Energy and Buildings

Energy and Buildings 41 (009) 175 181 Contents lists available at ScienceDirect Energy and Buildings journal homepage: www.elsevier.com/locate/enbuild Modeling solar-driven ejector refrigeration system offering air conditioning for office buildings J. Guo *, H.G. Shen School of Environmental Science and Engineering, Donghua University, 999# North Renmin Road, Shanghai 0160, PR China ARTICLE INFO ABSTRACT Article history: Received 6 June 008 Accepted 18 July 008 Keywords: Solar-driven ejector refrigeration Lumped method Dynamic model COP Solar fraction A lumped method combined with dynamic model is proposed for use in investigating the performance and solar fraction of a solar-driven ejector refrigeration system (SERS) using R134a, for office air conditioning application for buildings in Shanghai, China. Classical hourly outdoor temperature and solar radiation model were used to provide basic data for accurate analysis of the system performance. Results indicate that during the office working-time, i.e., from 9:00 to 17:00, the average COP and the average solar fraction of the system were 0.48 and 0.8 respectively when the operating conditions were: generator temperature (85 8C), evaporator temperature (8 8C) and condenser temperature varying with ambient temperature. Compared with traditional compressor based air conditioner, the system can save upto 80% electric energy when providing the same cooling capacity for office buildings. Hence, the system offers a good energy conservation method for office buildings. ß 008 Elsevier B.V. All rights reserved. 1. Introduction Energy is considered as a major agent in the generation of wealth and an important factor in economic development. With the sharp increase in the cost of the energy and the high energy consumed by the conventional air conditioners, the solar-driven ejector refrigeration system has recently received considerable attention as alternative refrigeration for residential and commercial space cooling application. An ejector driven by solar energy can be used to replace the compressor which makes the refrigeration system to consume much less electric power than traditional compressor based air conditioner. Moreover, the SERS is simple, reliable, and convenient for integration with buildings and can use environmentally friendly working fluid. In addition, they utilize solar energy which is essentially non-hazardous, unlimited and always 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 as system optimization works have been reported in literatures [4,5]. Various experimental studies [6 11] have examined the effect of the operation conditions such as the generator temperature, evaporator temperature and condenser temperature, the geometrical conditions such as the area ratio (the cross section area ratio of constant area 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 as refrigerant and collector selections on the performance of the system and presented abundant experimental data for reference during system design. Other researchers [1] have presented numerical methods of simulating the ejector and studied the parametric effect on the system performance. System optimization investigations [13 15] have focused on various combined ejector refrigeration systems for performance improvement. An accurate SERS performance forecasting is an important precondition for the optimal control and energy saving operation of air conditioning systems. Numerous prediction techniques, which mainly include thermodynamic method, dynamic method, lumped method, exergy analysis method and the use of artificial neural network (ANN) have been applied to predict the performance of SERS. Dynamic method is widely accepted as a technique which can describe in details what happens in the ejector while lumped method offers a good way to tackle complex problems in actual situations. The advantage of the dynamic method with respect to other models is its ability to model the choking, shock and mixing phenomena occuring in the ejector and can give detailed information on the mass flow along the ejector. In this paper, the lumped method combined with dynamic model was used to forecast the performance of a solar-driven ejector refrigeration system.. System description The SERS is shown in Fig. 1. It comprises of two loops, one is solar collection loop which is the main energy source of ejector 0378-7788/$ see front matter ß 008 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.008.07.016

