrical Glass transmittance 95% 2.2. CFD ModelCollector of the Collector total area 2.2 m2 Receiver area 0.362 m2 2.2. CFDRadiation, Model of theconvection Collector and conduction are the three ways of heat transfer that take place inside of the collector.Concentration The receiver ratio and PV cells are heated by the sun’s radiation 1.52 and then cooled by an Radiation,Reflector convection reflectivity and conduction are 96% the for three the full ways spectrum of heat and transfer 92% for the that visible take spectrum place inside of the collector.Receiver The receiver channel area and PV cells are heated 8by channels the sun’s with 154radiation mm2 (one and channel) then cooled by an Silicone thickness 1 mm on both side of PV cells Solar cell efficiency 18.7% (STC) Solar cell Temperature coefficient 0.4%/C Glass transmittance 95% Energies 2020, 13, 1669 6 of 21

2.2. CFD Model of the Collector Radiation, convection and conduction are the three ways of heat transfer that take place inside of the collector. The receiver and PV cells are heated by the sun’s radiation and then cooled by an HTF. The air inside of the collector starts moving due to the buoyancy-induced density gradient, creating Energies 2020, 13, x FOR PEER REVIEW 6 of 21 free convection inside the collector. The physical behavior can be described by the continuity equation (EquationHTF. The (1)), air energyinside of equation the collector (Equation starts (2)) movi andng the due Navier to the Stokes buoyancy-i equationnduced (Equation density (3)). gradient, These equationscreating free are convection Partial Diff erentialinside the Equations collector. (PDE),The phys nonlinearical behavior and coupled,can be desc thereforeribed by they the continuity need to be discretizedequation (Equation and solved (1)), numerically energy equation [25]. (Equation (2)) and the Navier Stokes equation (Equation (3)). These equations are Partial Differential Equations (PDE), nonlinear and coupled, therefore they ∂ρ need to be discretized and solved numerically+ [25].(ρ u ) = 0 (1) ∂t ∇· ∂ρ (1) + ∇∙(ρu)=! 0 ∂T∂t ρCp + u T + qc = Q (2) ∂T∂t ·∇ ∇· (2) ρC +u∙∇T+∇∙q =Q ∂u ∂t 1 + ( u)u ν 2u = P + F (3) ∂t ∇· − ∇ −ρ∇ ∂u 1 (3) + (∇∙u)u−ν∇u=− ∇P + F where ρ is the fluid density, Cp is the∂t specific heat constant, uρ is the fluid velocity, P is the fluid pressure, Twhere is the fluidρ is temperaturethe fluid density, and q cCcanp is bethe defined specific by heat Fourier’s constant, law—k u is T.the Q fluid andF velocity, are the heat P is generation the fluid ∇ andpressure, external T is forces, the fluid respectively. temperature and qc can be defined by Fourier’s law—k∇T. Q and F are the heat generation and external forces, respectively. 2.2.1. Simulation Procedure 2.2.1.The Simulation CFD simulation Procedure has been developed by the finite volume method performed by ANSYS® v2019The R3 fluentCFD simulation [26]. Firstly, has the been geometry developed of the by collector the finite was volume defined method in the performed software andby ANSYS meshed® optimally.v2019 R3 Secondly,fluent [26]. from Firstly, the the experimental geometry of results, the collector the specific was setup,defined variable in the software and solution and meshed method wereoptimally. defined. Secondly, Finally, from the results the experi of themental model results, were analyzedthe specific and setu thenp, variable compared and with solution experimental method results.were defined. The simulation Finally, the model results solved of the the model continuity, were analyzed energy and and then momentum compared equations with experimental inside the collector.results. The Flow simulation field, heat model transfer, solved temperature the contin gradientuity, energy inside and the momentum receiver, thermal equations and inside electrical the yield,collector. and radiationFlow field, field heat were transfer, obtained temperature from these gradient set of simulations. inside the receiver, thermal and electrical yield, and radiation field were obtained from these set of simulations. 2.2.2. Geometry and Mesh of the Collector 2.2.2.A Geometry profile view and (2D Mesh model) of the of Collector the collector was used for the simulation (Figure5). This geometry includesA profile one trough view of(2D the model) collector, of the front collector box and was detailed used for receiver the simulation with HTF (Figure channels, 5). This PV geometry cells and siliconeincludes layers. one trough of the collector, front box and detailed receiver with HTF channels, PV cells and silicone layers.

FigureFigure 5. 5.The The geometrygeometry ofof thethe collectorcollector and details of the receiver.

An air domain was defined inside the collector between the reflector, glass and receiver for the calculation of the fluid flow, free convection and radiation field. To simplify the geometry, some of the small parts of the collector were not considered. The 2D mesh was generated by ANSYS® meshing tool (Figure 6). The collector has been meshed with a total number of 180,000 elements. The space around the receiver, the reflector and the surrounding edges were meshed carefully due to the strong temperature and velocity gradients.

Energies 2020, 13, 1669 7 of 21

An air domain was defined inside the collector between the reflector, glass and receiver for the calculation of the fluid flow, free convection and radiation field. To simplify the geometry, some of the small parts of the collector were not considered. The 2D mesh was generated by ANSYS® meshing tool (Figure6). The collector has been meshed with a total number of 180,000 elements. The space around the receiver, the reflector and the surrounding edges were meshed carefully due to the strong temperatureEnergies 2020, 13 and, x FOR velocity PEER REVIEW gradients. 7 of 21

Figure 6. Mesh of the collector. Figure 6. Mesh of the collector. 2.2.3. Solution Methods 2.2.3. Solution Methods The simulation was performed in a pressure-based method and steady-state conditions, with the effTheect simulation of gravity. Thewas SIMPLEperformed (Semi in a Implicit pressure-bas Methoded formethod Pressure and Linkedsteady-state Equations) conditions, algorithm with wasthe effect used forof gravity. pressure The velocity SIMPLE coupling, (Semi Implicit first-order Method upwind for Pressure discretization Linked for Equations) the radiation, algorithm and a second-orderwas used for upwindpressure discretization velocity coupling, for the first-orde momentumr upwind and energy. discretization The simulations for the wereradiation, performed and a second-order upwind discretization for the momentum and energy. The simulations were performed by using the double-precision solver and standard under-relaxation factor. Body force weighted was by using the double-precision solver and standard under-relaxation factor. Body force weighted was used for pressure calculations. Due to the range of Rayleigh number (Ra = 107), the laminar model used for pressure calculations. Due to the range of Rayleigh number (Ra = 107), the laminar model was an excellent approximation to model the behavior of fluid inside the collector. was an excellent approximation to model the behavior of fluid inside the collector. The PV cells produce electricity and reduce the total amount of heat transfer through the receiver. The PV cells produce electricity and reduce the total amount of heat transfer through the Then, a volumetric heat absorption was applied to the PV cells layer by using a UDF (User Defined receiver. Then, a volumetric heat absorption was applied to the PV cells layer by using a UDF (User Function) code. The efficiency of the PV cells was affected by their temperature. Therefore, the PV Defined Function) code. The efficiency of the PV cells was affected by their temperature. Therefore, cells’ efficiency can be calculated by [4,27]: the PV cells’ efficiency can be calculated by [4,27]: ƞη((T)T) = ƞη[1[1 −β β(T −TT +ϒ+ loglog((G) G))])] (4)(4) cell 0 − PV PV − 0 G

