Design and Analysis of the Domestic Micro-Cogeneration Potential for an ORC System Adapted to a Solar Domestic Hot Water System

entropy

Article Design and Analysis of the Domestic Micro-Cogeneration Potential for an ORC System Adapted to a Solar Domestic Hot Water System

Daniel Leal-Chavez 1, Ricardo Beltran-Chacon 1,* , Paola Cardenas-Terrazas 1, Saúl Islas 2 and Nicolás Velázquez 2 1 Centro de Investigación en Materiales Avanzados, S.C., CIMAV, Chihuahua 31136, Mexico; [email protected] (D.L.-C.); [email protected] (P.C.-T.) 2 Instituto de ingeniería, Universidad Autónoma de Baja California, Mexicali 21100, Mexico; [email protected] (S.I.); [email protected] (N.V.) * Correspondence: [email protected]; Tel.: +52-614-439-1155

Received: 30 July 2019; Accepted: 11 September 2019; Published: 19 September 2019

Abstract: This paper proposes the configuration of an Organic Rankine Cycle (ORC) coupled to a solar domestic hot water system (SDHWS) with the purpose of analyzing the cogeneration capacity of the system. A simulation of the SDHWS was conducted at different temperatures, observing its performance to determine the amounts of useable heat generated by the solar collector; thus, from an energy balance point of view, the amount of heat that may be used by the ORC could be determined. The working fluid that would be suitable for the temperatures and pressures in the system was selected. The best fluid for the given conditions of superheated vapor at 120 ◦C and 604 kPa and a condensation temperature of 60 ◦C and 115 kPa was acetone. The main parameters for the expander thermodynamic design that may be used by the ORC were obtained, with the possibility of generating 443 kWh of annual electric energy with 6.65% global efficiency of solar to electric power, or an overall efficiency of the cogeneration system of 56.35% with a solar collector of 2.84 m2.

Keywords: solar domestic cogeneration; Organic Rankine Cycle; acetone; evacuated tube solar collector

1. Introduction The growing demand for energy and the current dependence on fossil fuels require more efficient processes and technologies to be developed, to allow a transition into a system with sustainable energy sources. In general terms, the objective is that buildings have zero net energy consumption through an efficient use of energy, and the adoption of renewable sources of energy and other technologies [1]. Photovoltaic, solar, thermal, and biomass technologies can contribute to reducing consumption for heating of spaces in the Mediterranean region [2], in order to reduce high energy costs, create energy security, and mitigate local air pollution [3–5]. Solar energy systems allow consumption to be reduced to almost zero net energy in buildings. For combined heat and power (CHP) systems, return periods are between 5.5–6.5 years, while for photovoltaic systems it takes 7 years [6]. Organic Rankine Cycle technology has intensified in recent years, and is being used as the main alternative to convert energy at low temperatures [7]. Solar water heaters generally capture a greater amount of solar energy during seasons with low hot water consumption, such as summer. In these circumstances, a lot of solar energy is wasted. Extending the utilization of energy captured by solar collectors through a second application would favor a technological alternative for electric production through renewable energies and a reduction of CO2 emissions associated with conventional fossil fuel-based generation techniques.

Entropy 2019, 21, 911; doi:10.3390/e21090911 www.mdpi.com/journal/entropy Entropy 2019, 21, x FOR PEER REVIEW 2 of 23

EntropyExtending2019, 21, 911 the utilization of energy captured by solar collectors through a second application2 of 23 would favor a technological alternative for electric production through renewable energies and a reduction of CO2 emissions associated with conventional fossil fuel-based generation techniques. An option to improve the utilization factor of solar systems is by integratingintegrating ORC systems to generate electricity in standard domestic use. Th Thee ORC is a proven technique to convert unused low temperature heat into useable mechanicalmechanical or electric energy [[8],8], and is characterized by its simplicity and flexibilityflexibility at a relatively lowlow operatingoperating temperaturetemperature [[9].9]. This techniquetechnique has has been been widely widely used used in recent in recent years withyears di ffwitherent different heat sources, heat such sources, as geothermal, such as heatgeothermal, recovery, heat biomass, recovery, and solar biomass, systems. and There sola arer manysystems. applications There andare configurationsmany applications at diff erentand temperaturesconfigurations and at capacitiesdifferent temperat [10]. In recentures and years, capacities there have [10]. been In recent many studiesyears, there on ORC, have ranging been many from optimization,studies on ORC, through ranging component from optimization, and working thro fluidugh selection, component to techno-economic and working fluid and experimentalselection, to studiestechno-economic [11]. and experimental studies [11]. Currently, therethere areare aa numbernumber ofof domestic-sized solarsolar ORC systems [[12–16];12–16]; their main operation characteristics are shown in Table1 1.. However,However, nonenone ofof themthem hashas aa configurationconfiguration usingusing directdirect vaporvapor generation with evacuatedevacuated tubetube collectors.collectors. These These configurations configurations generally generally use use an indirect heat exchanger between thethe solar heating systemsystem andand thethe ORCORC systemsystem (see(see FigureFigure1 1).). TheThe aimaim isis toto useuse thethe solar systemsystem only only for for pre-heating pre-heating the workingthe working fluid, andfluid, to laterand evaporateto later evaporate the fluid with the afluid conventional with a heatconventional source under heat controlledsource under conditions. controlled conditions.

Figure 1. (a) Proposed configuration, (b) typical configuration. Figure 1. (a) Proposed configuration, (b) typical configuration. Table 1. Performance of different Organic Rankine Cycles (ORCs). Table 1. Performance of different Organic Rankine Cycles (ORCs). Author Output Power Isentropic Efficiency (%) Global Efficiency (%) Output Isentropic Global Helvaci and Khan 2016Author [12] 135.96 W 58.66 3.81 Taccani et al. 2016 [13] 670 Wepower Efficiency 62 (%) Efficiency 8(%) VittoriniHelvaci et al. 2018 and [ 14Khan] 2016 [12] 700 W 135.96 W Not shown 58.66 3.81 3 * J. FreemanTaccani et al. 2017 et [al.15] 2016 [13] ~1 kWe 670 We 75 * 62 8 7.3 Cioccolanti, et al. 2017 [16] 2 kWe 60 * 4.98 Vittorini et al. 2018 [14] 700 W Not shown 3 * J. Freeman et al. 2017 [15] * assumed ~1 kWe by the author. 75* 7.3 Cioccolanti, et.al 2017 [16] 2 kWe 60* 4.98 There are different studies in the field of optimization of residential solar ORC configurations. * assumed by the author. A system with flat plate collectors with a heat source of 3.542 kW [12] uses a heat exchanger for condensationThere are and different a subsystem studies for in waste the field heating of optimi to heatzation the water of residential in a hot water solar tank.ORC Aconfigurations. configuration ofA 100system m2 of with a parabolic flat plate channel collectors with ORCwith [a13 heat] uses so aurce heat of exchanger 3.542 kW to [12] transfer uses heat a heat from exchanger the parabolic for channel,condensation and operates and a subsystem as an evaporator for waste for heating the ORC. to heat A configuration the water in a of hot an water evaporator tank. SDHWSA configuration used as anof 100 intermediate m2 of a parabolic heat exchanger channel to with heat theORC working [13] uses fluid a heat of the exchanger ORC system to transfer [14] additionally heat from uses the aparabolic system of channel, indirect heatingand operates for the as DHWS an evaporator and three flatfor platethe ORC. solar thermalA configuration collectors. of A an configuration evaporator withSDHWS a solar used area as ofan 15 intermediate m2 and thermal heat energy exchanger storage to heat [15] maintainsthe working and fluid uses of energy the ORC to mitigate system solar [14] energyadditionally variations uses ina thesystem ORC. of A solarindirect system heatin withg for a linear the DHWS Fresnel collector,and three with flat aplate total surfacesolar thermal area of 148collectors. m2, thermal A configuration storage with with phase a solar change, area and of 15 an m ORC2 and [16 thermal], uses the energy tank indirectlystorage [15] for maintains phase change and asuses the energy evaporator to mitigate from the solar ORC. energy variations in the ORC. A solar system with a linear Fresnel The proposed system presents a fundamental difference to other applications reported in the literature, in that the heat transfer is carried out directly from the evacuated tube solar collectors,