176 J. Guo, H.G. Shen / Energy and Buildings 41 (009) 175 181 Nomenclature A area (m ) COP coefficient of performance Cp specific heat of gas at constant pressure (kj/(kg K)) D diameter (mm) f solar fraction h enthalpy (kj/kg) I solar radiation (W/m ) m mass flow rate (kg/s) M Mach number P pressure (Pa) Q heat (W) R gas constant (kj/(kg K)) T temperature (K) V velocity (m/s) Greek symbols g specific heat ratio h coefficient F m isoentropy coefficient of mixture v entrainment ratio, v = m e /m m Subscripts AS after shock c cooling DO diffuser outlet e entrained fluid HR heat required I calculation step in inlet m motive fluid mt mixture NO nozzle outlet t nozzle throat y section y y 3 constant area tube refrigeration system (ERS) and the other is ejector refrigeration loop which supplies useful cooling to the user. The solar collection loop is composed of collector, a hot water storage tank, an auxiliary heater and a circulating pump. The auxiliary heater is located between the hot water storage tank and the generator of the ejector refrigeration loop. When the hot water temperature in the tank is not high enough to drive the ejector refrigeration loop, the auxiliary heater will start automatically. The ejector refrigeration loop consists of two subsystems: the power subsystem, and the refrigeration subsystem. In the power subsystem, the refrigerant flows through the generator, the ejector, the condenser and the circulating pump, and finally flows back to the generator to supply high pressure motive fluid to the ejector. In the refrigeration subsystem, the refrigerant flows through the ejector, the condenser, the expansion valve, the evaporator, and then back to the suction of the ejector to supply the required cooling capacity. The main part of the ejector refrigeration loop is the ejector (Fig. ), which is composed of a convergent divergent nozzle, suction chamber, mixing chamber and a diffuser. The motive fluid is first accelerated to supersonic velocity in the convergent divergent nozzle, which entrains the evaporated fluid (named entrained fluid hereinafter) from the evaporator and the two fluids mix together in the mixing chamber. In the diffuser, the velocity of the mixed fluid is stepped down and the pressure is lifted to the condenser pressure. 3. Mathematical model Being driven by solar energy, the performance of the SERS is affected not only by geometrical parameters of the ejector, but also by local climatic conditions. Taking these into considerations, a lumped method combined with dynamic model was developed to investigate the performance of the SERS. The environmental friendly refrigerant R134a was used as the working fluid. And the climatic conditions of Shanghai were used for field modeling. The designed cooling capacity of the system was 6 kw with evaporation temperature at 8 8C. A vacuum tube collector of 15 m was employed for analysis. 3.1. Modeling the ejector performance The main geometrical parameters of the designed ejector are shown in Fig.. The dynamic model of ejector performance prediction similar to that given in reference [16] with the outlet of the convergent divergent nozzle located at somewhere in front of the constant area tube was adopted to analyze the system with real gas property derived from NIST REFPROP (Version 6.01) [17]. Suppose two chokes occur for both the motive and the entrained fluids, then the mass flow follows the gas dynamic equations: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m ¼ P ina t gh ðgþ1þ=ðg 1Þ pffiffiffiffiffiffi (1) R g þ 1 A iþ1 A i P i P iþ1 ¼ T in " # ¼ M i 1 þððg 1Þ=ÞMiþ1 ðgþ1þ=ðg 1Þ () M iþ1 1 þððg 1Þ=ÞMi 1 þððr 1Þ=ÞM iþ1 1 þððr 1Þ=ÞM i! r=ðr 1Þ (3) For a given ejector, the area is known, and the Mach number and pressure P NO at convergent divergent nozzle exit can be obtained by Eqs. () and (3). Assuming that the entrained fluid mixed with the motive fluid at section y y, where it forms the dynamic throat for the entrained fluid, i.e., M ey = 1. For a given inlet stagnant pressure P e, the pressure of the entrained fluid (P ey ) at the mixing section can be calculated by Eq. (3). Also, supposing the motive fluid and the entrained fluid mixed at section y y with uniform pressure, i.e. P my = P ey, known the convergent divergent nozzle outlet Mach number and with pressure obtained as mentioned above, the Mach number of the motive fluid at section y y can be calculated by Eq. (3) if P NO > P ey. Otherwise, shock happens at the outlet of the convergent divergent nozzle, and the flow abides by the shock wave theory. Then the cross-section area of the motive fluid core A my at section y y and that of the ejector at section y y A y can be obtained from Eq. () and the geometrical parameter of the ejector, and consequently, the cross-section area of 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 e m m (5)

