Modeling solar-driven ejector refrigeration system offering air ...

Energy and Buildings 41 (2009) 175–181Contents lists available at ScienceDirectEnergy and Buildingsjournal homepage: www.elsevier.com/locate/enbuildModeling solar-driven ejector refrigeration system offering air conditioningfor office buildingsJ. Guo *, H.G. ShenSchool of Environmental Science and Engineering, Donghua University, 2999# North Renmin Road, Shanghai 201620, PR ChinaARTICLEINFOABSTRACTArticle history:Received 26 June 2008Accepted 18 July 2008Keywords:Solar-driven ejector refrigerationLumped methodDynamic modelCOPSolar fractionA lumped method combined with dynamic model is proposed for use in investigating the performanceand solar fraction of a solar-driven ejector refrigeration system (SERS) using R134a, for office airconditioning application for buildings in Shanghai, China. Classical hourly outdoor temperature and solarradiation model were used to provide basic data for accurate analysis of the system performance. Resultsindicate that during the office working-time, i.e., from 9:00 to 17:00, the average COP and the averagesolar fraction of the system were 0.48 and 0.82 respectively when the operating conditions were:generator temperature (85 8C), evaporator temperature (8 8C) and condenser temperature varying withambient temperature. Compared with traditional compressor based air conditioner, the system can saveupto 80% electric energy when providing the same cooling capacity for office buildings. Hence, the systemoffers a good energy conservation method for office buildings.ß 2008 Elsevier B.V. All rights reserved.1. IntroductionEnergy is considered as a major agent in the generation ofwealth and an important factor in economic development. Withthe sharp increase in the cost of the energy and the high energyconsumed by the conventional air conditioners, the solar-drivenejector refrigeration system has recently received considerableattention as alternative refrigeration for residential and commercialspace cooling application. An ejector driven by solar energy canbe used to replace the compressor which makes the refrigerationsystem to consume much less electric power than traditionalcompressor based air conditioner. Moreover, the SERS is simple,reliable, and convenient for integration with buildings and can useenvironmentally friendly working fluid. In addition, they utilizesolar energy which is essentially non-hazardous, unlimited andalways available.Since the idea of a SERS was advanced in the beginning of 1990s[1–3], a great deal of numerical and experimental works as well assystem optimization works have been reported in literatures [4,5].Various experimental studies [6–11] have examined the effect of theoperation conditions such as the generator temperature, evaporatortemperature and condenser temperature, the geometrical conditionssuch as the area ratio (the cross section area ratio of constantarea tube to the nozzle throat), the distance of the nozzle exit to the* Corresponding author.E-mail address: shuheguo@163.com (J. Guo).inlet of the constant area tube, the system conditions such asrefrigerant and collector selections on the performance of thesystem and presented abundant experimental data for referenceduring system design. Other researchers [12] have presentednumerical methods of simulating the ejector and studied theparametric effect on the system performance. System optimizationinvestigations [13–15] have focused on various combined ejectorrefrigeration systems for performance improvement.An accurate SERS performance forecasting is an importantprecondition for the optimal control and energy saving operation ofair conditioning systems. Numerous prediction techniques, whichmainly include thermodynamic method, dynamic method, lumpedmethod, exergy analysis method and the use of artificial neuralnetwork (ANN) have been applied to predict the performance ofSERS. Dynamic method is widely accepted as a technique which candescribe in details what happens in the ejector while lumpedmethod offers a good way to tackle complex problems in actualsituations. The advantage of the dynamic method with respect toother models is its ability to model the choking, shock and mixingphenomena occuring in the ejector and can give detailed informationon the mass flow along the ejector. In this paper, the lumpedmethod combined with dynamic model was used to forecast theperformance of a solar-driven ejector refrigeration system.2. System descriptionThe SERS is shown in Fig. 1. It comprises of two loops, one issolar collection loop which is the main energy source of ejector0378-7788/$ – see front matter ß 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.enbuild.2008.07.016