Entropy 2019, 21, x FOR PEER REVIEW 3 of 23 collector, with a total surface area of 148 m2, thermal storage with phase change, and an ORC [16], uses the tank indirectly for phase change as the evaporator from the ORC. EntropyThe2019 proposed, 21, 911 system presents a fundamental difference to other applications reported in3 ofthe 23 literature, in that the heat transfer is carried out directly from the evacuated tube solar collectors, using it as an evaporator. This improves the cycle efficiency due to the elimination of heat losses in using it as an evaporator. This improves the cycle efficiency due to the elimination of heat losses in the intermediate heat exchanger. When intermediate heat exchangers are added, each heat exchanger the intermediate heat exchanger. When intermediate heat exchangers are added, each heat exchanger requires a temperature difference to be effective. Therefore, each added heat exchanger decreases the requires a temperature difference to be effective. Therefore, each added heat exchanger decreases the maximum source temperature. In other words, the heat transfer increases the generation of entropy maximum source temperature. In other words, the heat transfer increases the generation of entropy of of the system, thus reducing the ability to produce work. the system, thus reducing the ability to produce work. This configuration is simpler because it eliminates the need for using two separate systems (a This configuration is simpler because it eliminates the need for using two separate systems (a solar solar system and ORC system), thus avoiding the need for two pumps to recirculate the fluid in both system and ORC system), thus avoiding the need for two pumps to recirculate the fluid in both systems. systems. The objective is that the proposed system can simultaneously provide two services: hot water The objective is that the proposed system can simultaneously provide two services: hot water and electricity production, instead of using the solar collector to provide only one service (hot water). and electricity production, instead of using the solar collector to provide only one service (hot water). It also increases the annual thermal performance of the collector because of the utilization of extra It also increases the annual thermal performance of the collector because of the utilization of extra heat for electricity production. The integration of an ORC system into a solar domestic hot water heat for electricity production. The integration of an ORC system into a solar domestic hot water system (SDHWS) is presented to achieve a domestic micro-cogeneration, taking into consideration system (SDHWS) is presented to achieve a domestic micro-cogeneration, taking into consideration the pressures and temperatures at which these two systems may work properly. The energy of the the pressures and temperatures at which these two systems may work properly. The energy of the fluid that does not produce work in the expander is utilized in the hot water tank for simultaneous fluid that does not produce work in the expander is utilized in the hot water tank for simultaneous production of hot water and electricity. production of hot water and electricity. The use of a variable flow pump is proposed for the vapor generation to occur directly in the solar The use of a variable flow pump is proposed for the vapor generation to occur directly in the collector, ensuring a constant vapor pressure and temperature at the collector outlet, while for the solar collector, ensuring a constant vapor pressure and temperature at the collector outlet, while for condensation zone of the system, a heat exchanger integrated within the SDHWS hot water tank will the condensation zone of the system, a heat exchanger integrated within the SDHWS hot water tank be used (see Figure2). will be used (see Figure 2).

Figure 2. SchemeScheme of of ORC ORC adapted adapted to to solar solar domestic domestic hot hot water system (SDHWS).

There are a number of studies related to to workin workingg fluid fluid selection selection for for the the ORC ORC [17–21]; [17–21]; however, however, theythey generallygenerally focus focus on on operation operation temperatures. temperatures. In contrast, In contrast, in this in study this thestudy (relatively the (relatively low) operation low) operationpressures thatpressures the SDHWS that the may SDHWS withstand may werewithstand first considered, were first considered, and later their and influence later their on influence the fluid onproperties the fluid and properties the thermal and performancethe thermal performance system were system evaluated. were evaluated. For the basic engineering design of this system a dimensioning method is proposed, including (A) an analysis of the thermal energy potential available in the SDHWS for a secondary use (ORC); (B) identification of operation conditions (the most adequate temperature and mass flow for an efficient Entropy 2019, 21, 911 4 of 23 operation of the SDHWS and ORC integrated system); and (C) the identification of working fluids that may allow a better performance to be obtained under these conditions. For this proposal a year-long simulation was conducted in Transient System Simulation Tool (TRNSYS) of a conventional solar hot water system with an evacuated tube collector. The results of the simulation of the main components in the system were validated with experimental data available in the literature. In this analysis the year-long climatic characteristics, the hourly solar energy utilization in the collector, and the hot water needs for an average-sized household were considered. The results of the simulation in TRNSYS show the energy flows and their destination, classifying them into thermal losses, useable heat for hot water, and potential useable (unutilized) heat, as well as the amount of energy that the cogeneration system can produce is calculated. From this study, it is possible to analyze the system performance when working at different temperature levels and to estimate the cogeneration potential.

2. Description of the System A cogeneration system is proposed for integration into solar water heating systems [22], as shown in Figure2 and Table2 describes in detail the main system components. It comprises a solar collector (evaporator) (2) which is interconnected to a two-position, three-way valve (9). In one position, the valve (9) allows the working fluid to flow towards the condenser (5), and in the other valve position the working fluid is directed towards an expansion device (3). The working fluid that comes out of the expansion device (3) is directed towards the condenser (5). The condenser (5) is a heat exchanger submerged inside the hot water tank (4). The system uses an auxiliary heat exchanger (7), in which a two-position, three-way valve (8) directs the working fluid towards the heat exchanger when heat removal in the condenser (5) is not sufficient. When the system changes from heating mode to ORC mode, the fluid pump (1) reduces the flow, causing part of the working fluid to be stored in a receptor tank (6).

Table 2. Basic speciﬁcations of the system components.

Solar Collector Cooling Coil Aperture area 2.84 m2 Length 18.6 m Fluid capacity 0.790 L Area 0.929 m2 Flow rate 0.0333 L/s Coil material cooper Max flow rate 0.25 L/s Coil internal diameter 1.27 cm Max operating pressure 800 kPa Coil external diameter 1.59 cm Hot Water Tank Expander Capacity 270 L Max. Output Power 245W Height 1.5 m Nominal expander power 194 W Internal diameter 0.45 m Nominal Volumetric flow 850 L/h Insulation thickness 0.047 m Expansion ratio 4.85 Insulation conductivity 0.036 W/mK Isentropic efficiency 0.85 Pump Design Point of the ORC Required power for ORC 1.5 W Irradiance 950 W/m2 Flow rate 15.4 L/h Collector thermal efficiency 62.50% Input pressure 115 kPa Output collector power 1687 W Output pressure 604 kPa Expander output 194 W Fluid temperature 60 ◦C Global efficiency 7.20%

One characteristic of the proposed system is that it may work under two operation modes; either water heating only, or combined heat and power production, depending on the requirements. Entropy 2019, 21, 911 5 of 23

2.1. Operation Mode: Water Heating The system configuration for exclusive production of hot water requires that the working fluid at the collector output is directed towards the heat exchanger inside the hot water tank. Through the heat exchanger/condenser, the working fluid transfers heat indirectly (without direct contact) to the water in the hot water tank. To achieve an efficient operation, the working fluid mass flow is controlled so that the working fluid temperature at the collector output is higher than the preset average tank water temperature. The working fluid that leaves the condenser out of the hot water tank is then directed towards the fluid pump and then to the evaporator inlet. This cycle is operated as long as the working fluid temperature at the solar collector output is higher than the water temperature in the hot water tank, or until the preset temperature (60 ◦C) is reached. In this mode of operation, the expander is not used; the fluid instead flows directly from the collector to the submerged heat exchanger. In this mode of operation, there is no phase change of the working fluid within the cycle, so the pump only circulates the working fluid, and thus it does not impose a high pressure change across the cycle.

2.2. Operation Mode: Organic Rankine Cycle The contribution of thermal energy to the water in the hot water tank when there is low hot water demand causes a progressive increase of water temperature in the hot water tank. Once the hot water tank temperature reaches a preset operation temperature (60 ◦C), the valve (9) (Figure2) changes position and directs the working fluid towards the volumetric expander. Simultaneously, the pump turns off momentarily to drain the working fluid partially into the receptor tank (6), which stores the unused working fluid when working in the Rankine cycle. After this, the pump starts to operate with a mass flow that allows the production of superheated vapor (at 120 ◦C) at the evaporator outlet. Variations in the solar resource and the useable heat produced require that the flow is regulated depending on the solar irradiance to produce steadily superheated vapor at the evaporator outlet. The expander may start working at a moment when there is a pressure differential between the hot side (collector outlet) and the cold side (hot water tank and/or condenser) of the system and convert some useful heat into useable mechanical work. This way, some of the solar energy captured by the solar collector which is not required to heat water (once it has reached a preset temperature) is used to produce mechanical work. The working fluid at a high temperature at the expander output is used to heat the water in the hot water tank when the conditions of the hot water tank temperature allow it, thus achieving a cogeneration of electrical and thermal energy. As heat is transferred into the hot water tank, its temperature increases, and the temperature difference between the working fluid and the hot water tank decreases; this eventually reduces the condenser cooling capacity to remove the necessary energy to condense the working fluid. Under these circumstances, it is necessary to have an auxiliary heat exchanger that allows the removal of the necessary energy to condensate the working fluid before it reaches the fluid pump. To achieve this energy removal, the valve (8) changes position so it directs the working fluid towards the auxiliary heat exchanger, where it is subcooled and stored in the receptor tank, completing the Rankine cycle. When all the energy provided by the collector is required for water heating, or when there is not enough irradiance for working fluid evaporation, the valve (9) changes position so the fluid flows directly towards the condenser in the hot water tank, thus homogenizing pressure in the whole system. Heat transfer is conducted directly from the solar collector towards the ORC working fluid, and the fluid energy not extracted by the expander is conducted towards the hot water tank for the simultaneous production of hot water and electricity. Entropy 2019, 21, 911 6 of 23 Entropy 2019, 21, x FOR PEER REVIEW 6 of 23

3.3. Thermodynamic Thermodynamic Model Model of of the the SDHWS SDHWS TheThe SDHWS SDHWS was was analyzed analyzed in in TRNSYS, TRNSYS, describing describing a a conventional conventional evacuated evacuated tube tube collector collector solar solar hothot water water system. system. These These simulations simulations allow allow the the prediction prediction of of the the performance performance of a a system system by by analyzing analyzing performance under dynamic conditions, allowing a pr properoper system sizing. Figure Figure 33 showsshows thethe schemescheme usedused for the study of the TRNSYS simulation.

