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Initial ratio optimization for the ejector cooling system with thermal pumping effect (ECSTPE)
Energy Conversion and Management 113 (2016) 281–289
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Initial ratio optimization for the ejector cooling system with thermal pumping effect (ECSTPE) Yijian He a, Yongjun Sun b, Sheng Zhang a,b,⇑, Yuanli Lyu b, Guangming Chen a a b
Institute of Refrigeration and Cryogenics, Zhejiang University, Hangzhou, China Division of Building Science and Technology, City University of Hong Kong, Kowloon, Hong Kong
a r t i c l e
i n f o
Article history: Received 24 August 2015 Accepted 28 January 2016
Keywords: Optimal initial ratio Optimal time length of cooling stage Performance optimization Ejector cooling Thermal pumping effect
a b s t r a c t An ejector cooling system with thermal pumping effect (ECSTPE) could operate without consumption of electric power, but it discards a great amount of thermal energy, which generally results in a lower COP value and a greater chilling load. An innovative concept for the optimal initial ratio is therefore proposed to develop the optimal time length of cooling stage (TLCS) control method. The optimal TLCS control method effectively improves the ECSTPE performance. First, in this context, it was theoretically proven that the optimal initial ratio could be used to reduce the energy loss and the chilling load. Second, it was formulated how to achieve the optimal initial ratio; and the optimal TLCS control method was determined by identifying the relationship between the TLCS and the initial ratio. Third, case studies were conducted to demonstrate the effectiveness of the developed optimal TLCS control method on ECSTPEs with different refrigerants. The results showed that for ECSTPE with R134a, a 10-second deviation from the optimal TLCS led to a decrease of 5.6% in the COP value and an increase of 23.7% in the chilling load. For ECSTPEs with R141b and R365mfc, a 10-second deviation led to relatively slight performance deterioration; however, an excessive deviation (e.g., 100 s) would lead to severe performance deterioration (e.g., increases of 35% and 58% in the chilling loads for ECSTPEs with R134b and R365mfc, respectively). The developed optimal TLCS control method could certainly improve the performance of ECSTPEs with other refrigerants. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Because the building sector accounts for approximately 40% of primary energy consumption, reducing the energy consumption of buildings is widely regarded as an effective means by which to mitigate increasing energy and environmental problems [1]. Refrigeration and air conditioning in buildings constitute a large portion of energy consumption, and this portion continues to increase [2]. Thus, improvement in the energy efficiency of refrigeration and air conditioning systems is a crucial step for the reduction of global energy demand and emissions. Ejector cooling systems present promising alternatives to conventional mechanical cooling systems [3]. The ejector in an ejector cooling system is responsible for pressurizing the refrigerant from the evaporator, as the mechanical compressor does in a conventional mechanical cooling system [4]. Ejector cooling systems are preferable for two reasons. First, ejector cooling systems can be ⇑ Corresponding author at: Division of Building Science and Technology, City University of Hong Kong, Kowloon, Hong Kong. Tel.: +852 34425290; fax: +852 34429716. E-mail address: [email protected] (S. Zhang). http://dx.doi.org/10.1016/j.enconman.2016.01.067 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.
powered by low-grade thermal energy such as solar energy, which contributes significantly to energy conservation and reduction of emissions [5]. Second, ejector cooling systems are superior to other solar-powered cooling systems (e.g., solar-powered adsorption cooling systems and solar-powered absorption cooling systems) in several aspects, including their low cost and their simple system design, installation, and operation [6]. Unfortunately, ejector cooling systems have not been widely accepted in the refrigeration and air conditioning market because their COPs (e.g., 0.18–0.6 [7]) are generally lower than those of conventional mechanical cooling systems (e.g., approximately 3–6 [8–10]) [6,11]. However, conventional mechanical cooling systems consume a large amount of electricity, while ejector cooling systems can use low-grade thermal energy and show other obvious superiorities. Thus, improvement of energy efficiency of ejector cooling systems could greatly promote their application.
1.1. Ejector cooling system without pump Ejector cooling technologies are generally classified into eight types [3], including single-ejector cooling systems [12,13],
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Nomenclature COP h P q Q t T v Vol w
coefficient of performance (–) enthalpy (kJ/kg) pressure (kPa) cooling power (kJ) chilling load (kJ/kg) time (s) temperature (°C) specific volume ðm3 =kgÞ volume (m3 ) entrainment ratio (–)
Greek symbols c initial ratio (–) Abbreviations ECSTPE ejector cooling system with thermal pumping effect HPVHT high pressure vapor with high temperature
combined ejector-absorption cooling systems [14,15], and ejector cooling systems without a pump [16,17], etc. The ejector cooling system without a pump eliminates the requirement for a mechanical pump to transfer the refrigerant from the condenser to the generator. The main motivations for elimination of the mechanical pump are as follows. In ejector cooling systems, the mechanical pump is the only moving part that requires relatively frequent maintenance and the only part that consumes electricity [18,19]. Thus, the ejector cooling system without a pump has two advantages over other ejector cooling technologies. First, it has the potential to work with greater stability and have a longer lifetime [20], and second, it consumes no electricity [21]. Four main types of ejector cooling systems without a pump have been proposed: the bi-ejector cooling system [16], the heat pipe/ejector cooling system [22], the gravitational ejector cooling system [19], and the ejector cooling system with thermal pumping effect (ECSTPE) [17]. The working principles and characteristics of these ejector cooling systems without a pump are as follows. The bi-ejector cooling system replaces the mechanical pump with a vapor/liquid ejector that uses the high pressure vapor from the generator to carry condensate back to the generator [16,23]. The heat pipe/ejector cooling system integrates the ejector and the heat pipe and exploits the heat pipe’s wick action to transfer condensate back to the generator [22,24]. Although the bi-ejector cooling system and the heat pipe/ejector cooling system seem theoretically promising, their practicality has not been proven experimentally [3]. The practicality of the gravitational ejector cooling system and the ECSTPE have been proven experimentally [19,25]. The gravitational ejector cooling system makes use of the height difference to equalize the pressure between the condenser and the generator and thus assist the refrigerant to successfully circulate; however, the height difference requires a large installation room and long conduction pipes (which causes friction and heat losses) [19,26]. The drawbacks of the gravitational ejector cooling system can be overcome with the use of rotary motion [27]. The roto-gravitational ejector cooling system makes use of the large accelerations of rotary motion to significantly decrease the system size; however, the rotating cylinder consumes electricity, which leads to the loss of one of the above-mentioned attractions of an ejector cooling system without a pump [27]. An ECSTPE uses a thermal pumping effect instead of a mechanical pump [28]. The thermal pumping effect has been widely studied but requires a special design for use in an ejector cooling system
TLCS time length of cooling stage Subscripts c condenser e evaporator ev evacuation chamber g gaseous/generator L liquid opt optimal wn primary fluid 1 cooling stage 2 pressuring stage 21 pressurization sub-process 22 feeding back sub-process 23 chilling sub-process i point at the beginning of the pressurization sub-process ii point at the beginning of the feeding back sub-process iii point at the beginning of the chilling sub-process
[29–32]. In an ECSTPE, the thermal pumping effect uses the high-pressure vapor from the vapor generator to pressurize the condensate in the evacuation chamber by means of thermal balance. Experiments have shown that an ECSTPE could be driven by thermal energy alone without other power input, and it is smaller than a gravitational ejector cooling system [25,33]. Thus, the ECSTPE is the most applicable ejector cooling system without a pump, and this study focuses on improvement of its thermal energy efficiency. 1.2. Low thermal energy efficiency of ECSTPEs Existing ECSTPEs have severe problems with the waste of thermal energy and chilling water. ECSTPEs come in two types: those with a workless boiler feeding system and those with a multifunction generator. Both types have low thermal energy efficiency due to the thermal pumping effect. Srisastra and Aphornratana [33] proposed an ECSTPE that used a workless boiler feeding system that transferred the condensate from the condenser to the boiler with the help of gravity and boiler pressure, which was similar to the ‘‘transfer-tank” used in an absorption cooling system [33,34]. However, the tank in this feeding system was chilled down by the condenser, which led to a great increase in energy consumption (e.g., 10–15%) [35]. Huang et al. [17] proposed an ECSTPE, in which a multi-function generator separated the tank (also called an ‘‘evacuation chamber”) and the condenser, and the evacuation chamber was chilled by the surrounding chilling jacket. The experimental results showed a decrease of 15% (from 0.218 to 0.185) in the COP after taking into account the extra thermal energy required by the thermal pumping effect at a generation temperature of 90 °C, a condensing temperature of 32.4 °C, and an evaporation temperature of 8.2 °C [17]. That is, approximately 15% of the thermal energy was discarded by the thermal pumping effect, because the thermal energy used to pressurize the condensed refrigerant in the evacuation chamber was negligible (e.g., 0.18% [36]). This considerable amount of thermal energy was discarded because the chilling jacket chilled down not only the evacuation chamber but also the vapor generator [17,37]. Accordingly, the high-pressure vapor with high temperature (HPVHT) in the vapor generator and the evacuation chamber was chilled directly. As a result, the thermal energy within the HPVHT was discarded, and the chilling water was largely required to remove the discarded thermal energy. The thermal energy discarded by chilling the vapor
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Out of the dotted rectangle: ejector cooling subsystem Ejector Solenoid valve 1
Condenser
Evaporator
Throttle valve
Solenoid valve 2
Solenoid valve 5
Solenoid valve 3
Chilling jacket Evacuation chamber Solenoid valve 4 Vapor generator
Heat
Solenoid valve 6 Within the dotted rectangle: multi-functional generator subsystem
Fig. 1. Schematic of the ejector cooling system with thermal pumping effect.