J. Guo, H.G. Shen / Energy and Buildings 41 (009) 175 181 177 Fig. 1. Schematic diagram of solar-driven ejector refrigeration system. According to gas dynamic equations (6) and (7), the temperature and velocity of motive and entrained fluids are: T in ¼ 1 þ g 1 T y M y (6) V y ¼ M y qffiffiffiffiffiffiffiffiffiffiffi grt y Based on energy and momentum conservation of the motive, entrained and the mixed fluid, and taking the energy loss into consideration, 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! py þ m e CpT ey þ V! ey ¼ðm m þ m e Þ CpT mt þ V mt (9) Call for the database NIST REFPROP (Version 6.01) for the properties 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 h 6 Þ (10) Q HR ¼ m m ðh 1 h 5 Þ (11) COP ERS ¼ Q c ¼ v h h 6 (1) Q g h 1 h 5 Under the condition that the motive fluid undergoes a shock wave at the outlet of the nozzle, the pressure and Mach number after the shock wave are described by Eqs. (13) and (14). P AS ¼ 1 þ g P NO g þ 1 ðm NO 1Þ (13) M AS ¼ 1 þððg 1Þ=ÞM NO gm NO ððg 1Þ=Þ (14) 3.. Modeling the performance of the system Once the performance of the ejector and its refrigeration system is obtained, the performance of the SERS can be described by: COP SERS ¼ COP ERS h col (15) Fig.. Schematic diagram of ejector geometry.

178 J. Guo, H.G. Shen / Energy and Buildings 41 (009) 175 181 Where, h col is the efficiency of the solar collector, given by: h col ¼ F R ðatþ F R U L T col T a I (16) Where, F R is the heat transfer factor, t and a are the solar incident ratio and absorption, respectively. U L is the total heat loss coefficient of collector, T col is the water temperature of the collector, and T a is the ambient temperature. Then the effective solar energy gain and the solar fraction can be calculated by the following equations: Q col ¼ A col I h col (17) heat geained from solar energy f ¼ heat required for the generator=h ¼ Q col Q HR =h where, A col is the collector area, m, I is solar radiation, W/m. (18) Fig. 3. Schematic schedule of the program.

J. Guo, H.G. Shen / Energy and Buildings 41 (009) 175 181 179 Fig. 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 the circulating pumps and that by the control system is neglectable; () the velocity at the ejector inlet, outlet and evaporator outlet is neglectable; (3) the condenser temperature is 5 8C higher than the ambient temperature; and (4) the collector temperature is 10 8C higher than the generator temperature, then the performance of the system can be predicted by the program descript in Fig. 3. 4. Results and discussions 4.1. Performance of the ejector and its refrigeration system For a given ejector, the performance can be calculated based on the mathematical model mentioned in Section 3.1. For validation, the results calculated by the model were compared with the experimental values and also with the one-dimension model by Huang et al. [16], and with that calculated by CFD software package Fluent 6. [18]. The deviations are shown in Fig. 4. The results were found to be in good agreement with experimental values with deviations no more than 10%, which means the model is effective for analysis the performance of the ejector and can be used as basis for performance analysis of the SERS. The entrainment ratio of the ejector used for the system analysis is shown in Fig. 5. For a given ejector, higher generator temperature means higher motive fluid pressure, which leads to a higher velocity at the exit of the convergent divergent nozzle and more fluid from the evaporator is entrained. When the inlet temperature of the motive fluid is higher than the designed temperature, shock wave will happen. With energy loss during the shock wave, the entrainment capacity of the motive fluid after the shock wave is decreased sharply. The COP of the ERS is shown in Fig. 6, and it has a similar trend as the entrainment ratio of the ejector because the performance of the system is greatly affected by the entrainment ratio of the ejector. More refrigerant fluid entrained by the ejector means the system supplies more cooling capacity, with a small increase in heat requirement for heating the motive fluid. Hence, the system offers better performance. Fig. 7 shows the cooling capacity of the designed ejector under critical condenser pressure. The critical cooling capacity of 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 wave happens at the exit of the nozzle which leads to energy loss, consequently, the performance and the cooling capacity of the ERS decrease sharply. Fig. 5. Entrainment ratio of the designed ejector. Fig. 7. Cooling capacity of the ERS under various generator temperature.