176J. Guo, H.G. Shen / Energy and Buildings 41 (2009) 175–181NomenclatureA area (m 2 )COP coefficient of performanceCp specific heat of gas at constant pressure (kJ/(kg K))D diameter (mm)f solar fractionh enthalpy (kJ/kg)I solar radiation (W/m 2 )m mass flow rate (kg/s)M Mach numberP pressure (Pa)Q heat (W)R gas constant (kJ/(kg K))T temperature (K)V velocity (m/s)Greek symbolsg specific heat ratioh coefficientF m isoentropy coefficient of mixturev entrainment ratio, v = m e /m mSubscriptsAS after shockc coolingDO diffuser outlete entrained fluidHR heat requiredI calculation stepin inletm motive fluidmt mixtureNO nozzle outlett nozzle throaty section y–y3 constant area tuberefrigeration system (ERS) and the other is ejector refrigerationloop which supplies useful cooling to the user.The solar collection loop is composed of collector, a hot waterstorage tank, an auxiliary heater and a circulating pump. Theauxiliary heater is located between the hot water storage tank andthe generator of the ejector refrigeration loop. When the hot watertemperature in the tank is not high enough to drive the ejectorrefrigeration loop, the auxiliary heater will start automatically.The ejector refrigeration loop consists of two subsystems: thepower subsystem, and the refrigeration subsystem. In the powersubsystem, the refrigerant flows through the generator, the ejector,the condenser and the circulating pump, and finally flows back tothe generator to supply high pressure motive fluid to the ejector. Inthe refrigeration subsystem, the refrigerant flows through theejector, the condenser, the expansion valve, the evaporator, andthen back to the suction of the ejector to supply the requiredcooling capacity. The main part of the ejector refrigeration loop isthe ejector (Fig. 2), which is composed of a convergent–divergentnozzle, suction chamber, mixing chamber and a diffuser. Themotive fluid is first accelerated to supersonic velocity in theconvergent–divergent nozzle, which entrains the evaporated fluid(named entrained fluid hereinafter) from the evaporator and thetwo fluids mix together in the mixing chamber. In the diffuser, thevelocity of the mixed fluid is stepped down and the pressure islifted to the condenser pressure.3. Mathematical modelBeing driven by solar energy, the performance of the SERS isaffected not only by geometrical parameters of the ejector, but alsoby local climatic conditions. Taking these into considerations, alumped method combined with dynamic model was developed toinvestigate the performance of the SERS. The environmentalfriendly refrigerant R134a was used as the working fluid. And theclimatic conditions of Shanghai were used for field modeling.The designed cooling capacity of the system was 6 kW withevaporation temperature at 8 8C. A vacuum tube collector of 15 m 2was employed for analysis.3.1. Modeling the ejector performanceThe main geometrical parameters of the designed ejector areshown in Fig. 2. The dynamic model of ejector performanceprediction similar to that given in reference [16] with the outlet ofthe convergent–divergent nozzle located at somewhere in front ofthe constant area tube was adopted to analyze the system with realgas property derived from NIST REFPROP (Version 6.01) [17].Suppose two chokes occur for both the motive and theentrained fluids, then the mass flow follows the gas dynamicequations:sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffim ¼ P inA t gh 2 ðgþ1Þ=ðg 1Þpffiffiffiffiffiffi(1)R g þ 1A iþ1A iT in" # ðgþ1Þ=2ðg¼ M i1 þððg 1Þ=2ÞMiþ12 1Þ(2)M iþ1 1 þððg 1Þ=2ÞMi2P iP iþ1¼ 1 þððr 1Þ=2ÞM2 iþ11 þððr 1Þ=2ÞM 2 i! r=ðr 1Þ(3)For a given ejector, the area is known, and the Mach number andpressure P NO at convergent–divergent nozzle exit can be obtainedby Eqs. (2) and (3). Assuming that the entrained fluid mixed withthe motive fluid at section y–y, where it forms the ‘‘dynamicthroat’’ for the entrained fluid, i.e., M ey = 1. For a given inletstagnant pressure P e , the pressure of the entrained fluid (P ey ) at themixing section can be calculated by Eq. (3). Also, supposing themotive fluid and the entrained fluid mixed at section y–y withuniform pressure, i.e. P my = P ey , known the convergent–divergentnozzle outlet Mach number and with pressure obtained asmentioned above, the Mach number of the motive fluid at sectiony–y can be calculated by Eq. (3) if P NO > P ey . Otherwise, shockhappens at the outlet of the convergent–divergent nozzle, and theflow abides by the shock wave theory. Then the cross-section areaof the motive fluid core A my at section y–y and that of the ejector atsection y–y A y can be obtained from Eq. (2) and the geometricalparameter of the ejector, and consequently, the cross-section areaof the entrained fluid A y at section y–y is given by:A ey ¼ A y A my (4)The mass flow of the entrained fluid m e can be calculated by Eq. (1)and the entrainment ratio is:v ¼ m em m(5)