FigureFigure 3. SDHWSSDHWS scheme scheme in in the the TRNSYS TRNSYS simulation simulation studio. studio.

TheThe weatherweather datadata location location used used in thisin this study study was Chihuahua,was Chihuahua, Mexico, Mexico, with 1 /64with hour 1/64 time hour intervals time intervalsfor the simulation for the simulation in order toin obtainorder to consistent obtain consistent results. results. TheThe objective of of this analysis was to characterize system performance at at different different operation temperatures,temperatures, and and to to identify identify the the parameters parameters that that influence influence heat heat gain. gain. The The model model refers refers only only to the to operationthe operation of the of theSDHWS, SDHWS, without without considering considering the the operation operation within within the the ORC. ORC. The The focus focus of of this simulationsimulation is to analyze thethe collectorcollector usefuluseful energy energy and and the the domestic domestic hot hot water water energy energy requirements requirements in inorder order to to estimate estimate the the energy energy that that could could be be used used within within the the ORC ORC system. system. TheThe resultsresults allowallow for for a quantificationa quantification of the of heatthe transferheat transfer rate, the rate, extra the heat extra that heat could that be harnessedcould be harnessedfor a secondary for a use,secondary and the use, mass and flows the andmass physical flows and conditions physical of workingconditions fluids of working that will fluids be used that in willthe system.be used in the system. TheThe collector collector converts converts solar solar irradiance irradiance into into useabl useablee heat heat and and transfers transfers it to it the to working the working fluidfluid that flowsthat flows through through the collector the collector manifold manifold towards towards the cooling the cooling coil submerged coil submerged in the hot in the water hot tank, water where tank, itwhere heatsit water heats for water domestic for domestic use. The use. pump The keeps pump working keeps working until the until top of the the top hot of water the hot tank water reaches tank anreaches operation an operation temperature temperature of ~75 °C, of as ~75 recommended◦C, as recommended by the manufacturer by the manufacturer [23]. If the hot [23 ].water If the does hot notwater reach does the not desired reach temperature the desired temperatureupon its utilization, upon its it utilization,may be heated it may by an be auxiliary heated by conventional an auxiliary heater.conventional heater. TheThe operation andand simulation simulation conditions conditions for for the the main main components components (i.e., (i.e. solar solar collector, collector, hot waterhot water tank, tank,and internal and internal heat exchanger) heat exchanger) were validatedwere validated with experimental with experimental data available data available in the literature in the literature [24–26]. [24–26].The results The shown, results verifyshown, that verify the modelsthat the havemodels been have correctly been correctly implemented implemented in the simulation, in the simulation, and also andshow also the show detail the of eachdetail one. of each one.

Entropy 2019, 21, 911 7 of 23 Entropy 2019, 21, x FOR PEER REVIEW 7 of 23

3.1.3.1. Solar Collector Solar collectorscollectors are aa specialspecial typetype ofof heatheat exchangersexchangers thatthat transformtransform solarsolar radiationradiation intointo useableuseable heat,heat, whichwhich isis transferredtransferred intointo aa ﬂuidfluid thatthat circulatescirculates throughthrough thethe collectorcollector [[27].27]. The resultsresults obtainedobtained in thethe ﬁeldfield teststests conductedconducted byby KottwitzaKottwitza [[28]28] werewere consideredconsidered forfor thethe validationvalidation ofof thethe mathematicalmathematical modelmodel usedused inin thisthis study,study, whilewhile QQmodelmodel showsshows thethe resultsresults obtainedobtained throughthrough thethe modelmodel usedused byby typetype 71,71, asas shownshown inin FigureFigure4 4..

Figure 4. Comparison of experimental tests versus the numerical model of the solar collector.

As maymay bebe seenseen inin FigureFigure4 4,, there there are are very very close close approximations approximations to to the the values values obtained obtained inin the the collectorcollector experimentalexperimental data,data, withwith aa maximummaximum errorerror ofof 1.44%1.44% atat thethe outletoutlet power.power.

3.2.3.2. Hot Water Tank The hothot water water tank tank is an is importantan important component component of a solar of hota solar water hot system water since system it may since considerably it may improveconsiderably its e ffiimproveciency andits efficiency profitability, and allowingprofitability, better allowing use of thebetter solar use system, of the solar and equatingsystem, and the usefulequating heat the of useful the solar heat resource of the andsolar energy resource demand and energy [29]. Solar demand energy [29]. is a time-dependentSolar energy is a energy time- resource,dependent just energy like theresource, energy just requirement, like the energy but bothrequirement, occur at but diff erentboth occur times at than different the solar times energy than supply;the solar therefore, energy supply; energy therefore, storage isenergy necessary storage if solar is necessary energy isif solar to be energy used to is meet to be a used major to partmeet of a energymajor part needs. of energy needs. For thethe validationvalidation ofof thethe hothot waterwater tanktank modelmodel andand submergedsubmerged coolingcooling coil,coil, thethe experimentalexperimental datadata inin thethe literatureliterature werewere comparedcompared toto datadata obtainedobtained throughthrough thethe simulation.simulation. TheThe resultsresults obtainedobtained byby CruickshankCruickshank and HarrisonHarrison [[29],29], whowho usedused aa commercialcommercial 270270 Ll hot water tank, were considered. ThisThis tank uses fiberglassfiberglass insulation with a 0.047 m thickness, thickness, and and a a 0.036 0.036 W/mK W/mK thermal thermal conductivity. conductivity. TheThe hothot waterwater tanktank hashas aa heightheight ofof 1.51.5 mm andand a 0.45 m internal diameter. In the experiment, the water was heated and mixed at a temperature of 54.0 C in an environment of 20 0.03 C over 48 h. Readings was heated and mixed at a temperature of 54.0◦ °C in an environment of± 20 ± ◦0.03 °C over 48 hours. wereReadings carried were out carried every 3 out min, every with temperature3 min, with temper sensorsature spaced sensors every 15spaced cm in every a vertical 15 cm array in a to vertical obtain stratificationarray to obtain readings. stratification The heat readings. loss coe Thefficients heat forloss each coefficients node were for consideredeach node were for the considered validation for of thisthe validation model, as shownof this model, in Figure as5 shown. in Figure 5. From thethe datadata of the experimental cool down test conducted by Cruickshank and Harrison [29], [29], aa loss of 14,580 14,580 kJ kJ was was obtained obtained over over 48 48 hours. h. The The result result of of the the simulation simulation of of type type 6060 waswas 14,83514,835 kJ, withwith anan error error of of 1.74%, 1.74%, which which shows shows that that the mathematicalthe mathematical model model of the hotof the water hot tank water is verytank accurate. is very accurate.From the same loss calculation, taking a single average loss coefficient from the insulation 2 characteristics,From the Usame= 0.86 loss W calculation,/m K, a significantly taking a reducedsingle average heat loss loss is obtained,coefficient with from a 19%the diinsulationfference withcharacteristics, respect to theU = experiment. 0.86 W/m2K, a significantly reduced heat loss is obtained, with a 19% difference with respect to the experiment.

Entropy 2019, 21, 911 8 of 23

EntropyEntropy 20192019,, 2121,, xx FORFOR PEERPEER REVIEWREVIEW 88 ofof 2323

FigureFigure 5.5. UU coefficientcoecoefficientﬃcient weighing weighing by by no nodesnodesdes in in the the hothot waterwater tank.tank.