180 J. Guo, H.G. Shen / Energy and Buildings 41 (009) 175 181 Fig. 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.. Performance of the SERS The climate conditions of Shanghai were used for the performance prediction of the SERS. Figs. 8 and 9 show the hourly outdoor ambient temperature and total solar radiation on a typical day in July calculated from the model proposed by Liu and Jordan [19]. Given the performance of the ejector as mentioned above and the climate conditions as shown in Figs. 8 and 9, the hourly performance of the ERS and SERS can be obtained (Figs. 10 and 11). Fig. 10 shows the hourly COP of the ERS with the evaporator temperature at 8 8C and the condenser temperature varying with the ambient temperature. Under fixed inlet pressures of motive fluid and entrained fluid, the mixed fluid is easier to flow through with higher condenser temperature, therefore, more refrigerant fluid can be entrained and the entrainment ratio of the ejector increases, consequently, the cooling capacity and the COP of the ERS also increase. Comparing Figs. 8 10, although the solar radiation reaches maximum at 1:00, the ambient temperature and the entrainment ratio of the ejector reach maximum at 14:00. It indicates that the condenser temperature has greater effect on the performance of the ERS than the generator temperature. As the condenser temperature not only determines the condenser pressure which in turn influences the entrainment ratio and COP of the ERS as mentioned above, but it also influences the heat required by the generator. Under a higher condenser temperature, the ejector entrains more refrigerant and supplies more cooling capacity. Furthermore, a higher condenser temperature causes a decrease in the heat required by the generator when it generates the same quality and quantity of motive fluid. Fig. 10. Variation of COP of ERS with time. Fig. 1. Hourly solar fraction.

J. Guo, H.G. Shen / Energy and Buildings 41 (009) 175 181 181 Considering the efficiency of the solar collector, heat loss of the storage tank and pipes as well as the heat transfer efficiency in the generator, the hourly overall performance of the SERS is as shown in Fig. 11. From 8:00. to 16:00, the system worked under steady performance between 0.43 and 0.53 with cooling capacity of 6 kw. During other times, the solar radiation intensity weakens and the ambient temperature drops, therefore, the overall COP of the system decreases sharply. From the view of this character, the system exerts its best performance when being used in daytime. Therefore, it s appropriate for the system to supply air conditioning for office buildings. The hourly solar fraction of the system is shown in Fig. 1. With more solar energy gain from 10:00 to 13:00, the solar fraction during this period is more than 1.0, which means no additional electric energy is needed (except that used for the instrument and circulation pumps) for the system to supply air conditioning. During other hours at daytime, the solar fraction of the system is between 0.45 0.94 except at 17:00, the solar fraction drops to as low as 0.15. When the system is equipped in office buildings, and the office time is from 9:00 to 17:00, the average solar fraction of the system is 0.8. That is to say, only 18% electric energy is needed to provide the same cooling capacity. Compared with traditional compressed air conditioning system, the SERS can conserve more than 75% of electric energy. 5. Conclusions In this study, the lumped method combined with dynamic model for performance prediction of solar-driven ejector refrigeration system for providing air conditioning to office buildings was investigated. The results of the mathematical simulation have demonstrated that the solar-driven ejector refrigeration system can be designed to meet the cooling requirements of air conditioning for office buildings. The following conclusions were obtained: (1) For the studied case, the condenser temperature influences more on the performance of the SERS than the generator temperature. () From 9:00 to 17:00, on typical clear sky days, the average COP of the system is 0.48 with most of the daytime remaining steady between 0.43 0.53, except at 17:00, when it drops as low as 0.9. The average solar fraction is 0.8. (3) Compared with traditional compressor based air conditioner, the SERS conserves more than 75% of electric energy when it is used to supply air conditioning during daytime for office buildings. (4) The system offers a good energy conservation method for air conditioning of office buildings. References [1] Srinivasa Murthy, R. Balasubramanian, M.V. 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