Thermodynamic performance analysis of dedicated mechanically subcooled vapour compression refrigerat

Abstract

Keywords: VCR; Subcooling; COP; R1234ze; R1234yf; Exergetic Efficiency; Dedicated; R134a

Introduction

Demand of energy, economy and eco-sustainability are the major considerations of a refrigeration system design. The demand of high grade energy is growing continuously in the developing countries viz. India. The cost of electricity is also increasing with its demand. The distortion of surrounding ecosystem with the use of high GWP refrigerants (HFCs) in the refrigeration and air-conditioning systems is a current issue. The high GWP HFCs have to be phased out as per the European Union (EU) regulation (Regulation (EU) No 517/2014 [1]). Many researchers have proved that the mechanically sub-cooling of vapour compression refrigeration (VCR) cycle improves its performance. Zubair [2, 3] and Zubair et al. [4] have investigated a dedicated and an integrated mechanical sub-cooling system from the thermodynamic standpoint. In these studies, it was found that the system performance had improved when operating in situations where the difference between the condensing and evaporating temperatures is large. Couvillion et al. [5] developed a mathematical model of a dedicated mechanical sub-cooling system by considering the individual component models of the equipment involved in the system. They found an improvement of 6-8% in the coefficient of performance (COP) and 20170% in the capacity over a conventional simple cycle. Qureshi et al. [6] analysed that the load carrying capacity of the evaporator increased by approximately 0.5kW when R22 was subcooled in the main cycle by 580C. They noted that using the sub-cooling, the second-law efficiency of the cycle increased by an average 21% and this percentage increase is direcltly proportional to the ambient temperature. Khan and Zubair [7] have investigated finite time thermodynamic models of simple vapour compression refrigeration, two stage VCR system (TSS), dedicated mechanical sub-cool VCR system (DMSS), integrated mechanical sub-cooling VCR system (IMSS). They predicted that the optimum value of COP is obtained by varying the parameters of heat exchanger and reduced sub-cooler saturation temperature. Thornton et al. [8] have used dedicated mechanical sub-cooling VCR cycle to sub-cool the condenser exit of main VCR cycle. They predicted the optimum value of sub-cooling evaporator temperature which established the design rule for optimum distribution of heat exchanger area. Arora et al. [9, 10, 11], Arora and Kaushik [12] and Arora [13] have analysed vapour compression and absorption refrigeration systems for energetic and exergetic performance improvement. Llopis et al. [14, 15] have theoretically analysed the energy performance enhancement of CO 2 transcritical refrigeration system using dedicated mechanical sub-cooling cycle. They observed 20% increase in COP and 28.8% increases in cooling capacity of combined and reviewed sub-cooling method viz. internal heat exchanger, economizers, thermoelectric systems, dedicated sub-cooling methods of CO2 refrigeration cycle. They concluded that the subcooling is a worth method to increase the performance of refrigeration cycle and deserve future development. Many researchers have suggested the replacement of R134a with R1234ze and R1234yf in refrigeration This paper was recommended for publication in revised form by Regional Editor Sandip Kale 1 Department of Mechanical Engineering, Delhi Technological University, Delhi-110042, India. *E-mail address: profakhilesharora@gmail.com Orcid id: 0000-0002-2363-7296, 0000-0002-5984-406X, 0000-0001-8022-5573 Manuscript Received 9 August 2017, Accepted 11 November 2017

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systems. Mota-Babiloni et al. [16] reviewed the recent developments in commercial refrigeration and focused on system modifications (as dedicated sub-cooling or the implementation of ejectors), tri-generation technologies (electrical, heating and cooling demand) and better evaporation conditions control. They concluded that the hydrocarbon, HFO and CO2 are HFC replacements. Kalla et al. [17, 18] reviewed alternative refrigerants for vapour compression refrigeration system and investigated the performance of R22 and its substitutes in airconditioners. Yataganbaba et al. [19] performed exergy analysis on a two evaporator vapour compression refrigeration system using R1234yf, R1234ze and R134a as refrigerants. The two refrigerants R1234yf and R1234ze were good alternatives to R134a regarding their environment friendly properties. Dixit et al. [24-26] carried out energy and exergy analysis of absorption-compression cascade and waste heat driven triple effect refrigeration cycles. The literature survey gathered from different established data sources viz. Google Scholar, Research gate, Science direct etc. reveals that the extensive research have been done on simple VCR cycle. Out of these, some studies based on dedicated mechanical sub-cool cycle have been considered to enhance the performance of the cycle. It is observed that limited work has been carried out to explore the performance of dedicated mechanical subcool cycle using HFO refrigerants viz. R1234yf and R1234ze.