3.3.3.3. Cooling Cooling Coil Coil TheThe hothothot water waterwater tank tanktank sub-system sub-systemsub-system for waterforfor waterwater heating heatingheating in this inin study thisthis consists studystudy ofconsistsconsists a cooling ofof coilaa coolingcooling submerged coilcoil insubmergedsubmerged the storage inin tank, thethe wherestoragestorage the tank,tank, high wherewhere temperature thethe highhigh working tetemperaturemperature ﬂuid coming workingworking from fluidfluid the solar comingcoming collector fromfrom exchanges thethe solarsolar heatcollectorcollector with exchangesexchanges the water inheatheat the withwith hot waterthethe waterwater tank. inin thethe hothot waterwater tank.tank. DataData presentedpresented byby R.R. FarringtonFarrington [[24][24]24] werewere usedused forfoforr thethe validationvalidation ofofof thethe coolingcooling coil.coil. This This cooling cooling 2 coilcoil hashashas a aa total totaltotal length lengthlength of ofof 18.6 18.618.6 m andmm andand an areaanan areaarea of 0.929 ofof 0.9290.929 m ; it mm is22;; made itit isis mademade of a plain ofof aa copper plainplain coppercopper tube with tubetube an with internalwith anan diameterinternalinternal diameterdiameter of 1.27 cm ofof and 1.271.27 an cmcm external andand anan external diameterexternal diameterdiameter of 1.59 cm. ofof 1.591.59 cm.cm. TheThe experimentalexperimental data data presented presented by by R.R. FarringtonFarrington [24] [[24]24] werewere takentaken intointo accountaccount toto validatevalidate thethe heatheat exchangerexchanger simulation.simulation. TheThe curvescurvescurves displayed displayeddisplayed by byby the thethe model modelmodel developed developeddeveloped in TRNSYS inin TRNSYSTRNSYS by type byby 60 showtypetype a6060 very showshow good aa adjustmentveryvery goodgood withadjustmentadjustment respect withwith to the respectrespect experimental toto thethe experimentalexperimental data obtained datadata by R.obtainedobtained Farrington byby R.R. [ 24 FarringtonFarrington], with an [24],[24], average withwith di ananﬀerence averageaverage of 1.6%differencedifference between ofof 1.6%1.6% the three betweenbetween models thethe three (Figurethree modelsmodels6). (Figure(Figure 6).6).

FigureFigure 6.6. ComparisonComparison of of experimental experimental data data versus versus TRNSYS TRNSYS ofof thethe submergedsubmerged coolingcooling coil.coil. 4. Energy Balance 4.4. EnergyEnergy BalanceBalance It is a common practice to use computer simulation to predict the performance of a solar domestic ItIt isis aa commoncommon practicepractice toto useuse computercomputer simusimulationlation toto predictpredict thethe performanceperformance ofof aa solarsolar hot water system. This process is based on the precise speciﬁcation of the system characteristics, domesticdomestic hothot waterwater system.system. ThisThis processprocess isis basedbased onon thethe preciseprecise specificationspecification ofof thethe systemsystem characteristics,characteristics, withwith thethe purposepurpose ofof integratingintegrating allall thesethese sub-systemssub-systems andand toto analyzeanalyze thethe behaviorbehavior thatthat

Entropy 2019, 21, 911 9 of 23 with the purpose of integrating all these sub-systems and to analyze the behavior that would be obtained through the interaction of all these components in a time-variable transitory state, according to the weather changes at the site.

4.1. Operation of the Solar SDHWS A typical meteorological year (TMY) of Chihuahua, Mexico, was considered for the simulation of the SDHWS; and the solar energy captured by the collector and the hot water needs were assumed for an average-sized household in Mexico. The required heat for a year-long supply of hot water was determined after analyzing the requirements, as well as the main devices in the system and the collector performance. In this study are considered the requirements of an average-sized household in Mexico of 3.7 (~4) members, according to INEGI [25]. A daily average hot water consumption of 236 L is assumed (Table3), at an average temperature of 45 ◦C[26].

Table 3. Typical residential hot water consumption [29].

Usage Amount of Hot Water (L) Daily Total Consumption per Household (L) 1 x Handwashing 3 (12 Uses) 36 1 x Shower 35 (4 Uses) 140 1 x Dishwashing 20 (2 Uses) 40 Cleaning 3 per person per day 12 Cooking 2 per person per day 8 Total Daily Requirement: 236 L

Considering Table3, the hourly consumption is adjusted to the typical household consumption reported by ASHRAE [30]. A daily consumption of 236 L at 45 ◦C was considered, representing 86,140 L and 4464 kWh of thermal energy per year. Three energy inputs were considered to obtain this required heat, in addition to the heat losses in the system: the solar collector, the auxiliary system, and the network water supply. In the system, using type 31, a piping section of 10 m and 1.27 cm in diameter from the hot water tank to the tap was considered, located outdoors with a thermal insulation of 13 mm. For the connection between the solar collector and the hot water tank, 5 m of piping with a 19 mm thickness was used. For the thermal conductivity of the insulated copper tube, the data reported by Marini et al. [31] of k = 0.031 W/mK was used. The results obtained show values similar to those reported by ASHRAE [30] of UA = 0.346 W/mK, U = 8.48 W/m2K, based on the internal diameter of the pipe. The system must maintain the water in the hot water tank at a minimum temperature of 60 ◦C to avoid the growth of bacteria such as Legionella [26,30]. Therefore, there will be heat losses at the hot water tank which should be accounted for by the water heating system. These temperatures may vary depending on the internal temperature of the hot water tank and the ambient temperature. Taking these data into consideration, as well as the behavior of the types of components described above, the simulation was carried out in TRNSYS, obtaining the energy balance shown in Figure7. The energy inputs for each inlet, as well as the heat losses for each part of the system, can be identiﬁed. Under these conditions, the solar collector and the water supply input at ambient temperature provides 96% of the required energy, with a total energy of 5673 kWh, whereas the auxiliary heater must provide the remaining 4% with 221 kWh to meet the annual hot water requirement. There are partial losses through the environment of 1858 kWh, taking into consideration the losses of the solar collector, the hot water tank, and the supply pipes. However, the solar collector may supply a greater amount of energy if the re-circulation pump is kept operating during sunny hours; that is, not turning oﬀ the recirculation pump when the water reaches the set temperature point. This may be attractive if this useable heat is used in another process, such as an ORC. Entropy 2019, 21, 911 10 of 23 Entropy 2019, 21, x FOR PEER REVIEW 10 of 23

FigureFigure 7.7. EnergyEnergy balance in the domestic hot water system. system. 4.2. Collector Performance at Different Temperatures 4.2. Collector Performance at Different Temperatures As the temperature difference between the working fluid and the ambient temperature increases, As the temperature difference between the working fluid and the ambient temperature the collector efficiency decreases. However, there is a higher gain of enthalpy in the working fluid increases, the collector efficiency decreases. However, there is a higher gain of enthalpy in the throughworking a fluid lower through volumetric a lower flow. volumetric flow. TakingTaking into into consideration consideration that that one one of theof objectivesthe object ofives this of study this study is to identify is to identify the thermal the potentialthermal ofpotential a solar collectorof a solar collector for a secondary for a secondary use, additional use, addi totional water to water heating, heating, it is necessaryit is necessary to analyze to analyze the collectorthe collector thermal thermal performance performance at diff erentat different mass flows mass and flows temperatures. and temperatures. Identifying Identifying these conditions these willconditions allowan will estimation allow an of estimation the different of workingthe different fluid working performances fluid performances under these circumstances.under these Forcircumstances. cogeneration For applications, cogeneration these applications, conditions involve these conditions superheated involve vapor atsuperheated the evaporator vapor (collector) at the andevaporator subcooled (collector) liquid at and the subc condenser.ooled liquid at the condenser. ForFor a a higher higher e efficiencyfficiency in in the the ORC, ORC, a a higher higher pressure pressure di differencefference is is required; required; therefore, therefore, the the aim aim is is to haveto have the highestthe highest permissible permissible pressure pressure in the system.in the system. In the case In the of this case study, of this a maximum study, a permissiblemaximum pressurepermissible of 800 pressure kPa is consideredof 800 kPa is in considered the collector, in the with collector, a stagnation with temperaturea stagnation oftemperature 228 ◦C according of 228 to°C the according manufacturer to the datamanufacturer sheet [23 ].data In thesheet condenser [23]. In the the condenser objective isthe to objective condense iswith to condense the hot waterwith tankthe hot operation water temperaturetank operation at atemperature relatively low at a pressure. relatively This low way, pressure. different This scenarios way, different may be scenarios analyzed consideringmay be analyzed different considering operation different temperatures, operation in order temp toeratures, select the in bestorder operating to select the condition. best operating condition.The condensation temperature parameter has a direct impact on the system performance. Therefore, whenThe defining condensation the condensation temperature temperature, parameter it should has a be direct considered impact that on settingthe system a temperature performance. lower thanTherefore, 60 ◦C implieswhen defining that a certain the condensation amount of energytemperature, should it beshould removed be co fromnsidered the system that setting through a antemperature external heat lower exchanger. than 60 °C These implies may that compromise a certain theamount amount of energy of useable should energy be removed for heating from water the andsystem increase through the needan external for auxiliary heat exchanger. heating. These may compromise the amount of useable energy for heatingOn the otherwater hand,and increase if there the is an need exceedingly for auxiliary high heating. temperature, the heat losses in the piping and hot waterOn the tank other may hand, increase, if there decreasing is an exceedingly the collector high etemperature,fficiency. Thus, the itheat is necessary losses in the to findpiping a point and wherehot water the needtank may for theincrease, required decreasing useable the energy collector may efficiency. be met, andThus, at it the is necessary same time to it find operates a point at temperatureswhere the need and for pressures the required that allow useable effi cientenergy operation may be in met, an ORC.and at the same time it operates at temperaturesWhen a constant and pressures temperature that allo isw required efficient and operation operation in an is ORC. continuous in a transitory state, it is necessary When to havea constant a control temperature system foris required regulation. and Inoperation order to is do continuous this a variable in a transitory flow pump state, can it is be considered,necessary to which have isa ablecontrol to controlsystem thefor systemregulation. optimally. In order The to considereddo this a variable expander flow must pump work can with be aconsidered, variable mass which flow is asable well, to control where the system expander optimally. would haveThe considered a constant expander pressure andmust temperature work with conditions,a variable mass and byflow having as well, the where expander the expander of a fixed would built-in have volume a constant ratio, pressure the angular and speedtemperature would increaseconditions, or decrease and by having depending the onexpander operating of a conditions. fixed built-in volume ratio, the angular speed would increase or decrease depending on operating conditions.