ββPV isis the the temperature temperature coefficient coefficient of of the the PV PV cell cell (0 (0.4%.4%/K/K for for mono-crystalline mono-crystalline cells) and is defineddefined asas thethe following:following: 11 β = (5)(5) βPV = T T T′0 − − T0 wherewhere T’T' is thethe highest operating temperature of the PV cells, for which the efficiency efficiency drops to zero, TT00 is the standardstandard temperaturetemperature ofof 2525 ◦°C,C, andand ηƞ00 isis thethe eefficiencyfficiency ofof thethe PVPV cellcell operatingoperating atatSTC. STC.Υ ϒGG isis thethe intensityintensity ofof thethe PVPV cellcell andand inin thisthis condition,condition, isis setset to zero becausebecause thethe eeffectffect ofof solarsolar radiationradiation onon thethe PVPV cellcell isis negligible. The electrical power output by the PV cells as the volumetric heat absorption isis calculatedcalculated byby EquationEquation (5),(5), asas cancan bebe seenseen below.below. L. W (6) E(T) =ƞ(T).G.L.W E(T) = ηcell(T).G. V (6) Vcell where L.W are the dimensions (m), Vcell is the volume of the PV cell (m3) and G is the solar radiation where(W/m2). L.W This are equation the dimensions was applied (m), Vcell as a UD is theF code volume for the of the PV PV cell cell in (m3)the model. and G is the solar radiation (W/m2). This equation was applied as a UDF code for the PV cell in the model. 2.2.4. Material Parameter Parameters such as materials, density, thermal conductivity, specific heat capacity and viscosity were considered independent from the temperature, except for the air. The air inside the collector was considered an incompressible ideal gas with a temperature-dependent density, as the free convection takes place inside the collector. Table 3 shows the properties of different materials.

Energies 2020, 13, 1669 8 of 21

2.2.4. Material Parameter Parameters such as materials, density, thermal conductivity, speciﬁc heat capacity and viscosity were considered independent from the temperature, except for the air. The air inside the collector was considered an incompressible ideal gas with a temperature-dependent density, as the free convection takes place inside the collector. Table3 shows the properties of di ﬀerent materials.

Table 3. Properties of diﬀerent materials.

Thermal Conductivity Density Speciﬁc Heat Capacity (W/m.K) (kg/m3) (J/kg.K) Front Glass 1 2500 720 Reﬂector 200 2700 901 Receiver 210 2700 901 Silicon 0.2 970 1550 PV cell 124 2320 678 Collector Box 0.033 500 100

2.2.5. Radiation Model To model the radiation field in the collector, the Radiative Transfer Equation (RTE) (Equation (6)) must be solved [28]: dI →r .→s 4 Z 4π 2 σ.T σs + (κ + σs).I →r .→s = κ.n . + . I →r .→s .Φ →s .→s dΩ (7) ds π 4π 0 0 where r and s are the position and direction vectors, I is the radiation intensity, n is the refraction -8 index, σ is the Stefan–Boltzmann constant (5.67 10 W/m2.K4), and σs and κ are the scattering and × absorption coefficients, respectively. T is the local temperature and Φ is the scattering phase function that describes the probability that a ray from one direction (s) will be scattered into a certain direction (s’). The numerical method used to solve the RTE equation was the Discrete Ordinate Method (DOM), as this model allows a specular surface to be defined. This method solves the radiation field inside the model for a finite number of discrete solid angle and direction vectors. The DOM method requires a directional discretization and, to avoid the ray effect, an angular discretization of 15 15 divisions × (Theta divisions and Phi division) and 3 3 pixels (Theta pixels and Phi pixels) was specified [29]. × All the surfaces were set as opaque with diffuse reflectivity, except for the glass and reflector. The glass was set as a semi-transparent surface and the reflector was set as a specular surface. The absorption and scattering coefficient were not considered for the air.

2.2.6. Boundary Conditions Different categories of boundary conditions were defined. The forced convection heat transfer coefficient with an average temperature was used to model the fluid channels. From the experimental results, the average value for HTF was found. The heat transfer in the HTF domain was not solved. The heat transfer coefficient inside the channels is a function of the Nusselt number (Nud), the thermal conductivity of the fluid (kf) and the hydraulic diameter (Dh), and is defined as [25]:

Nudkf hw.forced = (8) Dh

Reynolds calculations showed that the ﬂow regime inside the channels was laminar. Because of the high thermal conductivity of the receiver, the temperature of the channels was uniform. Then, the Nusselt number was constant Nud = 3.66 [25]. The thermal generation of the collector is calculated Energies 2020, 13, 1669 9 of 21

by Equation (8), where hw,forced is the heat transfer coefficient, Tf is fluid temperature and Tw is the temperature of the channels. Q = Ah (T Tw) (9) th w.forced f − The glass cover was modeled as a semi-transparent surface with an emissivity of 0.95 and with a thickness of 4 mm. The solar glass is made out of the iron glass with a solar weighted transmittance of 95%. Solar beam and diffuse radiation were defined according to the experimental measurements and solar angles were calculated using the setup place coordinates. The glass has a radiative heat loss to the sky (Tsky) and a forced convective heat loss to the ambient because of wind (Tamb). The heat transferEnergies 2020 coe, 13ffi, cientx FOR causedPEER REVIEW by wind and sky temperature is calculated as described by Kalogirou9 of [4 ]:21