initial ratio is formulated and the optimal TLCS control strategy is determined by identifying the relationship between the TLCS and the initial ratio. In Section 4, case studies are conducted to demonstrate the effectiveness of the developed optimal TLCS control method for ECSTPEs with different refrigerants. 2. Effects of initial ratio on ECSTPE performance In this section, the positive effects of the optimal initial ratio on ECSTPE performance are proven. First, the ECSTPE work mechanism is described. Based on the description of the work mechanism, the thermal energy and chilling water waste problems of the ECSTPE are exposed, and the optimal initial ratio is proven to be effective in mitigating those problems. To clearly illustrate the positive effects of the optimal initial ratio, the ECSTPE analyzed here is only equipped with one set of the multi-function generator, as shown in Fig. 1. An ECSTPE with one set of the multi-function generator produces intermittent cooling. However, the conclusions can be extrapolated to ECSTPEs with multiple sets of the multi-function generators. ECSTPEs with multiple sets of the multi-function generators in parallel can produce cooling power consecutively. 2.1. Description of ECSTPE work mechanism
generator can be avoided by separating the vapor generator and the evacuation chamber [35], as shown in Fig. 1. The ECSTPE in the following context refers to the ECSTPE shown in Fig. 1. However, the thermal energy and chilling water waste problems caused by chilling the evacuation chamber require further mitigation. To reduce the discarded thermal energy and the associated chilling load, the time length of cooling stage (TLCS) must be accurately controlled. The cooling stage refers to the stage during which the ECSTPE produces cooling. The main reasons are as follows. The TLCS determines the mass of the condensed refrigerant in the evacuation chamber, which equals the mass of the HPVHT used as the primary fluid in the ejector due to the mass conservation law. More primary fluid indicates more cooling production. More cooling production indicates larger thermal energy efficiency and less demand for chilling water, because the discarded thermal energy is constant for every work period (i.e., HPVHT in one evacuation chamber). In other words, the TLCS determines the cooling production, and the TLCS should be controlled to produce the most cooling in one work period. However, existing ECSTPE studies place little emphasis on optimization of TLCS control; the TLCS was simply determined to target high thermal energy efficiency without consideration of the thermal energy and chilling water waste problems caused by the thermal pumping effect [17,25,37]. In [17,37], the cooling stage was terminated when the generator pressure dropped to a level that could not effectively drive the ejector. In [25], the cooling stage was terminated when the evaporator pressure exceeded a set point (e.g., 0.004 MPa) at which cooling production would be unstable. Without optimization of TLCS control, experimental results showed that a large portion of the thermal energy was discarded (e.g., 26.6%) [25]. Moreover, Srisastra and Aphornratana [33] controlled the TLCS according to a desired amount of condensed refrigerant in the evacuation chamber; however, no explanations on the desired amount of condensed refrigerant were given, and low thermal energy efficiency was observed [35]. Therefore, an innovative concept for the optimal initial ratio is proposed to develop an optimal TLCS control method. The initial ratio is defined as the volume ratio of vapor refrigerant to liquid refrigerant in the evacuation chamber just before pressurization. The structure of the paper is arranged as follows. In Section 2, it is shown that the optimal initial ratio can mitigate the thermal energy and chilling water waste problems. Section 3, the optimal
As shown in Fig. 1, an ECSTPE consists of two subsystems: the multi-function generator subsystem within the dotted rectangle and the ejector cooling subsystem outside the dotted rectangle. The multi-function generator incorporates a vapor generator and an evacuation chamber and is designed to provide HPVHT. HPVHT is used for three tasks: for use as a primary fluid, to pressurize the condensed refrigerant in the evacuation chamber, and to balance the pressure between the vapor generator and the evacuation chamber to facilitate circulation of the refrigerant. One work period of the ECSTPE is partitioned into a cooling stage and a pressuring stage by controlling solenoid valves, as shown in Table 1. Before start-up, all solenoid valves are closed. To start the cooling stage, solenoid valves 1, 2, and 6 are switched on. The HPVHT generated in the vapor generator then flows into the ejector to extract the refrigerant from the evaporator, and the mixed refrigerant is obtained. The mixed refrigerant then flows into the condenser to be condensed. After leaving the condenser, the liquid refrigerant is separated into two portions, one that produces cooling in the evaporator and one that is fed back into the vapor generator after first being stored in the evacuation chamber. When the liquid refrigerant in the evacuation chamber reaches a certain level, the cooling stage ends and the pressuring stage begins by inversion of solenoid valves 1, 2, and 3. The pressuring stage consists of three successive sub-processes: pressurization, feeding back, and chilling. During the pressurization sub-process, HPVHT flows into the evacuation chamber to pressurize the liquid refrigerant until a thermal balance is achieved. The feeding back sub-process is then triggered by switching on solenoid valve 4.
Table 1 Actions of solenoid valves during one work period. Cooling stage t1 p p
SV1 SV2 SV3 SV4 SV5 SV6
p p
Pressuring stage Pressurization t21
Feeding back t 22
Chilling t23
p
p p
p
p
p
Note, ‘‘ ” and ‘‘”indicate ‘‘open” and ‘‘closed”, respectively; t indicates time.
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With the help of gravity, the pressurized liquid refrigerant is fed back into the vapor generator. To further facilitate the feeding back sub-process, HPVHT continues to flow into the evacuation chamber to balance the pressure between the vapor generator and the evacuation chamber. When no liquid refrigerant remains in the evacuation chamber, the chilling sub-process is initiated by inversion of solenoid valves 3, 4, 5 and 6. Chilling water flows within the chilling jacket (around the external surface of the evacuation chamber, as shown in Fig. 1) and chills the evacuation chamber. When the temperature in the evacuation chamber declines to a degree at which the liquid refrigerant can be received from the condenser, the work period is complete. The ECSTPE mechanism reveals that the ECSTPE has inherent problems of thermal energy and chilling water waste. The evacuation chamber is full of HPVHT after the feeding back sub-process. However, the HPVHT is directly chilled during the chilling subprocess. As a result, the thermal energy in the HPVHT and the associated chilling water used to chill the HPVHT are wasted. 2.2. Effects of initial ratio on ECSTPE performance
3. Identification of optimal initial ratio and optimal TLCS 3.1. Identification of optimal initial ratio The optimal initial ratio is identified by mathematical analysis of the pressuring stage. The initial ratio (c) is defined as the volume ratio of vapor refrigerant ðVolev ig Þ to liquid refrigerant ðVolev iL Þ in the evacuation chamber at the beginning of the pressurization sub-process, as shown in Eq. (1).
c¼
The initial ratio is an innovative concept that is defined as the ratio of the volume of vapor refrigerant to the volume of liquid refrigerant in the evacuation chamber just before the pressurization sub-process begins. Optimization of the initial ratio could mitigate the aforementioned thermal energy and chilling water waste problems which is explained as follows. An excessively large initial ratio would lead to rather poor ECSTPE performance. A larger initial ratio indicates the presence of less liquid refrigerant in the evacuation chamber. Less liquid refrigerant in the evacuation chamber indicates that less primary fluid has been provided according to the mass conservation law, which leads to less cooling production. However, the amount of HPVHT directly chilled is constant (i.e., one evacuation chamber during one work period), which means that the wasted thermal energy and chilling water are constant. As a result, to provide per unit mass cooling production, the wasted thermal energy and chilling water would increase when the initial ratio increases. Thus, a smaller initial ratio is more preferred to mitigate the thermal energy and chilling water waste problems. However, the initial ratio cannot be excessively small. If the initial ratio is too small, there will be too much liquid refrigerant in the evacuation chamber at the beginning of the pressurization sub-process. The liquid refrigerant expands during the pressurization sub-process because its density decreases as its temperature
1200
Liquid refrigerant density (kg/m3)
rises. The liquid density variations of R134a, R141b, and R365mfc with temperature are shown in Fig. 2. As a result, the liquid refrigerant expands and spills over the evacuation chamber, which causes the ECSTPE to work unsteadily and even break down. Therefore, an optimal value of the initial ratio must exist at which the best ECSTPE performance can be obtained. The optimal initial ratio is achieved when the liquid refrigerant just occupies the entire evacuation chamber at the end of the pressurization sub-process and no liquid refrigerant spills over.
Volev ig Volev il
During the pressurization sub-process, the refrigerant in the evacuation chamber acquires energy, which is governed by the energy conservation law, as shown in Eq. (2).
Mg2 hgg þ Mev iL hev iL þ M ev ig hev ig ¼ M ev iiL hev iiL þ M ev iig hev iig
Mev i þ Mg2 ¼ M ev ii
R134a R141b R365mfc 900
During the feeding back sub-process, HPVHT continues to flow into the evacuation chamber to facilitate the feeding back subprocess by balancing the pressure between the vapor generator and the evacuation chamber. This portion of the HPVHT occupies the volume in the evacuation chamber left by the liquid refrigerant that is fed back into the vapor generator. When the initial ratio reaches its optimal value, the volume of the liquid refrigerant fed back into the vapor generator equals the volume of the entire evacuation chamber. Thus, the volume of this portion of the HPVHT ðVolg3 Þ equals the volume of the evacuation chamber ðVolev Þ, as shown in Eq. (4).
Mev iiL ¼ Mg1 þ M g2 þ Mg3
82
84
86
88
Temperature ( ) Fig. 2. Liquid refrigerant density variations with temperatures.
ð3Þ
ð4Þ
The mass ðM ev iiL Þ of the liquid refrigerant fed back into the vapor generator is supposed to compensate for the refrigerant loss in the vapor generator due to the generation of HPVHT. The HPVHT is in three parts: the first for the ejector as primary fluid ðM g1 Þ, the second for the evacuation chamber to pressurize the liquid refrigerant ðM g2 Þ, and the third for the evacuation chamber to facilitate the feeding back sub-process ðM g3 Þ, as shown in Eq. (5).
1100
800
ð2Þ
During the pressurization sub-process, the total mass of the refrigerant in the evacuation chamber increases from M ev i to Mev ii . M ev i and M ev ii are the total mass of the refrigerant in the evacuation chamber at the beginning and the end of the pressurization sub-process, respectively. According to the mass conservation law, the mass ðM g2 Þ of HPVHT used for the pressurization sub-process complies with Eq. (3).
Volg3 ¼ Volev
1000
ð1Þ
90
ð5Þ
From the perspective of the entire work period, the total mass ðM ev i Þ of the refrigerant in the evacuation chamber at the beginning of the pressurization sub-process is determined by the mass of the liquid refrigerant from the condenser during the cooling stage and the mass ðM ev iii Þ of the remaining refrigerant after the chilling sub-process of the last work period, as shown in Eq. (6).
Y. He et al. / Energy Conversion and Management 113 (2016) 281–289
The mass of the liquid refrigerant in the evacuation chamber from the condenser equals the mass ðM g1 Þ of the HPVHT used as primary fluid according to the mass conservation law. Thus, the mass of the liquid refrigerant in the evacuation chamber from the condenser is determined by the mass flow rate of the primary fluid ðmwn Þ and the TLCS ðt 1 Þ, as shown in Eq. (7).
M ev i ¼ M g1 þ Mev iii M g1 ¼ mwn t 1
ð6Þ ð7Þ
The optimal initial ratio (copt ) is obtained by merging Eqs. (1)– (6), as shown in Eq. (8). The optimal initial ratio is determined by the generation temperature, the condensing temperature, and the type of refrigerant. In other words, regardless of the design details of ECSTPE, the optimal initial ratio remains constant as long as the generation temperature, the condensing temperature, and the type of refrigerant are invariable. Thus, the optimal initial ratio can be easily calculated in practice.