J. Guo, H.G. Shen / Energy and Buildings 41 (2009) 175–181 177Fig. 1. Schematic diagram of solar-driven ejector refrigeration system.According to gas dynamic equations (6) and (7), the temperatureand velocity of motive and entrained fluids are:T in¼ 1 þ g 1T y 2 M2 y (6)V y ¼ M yqffiffiffiffiffiffiffiffiffiffiffigRT yBased on energy and momentum conservation of the motive,entrained and the mixed fluid, and taking the energy loss intoconsideration, the parameters of the mixture are:F m ½m m V my þ m e V ey Š¼ðm m þ m e ÞV mt (8)m m CpT my þ V !py2 þ m e CpT ey þ V !ey222¼ðm m þ m e Þ CpT mt þ V mt2 (9)2Call for the database NIST REFPROP (Version 6.01) for theproperties of the gas, the cooling capacity, heat required by the(7)generator and the performance of the ERS are:Q c ¼ m e ðh 2 h 6 Þ (10)Q HR ¼ m m ðh 1 h 5 Þ (11)COP ERS ¼ Q c¼ v h 2 h 6(12)Q g h 1 h 5Under the condition that the motive fluid undergoes a shock waveat the outlet of the nozzle, the pressure and Mach number after theshock wave are described by Eqs. (13) and (14).P AS¼ 1 þ2gP NO g þ 1 ðM2 NO 1Þ (13)MAS 2 ¼ 1 þððg 1Þ=2ÞM2 NOgMNO 2 ððg 1Þ=2Þ3.2. Modeling the performance of the system(14)Once the performance of the ejector and its refrigeration systemis obtained, the performance of the SERS can be described by:COP SERS ¼ COP ERS h col (15)Fig. 2. Schematic diagram of ejector geometry.

178J. Guo, H.G. Shen / Energy and Buildings 41 (2009) 175–181Where, h col is the efficiency of the solar collector, given by:h col ¼ F R ðatÞ F R U LT col T aI(16)Where, F R is the heat transfer factor, t and a are the solar incidentratio and absorption, respectively. U L is the total heat losscoefficient of collector, T col is the water temperature of thecollector, and T a is the ambient temperature.Then the effective solar energy gain and the solar fraction can becalculated by the following equations:Q col ¼ A col I h col (17)heat geained from solar energyf ¼heat required for the generator=h ¼ Q colQ HR =hwhere, A col is the collector area, m 2 , I is solar radiation, W/m 2 .(18)Fig. 3. Schematic schedule of the program.

J. Guo, H.G. Shen / Energy and Buildings 41 (2009) 175–181 179Fig. 4. Validation of the model.Fig. 6. COP of the ERS under various generator temperature.Based on the assumption that: (1) the power consumed by thecirculating pumps and that by the control system is neglectable;(2) the velocity at the ejector inlet, outlet and evaporator outlet isneglectable; (3) the condenser temperature is 5 8C higherthanthe ambient temperature; and (4) the collector temperature is10 8C higher than the generator temperature, then the performanceof the system can be predicted by the program descriptin Fig. 3.4. Results and discussions4.1. Performance of the ejector and its refrigeration systemFor a given ejector, the performance can be calculated basedon the mathematical model mentioned in Section 3.1. Forvalidation, the results calculated by the model were comparedwith the experimental values and also with the one-dimensionmodel by Huang et al. [16], and with that calculated by CFDsoftware package Fluent 6.2 [18]. The deviations are shown inFig. 4. The results were found to be in good agreement withexperimental values with deviations no more than 10%, whichmeans the model is effective for analysis the performance ofthe ejector and can be used as basis for performance analysis ofthe SERS.The entrainment ratio of the ejector used for the systemanalysis is shown in Fig. 5. For a given ejector, higher generatortemperature means higher motive fluid pressure, which leads to ahigher velocity at the exit of the convergent–divergent nozzle andmore fluid from the evaporator is entrained. When the inlettemperature of the motive fluid is higher than the designedtemperature, shock wave will happen. With energy loss during theshock wave, the entrainment capacity of the motive fluid after theshock wave is decreased sharply.The COP of the ERS is shown in Fig. 6, and it has a similar trendas the entrainment ratio of the ejector because the performance ofthe system is greatly affected by the entrainment ratio of theejector. More refrigerant fluid entrained by the ejector means thesystem supplies more cooling capacity, with a small increase inheat requirement for heating the motive fluid. Hence, the systemoffers better performance.Fig. 7 shows the cooling capacity of the designed ejectorunder critical condenser pressure. The critical cooling capacityof the ejector increases with increasing generator temperature.Under the design condition of generator temperature at 85 8C,the cooling capacity reaches maximum. After that, shock wavehappens at the exit of the nozzle which leads to energy loss,consequently, the performance and the cooling capacity of theERS decrease sharply.Fig. 5. Entrainment ratio of the designed ejector.Fig. 7. Cooling capacity of the ERS under various generator temperature.