8.6 .V0.6 hwind = (10) 8.6L 0.4. V. (10) h = L. = 1.5 Tsky 0.0552Tamb (11) T = 0.0552T. (11) where V is the wind speed (m/s) and L is the characteristic length of the collector (m). The average windwhere speed V is the in thewind model speed was (m/s) set toand 3.14 L mis /thes and charac the characteristicteristic length length of the wascollector set to (m). 2.31 The m. average windThe speed receiver in the ismodel made was out set of to aluminum 3.14 m/s and with the an characteristic emissivity of length 0.4. Thewas PVset to cells 2.31 have m. 0.4 mm thicknessThe receiver and are placedis made between out of two-siliconealuminum with layers an with emissivity 1 mm thickness. of 0.4. The The PV boundary cells have conditions 0.4 mm ofthickness the PV and cells are and placed silicone between were thetwo-silicone conjugated laye wallrs with because 1 mm of thickness. conduction The heat boundary transfer conditions between them.of the PV The cells temperature and silicone of these were layers the conjugated was analyzed wall andbecause later of on conduction compared withheat thetransfer experimental between them. The temperature of these layers was analyzed and later on compared with the experimental data retrieved from the outdoor tests. The reflector was modeled with a specular surface (=0.05) with data retrieved from the outdoor tests. The reflector was modeled with a specular surface (ϵ=0.05) with a 96% reflectivity and a 0.4 mm thickness. On the other hand, the backside of the reflector has been a 96% reflectivity and a 0.4 mm thickness. On the other hand, the backside of the reflector has been modeled as a diffuse surface (=0.3). modeled as a diffuse surface (ϵ=0.3). The collector box is made out of polycarbonate (=0.95) with a thickness of around 4 mm. The collector box is made out of polycarbonate (ϵ=0.95) with a thickness of around 4 mm. It is It is exposed to the surrounding area and has a convective heat loss to the ambient. A forced exposed to the surrounding area and has a convective heat loss to the ambient. A forced convection convection heat transfer coefficient (hwind) with ambient temperature was defined for the collector box heat transfer coefficient (hwind) with ambient temperature was defined for the collector box boundary boundary conditions. conditions. 2.3. Experimental Test Method and Equipment Description 2.3. Experimental Test Method and Equipment Description Figure7 describes the experimental setup. The setup consists of temperature, flow and radiation Figure 7 describes the experimental setup. The setup consists of temperature, flow and radiation measurements. The collector has been installed in the outdoor testing laboratory (coordinates: 60◦N; measurements. The collector has been installed in the outdoor testing laboratory (coordinates: 60°N; 17◦E) at Gävle University, with a surface tilt angle (β) of 30◦ (south-oriented). 17°E) at Gävle University, with a surface tilt angle (β) of 30° (south-oriented).

(a) (b)

FigureFigure 7. ((aa)) Solar Solar Collector Collector Test Test Rig at Gävle University. ( b) The tested Solarus CPVT collector.collector.

Figure 8 shows a schematic of the experimental setup. The setup consists of two loops: a solar collector loop (closed loop) and a secondary loop (open loop). The solar collector loop relates to the HTF flowing between the collector and heat exchanger, supplied by a fixed flow by pump 2. Furthermore, on the solar loop, measurement equipment has been installed in order to measure the system operation, and these are presented below. • KippZonen CMP3 and CMP6 pyrometers were used to measure solar direct and diffuse radiation. • PT100 thermal resistances were used to measure the inlet and outlet fluid temperature and ambient temperature. • K-type thermocouples were used for measuring the PV cells’ temperature. • 2 Omega FMG80 flowmeters were used to measure the flow rate in each trough. • A PicoLog USB TC08 datalogger was used to collect the data from the K-type thermocouples.

Energies 2020, 13, 1669 10 of 21

KippZonen CMP3 and CMP6 pyrometers were used to measure solar direct and diffuse radiation. • EnergiesPT100 2020, 13 thermal, x FOR PEER resistances REVIEW were used to measure the inlet and outlet fluid temperature10 of and 21 • ambient temperature. • A datalogger CR1000 from Campbell Scientific was used to visualize/store the parameters K-type thermocouples were used for measuring the PV cells’ temperature. • obtained by the PT100 ambient and water flow temperature sensors, the CMP3 and CMP6, 2 Omega FMG80 flowmeters were used to measure the flow rate in each trough. • and flowmeters. A PicoLog USB TC08 datalogger was used to collect the data from the K-type thermocouples. • The secondary loop relates to the outlet water from the heat exchanger. The heater and mixing A datalogger CR1000 from Campbell Scientific was used to visualize/store the parameters obtained •tank were used to have a different value of HTF temperature. Whenever the heater is working, pump 1 recirculatesby the PT100 the fluid, ambient in order and water to achieve flow temperature a uniform temperature. sensors, the CMP3 and CMP6, and flowmeters.

Figure 8. Schematic of the experimental setup. Figure 8. Schematic of the experimental setup. The secondary loop relates to the outlet water from the heat exchanger. The heater and mixing tank wereSix measurements used to have a di(A,fferent B, C, value D, E of and HTF F) temperature. were taken Whenever on three the different heater is dates working, and pump times. 1 recirculatesMeasurements the A fluid, and inB orderon day to one achieve (August a uniform 17), C and temperature. D on day two (August 18) and E and F on day threeSix (August measurements 25) were (A, conducted. B, C, D, E andThe F)stagnation were taken test on was three conducted different dates on measurement and times. Measurements F, where no AHTF and flow B on rate day has one been (August implemented 17), C and and D onthe day heat two losses (August were 18)equal and to E the and energy F on day received three from (August the 25)sun were[20]. For conducted. each measurement, The stagnation the inlet test and was outlet conducted water temperature on measurement for one F, trough where of no the HTF collector, flow rateambient has beentemperature, implemented solar andbeam the and heat diffuse losses radiation, were equal and to thetemperature energy received of different from layers the sun of [ 20the]. Forcollector each measurement,were measured the (Table inlet 4). and Table outlet 4 shows water temperaturethe average values for one for trough each ofparameter. the collector, The ambientincident temperature,angle is the angle solar between beam and the di ffsun’suse radiation, rays and andthe normal temperature on the of surface different of layersthe collector. of the collector were measured (Table4). Table4 shows the average values for each parameter. The incident angle is the angle between the sun’s rays and the normal on the surface of the collector.

Energies 2020, 13, 1669 11 of 21

Table 4. Diﬀerent parameters of each measurement.