ðhgg hev iiL Þ
v ev iiL
¼
copt ðhgg hev ig Þ hgg hev iL þ : ð1 þ copt Þ v ev ig ð1 þ copt Þ v ev iL
ð8Þ
3.2. Identification of optimal TLCS The initial ratio can be used as a signal to end the cooling stage and trigger the pressuring stage. A smaller initial ratio means a larger TLCS. Thus, the optimal TLCS can be obtained on the basis of the optimal initial ratio. By accurately controlling the TLCS according to its optimal value, the thermal energy and chilling water waste problems can be mitigated. The optimal TLCS ðt1;opt Þ can be calculated by merging Eqs. (1)– (7), as shown in Eq. (9). The optimal TLCS is determined by the optimal initial ratio, the entrainment ratio, the cooling power, the volume of the evacuation chamber, the generation temperature, the condensing temperature, the evaporation temperature, and the specific volume of the refrigerant. The volume of the evacuation chamber, the generation temperature, the condensing temperature, the evaporation temperature, and the specific volume of the refrigerant are either predefined or easily measured. The entrainment ratio and cooling power can be obtained by measurement or numerical simulation. Thus, the optimal TLCS ðt1;opt Þ can be easily obtained on the basis of the optimal initial ratio ðcopt Þ in practice.
copt
ð1 þ copt Þ v ev ig ¼
þ
1 ð1 þ copt Þ v ev iL
q t1;opt 1 : þ Volev w ðheg heL Þ v gg
ð9Þ
4. Validation case studies In this section, case studies were conducted to demonstrate the effectiveness of the optimal TLCS control method. First, the simulation model was validated. Second, the developed optimal TLCS control method was implemented on the ECSTPE with R134a. Finally, the optimal TLCS control method was extended to ECSTPEs with other common refrigerants (e.g., R141b and R365mfc). 4.1. Simulation model and validation 4.1.1. Description of simulation model The simulation model consisted of two parts: the model of the ejector cooling subsystem and that of the multi-function generator subsystem. The model of the multi-function generator subsystem is illustrated in Section 3.1. The model of the ejector cooling sub-
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system was updated from that of Cizungu et al. [38]. In 2001, Cizungu et al. proposed a succinct method with which to model ejector cooling systems. In 2011, Khalil et al. [39] used this method to study the performance of an ejector cooling system with R134a. This method only included the conservation laws of mass, energy and momentum, and was suitable for ejectors under both singlephase and two-phase work situations. Meanwhile, it had no limitations regarding the type of refrigerant. Due to these merits, this method was adopted to model the ejector cooling subsystem with slight modifications, as shown in Fig. 3. Instead of empirical identification of the entrainment ratio, a dichotomy algorithm was used to quickly achieve an accurate result. Khalil et al. empirically assigned the value of the entrainment ratio, which may cause unnecessary errors and a heavy computation burden. The entire model of the ECSTPE was based on only the conservation laws of mass, energy and momentum. Meanwhile, it had no limitations on work situations in the ejector and was suitable for any type of refrigerant. Some assumptions were made in this model: (1) The ejector was a constant-pressure type, as shown in Fig. 4 [39]. (2) At the inlet and outlet of the ejector, the kinetics of the refrigerant, which were rather small compared with the enthalpy of the refrigerant, were negligible. (3) At the outlet section of the primary nozzle ‘‘pno”, the secondary flow reached sound speed and had the same pressure as the primary flow [40]. (4) The mixing process took place in the suction chamber between the outlet section of the primary nozzle ‘‘pno” and the inlet section of the constant-area chamber ‘‘cci”. (5) The ejector worked at a critical mode in which the entrainment was constant and the primary and secondary flows were both chocked [38]. When the chock took place, the Mach number suddenly dropped and the pressure suddenly increased [41]. (6) A normal shock occurred at the outlet section of the constant-area chamber ‘‘cco” [42]. (7) The thermodynamic process within the ejector was steady and adiabatic. 4.1.2. Validation of simulation model Model validation was carried out in two steps. First, the entrainment ratio variations with generation temperature of the ECSTPE model were compared with those of Khalil et al. [39], which were taken from their numerical model. Their numerical model had been validated by experimental data [39]. Second, the COPs of the ECSTPE model were compared with the experimental COPs of Huang et al. [17] and Wang et al. [25]. The COP refers to the ratio of the cooling obtained from the evaporator to the thermal energy inputted into the vapor generator during one work period. With the good accordance of the entrainment ratio comparisons and the reasonable COP comparison results, the accuracy of the ECSTPE model was proven to be credible. Fig. 5 shows the entrainment ratio variations with generation temperatures when the vapor generator was over heated by 10 °C and the condensing temperature was 30 °C. The simulated entrainment ratios of the ECSTPE model were in good agreement with those of Khalil et al. [39]. When the evaporation temperature was set at 5 °C, the average deviation of the simulation entrainment ratios from those of Khalil et al. was 4.7%. When the evaporation temperature rose to 10 °C, the average deviation was 1.8%. Table 2 shows the COP comparison results of the model validation. The dimensions of the ejectors in the simulation and the experiment had some discrepancies due to the assumptions in the ECSTPE model, but such assumptions have been proven to be
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Fig. 3. Flow chart of the simulation program.
Suction chamber
Primary flow (from generator )
Constant- area chamber
Diffuser
Mixed refrigerant (to condenser) pnt
pno
cci
cco
Secondary flow (from evaporator ) Fig. 4. Schematic of ejector of constant pressure type.
acceptable [38,39]. Two sets of comparisons were conducted, one for ECSTPEs with R141b and one for ECSTPEs with 365mfc. In both comparisons, the simulation COPs were higher than the reference COPs (i.e., the experimental COPs). The main reasons were as follows. In the ECSTPEs of Huang et al. and Wang et al., the vapor generator and evacuation chamber were connected by ducts without any block. The remaining HPVHT in the vapor generator was also chilled during the chilling sub-process, which resulted in extra thermal energy waste. To avoid this problem, the vapor generator and evacuation chamber in the ECSTPE of this study were separated by solenoid valves 3 and 4, as shown in Fig. 1. Thus, the simulation COPs were higher than the reference COPs.
4.2. Study on ECSTPE with R134a 4.2.1. Optimal initial ratio and associated optimal TLCS In this case, the refrigerant was R134a; the condensing temperature and evaporation temperature were set at 35 °C and 10 °C, respectively; the volume of the evacuation chamber was set at 2 m3; and the cooling capacity of the ECSTPE was set at 200 kW. The optimal initial ratio was calculated according to Eq. (8). The optimal initial ratio consecutively increased when the generation temperature increased, as shown in Fig. 6. This phenomenon can be explained as follows. When the generation temperature increased, the temperature increase of R134a during the
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2
0.35 Simulation 10 Simulation 5 Reference 10
0.25
1.8
Optimal initial ratio (-)
Entrainment ratio (-)
0.30
Reference 5
0.20 0.15 0.10
1.6
1.4
0.05 0.00
66
70
74
78
82
1.2
Generator temperature ( )
pressurization sub-process became greater. Consequently, the expansion of the liquid R134a in the evacuation chamber became more severe. Thus, more room was required in the evacuation chamber for the expansion of the liquid R134a, which resulted in an increase in the optimal initial ratio. The associated optimal TLCS was calculated on the basis of the optimal initial ratio according to Eq. (9). Fig. 7 shows the optimal TLCS variations with the optimal initial ratios. The optimal TLCS decreased when the optimal initial ratio increased, which can be explained as follows. When the optimal initial ratio increased, there was less liquid refrigerant in the evacuation chamber at the beginning of the pressurization sub-process. Thus, less time was required to accumulate liquid refrigerant from the condenser, which resulted in a decrease in the optimal TLCS.
84
86
88
90
Generation temperature (oC) Fig. 6. Optimal initial ratio variations with generation temperatures.
90 85
Optimal TLCS (s)
Fig. 5. Entrainment ratio comparison results of the model validation.
82
80 75 70 65 60 1.2
1.4
1.6
1.8
2
Optimal initial ratio (-) 4.2.2. Effectiveness of optimal TLCS control method The effectiveness of the optimal TLCS control method was demonstrated in terms of the performance deterioration that resulted from the deviation of the TLCS from its optimal value. The TLCS deviation was determined by the initial ratio deviation. Fig. 8 shows the variations of the TLCS deviation with the initial ratio deviations when the generation temperature was set at 85 °C. When the initial ratio deviation increased, the TLCS deviation increased. The reasons for this were similar to those given in Section 4.2.1. Fig. 9 shows COP variations with TLCS deviations. The COP consecutively decreased as the TLCS deviation increased. It was observed that the COP decreased by 5.6% when the TLCS deviated by 10 s from its optimal value. Fig. 10 shows the chilling load variations with TLCS deviations. The chilling load refers to the chilling load needed to remove the discarded thermal energy in the HPVHT when per unit mass of primary fluid was provided for
Fig. 7. Optimal TLCS variations with optimal initial ratios.
the ejector. The chilling load increased when the TLCS deviation increased. It was observed that the chilling load increased by 23.7% when the TLCS deviated by 10 s. Therefore, accurate control of the TLCS according to the optimal TLCS could effectively improve ECSTPE performance.
4.3. Study on ECSTPEs with other refrigerants Further case studies were conducted on ECSTPEs with other potential refrigerants (e.g., R141b and R365mfc). Fig. 11 shows the optimal initial ratio variations of ECSTPEs with R141b, R365mfc, and R134a with generation temperatures when the other
Table 2 COP comparison results of the model validation. Comparison 1
Comparison 2
Ref. [17]
Simulation
Ref. [25]
Simulation
Ejector dimension Primary nozzle throat diameter/mm Primary nozzle exit diameter/mm Constant area diameter/mm Area ratio
2.64 4.50 7.34 7.73
2.98 6.55 7.93 7.08
2.64 4.50 7.34 7.73
2.85 5.73 7.26 6.48
COP Absolute data Percentage discrepancy (%)
0.185 (measuring error 4.82%) 8.11
0.200
0.215 (measuring error 4.82%) 19.07
0.256
Note, the boundary conditions of comparison 1 were as follows: R141b, T b ¼ 90 C, T c ¼ 32:4 C, T e ¼ 8:2 C. The boundary conditions of comparison 2 were as follows: R365mfc, T b ¼ 90 C, T c ¼ 39:6 C, T e ¼ 20 C.
Y. He et al. / Energy Conversion and Management 113 (2016) 281–289
50
2.1
40
1.8
Optimal initial ratio (-)
TLCS deviation from its optimal value(s)
288
30
20
10
1.5
R134a R141b
1.2
R365mfc 0.9
0.6
0 0
20
40
60
80
100
Initial ratio deviation from its optimal value (%)
0.3
Fig. 8. TLCS deviation variations with initial ratio deviations.
82
84
86
88
90
Generation temperature (oC)
20
0.095
15
0.090 COP decrease percent COP
10
0.085
5
0.080
0 0
5
10
15
20
25
30
35
Table 3 ECSTPE performance deterioration with each 10-second deviation of TLCS.
0.075 45
40
TLCS deviation (s) Fig. 9. COP variations with TLCS deviations.