180J. Guo, H.G. Shen / Energy and Buildings 41 (2009) 175–181Fig. 8. Hourly ambient temperature variations in Shanghai (July).Fig. 11. Variation of COP of the SERS with time.Fig. 9. Hourly solar radiation in Shanghai (July).4.2. Performance of the SERSThe climate conditions of Shanghai were used for theperformance prediction of the SERS. Figs. 8 and 9 show the hourlyoutdoor ambient temperature and total solar radiation on a typicalday in July calculated from the model proposed by Liu and Jordan[19]. Given the performance of the ejector as mentioned above andthe climate conditions as shown in Figs. 8 and 9, the hourlyperformance of the ERS and SERS can be obtained (Figs. 10 and 11).Fig. 10 shows the hourly COP of the ERS with the evaporatortemperature at 8 8C and the condenser temperature varying withthe ambient temperature. Under fixed inlet pressures of motivefluid and entrained fluid, the mixed fluid is easier to flow throughwith higher condenser temperature, therefore, more refrigerantfluid can be entrained and the entrainment ratio of the ejectorincreases, consequently, the cooling capacity and the COP of theERS also increase.Comparing Figs. 8–10, although the solar radiation reachesmaximum at 12:00, the ambient temperature and the entrainmentratio of the ejector reach maximum at 14:00. It indicates that thecondenser temperature has greater effect on the performance ofthe ERS than the generator temperature. As the condensertemperature not only determines the condenser pressure whichin turn influences the entrainment ratio and COP of the ERS asmentioned above, but it also influences the heat required by thegenerator. Under a higher condenser temperature, the ejectorentrains more refrigerant and supplies more cooling capacity.Furthermore, a higher condenser temperature causes a decrease inthe heat required by the generator when it generates the samequality and quantity of motive fluid.Fig. 10. Variation of COP of ERS with time.Fig. 12. Hourly solar fraction.

J. Guo, H.G. Shen / Energy and Buildings 41 (2009) 175–181 181Considering the efficiency of the solar collector, heat loss of thestorage tank and pipes as well as the heat transfer efficiency in thegenerator, the hourly overall performance of the SERS is as shownin Fig. 11. From 8:00. to 16:00, the system worked under steadyperformance between 0.43 and 0.53 with cooling capacity of 6 kW.During other times, the solar radiation intensity weakens andthe ambient temperature drops, therefore, the overall COP of thesystem decreases sharply. From the view of this character, thesystem exerts its best performance when being used in daytime.Therefore, it’s appropriate for the system to supply air conditioningfor office buildings.The hourly solar fraction of the system is shown in Fig. 12. Withmore solar energy gain from 10:00 to 13:00, the solar fractionduring this period is more than 1.0, which means no additionalelectric energy is needed (except that used for the instrument andcirculation pumps) for the system to supply air conditioning.During other hours at daytime, the solar fraction of the system isbetween 0.45–0.94 except at 17:00, the solar fraction drops to aslow as 0.15. When the system is equipped in office buildings, andthe office time is from 9:00 to 17:00, the average solar fraction ofthe system is 0.82. That is to say, only 18% electric energy is neededto provide the same cooling capacity. Compared with traditionalcompressed air conditioning system, the SERS can conserve morethan 75% of electric energy.5. ConclusionsIn this study, the lumped method combined with dynamicmodel for performance prediction of solar-driven ejector refrigerationsystem for providing air conditioning to office buildingswas investigated. The results of the mathematical simulation havedemonstrated that the solar-driven ejector refrigeration systemcan be designed to meet the cooling requirements of airconditioning for office buildings. The following conclusions wereobtained:(1) For the studied case, the condenser temperature influencesmore on the performance of the SERS than the generatortemperature.(2) From 9:00 to 17:00, on typical clear sky days, the average COPof the system is 0.48 with most of the daytime remainingsteady between 0.43–0.53, except at 17:00, when it drops aslow as 0.29. The average solar fraction is 0.82.(3) Compared with traditional compressor based air conditioner,the SERS conserves more than 75% of electric energy when it isused to supply air conditioning during daytime for officebuildings.(4) The system offers a good energy conservation method for airconditioning of office buildings.References[1] Srinivasa Murthy, R. Balasubramanian, M.V. 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