Entropy 2019, 21, x FOR PEER REVIEW 11 of 23 Entropy 2019, 21, 911 11 of 23

For the Rankine cycle, it is desirable to obtain the lowest temperature cycle to keep the heat lossesFor as thelow Rankine as possible, cycle, so it the isdesirable analysis is to focused obtain the on lowestinlet temperatures temperature of cycle 40, to50, keep and the60 °C. heat For losses the collectoras low as simulation, possible, so the analysisinput fluid is focused was evaluated on inlet temperaturesat different initial of 40, temperatures. 50, and 60 ◦C. ForA variable the collector flow pumpsimulation, with thea feedback input fluid controller was evaluated was used at di fftoerent obtain initial a constant temperatures. output A temperature variable flow at pump different with irradiances.a feedback controller was used to obtain a constant output temperature at different irradiances. Figure8 8shows shows the the thermal thermal energy energy produced produced annually an withnually each with established each established temperature temperature di fference, difference,and the required and the mass required flow. mass flow.

Figure 8. EnergyEnergy produced produced at different different operation temperatures. 5. ORC Efficiencies 5. ORC Efficiencies To select the operation temperatures in the cycle, it is necessary to analyze the performance of the To select the operation temperatures in the cycle, it is necessary to analyze the performance of heat source (solar collector), as well as the ORC, when operating at such temperatures. A point of the heat source (solar collector), as well as the ORC, when operating at such temperatures. A point of operation that allows the solar collector to have enough efficiency to supply the energy required by the operation that allows the solar collector to have enough efficiency to supply the energy required by SDHWS and for the ORC to have a good efficiency is desirable. the SDHWS and for the ORC to have a good efficiency is desirable. To condense at a temperature lower than 60 C in the Rankine cycle, it is necessary to remove To condense at a temperature lower than 60 ◦°C in the Rankine cycle, it is necessary to remove energy from the system, which implies a waste of the solar energy captured by the collector; therefore, energy from the system, which implies a waste of the solar energy captured by the collector; therefore, the total system efficiency decreases. Condensing at temperatures 60 C allows the utilization of the total system efficiency decreases. Condensing at temperatures ≥≥ 60 °C◦ allows the utilization of a a greater amount of heat for the generation of electric power, without compromising the energy greater amount of heat for the generation of electric power, without compromising the energy required to keep the water at 60 C. required to keep the water at 60 ◦°C. With an input temperature of 60 C and an output temperature of 120 C, this allows us to obtain With an input temperature of 60 ◦°C and an output temperature of 120 ◦°C, this allows us to obtain a useful energy of 3960 kWh and a Carnot efficiency of around 15% (Figure9). a useful energy of 3960 kWh and a Carnot efficiency of around 15% (Figure 9). Type 71 simulates solar collectors in which heating a working fluid occurs without phase change. Type 71 simulates solar collectors in which heating a working fluid occurs without phase change. Collector thermal efficiency and thermal losses depend mainly on the fluid average temperature. Collector thermal efficiency and thermal losses depend mainly on the fluid average temperature. The The energy balance in the solar collector when operating in ORC mode, where phase change occurs, energy balance in the solar collector when operating in ORC mode, where phase change occurs, takes takes into account the latent heat of vaporization. into account the latent heat of vaporization. When analyzing solar collectors with phase change, the filling factor is considered. The filling When analyzing solar collectors with phase change, the filling factor is considered. The filling factor is the ratio of volume occupied by liquid with respect to the total volume of the evaporator. factor is the ratio of volume occupied by liquid with respect to the total volume of the evaporator. A A filling factor near to one indicates that most of the volume is occupied by liquid. A filling factor filling factor near to one indicates that most of the volume is occupied by liquid. A filling factor close close to zero indicates that most of the volume is occupied by vapor, which can involve overheating of to zero indicates that most of the volume is occupied by vapor, which can involve overheating of the the fluid and increase the average temperature, affecting the calculation of thermal efficiency. fluid and increase the average temperature, affecting the calculation of thermal efficiency. An experimental study [26] conducted with a filling factor of 55% showed a decrease in the An experimental study [26] conducted with a filling factor of 55% showed a decrease in the thermal efficiency of only 4.5%, compared to a collector without phase change. This shows that the thermal efficiency of only 4.5%, compared to a collector without phase change. This shows that the thermal efficiency of the solar collector depends mainly on the average temperature, even when the thermal efficiency of the solar collector depends mainly on the average temperature, even when the heat transfer coefficients with phase change are very different. heat transfer coefficients with phase change are very different.

Entropy 2019, 21, 911 12 of 23 Entropy 2019, 21, x FOR PEER REVIEW 12 of 23

FigureFigure 9.9. Energy and eefficiencyﬃciency of the cycle at different diﬀerent operation temperatures.

InIn thisthis study,study, thethe vaporvapor superheatedsuperheated temperaturetemperature (120(120 ◦°C)C) is close to saturation temperature (119.6(119.6◦ °C).C). Therefore,Therefore, it it is is considered considered that that the the variation variation of of mean mean temperature temperature over over thermal thermal e ffiefficiencyciency is negligible.is negligible. Thus, Thus, several several authors authors have usedhave di ffusederent different configurations configurations to use collectors to useas collectors evaporators, as obtainingevaporators, good obtaining efficiencies good [32 efficiencies–34]. [32–34].

5.1.5.1. WorkingWorking FluidFluid SelectionSelection AA greatgreat numbernumber ofof organicorganic fluidsfluids withwith aa boilingboiling temperature lower than water may be be used used to to operateoperate withwith lowlow temperaturestemperatures and pressures in an ORC. A proper selection of the working fluid fluid in in anan ORCORC isis extremelyextremely important,important, since it will not only affect affect the cycle efficiency, efficiency, but also the the size size of of components,components, thethe expanderexpander designdesign andand thethe systemsystem stability.stability. Firstly,Firstly, for for a propera proper selection selection of theof workingthe working fluid, fluid, a practical a practical pressure pressure and temperature and temperature are defined are withindefined the within cycle the limits. cycle A limits. high pressure A high pressure ratio favors ratio cycle favors effi cycleciency. efficiency. In this study, In this the study, highest the pressure highest ispressure limited is by limited the solar by the collector solar collector maximum maximum operating operating pressure. pressure. It is important It is important to also to also consider consider the isentropicthe isentropic efficiencies efficiencies that that would would be be obtained obtained in in the the pump pump and and the the expander expander whenwhen operating with with suchsuch fluid.fluid. InIn aa study study conducted conducted by by Qiu Qiu G. G. [20 [20],], the the main main criteria criteria for thefor the proper proper selection selection of the of working the working fluid, influid, decreasing in decreasing order oforder relevance, of relevance, are outlined are outlined as the following:as the following: • Not banned by relevant national standards. • Not banned by relevant national standards. • High enthalpy change in the expander; this translates into a higher work output. • High enthalpy change in the expander; this translates into a higher work output. • Working fluids should be easy to manage at ambient temperature, where the ambient temperature • Working fluids should be easy to manage at ambient temperature, where the ambient temperatureis not higher is than not 100higher◦C. than 100 °C. • Isentropic or “dry” fluids fluids are are preferred preferred to avoid superheating superheating in in the the cycle. cycle. • • High latent heat; this makes comp componentsonents in in the the system system smaller. smaller. • • Preferential physicalphysical properties, properties, such such as: chemicalas: chem stability,ical stability, high thermalhigh thermal conductivity, conductivity, low viscosity, low • viscosity,and operating and operating at low pressures. at low pressures. • High safety requirements requirements such such as as low low toxicity, toxicity, low low corrosion, corrosion, non-flammable, non-flammable, and and non-explosive. non-explosive. •• Accessibility and low cost. • ThroughThrough thethe EESEES softwaresoftware [[35],35], 29 didifferentfferent organic fluids fluids were analyzed, analyzed, chosen chosen from from BaoBao et et al. al. andand QuiQui and Rayegan et et al. al. [19–21]. [19–21]. It Itwas was found found that that only only 16 16may may be superheated be superheated at 120 at 120°C and◦C and800 800kPa kPa and and subcooled subcooled at 60 at °C 60 and◦C and 100 100kPa kPa (Figure (Figure 10). 10 A).dditionally, Additionally, 13 fluids 13 fluids (not (not shown) shown) could could not notbe beused used in inthe the cycle cycle because because the the saturation saturation pressures pressures obtained obtained at at the the required required temperatures temperatures were were not not feasiblefeasible inin thethe SDHWS.SDHWS.