Chilling load increase percent
simulation conditions were similar to those given in Section 4.2. The optimal initial ratios of all three systems increased as the generation temperature increased for reasons similar to those given in Section 4.2.1. Furthermore, the increased speeds of the ECSTPEs with R141b and R365mfc were lower than that of the ECSTPE with R134a. This phenomenon can be explained as follows. The increased speed of the optimal initial ratio was determined by density variations in the liquid refrigerant with temperatures. The
COP (%/10 s) Q (%/10 s)
R134a
R141b
R365mfc
5.6 23.7
0.06 3.5
0.14 5.8
more rapid density variations of liquid refrigerant indicated larger volume expansion during the pressurization sub-process, which resulted in a greater increase in the increased speed of the optimal initial ratio. The density variation speeds of liquid R141b and R365mfc were lower than that of liquid R134a, as shown in Fig. 2. When the TLCS deviated from its optimal value due to the initial ratio deviation, the COPs of the ECSTPEs with R141b and R365mfc decreased and their chilling loads increased. The reasons for this finding were similar to those given in Section 4.2.2. Table 3 shows the ECSTPE performance deterioration results. When the TLCS deviated 10 s from its optimal value, the COPs of the ECSTPEs with R141b and R365mfc decreased by 0.06% and 0.14%, respectively; and their chilling loads increased by 3.5% and 5.8%, respectively. The performance deterioration of the ECSTPEs with R141b and R365mfc was lower than that of the ECSTPE with R134a because the density variations of liquid R141b and R365mfc during the pressurization sub-process were smaller. In other words, the performance of the ECSTPE with R134a was the more sensitive to
120.0
260.0
100.0
230.0
Chilling load increase percent 200.0
80.0
Chilling load 60.0
170.0
40.0
140.0
20.0
110.0
80.0
0.0 0
5
10
15
20
25
30
35
40
TLCS deviation (s) Fig. 10. Chilling load variations with TLCS deviations.
45
Chilling load for unit mass primary fluid (kJ/kg)
0.100
COP (-)
COP decrease percent
Fig. 11. Optimal initial ratio variations with generation temperatures.
25
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the TLCS deviation. Thus, the optimal TLCS control method was the more effective on the ECSTPE with R134a. For the ECSTPEs with R141b and R365mfc, the small TLCS deviation inflicted little damage on the ECSTPE performance, but it was still necessary and beneficial to accurately control the TLCS for ECSTPEs with R141b and R365mfc for several reasons. First, a large TLCS deviation would cause severe performance deterioration. For example, a 100second TLCS deviation led to increases of 35% and 58% in the chilling loads of the ECSTPEs with R141b and 365mfc, respectively. Second, accurate control of the TLCS based on the optimal initial ratio was convenient because the optimal initial ratio could be easily calculated. The developed optimal TLCS control method was effective on ECSTPEs whose liquid refrigerant density varied with temperature. 5. Conclusions To alleviate the severe thermal energy and chilling water waste problems of ECSTPEs, an innovative concept for the optimal initial ratio has been proposed and an optimal TLCS control method has been developed. The optimal TLCS control method is base on the optimal initial ratio. Case studies have demonstrated the effectiveness of the developed optimal TLCS control method on ECSTPEs with different refrigerants. For the ECSTPE with R134a, with each 10-second TLCS deviation from its optimal value, the COP of the ECSTPE decreased by 5.6% and the chilling load increased by 23.7%. For ECSTPEs with R141b and R365mfc, each 10-second deviation led to relatively little performance deterioration; however, excessive deviation (e.g., 100 s) could lead to severe performance deterioration (e.g., a chilling load increase of 35% for R134b and 58% for R365mfc). The developed optimal TLCS control method can improve the performance of ECSTPEs with other refrigerants as long as the liquid refrigerant density varies with the temperature. Furthermore, the optimal TLCS control method can be conveniently used in practice because the optimal initial ratio is easy to determine from only the generation temperature, the condensing temperature, and the type of refrigerant. Improvement of ECSTPE performance helps to mitigate increasing energy and environmental problems. Acknowledgements This work was supported by the Natural Science Foundation of China (contract No. 51206140) and Science and Technology Department of Zhejiang Province (contract No. 2012C21072). The authors would like to express their gratitude to Dr. Yong Cheng from Chongqing University for his valuable suggestions. References [1] Kolokotsa D, Rovas D, Kosmatopoulos E, Kalaitzakis K. A roadmap towards intelligent net zero- and positive-energy buildings. Sol Energy 2011;85:3067–84. [2] Chua KJ, Chou SK, Yang VM, Yan J. Achieving better energy-efficient air conditioning – a review of technologies and strategies. Appl Energy 2013;104:87–104; Besagni G, Mereu R, Inzoli F. Ejector refrigeration: a comprehensive review. Renew Sustain Energy Rev 2016;53:373–407. [3] Besagni G, Mereu R, Inzoli F. Ejector refrigeration: a comprehensive review. Renew Sustain Energy Rev 2016;53:373–407. [4] Chen J, Jarall S, Havtun H, Palm B. A review on versatile ejector applications in refrigeration systems. Renew Sustain Energy Rev 2015;49:67–90. [5] Abdulateef JM, Sopian K, Alghoul KA, Sulaiman MY. Review on solar-driven ejector refrigeration technologies. Renew Sustain Energy Rev 2009;13:1338–49. [6] Gil B, Kasperski J. Efficiency analysis of alternative refrigerants for ejector cooling cycles. Energy Convers Manage 2015;94:12–8. [7] Chunnanond K, Aphornratana S. Ejectors: applications in refrigeration technology. Renew Sustain Energy Rev 2004;8(2):129–55.
289
[8] Huang P, Huang G, Wang Y. HVAC system design under peak load prediction uncertainty using multiple-criterion decision making technique. Energy Build 2015;91:26–36. [9] ASHRAE Handbook. HVAC systems and equipment. Atlanta, GA: American Society of Heating, Refrigerating, and Air Conditioning Engineers; 1996. [10] Grondzik WT, editor. Air-conditioning system design manual. Atlanta, USA: ASHRAE Inc.; 2007. [11] Chandra VV, Ahmed MR. Experimental and computational studies on a steam jet refrigeration system with constant area and variable area ejectors. Energy Convers Manage 2014;79:377–86. [12] Tashtoush B, Alshare A, Al-Rifai S. Performance study of ejector cooling cycle at critical mode under superheated primary flow. Energy Convers Manage 2015;94:300–10. [13] Huang BJ, Jiang CB, Hu FL. Ejector performance characteristics and design analysis of jet refrigeration system. J Eng Gas Turbines Power 1985;107:792–802. [14] Abed AM, Alghoul MA, Sirawn R, Al-Shamani AN, Sopian K. Performance enhancement of ejector–absorption cooling cycle by re-arrangement of solution streamlines and adding RHE. Appl Therm Eng 2015;77:65–75. [15] Khaliq A. Performance analysis of a waste-heat-powered thermodynamic cycle for multi-effect refrigeration. Int J Energy Res 2015;39:529–42. [16] Shen S, Qu X, Zhang B, Riffat S, Gillott M. Study of a gas–liquid ejector and its application to a solar-powered bi-ejector refrigeration system. Appl Therm Eng 2005;25:2891–902. [17] Huang BJ, Hu SS, Lee SH. Development of an ejector cooling system with thermal pumping effect. Int J Refrig 2006;29:476–84. [18] Chen X, Omer S, Worall M, Riffat S. Recent developments in ejector refrigeration technologies. Renew Sustain Energy Rev 2013;19:629–51. [19] Nguyen VM, Riffat SB, Doherty PS. Development of a solar-powered passive ejector cooling system. Appl Therm Eng 2001;21:157–68. [20] Dai Z, He Y, Huang Y, Tang L, Chen G. Ejector performance of a pump-less ejector refrigeration system driven by solar thermal energy. USA: International Refrigeration and Air Conditioning Conference Purdue; 2012. [21] Chuech SG, Chen C, Lu J, Yan M. Design and implementation of ejector driven micropump. Energy Convers Manage 2007;48:2657–62. [22] Ziapour BM, Abbasy A. First and second laws analysis of the heat pipe/ejector refrigeration cycle. Energy 2010;35:3307–14. [23] Wang F, Shen S. A novel solar bi-ejector refrigeration system and the performance of the added injector with different structures and operation parameters. Sol Energy 2009;83:2186–94. [24] Riffat SB, Holt A. A novel heat pipe/ejector cooler. Appl Therm Eng 1999;18 (3):93–101. [25] Wang JH, Wu JH, Hu SS, Huang BJ. Performance of ejector cooling system with thermal pumping effect using R141b and R365mfc. Appl Therm Eng 2009;29:1904–12. [26] Kasperski J. Two kinds of gravitational ejector refrigerator stimulation. Appl Therm Eng 2009;29:3380–5. [27] Kasperski J. Rotational type of a gravitational ejector refrigerator – a system balance of the refrigerant analysis. Int J Refrig 2010;33:3–11. [28] Huang BJ, Wu JH, Hsu HY, Wang JH. Development of hybrid solar-assisted cooling/heating system. Energy Convers Manage 2010;51(8):1643–50. [29] Wong YW, Sumathy K. Solar thermal water pumping systems: a review. Renew Sustain Energy Rev 1999;3:185–217. [30] Wong YW, Sumathy K. Thermodynamic analysis and optimization of a solar thermal water pump. Appl Therm Eng 2001;21:613–27. [31] Dobriansky Y. Concepts of self-acting circulation loops for downward heat transfer (reverse thermosiphons). Energy Convers Manage 2011;52 (1):414–25. [32] Bataineh KM. Optimization analysis of solar thermal water pump. Renew Sustain Energy Rev 2016;55:603–13. [33] Srisastra P, Aphornratana S. A circulating system for a steam jet refrigeration system. Appl Therm Eng 2005;25(14–15):2247–57. [34] Karthikeyan G, Mani A, Murthy SS. Analysis of an absorption refrigeration system with transfer tank. Renewable Energy 1994;4(1):129–32. [35] Srisastra P, Aphornratana S, Sriveerakul T. Development of a circulating system for a jet refrigeration cycle. Int J Refrig 2008;31(5):921–9. [36] Pridasawas W, Lundqvist P. An exergy analysis of a solar-driven ejector refrigeration system. Sol Energy 2004;76:369–79. [37] Xu ZL, Tao LR, Xiao X. Ejector refrigeration system without pump for air conditioning. Heat, Ventilating Air Cond 2008;38(1). [38] Cizungu K, Mani A, Groll M. Performance comparison of vapour jet refrigeration system with environment friendly working fluids. Appl Therm Eng 2001;21:585–98. [39] Khalil A, Fatouh M, Elgendy E. Ejector design and theoretical study of R134a ejector refrigeration cycle. Int J Refrig 2011;34:1684–98. [40] Ouzzane M, Aidoun Z. Model development and numerical procedure for detailed ejector analysis and design. Appl Therm Eng 2003;23:2337–51. [41] Riffat SB, Omer SA. CFD modelling and experimental investigation of an ejector refrigeration system using methanol as the working fluid. Int J Energy Res 2001;25(2):115–28. [42] Selvaraju A, Mani A. Analysis of an ejector with environment friendly refrigerants. Appl Therm Eng 2004;24:827–38.
Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
Initial ratio optimization for the ejector cooling system with thermal pumping effect (ECSTPE) Yijian He a, Yongjun Sun b, Sheng Zhang a,b,⇑, Yuanli Lyu b, Guangming Chen a a b
Institute of Refrigeration and Cryogenics, Zhejiang University, Hangzhou, China Division of Building Science and Technology, City University of Hong Kong, Kowloon, Hong Kong
a r t i c l e
i n f o
Article history: Received 24 August 2015 Accepted 28 January 2016
Keywords: Optimal initial ratio Optimal time length of cooling stage Performance optimization Ejector cooling Thermal pumping effect
a b s t r a c t An ejector cooling system with thermal pumping effect (ECSTPE) could operate without consumption of electric power, but it discards a great amount of thermal energy, which generally results in a lower COP value and a greater chilling load. An innovative concept for the optimal initial ratio is therefore proposed to develop the optimal time length of cooling stage (TLCS) control method. The optimal TLCS control method effectively improves the ECSTPE performance. First, in this context, it was theoretically proven that the optimal initial ratio could be used to reduce the energy loss and the chilling load. Second, it was formulated how to achieve the optimal initial ratio; and the optimal TLCS control method was determined by identifying the relationship between the TLCS and the initial ratio. Third, case studies were conducted to demonstrate the effectiveness of the developed optimal TLCS control method on ECSTPEs with different refrigerants. The results showed that for ECSTPE with R134a, a 10-second deviation from the optimal TLCS led to a decrease of 5.6% in the COP value and an increase of 23.7% in the chilling load. For ECSTPEs with R141b and R365mfc, a 10-second deviation led to relatively slight performance deterioration; however, an excessive deviation (e.g., 100 s) would lead to severe performance deterioration (e.g., increases of 35% and 58% in the chilling loads for ECSTPEs with R134b and R365mfc, respectively). The developed optimal TLCS control method could certainly improve the performance of ECSTPEs with other refrigerants. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Because the building sector accounts for approximately 40% of primary energy consumption, reducing the energy consumption of buildings is widely regarded as an effective means by which to mitigate increasing energy and environmental problems [1]. Refrigeration and air conditioning in buildings constitute a large portion of energy consumption, and this portion continues to increase [2]. Thus, improvement in the energy efficiency of refrigeration and air conditioning systems is a crucial step for the reduction of global energy demand and emissions. Ejector cooling systems present promising alternatives to conventional mechanical cooling systems [3]. The ejector in an ejector cooling system is responsible for pressurizing the refrigerant from the evaporator, as the mechanical compressor does in a conventional mechanical cooling system [4]. Ejector cooling systems are preferable for two reasons. First, ejector cooling systems can be ⇑ Corresponding author at: Division of Building Science and Technology, City University of Hong Kong, Kowloon, Hong Kong. Tel.: +852 34425290; fax: +852 34429716. E-mail address: [email protected] (S. Zhang). http://dx.doi.org/10.1016/j.enconman.2016.01.067 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.
powered by low-grade thermal energy such as solar energy, which contributes significantly to energy conservation and reduction of emissions [5]. Second, ejector cooling systems are superior to other solar-powered cooling systems (e.g., solar-powered adsorption cooling systems and solar-powered absorption cooling systems) in several aspects, including their low cost and their simple system design, installation, and operation [6]. Unfortunately, ejector cooling systems have not been widely accepted in the refrigeration and air conditioning market because their COPs (e.g., 0.18–0.6 [7]) are generally lower than those of conventional mechanical cooling systems (e.g., approximately 3–6 [8–10]) [6,11]. However, conventional mechanical cooling systems consume a large amount of electricity, while ejector cooling systems can use low-grade thermal energy and show other obvious superiorities. Thus, improvement of energy efficiency of ejector cooling systems could greatly promote their application.
1.1. Ejector cooling system without pump Ejector cooling technologies are generally classified into eight types [3], including single-ejector cooling systems [12,13],
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Nomenclature COP h P q Q t T v Vol w
coefficient of performance (–) enthalpy (kJ/kg) pressure (kPa) cooling power (kJ) chilling load (kJ/kg) time (s) temperature (°C) specific volume ðm3 =kgÞ volume (m3 ) entrainment ratio (–)
Greek symbols c initial ratio (–) Abbreviations ECSTPE ejector cooling system with thermal pumping effect HPVHT high pressure vapor with high temperature
combined ejector-absorption cooling systems [14,15], and ejector cooling systems without a pump [16,17], etc. The ejector cooling system without a pump eliminates the requirement for a mechanical pump to transfer the refrigerant from the condenser to the generator. The main motivations for elimination of the mechanical pump are as follows. In ejector cooling systems, the mechanical pump is the only moving part that requires relatively frequent maintenance and the only part that consumes electricity [18,19]. Thus, the ejector cooling system without a pump has two advantages over other ejector cooling technologies. First, it has the potential to work with greater stability and have a longer lifetime [20], and second, it consumes no electricity [21]. Four main types of ejector cooling systems without a pump have been proposed: the bi-ejector cooling system [16], the heat pipe/ejector cooling system [22], the gravitational ejector cooling system [19], and the ejector cooling system with thermal pumping effect (ECSTPE) [17]. The working principles and characteristics of these ejector cooling systems without a pump are as follows. The bi-ejector cooling system replaces the mechanical pump with a vapor/liquid ejector that uses the high pressure vapor from the generator to carry condensate back to the generator [16,23]. The heat pipe/ejector cooling system integrates the ejector and the heat pipe and exploits the heat pipe’s wick action to transfer condensate back to the generator [22,24]. Although the bi-ejector cooling system and the heat pipe/ejector cooling system seem theoretically promising, their practicality has not been proven experimentally [3]. The practicality of the gravitational ejector cooling system and the ECSTPE have been proven experimentally [19,25]. The gravitational ejector cooling system makes use of the height difference to equalize the pressure between the condenser and the generator and thus assist the refrigerant to successfully circulate; however, the height difference requires a large installation room and long conduction pipes (which causes friction and heat losses) [19,26]. The drawbacks of the gravitational ejector cooling system can be overcome with the use of rotary motion [27]. The roto-gravitational ejector cooling system makes use of the large accelerations of rotary motion to significantly decrease the system size; however, the rotating cylinder consumes electricity, which leads to the loss of one of the above-mentioned attractions of an ejector cooling system without a pump [27]. An ECSTPE uses a thermal pumping effect instead of a mechanical pump [28]. The thermal pumping effect has been widely studied but requires a special design for use in an ejector cooling system
TLCS time length of cooling stage Subscripts c condenser e evaporator ev evacuation chamber g gaseous/generator L liquid opt optimal wn primary fluid 1 cooling stage 2 pressuring stage 21 pressurization sub-process 22 feeding back sub-process 23 chilling sub-process i point at the beginning of the pressurization sub-process ii point at the beginning of the feeding back sub-process iii point at the beginning of the chilling sub-process
[29–32]. In an ECSTPE, the thermal pumping effect uses the high-pressure vapor from the vapor generator to pressurize the condensate in the evacuation chamber by means of thermal balance. Experiments have shown that an ECSTPE could be driven by thermal energy alone without other power input, and it is smaller than a gravitational ejector cooling system [25,33]. Thus, the ECSTPE is the most applicable ejector cooling system without a pump, and this study focuses on improvement of its thermal energy efficiency. 1.2. Low thermal energy efficiency of ECSTPEs Existing ECSTPEs have severe problems with the waste of thermal energy and chilling water. ECSTPEs come in two types: those with a workless boiler feeding system and those with a multifunction generator. Both types have low thermal energy efficiency due to the thermal pumping effect. Srisastra and Aphornratana [33] proposed an ECSTPE that used a workless boiler feeding system that transferred the condensate from the condenser to the boiler with the help of gravity and boiler pressure, which was similar to the ‘‘transfer-tank” used in an absorption cooling system [33,34]. However, the tank in this feeding system was chilled down by the condenser, which led to a great increase in energy consumption (e.g., 10–15%) [35]. Huang et al. [17] proposed an ECSTPE, in which a multi-function generator separated the tank (also called an ‘‘evacuation chamber”) and the condenser, and the evacuation chamber was chilled by the surrounding chilling jacket. The experimental results showed a decrease of 15% (from 0.218 to 0.185) in the COP after taking into account the extra thermal energy required by the thermal pumping effect at a generation temperature of 90 °C, a condensing temperature of 32.4 °C, and an evaporation temperature of 8.2 °C [17]. That is, approximately 15% of the thermal energy was discarded by the thermal pumping effect, because the thermal energy used to pressurize the condensed refrigerant in the evacuation chamber was negligible (e.g., 0.18% [36]). This considerable amount of thermal energy was discarded because the chilling jacket chilled down not only the evacuation chamber but also the vapor generator [17,37]. Accordingly, the high-pressure vapor with high temperature (HPVHT) in the vapor generator and the evacuation chamber was chilled directly. As a result, the thermal energy within the HPVHT was discarded, and the chilling water was largely required to remove the discarded thermal energy. The thermal energy discarded by chilling the vapor
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Out of the dotted rectangle: ejector cooling subsystem Ejector Solenoid valve 1
Condenser
Evaporator
Throttle valve
Solenoid valve 2
Solenoid valve 5
Solenoid valve 3
Chilling jacket Evacuation chamber Solenoid valve 4 Vapor generator
Heat
Solenoid valve 6 Within the dotted rectangle: multi-functional generator subsystem
Fig. 1. Schematic of the ejector cooling system with thermal pumping effect.