Ambient Inlet Water Outlet Water Direct Diﬀuse Duration of Incident Angle Solar Solar Flow Rate Measurement Temperature Temperature Temperature Radiation Radiation 0 0 0 Measurement 2 2 ( ) Altitude( ) Azimuth ( ) (L/min) (◦C) (◦C) (◦C) (W/m ) (W/m ) (min) A 18.6 33.6 36.6 978.3 93.1 18.5 48.5 199.4 2.2 10 B 19.1 42.9 46.2 922.8 77.2 26.4 56.3 231.9 1 5 C 20.1 46.3 48.4 946.0 77.2 17.9 47.8 189.4 2.2 10 D 20.8 44.7 47.5 892.9 76.4 28.1 58.1 235.7 1.2 5 E 21.6 36.2 39.0 757.8 145.5 21.4 51.4 200.9 2.1 3 F 23.1 - - 422.5 114.6 29.2 59.2 231.8 0 3 Energies 2020, 13, x FOR PEER REVIEW 11 of 21

Table 4. Different parameters of each measurement.

Diffus Inlet Outlet Direct Incide Flow Duration Ambient e Solar Solar Measure Water Water Radiati nt Rate of Temperat Radiati Altitu Azimu ment Temperat Temperat on(W/ Angle (L/mi Measurem ure (°C) on(W/ de(⁰) th (⁰) ure (°C) ure (°C) m2) (⁰) n) ent (min) m2) A 18.6 33.6 36.6 978.3 93.1 18.5 48.5 199.4 2.2 10 BEnergies 202019.1, 13, 1669 42.9 46.2 922.8 77.2 26.4 56.3 231.9 1 12 of 215 C 20.1 46.3 48.4 946.0 77.2 17.9 47.8 189.4 2.2 10 D 20.8 44.7 47.5 892.9 76.4 28.1 58.1 235.7 1.2 5 E Four21.6 K-type sensors36.2 (1, 2, 3 and39.0 4) were757.8 located 145.5 as described 21.4 in Figure51.4 9.200.9 Each K-Type2.1 sensor 3 Fwas soldered23.1 on a diﬀerent - part of the - receiver.422.5 The K-type114.6 temperature29.2 59.2 sensors 231.8 have been0 numbered 3 according to the list below. Four K-type sensors (1, 2, 3 and 4) were located as described in Figure 9. Each K-Type sensor Backwas soldered side sensor on a different 1: Temperature part of the over receiver. the cell The (second K-type temperature cell). sensors have been numbered • according to the list below. Top side sensor 2: Temperature on the receiver (fourth cell). • • Back side sensor 1: Temperature over the cell (second cell). Top• side sensor 3: Temperature under the cell (fourth cell). • Top side sensor 2: Temperature on the receiver (fourth cell). Top• side Top sensor side 4:sensor Temperature 3: Temperature over under the cell the (fourth cell (fourth cell). cell). • • Top side sensor 4: Temperature over the cell (fourth cell).

Silicone 4 Top Side Cells 3 Silicone 2 Receiver Silicone Back Side Cells 1 Silicone

Figure 9. The placement of each temperature sensor on the different layers of the receiver. Figure 9. The placement of each temperature sensor on the different layers of the receiver. 3. Results and Discussion 3. Results and Discussion 3.1. Experimental Results 3.1. Experimental Results In this section, experimental results are presented and analyzed. Figures 10–12 show the In this section, experimental results are presented and analyzed. Figures 10, 11 and 12 show the temperaturetemperature of di ffoferent different layers layers of the receiver,of the receiver ambient, ambient temperature, temperature, inlet and inlet outlet and water outlet temperatures, water and solartemperatures, radiation and for solar measurements radiation for measurements A and B. Top A side and sensorB. Top side 2 shows sensor a 2 valueshows closea value to close the HTF temperature,to the HTF showing temperature, a good showing thermal a good conductivity. thermal cond Solaructivity. radiation Solar radiation is focused is focused on the backon the side back of the receiverside with of the the receiver highest with temperature the highest temperature on the focal on point. the focal In point. these In measurements, these measurements, back back side side sensor 1 was locatedsensor 1 far was from located the focalfar from point the (as focal the point focal (as point the isfocal set bypoint the is reflector’s set by the specificreflector’s geometry specific and sun’sgeometry relative position).and sun’s relative Therefore, position). it shows Therefore, a temperature it shows a close temperature to the HTF. close Onto the the HTF. other On hand, the top side sensorsother hand, 3 and top 4 showside sensors nearly the3 and same 4 show values nearly due tothe the same high values thermal due conductivity to the high over thermal the very thin PVconductivity cells (124W over/m.K). the very Back thin side PV sensor cells (124W/m.K) 1 would be. expectedBack side sensor to show 1 would the highest be expected temperature to show value the highest temperature value located, but as the sensor is not under the focal point, this does not located,Energies but 2020 as, the13, x sensorFOR PEER is REVIEW not under the focal point, this does not happen. 12 of 21 happen.

Figure 10. Measurement A: layers, water and ambient temperatures and solar radiation. The ﬂow rate Figure 10. Measurement A: layers, water and ambient temperatures and solar radiation. The flow rate of measurement:of measurement: 2.2 2.2 L/min. L/min.

Figure 11. Measurement B: layers, water and ambient temperatures and solar radiation. The flow rate of measurement: 1 L/min.

Energies 2020, 13, x FOR PEER REVIEW 12 of 21

Energies 2020Figure, 13, 1669 10. Measurement A: layers, water and ambient temperatures and solar radiation. The flow rate 13 of 21 of measurement: 2.2 L/min.

Figure 11. Measurement B: layers, water and ambient temperatures and solar radiation. The ﬂow rate EnergiesFigure 2020, 11.13, Measurementx FOR PEER REVIEW B: layers, water and ambient temperatures and solar radiation. The flow rate13 of 21 of measurement:of measurement: 1 L 1/min. L/min.