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FigureFigureFigure 10. 10.10. Saturation SaturationSaturation pressurepressure of working fluidsfluids fluids forfor thethe ORC ORC conditions. conditions. conditions. 5.1.1. Enthalpy Change 5.1.1.5.1.1. Enthalpy Enthalpy ChangeChange TheTheThe main mainmain characteristic characteristiccharacteristic that that must must be takenbe taken into accountintoto accountaccount is a high isis aa enthalpy highhigh enthalpyenthalpy change change inchange the expander, in in the the becauseexpander,expander, this becausebecause means that thisthis most meansmeans of vaporthat most enthalpy of va maypor beenthalpyenthalpy transformed maymay be intobe transformedtransformed useable mechanical intointo useableuseable work. Therefore,mechanicalmechanical the work.work. isentropic Therefore,Therefore, enthalpy the change isentropic in the enthal cyclepypy is evaluated changechange inin with thethe a cyclecycle set temperature isis evaluatedevaluated and with with a pressure a aset set nottemperaturetemperature higher than and and 800 aa pressurekPa.pressure notnot higherhigher than 800 kPa.kPa. ForForFor fluids fluidsfluids with withwith a aa saturation saturationsaturation pressurepressure higherhigher th thananan 800 800 kPakPa atat 120120 °C,°C,◦C, thethe the enthalpyenthalpy enthalpy change change change is is is consideredconsideredconsidered limited limitedlimited at atat this thisthis pressure pressurepressure (shown(shown inin orangeorange in in Figures Figures 10–13).10–13).10–13). AA A similarsimilar similar consideration consideration consideration is is is mademademade for for for cooling cooling cooling down downdown conditions conditionsconditions atat 6060 ◦°C,C, in orderorderr to to maintain maintain thethe operation operation conditions conditions conditions within within within the the the permissiblepermissiblepermissible range. range. range. TheTheThe power powerpower produced producedproduced bybyby thethe expanderexpander is the product product ofof of enthalpyenthalpy enthalpy changechange change and and and the the the mass mass mass flow. flow. flow. Therefore,Therefore,Therefore, by byby having havinghaving aaa greatergreater enthalpy change, change, a asmaller smaller devicedevice device (or(or (or lowerlower lower volumetric volumetric volumetric flow flow flow rate) rate) rate)is is isrequired.required. required. FigureFigureFigure 11 1111 shows showsshows the thethe di differencedifferencefference of of enthalpy enthalpy for for the thethe di differentffdifferenterent fluids fluidsfluids analyzed. analyzed. analyzed. It It isIt is observedis observed observed that that that the fivethethe fluidsfive five fluidsfluids with a withwith higher aa higherhigher enthalpy enthalpyenthalpy difference difference between betweenbetween selected selectedselected temperatures temperaturestemperatures and pressures and and pressures pressures are: acetone, are: are: benzene,acetone,acetone, toluene,benzene, benzene, cyclohexane, toluene,toluene, cyclohexane,cyclohexane, and isohexane. and isohexane.

Figure 11. Enthalpy change of working fluids (at a condensation temperature of 60 °C). FigureFigure 11. 11.Enthalpy Enthalpy changechange ofof workingworking ﬂuidsfluids (at a condensation temperature of of 60 60 °C).◦C).

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5.1.2. Thermal Efficiency 5.1.2. Thermal Efficiency Another important point to consider for proper fluid selection is the thermal efficiency of the idealAnother cycle; this important is the ratio point between to consider the enthalpy for proper change fluid at selection the expander, is the thermal and the e increasefficiency of of enthalpy the ideal cycle;at the thiscycle, is theas shown ratio between in Equation the enthalpy (1): change at the expander, and the increase of enthalpy at the cycle, as shown in Equation (1): ℎ −ℎ 𝜂 =h3 h4 (1) ,ηORC ideal = − (1) , hℎ −ℎh 3 − 1 For a particular saturation temperature didifferfferenceence betweenbetween the evaporationevaporation and condensationcondensation states, there will be anan enthalpyenthalpy change.change. AccordingAccording to Equation (1), the thermal eefficiencyfficiency depends not only on on the the enthalpy enthalpy change change during during the the expans expansionion but but also also on onthe the enthalpy enthalpy change change required required for forevaporation; evaporation; that that is, is,the the latent latent heat heat of of vaporization. vaporization. For For each each saturation saturation temperature, temperature, different different working fluidsfluids have didifferentfferent latent heats of vaporizationvaporization due to their intrinsic properties. Therefore, Therefore, two working fluidsfluids can present the same enthalpy change for a given temperature didifferencefference but require a didifferentfferent latentlatent heatheat ofof vaporization.vaporization. UnderUnder these conditions, the fluidfluid with a bigger latent heat of vaporization will present aa lowerlower thermalthermal eefficiency.fficiency. The thermal eefficienciesfficiencies ofof the analyzed fluidsfluids in FigureFigure 12 show that the five five fluids fluids with a higher enthalpy change are those with a higher thermal eefficienfficiency.cy. ItIt isis important toto note that it is not always the fluids fluids with a higher enthalpy change change during during ex expansionpansion that that will will have have a a higher higher thermal thermal efficiency. efficiency. Some examples of this are isopentane, neopentane,neopentane, andand R123,R123, toto mentionmention aa few.few.

Figure 12. ThermalThermal efficiency efficiency of different different working fluidsfluids (at a condensation temperaturetemperature ofof 6060 ◦°C).C).

5.1.3. Expansion Ratio For the dimensioning of of the the expander, expander, it it is is necess necessaryary to to know know the the expansion expansion ratio ratio of ofthe the fluid. fluid. It Itmay may be beobserved observed that that the thefluids fluids with with a higher a higher expansion expansion ratio are ratio those are with those a withhigher a enthalpy higher enthalpy change changein the cycle, in the but cycle, not butin the not same in the order same (Figure order (Figure13). 13). It maymay bebe observed observed that that there there is no is directno direct relationship relationship between between the fluid the properties fluid properties and the and thermal the performancethermal performance parameters; parameters; therefore, therefore, it is important it is important to take noteto take of note them of to them make to the make right the choice. right Fromchoice. the From expansion the expansion ratio, it isratio, possible it is topossible choose to the choose type ofthe expander type of thatexpander could that be used could within be used the cycle.within Inthe the cycle. next In section, the next the section, performance the performa of thence cycle of the with cycle the with selected the selected working working fluid is shown,fluid is asshown, well asas otherwell as parameters other parameters required required for the selectionfor the selection and suitable and suitable design ofdesign the expansion of the expansion device. Thedevice. selected The selected expander expander type is atype volumetric is a volumetric expansion expansion device, device, because because it is more it is appropriate more appropriate for the ORCfor the at ORC small at capacities small capacities [36] due [36] to its due required to its requ lowerired flow lower rates, flow higher rates, pressure higher ratiospressure and ratios rotational and

Entropy 2019, 21, 911 15 of 23 Entropy 2019, 21, x FOR PEER REVIEW 15 of 23 rotationalspeeds, which speeds, are which lower inare comparison lower in comparison to the velocity to the expander velocity type. expander The basic type. expander The basic selection expander is selectiondescribed is in described Section6 .in Section 6.