initial ratio is formulated and the optimal TLCS control strategy is determined by identifying the relationship between the TLCS and the initial ratio. In Section 4, case studies are conducted to demonstrate the effectiveness of the developed optimal TLCS control method for ECSTPEs with different refrigerants. 2. Effects of initial ratio on ECSTPE performance In this section, the positive effects of the optimal initial ratio on ECSTPE performance are proven. First, the ECSTPE work mechanism is described. Based on the description of the work mechanism, the thermal energy and chilling water waste problems of the ECSTPE are exposed, and the optimal initial ratio is proven to be effective in mitigating those problems. To clearly illustrate the positive effects of the optimal initial ratio, the ECSTPE analyzed here is only equipped with one set of the multi-function generator, as shown in Fig. 1. An ECSTPE with one set of the multi-function generator produces intermittent cooling. However, the conclusions can be extrapolated to ECSTPEs with multiple sets of the multi-function generators. ECSTPEs with multiple sets of the multi-function generators in parallel can produce cooling power consecutively. 2.1. Description of ECSTPE work mechanism
generator can be avoided by separating the vapor generator and the evacuation chamber [35], as shown in Fig. 1. The ECSTPE in the following context refers to the ECSTPE shown in Fig. 1. However, the thermal energy and chilling water waste problems caused by chilling the evacuation chamber require further mitigation. To reduce the discarded thermal energy and the associated chilling load, the time length of cooling stage (TLCS) must be accurately controlled. The cooling stage refers to the stage during which the ECSTPE produces cooling. The main reasons are as follows. The TLCS determines the mass of the condensed refrigerant in the evacuation chamber, which equals the mass of the HPVHT used as the primary fluid in the ejector due to the mass conservation law. More primary fluid indicates more cooling production. More cooling production indicates larger thermal energy efficiency and less demand for chilling water, because the discarded thermal energy is constant for every work period (i.e., HPVHT in one evacuation chamber). In other words, the TLCS determines the cooling production, and the TLCS should be controlled to produce the most cooling in one work period. However, existing ECSTPE studies place little emphasis on optimization of TLCS control; the TLCS was simply determined to target high thermal energy efficiency without consideration of the thermal energy and chilling water waste problems caused by the thermal pumping effect [17,25,37]. In [17,37], the cooling stage was terminated when the generator pressure dropped to a level that could not effectively drive the ejector. In [25], the cooling stage was terminated when the evaporator pressure exceeded a set point (e.g., 0.004 MPa) at which cooling production would be unstable. Without optimization of TLCS control, experimental results showed that a large portion of the thermal energy was discarded (e.g., 26.6%) [25]. Moreover, Srisastra and Aphornratana [33] controlled the TLCS according to a desired amount of condensed refrigerant in the evacuation chamber; however, no explanations on the desired amount of condensed refrigerant were given, and low thermal energy efficiency was observed [35]. Therefore, an innovative concept for the optimal initial ratio is proposed to develop an optimal TLCS control method. The initial ratio is defined as the volume ratio of vapor refrigerant to liquid refrigerant in the evacuation chamber just before pressurization. The structure of the paper is arranged as follows. In Section 2, it is shown that the optimal initial ratio can mitigate the thermal energy and chilling water waste problems. Section 3, the optimal
As shown in Fig. 1, an ECSTPE consists of two subsystems: the multi-function generator subsystem within the dotted rectangle and the ejector cooling subsystem outside the dotted rectangle. The multi-function generator incorporates a vapor generator and an evacuation chamber and is designed to provide HPVHT. HPVHT is used for three tasks: for use as a primary fluid, to pressurize the condensed refrigerant in the evacuation chamber, and to balance the pressure between the vapor generator and the evacuation chamber to facilitate circulation of the refrigerant. One work period of the ECSTPE is partitioned into a cooling stage and a pressuring stage by controlling solenoid valves, as shown in Table 1. Before start-up, all solenoid valves are closed. To start the cooling stage, solenoid valves 1, 2, and 6 are switched on. The HPVHT generated in the vapor generator then flows into the ejector to extract the refrigerant from the evaporator, and the mixed refrigerant is obtained. The mixed refrigerant then flows into the condenser to be condensed. After leaving the condenser, the liquid refrigerant is separated into two portions, one that produces cooling in the evaporator and one that is fed back into the vapor generator after first being stored in the evacuation chamber. When the liquid refrigerant in the evacuation chamber reaches a certain level, the cooling stage ends and the pressuring stage begins by inversion of solenoid valves 1, 2, and 3. The pressuring stage consists of three successive sub-processes: pressurization, feeding back, and chilling. During the pressurization sub-process, HPVHT flows into the evacuation chamber to pressurize the liquid refrigerant until a thermal balance is achieved. The feeding back sub-process is then triggered by switching on solenoid valve 4.
Table 1 Actions of solenoid valves during one work period. Cooling stage t1 p p
SV1 SV2 SV3 SV4 SV5 SV6
p p
Pressuring stage Pressurization t21
Feeding back t 22
Chilling t23
p
p p
p
p
p
Note, ‘‘ ” and ‘‘”indicate ‘‘open” and ‘‘closed”, respectively; t indicates time.
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With the help of gravity, the pressurized liquid refrigerant is fed back into the vapor generator. To further facilitate the feeding back sub-process, HPVHT continues to flow into the evacuation chamber to balance the pressure between the vapor generator and the evacuation chamber. When no liquid refrigerant remains in the evacuation chamber, the chilling sub-process is initiated by inversion of solenoid valves 3, 4, 5 and 6. Chilling water flows within the chilling jacket (around the external surface of the evacuation chamber, as shown in Fig. 1) and chills the evacuation chamber. When the temperature in the evacuation chamber declines to a degree at which the liquid refrigerant can be received from the condenser, the work period is complete. The ECSTPE mechanism reveals that the ECSTPE has inherent problems of thermal energy and chilling water waste. The evacuation chamber is full of HPVHT after the feeding back sub-process. However, the HPVHT is directly chilled during the chilling subprocess. As a result, the thermal energy in the HPVHT and the associated chilling water used to chill the HPVHT are wasted. 2.2. Effects of initial ratio on ECSTPE performance
3. Identification of optimal initial ratio and optimal TLCS 3.1. Identification of optimal initial ratio The optimal initial ratio is identified by mathematical analysis of the pressuring stage. The initial ratio (c) is defined as the volume ratio of vapor refrigerant ðVolev ig Þ to liquid refrigerant ðVolev iL Þ in the evacuation chamber at the beginning of the pressurization sub-process, as shown in Eq. (1).
c¼
The initial ratio is an innovative concept that is defined as the ratio of the volume of vapor refrigerant to the volume of liquid refrigerant in the evacuation chamber just before the pressurization sub-process begins. Optimization of the initial ratio could mitigate the aforementioned thermal energy and chilling water waste problems which is explained as follows. An excessively large initial ratio would lead to rather poor ECSTPE performance. A larger initial ratio indicates the presence of less liquid refrigerant in the evacuation chamber. Less liquid refrigerant in the evacuation chamber indicates that less primary fluid has been provided according to the mass conservation law, which leads to less cooling production. However, the amount of HPVHT directly chilled is constant (i.e., one evacuation chamber during one work period), which means that the wasted thermal energy and chilling water are constant. As a result, to provide per unit mass cooling production, the wasted thermal energy and chilling water would increase when the initial ratio increases. Thus, a smaller initial ratio is more preferred to mitigate the thermal energy and chilling water waste problems. However, the initial ratio cannot be excessively small. If the initial ratio is too small, there will be too much liquid refrigerant in the evacuation chamber at the beginning of the pressurization sub-process. The liquid refrigerant expands during the pressurization sub-process because its density decreases as its temperature
1200
Liquid refrigerant density (kg/m3)
rises. The liquid density variations of R134a, R141b, and R365mfc with temperature are shown in Fig. 2. As a result, the liquid refrigerant expands and spills over the evacuation chamber, which causes the ECSTPE to work unsteadily and even break down. Therefore, an optimal value of the initial ratio must exist at which the best ECSTPE performance can be obtained. The optimal initial ratio is achieved when the liquid refrigerant just occupies the entire evacuation chamber at the end of the pressurization sub-process and no liquid refrigerant spills over.
Volev ig Volev il
During the pressurization sub-process, the refrigerant in the evacuation chamber acquires energy, which is governed by the energy conservation law, as shown in Eq. (2).
Mg2 hgg þ Mev iL hev iL þ M ev ig hev ig ¼ M ev iiL hev iiL þ M ev iig hev iig
Mev i þ Mg2 ¼ M ev ii
R134a R141b R365mfc 900
During the feeding back sub-process, HPVHT continues to flow into the evacuation chamber to facilitate the feeding back subprocess by balancing the pressure between the vapor generator and the evacuation chamber. This portion of the HPVHT occupies the volume in the evacuation chamber left by the liquid refrigerant that is fed back into the vapor generator. When the initial ratio reaches its optimal value, the volume of the liquid refrigerant fed back into the vapor generator equals the volume of the entire evacuation chamber. Thus, the volume of this portion of the HPVHT ðVolg3 Þ equals the volume of the evacuation chamber ðVolev Þ, as shown in Eq. (4).
Mev iiL ¼ Mg1 þ M g2 þ Mg3
82
84
86
88
Temperature ( ) Fig. 2. Liquid refrigerant density variations with temperatures.
ð3Þ
ð4Þ
The mass ðM ev iiL Þ of the liquid refrigerant fed back into the vapor generator is supposed to compensate for the refrigerant loss in the vapor generator due to the generation of HPVHT. The HPVHT is in three parts: the first for the ejector as primary fluid ðM g1 Þ, the second for the evacuation chamber to pressurize the liquid refrigerant ðM g2 Þ, and the third for the evacuation chamber to facilitate the feeding back sub-process ðM g3 Þ, as shown in Eq. (5).
1100
800
ð2Þ
During the pressurization sub-process, the total mass of the refrigerant in the evacuation chamber increases from M ev i to Mev ii . M ev i and M ev ii are the total mass of the refrigerant in the evacuation chamber at the beginning and the end of the pressurization sub-process, respectively. According to the mass conservation law, the mass ðM g2 Þ of HPVHT used for the pressurization sub-process complies with Eq. (3).
Volg3 ¼ Volev
1000
ð1Þ
90
ð5Þ
From the perspective of the entire work period, the total mass ðM ev i Þ of the refrigerant in the evacuation chamber at the beginning of the pressurization sub-process is determined by the mass of the liquid refrigerant from the condenser during the cooling stage and the mass ðM ev iii Þ of the remaining refrigerant after the chilling sub-process of the last work period, as shown in Eq. (6).
Y. He et al. / Energy Conversion and Management 113 (2016) 281–289
The mass of the liquid refrigerant in the evacuation chamber from the condenser equals the mass ðM g1 Þ of the HPVHT used as primary fluid according to the mass conservation law. Thus, the mass of the liquid refrigerant in the evacuation chamber from the condenser is determined by the mass flow rate of the primary fluid ðmwn Þ and the TLCS ðt 1 Þ, as shown in Eq. (7).
M ev i ¼ M g1 þ Mev iii M g1 ¼ mwn t 1
ð6Þ ð7Þ
The optimal initial ratio (copt ) is obtained by merging Eqs. (1)– (6), as shown in Eq. (8). The optimal initial ratio is determined by the generation temperature, the condensing temperature, and the type of refrigerant. In other words, regardless of the design details of ECSTPE, the optimal initial ratio remains constant as long as the generation temperature, the condensing temperature, and the type of refrigerant are invariable. Thus, the optimal initial ratio can be easily calculated in practice.