Figure 12. Measurement C: layers, water and ambient temperatures and solar radiation. The ﬂow rate Figure 12. Measurement C: layers, water and ambient temperatures and solar radiation. The flow rate of measurement: 2.2 L/min. of measurement: 2.2 L/min. 3.2. Validation of the CFD Model 3.2. Validation of the CFD Model In this section, the CFD model is validated with experimental results. Figure 13 shows the CFD In this section, the CFD model is validated with experimental results. Figure 13 shows the CFD resultsresults for a for temperature a temperature distribution distribution over over thethe cellscells on both both sides sides of of the the receiver receiver (outer (outer part) part) for the for the conditionsconditions of measurement of measurement A. A. This This Figure Figure showsshows that the the back back side side of ofthe the receiver receiver (where (where the focal the focal pointpoint is located) is located) can reachcan reach the highestthe highest temperature temperature and and sensor sensor 1 can 1 can show show this this temperature temperature if if it it is is under the focalunder line. the Thefocal top line. side The of top the side receiver of the hasreceiver a ﬂat has distribution a flat distribution due to due the uniformto the uniform solar radiationsolar (no focalradiation line). (no Both focal ends line). of Both the receiverends of the have receiver the same have value, the same which value, is lowerwhich thanis lower other than parts other of the receiverparts due of the to thereceiver convection due to the heat convection transfer heat from transf theer receiver from the to receiver the air to inside the air theinside collector. the collector. Figure 13 also showsFigure that13 also the shows placement that the of placement the sensor of 1 the on sensor the back 1 on side the ofback the side receiver of the isreceiver important is important because the because the PV cells might reach a ΔT of around 5 °C (44 to 39 °C) along the receiver width. This PV cells might reach a ∆T of around 5 C (44 to 39 C) along the receiver width. This accounts for the accounts for the back side sensor 1 showing◦ lower◦ temperatures than the top side sensor 4. back side sensor 1 showing lower temperatures than the top side sensor 4.

Figure 13. Simulated temperature distribution over the cells on both sides of the receiver (outer part) for measurement A.

Energies 2020, 13, x FOR PEER REVIEW 13 of 21

Figure 12. Measurement C: layers, water and ambient temperatures and solar radiation. The flow rate of measurement: 2.2 L/min.

3.2. Validation of the CFD Model In this section, the CFD model is validated with experimental results. Figure 13 shows the CFD results for a temperature distribution over the cells on both sides of the receiver (outer part) for the conditions of measurement A. This Figure shows that the back side of the receiver (where the focal point is located) can reach the highest temperature and sensor 1 can show this temperature if it is under the focal line. The top side of the receiver has a flat distribution due to the uniform solar radiation (no focal line). Both ends of the receiver have the same value, which is lower than other parts of the receiver due to the convection heat transfer from the receiver to the air inside the collector. Figure 13 also shows that the placement of the sensor 1 on the back side of the receiver is important becauseEnergies 2020 the, 13 PV, 1669 cells might reach a ΔT of around 5 °C (44 to 39 °C) along the receiver width.14 This of 21 accounts for the back side sensor 1 showing lower temperatures than the top side sensor 4.

Figure 13. Simulated temperature distribution over the cells on both sides of the receiver (outer part) EnergiesFigurefor measurement 2020 13., 13 Simulated, x FOR A.PEER temperature REVIEW distribution over the cells on both sides of the receiver (outer part)14 of 21 for measurement A. FiguresFigures 14 14,–16 15show and the 16 comparisonshow the comparison between experimental between experimental and CFD results.and CFD The results. temperature The oftemperature diEnergiesﬀerent 2020 layers, 13 of, x differentFOR of the PEER receiver REVIEWlayers of from the experimentalreceiver from resultsexperimental were compared results were with compared the CFD with results14 ofthe 21 for measurementsCFD results for A, measurements B and C. The experimentalA, B and C. The results experimental are average results values are average during thevalues measuring during the time Figures 14, 15 and 16 show the comparison between experimental and CFD results. The andmeasuring CFD results time are and weighted CFD results average are weighted values along average with values the receiveralong with (according the receiver to the (according temperature to temperature of different layers of the receiver from experimental results were compared with the distribution).the temperature distribution). CFD results for measurements A, B and C. The experimental results are average values during the measuringFigures 14 time–16 showand CFD a reasonable results are ﬁt weighted between theaverage experimental values along and with the CFD the receiver results, as(according the deviation to fromthe the temperature CFD model distribution). varies from 0.2% up to 11.4%. The average deviation value for four sensors is 7%.

Figure 14. Measurement A: experimental results versus Computational Fluid Dynamics (CFD) results. Figure 14. Measurement A: experimental results versus Computational Fluid Dynamics (CFD) results. Figure 14. Measurement A: experimental results versus Computational Fluid Dynamics (CFD) results.

Figure 15. Measurement B: experimental results versus CFD results. Figure 15. Measurement B: experimental results versus CFD results.

Figure 15. Measurement B: experimental results versus CFD results.

Figure 16. Measurement C: experimental results versus CFD results.

Figures 14, 15 and 16 show a reasonable fit between the experimental and the CFD results, as the deviation from the CFDFigure model 16. Measurement varies from C: 0.2% experimental up to 11.4%. results The versus average CFD results deviation. value for four sensors is 7%. Figures 14, 15 and 16 show a reasonable fit between the experimental and the CFD results, as the 3.3.deviation CFD Results from the CFD model varies from 0.2% up to 11.4%. The average deviation value for four sensors is 7%. The validation of the model allows further analysis of the CFD results. Figure 17 shows the distribution3.3. CFD Results of incident total radiation in the collector for a tilt angle of 30°, as in measurement A,

The validation of the model allows further analysis of the CFD results. Figure 17 shows the distribution of incident total radiation in the collector for a tilt angle of 30°, as in measurement A,

Energies 2020, 13, x FOR PEER REVIEW 14 of 21

Figures 14, 15 and 16 show the comparison between experimental and CFD results. The temperature of different layers of the receiver from experimental results were compared with the CFD results for measurements A, B and C. The experimental results are average values during the measuring time and CFD results are weighted average values along with the receiver (according to the temperature distribution).

Figure 14. Measurement A: experimental results versus Computational Fluid Dynamics (CFD) results.

Energies 2020, 13, 1669 15 of 21 Figure 15. Measurement B: experimental results versus CFD results.