FigureFigure 13. 13. PressurePressure ratio ratio of of different different working fluids fluids (at a condensation temperature of 60 ◦°C).C). 5.2. ORC with Acetone as the Working Fluid 5.2. ORC with Acetone as the Working Fluid At low pressures, the best candidates were hydrocarbons, due to a higher isentropic enthalpy At low pressures, the best candidates were hydrocarbons, due to a higher isentropic enthalpy change. Therefore, the pressure in the cycle may be more relevant than the operation temperature at change. Therefore, the pressure in the cycle may be more relevant than the operation temperature at the moment of selecting a working fluid for an ORC. the moment of selecting a working fluid for an ORC. Acetone was selected as the most suitable fluid to operate in the cycle with the given conditions. Acetone was selected as the most suitable fluid to operate in the cycle with the given conditions. In Figure 14, the Rankine cycle is shown, indicating that the saturation pressure is 604 kPa at 120 C In Figure 14, the Rankine cycle is shown, indicating that the saturation pressure is 604 kPa at 120 °C◦ and 115 kPa at 60 C at the expander output. and 115 kPa at 60 °C◦ at the expander output. The working fluid is one of the most important factors to take into consideration for the performance The working fluid is one of the most important factors to take into consideration for the of solar collectors [37], because it carries the heat absorbed by the solar collector to the load or to the hot performance of solar collectors [37], because it carries the heat absorbed by the solar collector to the water tank. Therefore, it is important to consider the thermal properties such as thermal conductivity. load or to the hot water tank. Therefore, it is important to consider the thermal properties such as This property has a major role in the search for equipment with high energy performance [38]. This is thermal conductivity. This property has a major role in the search for equipment with high energy because the higher the heat transfer to the fluid, the higher the collector efficiency [39]. Some studies performance [38]. This is because the higher the heat transfer to the fluid, the higher the collector have used acetone as the working fluid in heat pipe collectors, achieving a better performance than efficiency [39]. Some studies have used acetone as the working fluid in heat pipe collectors, achieving with other working fluids [37,40–43]. These results confirm that acetone is an adequate working fluid a better performance than with other working fluids [37,40–43]. These results confirm that acetone is to operate with phase changes in solar collectors. an adequate working fluid to operate with phase changes in solar collectors. Among the advantages of using acetone in a SDHWS are it prevents freezing, scaling, fouling and Among the advantages of using acetone in a SDHWS are it prevents freezing, scaling, fouling corrosion. This fluid has a low GWP (Global Warming Potential), which is a widely used parameter to and corrosion. This fluid has a low GWP (Global Warming Potential), which is a widely used show how much heat is trapped in the atmosphere by a greenhouse gas, being in this case 0.5 which is parameter to show how much heat is trapped in the atmosphere by a greenhouse gas, being in this considerably low when compared to typical refrigerants (i.e., R134a GWP = 1300; R410a GWP = 1700). case 0.5 which is considerably low when compared to typical refrigerants (i.e. R134a GWP = 1300; In addition to this, acetone is considered not to have Ozone Depletion Potential (ODP), therefore it R410a GWP = 1700). In addition to this, acetone is considered not to have Ozone Depletion Potential is a great candidate for this type of application [44]. The auto-ignition temperature for acetone is (ODP), therefore it is a great candidate for this type of application [44]. The auto-ignition temperature 465 C[45], and since this temperature cannot be reached within the cycle, flammability or explosiveness for acetone◦ is 465 °C [45], and since this temperature cannot be reached within the cycle, flammability is avoided. Flammability is also prevented because open flames and sparks are not present in the cycle or explosiveness is avoided. Flammability is also prevented because open flames and sparks are not under typical operating conditions. present in the cycle under typical operating conditions. Acetone has been experimentally used as a working fluid [1,27,44,46,47]. Other procedures to select working fluids for ORC systems indicate that acetone achieves a high performance for ORC at 130 °C [21].

Entropy 2019, 21, 911 16 of 23

EntropyAcetone 2019, 21 has, x FOR been PEER experimentally REVIEW used as a working ﬂuid [1,27,44,46,47]. Other procedures16 of to 23 select working ﬂuids for ORC systems indicate that acetone achieves a high performance for ORC at 130Entropy◦C[ 201921]., 21, x FOR PEER REVIEW 16 of 23

Figure 14. Rankine cycle with acetone as the working fluid.

Figure 14. Rankine cycle with acetone as the working fluid. 5.3. Analysis of Energy PotentialFigure 14. Delivered Rankine to cycle the withExpander aceton e as the working fluid. 5.3. AnalysisTo analyze of Energy the cogeneration Potential Delivered system, to thethe Expander process shown in Figure 15 was carried out, following 5.3. Analysis of Energy Potential Delivered to the Expander the Tomethodology analyze the described cogeneration in Section system, 2. Description the process shownof the system, in Figure as 15follows: was carried out, following the methodologyToOnce analyze the hot the described watercogeneration tank in Section temperature system,2. Description the processreaches of theshowna preset system, in operationFigure as follows: 15 wastemperature carried out, (60 following °C) and theavailable methodology irradiance described meets CHP in Section energy 2. requirementsDescription of, thethe workingsystem, as fluid follows: mass flow that the system Once the hot water tank temperature reaches a preset operation temperature (60 ◦C) and available irradiancecan deliveredOnce meets the ishot CHP determined water energy tank requirements,based temperature on: the theirradiance reaches working, thea fluid preset output mass operation thermal flow that powertemperature the system of the can collector(60 delivered °C) and isavailablethe determined enthalpy irradiance required based on:meets to the take CHP irradiance, the energy working the requirements fluid output from thermal subcooled, the working power liquid of fluid the at collector60 mass °C toflow superheated and that the the enthalpy system vapor canat 120 delivered °C and 604is determined kPa at the outputbased on: of thethe solar irradiance collector., the output thermal power of the collector and required to take the working fluid from subcooled liquid at 60 ◦C to superheated vapor at 120 ◦C and 604the kPa enthalpyAfter at the the required output mass flow of to the takeis solarcalculated, the collector. working it is possiblefluid from to subcooledobtain the liquidpower at delivered 60 °C to bysuperheated the expander vapor by atconsidering 120After °C and the the mass604 vapor kPa flow at mass isthe calculated, output flow, asof wellthe it is solar possibleas the collector. en tothalpy obtain drop the powerin the deliveredexpansion byprocess, the expander and the byisentropic consideringAfter theefficiency mass the vapor flow of the is mass calculated,expander. flow, as Therefore,it well is possible as the by enthalpy to the obtain integration dropthe power in over the delivered expansionthe periods by process, theof time expander and(when the by it isentropicconsideringis possible effi tociencythe use vapor ofthe the cogenerationmass expander. flow, as Therefore, system), well as the bythe the enamountthalpy integration ofdrop energy over in the thedelivered expansion periods by of process, timethe expander (when and it the isis possibleisentropiccalculated. to useefficiency the cogeneration of the expander. system), Therefore, the amount byof the energy integration delivered over by the the periods expander of time is calculated. (when it is possible to use the cogeneration system), the amount of energy delivered by the expander is calculated.

Power (∆h4-3, ṁ, ƞexp)

ṁ(I ,coll, ∆h ) 3-2 TankT ≥60 °C ṁ(I ,coll, ∆h ) ORCmode=on 3-2 TankT ≥60 °C ORCmode=on

FigureFigure 15. 15.ORC ORC mode mode scheme scheme in in the the TRNSYS TRNSYS simulation simulation studio. studio.

Once the workingFigure fluid 15. hasORC beenmode selectedscheme in and the TRthNSYSe heat simulation required studio. to change the state from subcooled liquid at 60 °C to superheated vapor at 120 °C has been defined, the required mass flows Once the working fluid has been selected and the heat required to change the state from subcooled liquid at 60 °C to superheated vapor at 120 °C has been defined, the required mass flows

Entropy 2019, 21, 911 17 of 23

EntropyOnce 2019 the, 21, workingx FOR PEER fluid REVIEW has been selected and the heat required to change the state from subcooled17 of 23 liquid at 60 ◦C to superheated vapor at 120 ◦C has been defined, the required mass flows are determined throughare determined an energy through balance. an Consequently,energy balance. it Conseque is possiblently, to calculate it is possible the volumetric to calculate flow the thatvolumetric would beflow obtained that would under be theobtained different under operation the different conditions. operation With conditions. these parameters With these defined, parameters it is possible defined, to selectit is possible the most to adequateselect the expansionmost adequate device. expansion device. TheThe collectorcollector simulation allowsallows for an estimation of the thermal power, the average useable heat, andand thethe irradianceirradiance levelslevels atat whichwhich thethe higherhigher energyenergy (2346(2346 kWhkWh/m/m22)) andand powerpower thatthat cancan bebe obtainedobtained (Figure(Figure 1616),), inin orderorder toto optimizeoptimize thethe eefficiencyfficiencyof ofthe thesystem system for for these these conditions. conditions.

Figure 16. Power and energy given at didifferentﬀerent irradianceirradiance levelslevels duringduring thethe year.year.

InIn TableTable4 4,, the the main main parameters parameters required required for for the the expander expander thermodynamic thermodynamic design design are are listed. listed.

TableTable 4.4. MainMain parametersparameters forfor thethe expanderexpander design.design.

WorkingWorking Fluid: AcetoneAcetone InletInlet OutletOutlet DifferenceDifference PressurePressure 604 604 kPa kPa 115 115 kPa kPa P1/P2 = 5.25 P1/ P2 = 5.25 TemperatureTemperature 120 120 °C◦C 60 ◦ 60C °C ∆T = 60 ◦C∆T = 60 °C EnthalpyEnthalpy 892 892 kJ/kg kJ/kg 815 815 kJ/kg kJ/kg ∆h = 77 kJ∆/kgh = 77 kJ/kg Viscosity 10.18 10 6 Pa s 23.12 10 5 Pa s ∆µ = 22 10 5 Pa s -6 − − -5 − -5 Viscosity 10.18x10× Pa∙3s · 23.12x10× 3 ·Pa∙s × ∆μ = 22.x10· Pa∙s Density 12.68 kg/m 2.612 kg/m ρ1/ρ2 = 4.85 Density 12.68 kg/mOperation3 Range2.612 kg/m3 ρ1/ρ2 = 4.85 Volumetric Flow V˙ min =180Operation L/h V ˙Rangemax = 900 L/h V˙ nominal = 850 L/h Volumetric FlowInlet Heat V Q̇minmin =180= 310 l/h W Qmax V=maẋ 1830 = 900 W l/h Qnominal = 1690 Vnominal̇ W = 850 l/h Inlet Heat Qmin = 310 W Qmax = 1830 W Qnominal = 1690 W 6. Expander 6. Expander Once the ORC configuration (Figure2) and the system operation conditions (Table4) have been establishedOnce the and ORC the workingconfiguration fluid has(Figure been 2) defined, and the itsystem is possible operation to select conditions the best (Table suited 4) expander have been to workestablished within and the the cycle. working fluid has been defined, it is possible to select the best suited expander to workThe within expansion the cycle. device is one of the four main components of an ORC system, with the most influenceThe expansion over the cycle device performance is one of the and four the totalmain system components cost. Adequate of an ORC selection system, of with the expanderthe most dependsinfluence on over the operationthe cycle performance conditions, working and the fluid, total size system of the cost. system, Adequate mass flow, selection chemical of the composition expander ofdepends the fluid, on temperature the operation diff erence,conditions, and pressureworking allowed fluid, size within of thethe system system, [48 mass]. flow, chemical composition of the fluid, temperature difference, and pressure allowed within the system [48]. Figure 17 shows the compilation of different types of expanders that have been used in different power ranges for micro-ORC [49]. The number of studies considered by the authors is shown in parentheses. It may be observed that the better volumetric expansion type for the power considered