ðhgg hev iiL Þ
v ev iiL
¼
copt ðhgg hev ig Þ hgg hev iL þ : ð1 þ copt Þ v ev ig ð1 þ copt Þ v ev iL
ð8Þ
3.2. Identification of optimal TLCS The initial ratio can be used as a signal to end the cooling stage and trigger the pressuring stage. A smaller initial ratio means a larger TLCS. Thus, the optimal TLCS can be obtained on the basis of the optimal initial ratio. By accurately controlling the TLCS according to its optimal value, the thermal energy and chilling water waste problems can be mitigated. The optimal TLCS ðt1;opt Þ can be calculated by merging Eqs. (1)– (7), as shown in Eq. (9). The optimal TLCS is determined by the optimal initial ratio, the entrainment ratio, the cooling power, the volume of the evacuation chamber, the generation temperature, the condensing temperature, the evaporation temperature, and the specific volume of the refrigerant. The volume of the evacuation chamber, the generation temperature, the condensing temperature, the evaporation temperature, and the specific volume of the refrigerant are either predefined or easily measured. The entrainment ratio and cooling power can be obtained by measurement or numerical simulation. Thus, the optimal TLCS ðt1;opt Þ can be easily obtained on the basis of the optimal initial ratio ðcopt Þ in practice.
copt
ð1 þ copt Þ v ev ig ¼
þ
1 ð1 þ copt Þ v ev iL
q t1;opt 1 : þ Volev w ðheg heL Þ v gg
ð9Þ
4. Validation case studies In this section, case studies were conducted to demonstrate the effectiveness of the optimal TLCS control method. First, the simulation model was validated. Second, the developed optimal TLCS control method was implemented on the ECSTPE with R134a. Finally, the optimal TLCS control method was extended to ECSTPEs with other common refrigerants (e.g., R141b and R365mfc). 4.1. Simulation model and validation 4.1.1. Description of simulation model The simulation model consisted of two parts: the model of the ejector cooling subsystem and that of the multi-function generator subsystem. The model of the multi-function generator subsystem is illustrated in Section 3.1. The model of the ejector cooling sub-
285
system was updated from that of Cizungu et al. [38]. In 2001, Cizungu et al. proposed a succinct method with which to model ejector cooling systems. In 2011, Khalil et al. [39] used this method to study the performance of an ejector cooling system with R134a. This method only included the conservation laws of mass, energy and momentum, and was suitable for ejectors under both singlephase and two-phase work situations. Meanwhile, it had no limitations regarding the type of refrigerant. Due to these merits, this method was adopted to model the ejector cooling subsystem with slight modifications, as shown in Fig. 3. Instead of empirical identification of the entrainment ratio, a dichotomy algorithm was used to quickly achieve an accurate result. Khalil et al. empirically assigned the value of the entrainment ratio, which may cause unnecessary errors and a heavy computation burden. The entire model of the ECSTPE was based on only the conservation laws of mass, energy and momentum. Meanwhile, it had no limitations on work situations in the ejector and was suitable for any type of refrigerant. Some assumptions were made in this model: (1) The ejector was a constant-pressure type, as shown in Fig. 4 [39]. (2) At the inlet and outlet of the ejector, the kinetics of the refrigerant, which were rather small compared with the enthalpy of the refrigerant, were negligible. (3) At the outlet section of the primary nozzle ‘‘pno”, the secondary flow reached sound speed and had the same pressure as the primary flow [40]. (4) The mixing process took place in the suction chamber between the outlet section of the primary nozzle ‘‘pno” and the inlet section of the constant-area chamber ‘‘cci”. (5) The ejector worked at a critical mode in which the entrainment was constant and the primary and secondary flows were both chocked [38]. When the chock took place, the Mach number suddenly dropped and the pressure suddenly increased [41]. (6) A normal shock occurred at the outlet section of the constant-area chamber ‘‘cco” [42]. (7) The thermodynamic process within the ejector was steady and adiabatic. 4.1.2. Validation of simulation model Model validation was carried out in two steps. First, the entrainment ratio variations with generation temperature of the ECSTPE model were compared with those of Khalil et al. [39], which were taken from their numerical model. Their numerical model had been validated by experimental data [39]. Second, the COPs of the ECSTPE model were compared with the experimental COPs of Huang et al. [17] and Wang et al. [25]. The COP refers to the ratio of the cooling obtained from the evaporator to the thermal energy inputted into the vapor generator during one work period. With the good accordance of the entrainment ratio comparisons and the reasonable COP comparison results, the accuracy of the ECSTPE model was proven to be credible. Fig. 5 shows the entrainment ratio variations with generation temperatures when the vapor generator was over heated by 10 °C and the condensing temperature was 30 °C. The simulated entrainment ratios of the ECSTPE model were in good agreement with those of Khalil et al. [39]. When the evaporation temperature was set at 5 °C, the average deviation of the simulation entrainment ratios from those of Khalil et al. was 4.7%. When the evaporation temperature rose to 10 °C, the average deviation was 1.8%. Table 2 shows the COP comparison results of the model validation. The dimensions of the ejectors in the simulation and the experiment had some discrepancies due to the assumptions in the ECSTPE model, but such assumptions have been proven to be
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Fig. 3. Flow chart of the simulation program.
Suction chamber
Primary flow (from generator )
Constant- area chamber
Diffuser
Mixed refrigerant (to condenser) pnt
pno
cci
cco
Secondary flow (from evaporator ) Fig. 4. Schematic of ejector of constant pressure type.
acceptable [38,39]. Two sets of comparisons were conducted, one for ECSTPEs with R141b and one for ECSTPEs with 365mfc. In both comparisons, the simulation COPs were higher than the reference COPs (i.e., the experimental COPs). The main reasons were as follows. In the ECSTPEs of Huang et al. and Wang et al., the vapor generator and evacuation chamber were connected by ducts without any block. The remaining HPVHT in the vapor generator was also chilled during the chilling sub-process, which resulted in extra thermal energy waste. To avoid this problem, the vapor generator and evacuation chamber in the ECSTPE of this study were separated by solenoid valves 3 and 4, as shown in Fig. 1. Thus, the simulation COPs were higher than the reference COPs.
4.2. Study on ECSTPE with R134a 4.2.1. Optimal initial ratio and associated optimal TLCS In this case, the refrigerant was R134a; the condensing temperature and evaporation temperature were set at 35 °C and 10 °C, respectively; the volume of the evacuation chamber was set at 2 m3; and the cooling capacity of the ECSTPE was set at 200 kW. The optimal initial ratio was calculated according to Eq. (8). The optimal initial ratio consecutively increased when the generation temperature increased, as shown in Fig. 6. This phenomenon can be explained as follows. When the generation temperature increased, the temperature increase of R134a during the
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2
0.35 Simulation 10 Simulation 5 Reference 10
0.25
1.8
Optimal initial ratio (-)
Entrainment ratio (-)
0.30
Reference 5
0.20 0.15 0.10
1.6
1.4
0.05 0.00
66
70
74
78
82
1.2
Generator temperature ( )
pressurization sub-process became greater. Consequently, the expansion of the liquid R134a in the evacuation chamber became more severe. Thus, more room was required in the evacuation chamber for the expansion of the liquid R134a, which resulted in an increase in the optimal initial ratio. The associated optimal TLCS was calculated on the basis of the optimal initial ratio according to Eq. (9). Fig. 7 shows the optimal TLCS variations with the optimal initial ratios. The optimal TLCS decreased when the optimal initial ratio increased, which can be explained as follows. When the optimal initial ratio increased, there was less liquid refrigerant in the evacuation chamber at the beginning of the pressurization sub-process. Thus, less time was required to accumulate liquid refrigerant from the condenser, which resulted in a decrease in the optimal TLCS.
84
86
88
90
Generation temperature (oC) Fig. 6. Optimal initial ratio variations with generation temperatures.
90 85
Optimal TLCS (s)
Fig. 5. Entrainment ratio comparison results of the model validation.
82
80 75 70 65 60 1.2
1.4
1.6
1.8
2
Optimal initial ratio (-) 4.2.2. Effectiveness of optimal TLCS control method The effectiveness of the optimal TLCS control method was demonstrated in terms of the performance deterioration that resulted from the deviation of the TLCS from its optimal value. The TLCS deviation was determined by the initial ratio deviation. Fig. 8 shows the variations of the TLCS deviation with the initial ratio deviations when the generation temperature was set at 85 °C. When the initial ratio deviation increased, the TLCS deviation increased. The reasons for this were similar to those given in Section 4.2.1. Fig. 9 shows COP variations with TLCS deviations. The COP consecutively decreased as the TLCS deviation increased. It was observed that the COP decreased by 5.6% when the TLCS deviated by 10 s from its optimal value. Fig. 10 shows the chilling load variations with TLCS deviations. The chilling load refers to the chilling load needed to remove the discarded thermal energy in the HPVHT when per unit mass of primary fluid was provided for
Fig. 7. Optimal TLCS variations with optimal initial ratios.
the ejector. The chilling load increased when the TLCS deviation increased. It was observed that the chilling load increased by 23.7% when the TLCS deviated by 10 s. Therefore, accurate control of the TLCS according to the optimal TLCS could effectively improve ECSTPE performance.
4.3. Study on ECSTPEs with other refrigerants Further case studies were conducted on ECSTPEs with other potential refrigerants (e.g., R141b and R365mfc). Fig. 11 shows the optimal initial ratio variations of ECSTPEs with R141b, R365mfc, and R134a with generation temperatures when the other
Table 2 COP comparison results of the model validation. Comparison 1
Comparison 2
Ref. [17]
Simulation
Ref. [25]
Simulation
Ejector dimension Primary nozzle throat diameter/mm Primary nozzle exit diameter/mm Constant area diameter/mm Area ratio
2.64 4.50 7.34 7.73
2.98 6.55 7.93 7.08
2.64 4.50 7.34 7.73
2.85 5.73 7.26 6.48
COP Absolute data Percentage discrepancy (%)
0.185 (measuring error 4.82%) 8.11
0.200
0.215 (measuring error 4.82%) 19.07
0.256
Note, the boundary conditions of comparison 1 were as follows: R141b, T b ¼ 90 C, T c ¼ 32:4 C, T e ¼ 8:2 C. The boundary conditions of comparison 2 were as follows: R365mfc, T b ¼ 90 C, T c ¼ 39:6 C, T e ¼ 20 C.
Y. He et al. / Energy Conversion and Management 113 (2016) 281–289
50
2.1
40
1.8
Optimal initial ratio (-)
TLCS deviation from its optimal value(s)
288
30
20
10
1.5
R134a R141b
1.2
R365mfc 0.9
0.6
0 0
20
40
60
80
100
Initial ratio deviation from its optimal value (%)
0.3
Fig. 8. TLCS deviation variations with initial ratio deviations.
82
84
86
88
90
Generation temperature (oC)
20
0.095
15
0.090 COP decrease percent COP
10
0.085
5
0.080
0 0
5
10
15
20
25
30
35
Table 3 ECSTPE performance deterioration with each 10-second deviation of TLCS.
0.075 45
40
TLCS deviation (s) Fig. 9. COP variations with TLCS deviations.