Figure 16. Measurement C: experimental results versus CFD results. Figure 16. Measurement C: experimental results versus CFD results. 3.3. CFD Results Figures 14, 15 and 16 show a reasonable fit between the experimental and the CFD results, as the deviationThe validation from the ofCFD the model model varies allows from further 0.2% up analysis to 11.4%. of theThe CFD average results. deviation Figure value 17 showsfor four the distributionEnergiessensors 2020 is, 137%. of, x incidentFOR PEER totalREVIEW radiation in the collector for a tilt angle of 30◦, as in measurement15 of A,21 where the temperature of different layers of the receiver, ambient temperature, solar radiation and flowwhere3.3. rate CFD the was temperatureResults measured. of Thedifferent reference layers case of the is the receiver, only measurement ambient temperature, A. Several solar parameters radiation were and changedflow rate towas study measured. their impact The reference on the collector case is performancethe only measurement and compared A. Several with the parameters reference were case. The validation of the model allows further analysis of the CFD results. Figure 17 shows the changed to study their impact on the collector performance and compared with the reference case. Thedistribution parameters of wereincident collector total radiation tilt angle, in di thefferent collector HTF for temperature, a tilt angle noof front30°, as glass, in measurement receiver material A, The parameters were collector tilt angle, different HTF temperature, no front glass, receiver material and insulation. Figure 17 shows how solar radiation is focused on the back side of the receiver. and insulation. Figure 17 shows how solar radiation is focused on the back side of the receiver.

Figure 17. Discrete Ordinates (DO) radiation contour inside the collector.

Figures 1818 and and 19 19 show show the the distribution distribution of temperature of temperature and velocity and velocity streamlines streamlines inside the inside collector the forcollector measurement for measurement A, respectively. A, respectively. Figure 18 Figureshows 18 that shows the hottest that the part hottest of the part collector of the is,collector as expected, is, as theexpected, receiver, the due receiver, to the highdue to absorbance the high absorbance of light by theof light solar by cells the and solar the cells concentration. and the concentration. The bottom ofThe the bottom collector of the and collector front glass and havefront theglass lowest have temperaturethe lowest temperature because of convectionbecause of convection heat transfer heat to thetransfer ambient. to the ambient. Figure 19 shows how the air moves inside the collector (an eddy movement). The air on both sides of the receiver gets hot, and due to the temperature-dependent density, travels upwards. Then, it moves under the front glass, and it’s temperature reduces because of heat losses to the ambient and goes down. The reﬂector absorbs a small fraction (4%) of solar radiation and gets hot then increases air temperature. The air goes upward and this circulation is repeated. In the collector box (under the reﬂector), the air warms up and goes up. The walls of the collector’s box show convective heat loss to the ambient. Therefore, the air temperature decreases and the air moves down.

Figure 18. Temperature contours inside the collector.

Figure 19 shows how the air moves inside the collector (an eddy movement). The air on both sides of the receiver gets hot, and due to the temperature-dependent density, travels upwards. Then, it moves under the front glass, and it’s temperature reduces because of heat losses to the ambient and goes down. The reflector absorbs a small fraction (4%) of solar radiation and gets hot then increases air temperature. The air goes upward and this circulation is repeated. In the collector box (under the

Energies 2020, 13, x FOR PEER REVIEW 15 of 21 where the temperature of different layers of the receiver, ambient temperature, solar radiation and flow rate was measured. The reference case is the only measurement A. Several parameters were changed to study their impact on the collector performance and compared with the reference case. The parameters were collector tilt angle, different HTF temperature, no front glass, receiver material and insulation. Figure 17 shows how solar radiation is focused on the back side of the receiver.

Figure 17. Discrete Ordinates (DO) radiation contour inside the collector.

Figures 18 and 19 show the distribution of temperature and velocity streamlines inside the collector for measurement A, respectively. Figure 18 shows that the hottest part of the collector is, as expected, the receiver, due to the high absorbance of light by the solar cells and the concentration. EnergiesThe bottom2020, 13 ,of 1669 the collector and front glass have the lowest temperature because of convection16 ofheat 21 transfer to the ambient.

Energies 2020, 13, x FOR PEER REVIEW 16 of 21 reflector), the air warms up and goes up. The walls of the collector’s box show convective heat loss Figure 18. Temperature contours inside the collector. to the ambient. Therefore, theFigure air 18.temper Temperatureature decreases contours and inside the the air collector moves. down.

Figure 19. Velocity streamlines inside the collector.collector.

3.3.1. Collector Tilt Angle Variation The collector tilt angle has been varied between 00°◦ and 6060°◦ under the condition of measurement AA (Table(table 44)) toto studystudy thethe eeffectffect of tilt angle on th thee electrical and thermal productions productions of of the the collector. collector. In FigureFigure 2020,, thethe thermalthermal andand electricalelectrical powerpower ofof thethe collectorcollector atat didifferentfferent tilttilt anglesangles is shownshown for a specificspecific time of thethe year.year. For a 4040°◦ tilttilt angle,angle, thethe incidentincident angleangle isis 8.58.5°◦ and the thermalthermal and electrical power reachesreaches thethe maximum maximum values values of of 539 539 W W and and 147 147 W, W, respectively. respectively. It should It should be mentionedbe mentioned that that this isthis not is the not optimum the optimum angle angle of installation of installation for the for collector the collector for the for whole the yearwhole and year just and shows just the shows effect the of tilteffect angle of tilt on theangle collector on the productions.collector productions. It also shows It also that shows the eff thatect of th tilte effect angle of on tilt thermal angle productionon thermal isproduction more serious is more than serious the electrical than the one. electrical one.

Figure 20. Thermal and electrical power of the collector for different tilt angles.

3.3.2. HTF Temperature Variation Different HTF temperatures were modeled and are presented in Figure 21. Figure 21 shows the performance of the collector versus ΔT (Tm-Tamb). Tm is mean HTF temperature and Tamb is the ambient temperature. At higher HTF temperature, the thermal efficiency of the collector decreases and that is due to the decreasing temperature gradient between the receiver and HTF.

Energies 2020, 13, x FOR PEER REVIEW 16 of 21

reflector), the air warms up and goes up. The walls of the collector’s box show convective heat loss to the ambient. Therefore, the air temperature decreases and the air moves down.

Figure 19. Velocity streamlines inside the collector.

3.3.1. Collector Tilt Angle Variation The collector tilt angle has been varied between 0° and 60° under the condition of measurement A (table 4) to study the effect of tilt angle on the electrical and thermal productions of the collector. In Figure 20, the thermal and electrical power of the collector at different tilt angles is shown for a specific time of the year. For a 40° tilt angle, the incident angle is 8.5° and the thermal and electrical power reaches the maximum values of 539 W and 147 W, respectively. It should be mentioned that this is not the optimum angle of installation for the collector for the whole year and just shows the Energieseffect2020 of, 13tilt, 1669 angle on the collector productions. It also shows that the effect of tilt angle on thermal17 of 21 production is more serious than the electrical one.