Entropy 2019, 21, 911 18 of 23

Figure 17 shows the compilation of different types of expanders that have been used in different power ranges for micro-ORC [49]. The number of studies considered by the authors is shown in parentheses.Entropy 2019, 21 It, x may FOR bePEER observed REVIEW that the better volumetric expansion type for the power considered18 of 23 in this study is the “trochoid” (gerotor) type. One of the advantages of this type of device is that, due to in this study is the “trochoid” (gerotor) type. One of the advantages of this type of device is that, due their configuration, there is a low relative speed between the rotor and stator, which generates lower to their configuration, there is a low relative speed between the rotor and stator, which generates frictionlower friction losses with losses respect with respect to other to type other of type positive of positive displacement displacement devices devices [50]. [50].

Figure 17. Power range produced by different expansion devices [49]. Figure 17. Power range produced by different expansion devices [49]. Currently, there is limited literature that reports on the use of this type of device as an expander Currently, there is limited literature that reports on the use of this type of device as an expander for an ORC, however, an ORC system has shown isentropic efficiency of 85% and a global efficiency for an ORC, however, an ORC system has shown isentropic efficiency of 85% and a global efficiency of 7.7% with a source temperature of 162.2 ◦C[50]. The expander isentropic efficiency ηexp = 85% of 7.7% with a source temperature of 162.2 °C [50]. The expander isentropic efficiency 𝜂 = 85% was selected from these results. The maximum capacity of electric power generation of the proposed was selected from these results. The maximum capacity of electric power generation of the proposed systemsystem isis estimatedestimated consideringconsidering the constant efficiency. efficiency. However, However, it it is is important important to to note note that that the the expansionexpansion isentropic isentropic eefficiencyfficiency cancan varyvary withwith time and conditions. InIn the the analysis analysis ofof thethe idealideal RankineRankine cycle, the the pump pump and and the the expander expander are are considered considered isentropic isentropic whilewhile the the evaporator evaporator andand condensercondenser dodo notnot involve any work. The The power power of of the the pump pump is is defined defined as as . 𝑊,W =𝑚=(ℎm−ℎ(h ) h ) (2) (2) pump,in 2 − 1 And the power of the expander is And the power of the expander is 𝑊, =𝑚 (ℎ −ℎ) (3) . Wexp,out = m(h h ) (3) However, one of the major deviations within the3 − ideal4 Rankine cycle is the irreversibilities occurring within the pump and the expander. To obtain more accurate results, it is necessary to take However, one of the major deviations within the ideal Rankine cycle is the irreversibilities into consideration the work involved within the cycle, and also the isentropic efficiencies. occurring within the pump and the expander. To obtain more accurate results, it is necessary to take For this particular study a pump efficiency of 𝜂 = 65% [12,15,16,51,52] is considered. The into consideration the work involved within the cycle, and also the isentropic efficiencies. power required by the pump can be calculated by For this particular study a pump efficiency of ηpump = 65% [12,15,16,51,52] is considered. ∆ℎ ∙𝑚 The power required by the pump can be calculated by (4) 𝑊 = 𝜂 . ∆h2 1 m The expander would be consideredW topump achieve= −85%,· so the power of the expander can be(4) calculated by ηpump

𝑊 =∆ℎ ∙𝑚 ∙𝜂 (5) When considering Equations (4) and (5), it is possible to calculate the amount of power generated by the expander, as well as the power required by the pump to maintain the flow of the working fluid

Entropy 2019, 21, 911 19 of 23

The expander would be considered to achieve 85%, so the power of the expander can be calculated by . Wexp = ∆h4 3 m ηexp (5) − · · When considering Equations (4) and (5), it is possible to calculate the amount of power generated by the expander, as well as the power required by the pump to maintain the flow of the working fluid in the cycle. To obtain the maximum power of the expander the maximum flow from Figure 16 is considered in Equation (5), which gives a value of 245 W. The efficiency of the ORC system can be calculated by considering these isentropic efficiencies, the constant temperatures and pressures in the cycle, obtaining 84.4% of the ideal ORC, as given below:

Wexp Wpump ηORC = . − (6) m(h h ) 4 − 3 The eﬃciency from solar to electric power can be obtained as follows:

Eelect ηsolar = . (7) Qu

The CHP eﬃciency is given by

. . Wnet + Wheat ηCHP = . (8) Qu

The proposed system has 2346 kWh/m2 annual irradiation, and a 2.84 m2 collector surface area; it is possible to generate a useful electric energy of 443 kWh, with a global eﬃciency of solar to electric power of 6.65% (Equation (7)). Additionally, the overall eﬃciency of the cogeneration system is 56.35% (Equation (8)) when considering CHP generation.

7. Conclusions In this paper the application of an ORC to a SDHWS was presented and analyzed with the purpose of observing the cycle feasibility, the system energy balances, and the proper working fluid selection. The collector performance was analyzed when operating at different temperatures, and it was observed that as the operation temperature increases, the collector efficiency decreases, but the theoretical efficiency of the ORC increases. Thus, a point of operation was determined to meet the needs of both systems. Different working fluids were analyzed below the maximum collector permissible pressures, showing that hydrocarbons (HCs) provide a better performance than other organic fluids at low pressures (100–1000 kPa). A multiple criteria analysis was conducted (i.e., enthalpy change, thermal efficiency, and expansion ratio), showing a similar performance, with some variations. This study found that acetone is the most suitable working fluid because of its higher enthalpy change under the operating conditions. This design method allows evaluation of the useable heat generated by a solar system under different operation conditions, selecting the most suitable working fluids for the cycle and therefore selecting the best design conditions for an ORC cycle expander. It is technically feasible to implement a CHP system with the proposed configuration with a better utilization of the heat that went unutilized by the SDHWS in a second application through a low temperature ORC. With a solar collector area of 2.84 m2 it is possible to generate 443 kWh of electric power annually with a solar to electric efficiency of 6.65%, or an overall cogeneration system efficiency of 56.35%. Entropy 2019, 21, 911 20 of 23

The objective of this study was to analyze the technical feasibility of the proposed cogeneration system, in order to obtain the main parameters for the design of the expander that can convert part of the heat delivered by the SDHWS into mechanical energy. Future work will include the development of said expander, as well as the implementation of the ORC system proposed within the SDHWS in order to validate the proposed technique. Once validated, larger capacity systems can be designed and developed.

8. Patents Patents related to this work:

Cogeneration System for Integration into Solar Water Heating Systems, U.S. Patent, Application • Number: 16,208,666. Dispositivo de cogeneración para integración en sistemas de calentadores solares de agua, IMPI: • MX/E/2017/094793.

Author Contributions: Cogeneration System proposal and evaluation, D.L.-C., Collector and thermo tank performance evaluation, R.B.-C., DHWS simulation, P.C.-T., Working fluid selection, S.I., Analysis of energy potential delivered to the expander, N.V. Funding: The open access publishing fees for this article have been covered by the Premio PRODETES 2017—SENER—World Bank—Global Environment Facility. Acknowledgments: D.L.-C. thanks the National Council for Science and Technology (CONACYT) and the Centro de Investigación en Materiales Avanzados for their support for the completion of doctorate studies (CVU 483872). Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

E total energy h specific enthalpy (kJ/kg) I solar radiation (W/m2) . m mass flow rate (kg/s) P pressure (kPa) Q heat (W) . Qu useful heat gain (W) s entropy (kJ/kg) t time (s) T temperature (◦C) U overall heat transfer coefficient (W/m2K) . V volumetric flow rate (m3/s) W work (W) Subscripts CHP combined heat and power coll solar collector cond condensation elect electric evap evaporation exp expander ORC organic Rankine cycle SDHWS solar domestic hot water system Greek Symbols ∆ difference η efficiency µ dynamic viscosity ρ density Entropy 2019, 21, 911 21 of 23

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