Chilling load increase percent
simulation conditions were similar to those given in Section 4.2. The optimal initial ratios of all three systems increased as the generation temperature increased for reasons similar to those given in Section 4.2.1. Furthermore, the increased speeds of the ECSTPEs with R141b and R365mfc were lower than that of the ECSTPE with R134a. This phenomenon can be explained as follows. The increased speed of the optimal initial ratio was determined by density variations in the liquid refrigerant with temperatures. The
COP (%/10 s) Q (%/10 s)
R134a
R141b
R365mfc
5.6 23.7
0.06 3.5
0.14 5.8
more rapid density variations of liquid refrigerant indicated larger volume expansion during the pressurization sub-process, which resulted in a greater increase in the increased speed of the optimal initial ratio. The density variation speeds of liquid R141b and R365mfc were lower than that of liquid R134a, as shown in Fig. 2. When the TLCS deviated from its optimal value due to the initial ratio deviation, the COPs of the ECSTPEs with R141b and R365mfc decreased and their chilling loads increased. The reasons for this finding were similar to those given in Section 4.2.2. Table 3 shows the ECSTPE performance deterioration results. When the TLCS deviated 10 s from its optimal value, the COPs of the ECSTPEs with R141b and R365mfc decreased by 0.06% and 0.14%, respectively; and their chilling loads increased by 3.5% and 5.8%, respectively. The performance deterioration of the ECSTPEs with R141b and R365mfc was lower than that of the ECSTPE with R134a because the density variations of liquid R141b and R365mfc during the pressurization sub-process were smaller. In other words, the performance of the ECSTPE with R134a was the more sensitive to
120.0
260.0
100.0
230.0
Chilling load increase percent 200.0
80.0
Chilling load 60.0
170.0
40.0
140.0
20.0
110.0
80.0
0.0 0
5
10
15
20
25
30
35
40
TLCS deviation (s) Fig. 10. Chilling load variations with TLCS deviations.
45
Chilling load for unit mass primary fluid (kJ/kg)
0.100
COP (-)
COP decrease percent
Fig. 11. Optimal initial ratio variations with generation temperatures.
25
Y. He et al. / Energy Conversion and Management 113 (2016) 281–289
the TLCS deviation. Thus, the optimal TLCS control method was the more effective on the ECSTPE with R134a. For the ECSTPEs with R141b and R365mfc, the small TLCS deviation inflicted little damage on the ECSTPE performance, but it was still necessary and beneficial to accurately control the TLCS for ECSTPEs with R141b and R365mfc for several reasons. First, a large TLCS deviation would cause severe performance deterioration. For example, a 100second TLCS deviation led to increases of 35% and 58% in the chilling loads of the ECSTPEs with R141b and 365mfc, respectively. Second, accurate control of the TLCS based on the optimal initial ratio was convenient because the optimal initial ratio could be easily calculated. The developed optimal TLCS control method was effective on ECSTPEs whose liquid refrigerant density varied with temperature. 5. Conclusions To alleviate the severe thermal energy and chilling water waste problems of ECSTPEs, an innovative concept for the optimal initial ratio has been proposed and an optimal TLCS control method has been developed. The optimal TLCS control method is base on the optimal initial ratio. Case studies have demonstrated the effectiveness of the developed optimal TLCS control method on ECSTPEs with different refrigerants. For the ECSTPE with R134a, with each 10-second TLCS deviation from its optimal value, the COP of the ECSTPE decreased by 5.6% and the chilling load increased by 23.7%. For ECSTPEs with R141b and R365mfc, each 10-second deviation led to relatively little performance deterioration; however, excessive deviation (e.g., 100 s) could lead to severe performance deterioration (e.g., a chilling load increase of 35% for R134b and 58% for R365mfc). The developed optimal TLCS control method can improve the performance of ECSTPEs with other refrigerants as long as the liquid refrigerant density varies with the temperature. Furthermore, the optimal TLCS control method can be conveniently used in practice because the optimal initial ratio is easy to determine from only the generation temperature, the condensing temperature, and the type of refrigerant. Improvement of ECSTPE performance helps to mitigate increasing energy and environmental problems. Acknowledgements This work was supported by the Natural Science Foundation of China (contract No. 51206140) and Science and Technology Department of Zhejiang Province (contract No. 2012C21072). The authors would like to express their gratitude to Dr. Yong Cheng from Chongqing University for his valuable suggestions. References [1] Kolokotsa D, Rovas D, Kosmatopoulos E, Kalaitzakis K. A roadmap towards intelligent net zero- and positive-energy buildings. Sol Energy 2011;85:3067–84. [2] Chua KJ, Chou SK, Yang VM, Yan J. Achieving better energy-efficient air conditioning – a review of technologies and strategies. Appl Energy 2013;104:87–104; Besagni G, Mereu R, Inzoli F. Ejector refrigeration: a comprehensive review. Renew Sustain Energy Rev 2016;53:373–407. [3] Besagni G, Mereu R, Inzoli F. Ejector refrigeration: a comprehensive review. Renew Sustain Energy Rev 2016;53:373–407. [4] Chen J, Jarall S, Havtun H, Palm B. A review on versatile ejector applications in refrigeration systems. Renew Sustain Energy Rev 2015;49:67–90. [5] Abdulateef JM, Sopian K, Alghoul KA, Sulaiman MY. Review on solar-driven ejector refrigeration technologies. Renew Sustain Energy Rev 2009;13:1338–49. [6] Gil B, Kasperski J. Efficiency analysis of alternative refrigerants for ejector cooling cycles. Energy Convers Manage 2015;94:12–8. [7] Chunnanond K, Aphornratana S. Ejectors: applications in refrigeration technology. Renew Sustain Energy Rev 2004;8(2):129–55.
289
[8] Huang P, Huang G, Wang Y. HVAC system design under peak load prediction uncertainty using multiple-criterion decision making technique. Energy Build 2015;91:26–36. [9] ASHRAE Handbook. HVAC systems and equipment. Atlanta, GA: American Society of Heating, Refrigerating, and Air Conditioning Engineers; 1996. [10] Grondzik WT, editor. Air-conditioning system design manual. Atlanta, USA: ASHRAE Inc.; 2007. [11] Chandra VV, Ahmed MR. Experimental and computational studies on a steam jet refrigeration system with constant area and variable area ejectors. Energy Convers Manage 2014;79:377–86. [12] Tashtoush B, Alshare A, Al-Rifai S. Performance study of ejector cooling cycle at critical mode under superheated primary flow. Energy Convers Manage 2015;94:300–10. [13] Huang BJ, Jiang CB, Hu FL. Ejector performance characteristics and design analysis of jet refrigeration system. J Eng Gas Turbines Power 1985;107:792–802. [14] Abed AM, Alghoul MA, Sirawn R, Al-Shamani AN, Sopian K. Performance enhancement of ejector–absorption cooling cycle by re-arrangement of solution streamlines and adding RHE. Appl Therm Eng 2015;77:65–75. [15] Khaliq A. Performance analysis of a waste-heat-powered thermodynamic cycle for multi-effect refrigeration. Int J Energy Res 2015;39:529–42. [16] Shen S, Qu X, Zhang B, Riffat S, Gillott M. Study of a gas–liquid ejector and its application to a solar-powered bi-ejector refrigeration system. Appl Therm Eng 2005;25:2891–902. [17] Huang BJ, Hu SS, Lee SH. Development of an ejector cooling system with thermal pumping effect. Int J Refrig 2006;29:476–84. [18] Chen X, Omer S, Worall M, Riffat S. Recent developments in ejector refrigeration technologies. Renew Sustain Energy Rev 2013;19:629–51. [19] Nguyen VM, Riffat SB, Doherty PS. Development of a solar-powered passive ejector cooling system. Appl Therm Eng 2001;21:157–68. [20] Dai Z, He Y, Huang Y, Tang L, Chen G. Ejector performance of a pump-less ejector refrigeration system driven by solar thermal energy. USA: International Refrigeration and Air Conditioning Conference Purdue; 2012. [21] Chuech SG, Chen C, Lu J, Yan M. Design and implementation of ejector driven micropump. Energy Convers Manage 2007;48:2657–62. [22] Ziapour BM, Abbasy A. First and second laws analysis of the heat pipe/ejector refrigeration cycle. Energy 2010;35:3307–14. [23] Wang F, Shen S. A novel solar bi-ejector refrigeration system and the performance of the added injector with different structures and operation parameters. Sol Energy 2009;83:2186–94. [24] Riffat SB, Holt A. A novel heat pipe/ejector cooler. Appl Therm Eng 1999;18 (3):93–101. [25] Wang JH, Wu JH, Hu SS, Huang BJ. Performance of ejector cooling system with thermal pumping effect using R141b and R365mfc. Appl Therm Eng 2009;29:1904–12. [26] Kasperski J. Two kinds of gravitational ejector refrigerator stimulation. Appl Therm Eng 2009;29:3380–5. [27] Kasperski J. Rotational type of a gravitational ejector refrigerator – a system balance of the refrigerant analysis. Int J Refrig 2010;33:3–11. [28] Huang BJ, Wu JH, Hsu HY, Wang JH. Development of hybrid solar-assisted cooling/heating system. Energy Convers Manage 2010;51(8):1643–50. [29] Wong YW, Sumathy K. Solar thermal water pumping systems: a review. Renew Sustain Energy Rev 1999;3:185–217. [30] Wong YW, Sumathy K. Thermodynamic analysis and optimization of a solar thermal water pump. Appl Therm Eng 2001;21:613–27. [31] Dobriansky Y. Concepts of self-acting circulation loops for downward heat transfer (reverse thermosiphons). Energy Convers Manage 2011;52 (1):414–25. [32] Bataineh KM. Optimization analysis of solar thermal water pump. Renew Sustain Energy Rev 2016;55:603–13. [33] Srisastra P, Aphornratana S. A circulating system for a steam jet refrigeration system. Appl Therm Eng 2005;25(14–15):2247–57. [34] Karthikeyan G, Mani A, Murthy SS. Analysis of an absorption refrigeration system with transfer tank. Renewable Energy 1994;4(1):129–32. [35] Srisastra P, Aphornratana S, Sriveerakul T. Development of a circulating system for a jet refrigeration cycle. Int J Refrig 2008;31(5):921–9. [36] Pridasawas W, Lundqvist P. An exergy analysis of a solar-driven ejector refrigeration system. Sol Energy 2004;76:369–79. [37] Xu ZL, Tao LR, Xiao X. Ejector refrigeration system without pump for air conditioning. Heat, Ventilating Air Cond 2008;38(1). [38] Cizungu K, Mani A, Groll M. Performance comparison of vapour jet refrigeration system with environment friendly working fluids. Appl Therm Eng 2001;21:585–98. [39] Khalil A, Fatouh M, Elgendy E. Ejector design and theoretical study of R134a ejector refrigeration cycle. Int J Refrig 2011;34:1684–98. [40] Ouzzane M, Aidoun Z. Model development and numerical procedure for detailed ejector analysis and design. Appl Therm Eng 2003;23:2337–51. [41] Riffat SB, Omer SA. CFD modelling and experimental investigation of an ejector refrigeration system using methanol as the working fluid. Int J Energy Res 2001;25(2):115–28. [42] Selvaraju A, Mani A. Analysis of an ejector with environment friendly refrigerants. Appl Therm Eng 2004;24:827–38.