Figure 20. Thermal and electrical power of the collector for different tilt angles. Figure 20. Thermal and electrical power of the collector for different tilt angles. 3.3.2. HTF Temperature Variation 3.3.2. HTF Temperature Variation Different HTF temperatures were modeled and are presented in Figure 21. Figure 21 shows Different HTF temperatures were modeled and are presented in Figure 21. Figure 21 shows the the performance of the collector versus ∆T (Tm-Tamb). Tm is mean HTF temperature and Tamb is the performance of the collector versus ΔT (Tm-Tamb). Tm is mean HTF temperature and Tamb is the ambient ambient temperature. At higher HTF temperature, the thermal efficiency of the collector decreases and Energiestemperature. 2020, 13, x AtFOR higher PEER REVIEW HTF temperature, the thermal efficiency of the collector decreases17 andof 21 that is that is due to the decreasing temperature gradient between the receiver and HTF. due to the decreasing temperature gradient between the receiver and HTF.

FigureFigure 21.21. Thermal and and electrical electrical efficiency eﬃciency of th ofe thecollector collector for different for diﬀ erentHTF temperatures HTF temperatures..

FigureFigure 21 21 shows shows that that thethe slopeslope of thermal efficiency efficiency line line and and Equation Equation (12) (12) [4] [4is] (U/G is (U /=G 0.005)= 0.005) and solarand radiation solar radiation for measurement for measurement A is 978.3W A is 978.3W/m/m2. The2. collector The collector heat lossheat coe lossffi cientcoefficient (U) is (U) calculated is as 2 4.89calculated W/m2.K. as 4.89 W/m .K. U. ΔTU.∆T (12) ƞ=ƞη = η− (12) 0 −G G FigureFigure 21 21 also also shows shows that that at at higher higher temperatures, temperatures, the the production production of of PV PV cells cells decreases, decreases, as as expected. Underexpected. stagnation Under stagnation (when the (when HTF nothe longer HTF no extracts longer heatextracts from heat the from collector), the collector), the PV the cell PV temperature cell temperature varies from 42 °C (measurement A (Tm ₋Tamb = 16.5)) to 105 °C. This 63 °C increase in the varies from 42 ◦C (measurement A (Tm -Tamb = 16.5)) to 105 ◦C. This 63 ◦C increase in the temperature temperature of the cells caused a 25% decrease in efficiency. This shows the importance of cooling of the cells caused a 25% decrease in efficiency. This shows the importance of cooling and thermal and thermal potential. The collector reaches a maximum of 52% in thermal and 13.3% in electrical potential. The collector reaches a maximum of 52% in thermal and 13.3% in electrical efficiency. efficiency. According to these results, the effect of HTF on thermal production was more pronounced Accordingthan on electrical to these production. results, the This eff ectis shown of HTF by ona steeper thermal curve production slope for the was thermal more pronouncedefficiency line than on than for the electrical efficiency line.

3.3.3. Collector Modification Table 5 presents three modifications, that have been suggested and studied, and later on compared with the base case presented in measurement A. To reduce the heat losses by convection in the collector box, insulation was applied on the backside of the reflector. This insulation increases the thermal power by 3% when working at a temperature of 23 °C above ambient (Figure 22). To increase the heat transfer rate between the receiver and HTF, the receiver material was changed from aluminum to copper, due to the higher conductance of the copper. This change had no significant relevance in the collector output, which indicates that the aluminum is not the bottleneck for the transfer of heat between the solar cells and the HTF. It is important to point out that there is a very small temperature gradient across the 158 mm of the receiver width. Another variation that has been studied was a collector without the front glass, in order to reduce the overall temperature inside the collector, since by removing the front glass, the hot air is released to the ambient. This effect also reduces the PV cells’ temperature and due to that, the electrical production increases by 2%. On the other hand, due to the lower temperature gradient, the thermal power decreased by 70% (Tamb = 18.6 °C, Tm = 35.1 °C). This result shows that, as expected, a glass cover is fundamental for any collector that has been expected to work at 10 °C above ambient temperatures.

Energies 2020, 13, 1669 18 of 21 electrical production. This is shown by a steeper curve slope for the thermal eﬃciency line than for the electrical eﬃciency line.

3.3.3. Collector Modification Energies 2020, 13, x FOR PEER REVIEW 18 of 21 Table5 presents three modifications, that have been suggested and studied, and later on compared with theTable base 5. case Performance presented of in the measurement different collector A. To variations reduce the studied heat losses (Tamb = by 18.6 convection °C, Tm = 35.1 in °C) the. collector box, insulation was applied on the backside of the reflector. This insulation increases the thermal Back Side Cell Top Side Cell power by 3% when working at a temperature of 23 ◦C aboveThermal ambient Power (Figure 22Electrical). Power Temperature Temperature (w) (w) Table 5. Performance(°C) of the different collector(°C) variations studied (Tamb = 18.6 ◦C, Tm = 35.1 ◦C). Measurement 42.4 Back Side Cell 42.2 Top Side Cell 511 Thermal Power Electrical 142.2 Power A (base case) Temperature (◦C) Temperature (◦C) (w) (w) Reflector Measurement A (base case)42.6 42.442.4 42.2 528 511 142.1 142.2 insulation Reflector insulation 42.6 42.4 528 142.1 Copper Copper receiver42.3 42.342.1 42.1 512 512 142.3 142.3 receiver No front glass 38.2 36.5 150 145.2 No front glass 38.2 36.5 150 145.2 No HTF 105.7 105.2 0 103.6 No HTF 105.7 105.2 0 103.6

Figure 22. The thermal and electrical efficiency for collector’s modifications. Figure 22. The thermal and electrical efficiency for collector’s modifications. To increase the heat transfer rate between the receiver and HTF, the receiver material was changed 4.from Conclusions aluminum to copper, due to the higher conductance of the copper. This change had no significant relevanceThe presented in the collector paper focused output, on which the CFD indicates modeling that theof a aluminum low concentrating is not the PVT bottleneck solar collector for the withtransfer an asymmetric of heat between reflector the solargeometry cells produced and the HTF. by Solarus It is important Sunpower. to point The outpresented that there CFD is model a very wassmall validated temperature by the gradient existing across experimental the 158 mm data. of theThe receiver design width.of the collector, the installation of the set-upAnother and the variation CFD model that were has been described, studied analyzed was a collector and discussed. without the After front the glass, validation in order of to results, reduce thethe CFD overall model temperature proved insideto be thea powerful collector, tool since for by solving removing the the continuity, front glass, energy the hot and air ismomentum released to equationsthe ambient. inside This the effect collector, also reduces as well the PVas cells’helping temperature to understand and due the to that,collector´s the electrical behavior production when variationsincreases to by the 2%. design On theare otherintroduced. hand, Several due to variations the lower were temperature considered gradient, and compared the thermal with powera base casedecreased of measurement by 70% (Tamb A. =Top18.6 side◦C, sensors Tm = 35.1 3 and◦C). 4 This showed result higher shows temperatures that, as expected, due ato glass direct cover solar is radiation.fundamental Top for side any sensor collector 2, located that has on been the expectedreceiver core, to work showed at 10 nearly◦C above the ambient same temperatures temperatures. as the ones registered for the HTF. The back side sensor 1 (located far from the focal point) showed lower temperatures than the ones registered for the top side sensor 4. As expected, the temperature of the HTF greatly affects the collector power, with both thermal and electrical efficiency decreasing with an increment in temperature. Under stagnation, the PV cells temperature reached a maximum of 105 °C (80 °C higher than standard temperature (25°C)) and the electrical production of the collector decreased by 32%. HTF, with an average temperature of 35.1 °C and 2.2 L/min flow rate, can decrease temperature to 42 °C. This 63 °C reduction in cell temperature caused a 25% increase in electrical efficiency. This result shows the importance of cooling. With the aim of increasing the overall collector production, three modifications were studied. Firstly, by applying insolation on the back side of the reflector, the thermal power increased by 3%.

Energies 2020, 13, 1669 19 of 21

4. Conclusions The presented paper focused on the CFD modeling of a low concentrating PVT solar collector with an asymmetric reflector geometry produced by Solarus Sunpower. The presented CFD model was validated by the existing experimental data. The design of the collector, the installation of the set-up and the CFD model were described, analyzed and discussed. After the validation of results, the CFD model proved to be a powerful tool for solving the continuity, energy and momentum equations inside the collector, as well as helping to understand the collector´s behavior when variations to the design are introduced. Several variations were considered and compared with a base case of measurement A. Top side sensors 3 and 4 showed higher temperatures due to direct solar radiation. Top side sensor 2, located on the receiver core, showed nearly the same temperatures as the ones registered for the HTF. The back side sensor 1 (located far from the focal point) showed lower temperatures than the ones registered for the top side sensor 4. As expected, the temperature of the HTF greatly affects the collector power, with both thermal and electrical efficiency decreasing with an increment in temperature. Under stagnation, the PV cells temperature reached a maximum of 105 ◦C (80 ◦C higher than standard temperature (25◦C)) and the electrical production of the collector decreased by 32%. HTF, with an average temperature of 35.1 ◦C and 2.2 L/min flow rate, can decrease temperature to 42 ◦C. This 63 ◦C reduction in cell temperature caused a 25% increase in electrical efficiency. This result shows the importance of cooling. With the aim of increasing the overall collector production, three modifications were studied. Firstly, by applying insolation on the back side of the reflector, the thermal power increased by 3%. Secondly, by changing the receiver material from aluminum to copper (due to the higher conductance), no relevant variations have been found, due to the low temperature gradient in the receiver. Lastly, by removing the front glass, the electrical yield increased by 2%, which is caused by the lower temperature of PV cells. However, this also implies that the thermal yield is reduced by 70%, which means that this would not be a good trade-off from an energy output perspective. This result shows, as expected, that collectors for DHW require a front glass.

Author Contributions: All authors contributed to write the paper. P.N., H.A.G., J.G. and T.L. analyzed the experimental data. P.N. and H.A.G. performed the CFD simulations and analyzed the CFD results. J.G. and T.L. performed the experimental setup, reviewed and edited the paper. D.C., M.S. and A.H. reviewed and edited the paper. All authors have read and agreed to the published version of the manuscript. Funding: This research was partly supported with funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 814865 (RES4BUILD). The authors are also grateful for the support provided by the STINT mobility program and are thankful for the fruitful cooperation with the project partners. The outputs reflect only the author’s view and the European Union cannot be held responsible for any use that may be made of the information contained therein. Acknowledgments: The author would like to acknowledge the support given by Björn Karlsson. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

Symbol Description, (Unit) Acronyms κ Absorption coeﬃcient, (1/m) CPC Compound Parabolic Collector Tamb Ambient temperature, (◦C) CFD Computational Fluid Dynamics A Area, (m2) CPV Concentrating Photovoltaic Concentrating L Characteristic length of the collector, (m) CPVT Photovoltaic-Thermal ρ Density, (kg/m3) CT Concentrating Thermal L, W Dimensions of the PV, (m) DOM Discrete Ordinate Method Energies 2020, 13, 1669 20 of 21

η0 Efficiency of the PV cell operating at STC, (–) DHW Domestic Hot Water ηcell Efficiency of the PV cell, (–) HTF Heat Transfer Fluid E Electrical production of the PV cell, (W) MCRT Monte Carlo Ray Tracing Emissivity, (–) PVT Photovoltaic-Thermal F External forces, (N) RTE Radiative Transfer Equation Kf Fluid Conductivity, (W/m.K) STC Standard Test Condition P Fluid Pressure, (Pa) UDF User-Defined Function Tf Fluid temperature, (◦C) u Fluid velocity, (m/s) Q Heat generation, (W/m3) U Heat loss coefficient, (W/m2.K) ’ T Highest operating temperature of the PV cells, (◦C) Dh Hydraulic diameter, (m) υG Intensity of the PV cell, (–) Tm Mean water temperature, (◦C) Nud Nusselt number, (–) →r .→s Position and direction vector, (m) I Radiation intensity, (W/m2) Ra Rayleigh number, (–) n Refraction index, (–) σs Scattering coefficient, (1/m) Φ Scattering phase function, (–) Tsky Sky temperature, (◦C) G Solar radiation, (W/m2) Cp Specific Heat Capacity, (J/kg.K) T0 Standard temperature, (25 ◦C) σ Stefan–Boltzmann constant, (5.669 * 10-8 W/m2.K4) βPV Temperature coefficient of the PV cell, (%/K) Tpv Temperature of PV cell, (◦C) Tw Temperature of the receiver channels, (◦C) k Thermal Conductivity, (W/m.K) Qth Thermal production of the collector, (W) β Tilt angle, (degree) t Time, (s) 3 Vcell Volume of the PV cell, (m ) 2 hw forced Water convection heat transfer, (W/m .k) 2 hwind Wind convection heat transfer, (W/m .k) V Wind speed, (m/s)

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