(b) Figure 1. (a) Saturated Vapour Compression Refrigeration Cycle, (b) P-h diagram of saturated vapour compression refrigeration cycle The present work investigates the thermodynamic performance of dedicated mechanically subcooled VCR cycle using R1234yf, R1234ze and R134a. The comparison of considered refrigerant has also been explored for drop-in replacement of R134a to R1234ze and R1234yf. The first and second law based performance parameters viz. COP and exergetic efficiency have been computed with the variation in degree of sub-cooling (DOS), evaporator temperature and condenser temperature.

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Description Of System And Modelling

Description of System The current work presents first and second law based thermodynamic analysis of dedicated mechanically subcooled vapour compression refrigeration system (DSC) using R1234ze, R1234yf and R134a. The mechanical sub-cooling of main VCR cycle has been carried out through the subcooler or evaporator of another simple VCR cycle designated as subcooler VCR cycle.

(b) Figure 2. (a) Schematic diagram of dedicated mechanically subcooled vapour compression refrigeration cycle, (b) P-h diagram of dedicated sub-cooled vapour compression cycle Figure 2(a) and 2(b) illustrate the schematic and P-h diagrams of dedicated mechanically subcooled vapour compression refrigeration system respectively. It comprises of two sections i.e. subcooled and subcooler vapour compression refrigeration cycles. The evaporator of subcooler VCR cycle receives the heat rejected by the condensate liquid refrigerant of subcooled VCR cycle and acts as subcooler. In this way, the two cycles are coupled together through subcooler or evaporator 2 in order to achieve low temperature in evaporator1. The refrigerants considered for the energy and exergy analysis of the system are R134a, R1234yf and R1234ze. The same refrigerant has been considered in the two sections simultaneously. The subcooled VCR cycle is in lower section which consists of compressor1, evaporator1, expansion valve1, subcooler and condenser1 and the subcooler VCR cycle is upper section which consists of compressor2, condenser2, expansion valve2 and evaporator2 or subcooler. The vapour refrigerant leaving the evaporator1 of subcooled VCR cycle at state point1 enters into the compressor1 and is being compressed. The refrigerant at high temperature and pressure leaving the compressor1 at state point 2 and enters in to the condenser1. The liquid condensate has been subcooled from state point 3-3a by the evaporator2 of the subcooler cycle. The subcooled liquid refrigerant is throttled by the expansion valve1 from state point 3a-4. The low temperature liquid-vapour mixture of refrigerant enters in to the evaporator1 and low temperature is achieved in the evaporator1.

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Similarly, the saturated vapour of the refrigerant leaving the evaporator2 or subcooler at state point 5 enters in to the compressor2. The compressed high pressure, high temperature vapour refrigerant enters into the condenser2 at state point 6. The vapour phase of the refrigerant is converted in to liquid in the condenser2. The liquid condensate refrigerant leaving the condenser2 at state point7 is expanded freely by the expansion valve2 from state 7-8. The low temperature liquid-vapour mixture of refrigerant enters into the evaporator2 or subcooler and absorbs heat from the condensate of condenser1 from state 8-5 and transformed into saturated vapour. In this way, the mechanical sub-cooling is produced by the subcooler VCR cycle in the subcooler from states 3-3a. The evaporator temperature (Te,SC ) of the subcooler cycle is more than the evaporator temperature of subcooled cycle. The sub-cooling of liquid condensate refrigerant of subcooled cycle enhances the net specific refrigerating effect as shown in Figure 2 from states 4-1. The increase in refrigerating effect enhances the coefficient of performance (COP) of the subcooled cycle. However, the compressor work of the subcooler cycle reduces the COP of the overall cycle. Thermodynamic Modelling In the present work, the energy and exery analysis of dedicated mechanically subcooled vapour compression cycle have been carried out. In which the subcooler VCR cycle produces mechanical sub-cooling in the subcooled VCR cycle through subcooler using considered refrigerants R134a, R1234yf and R1234ze. The various performance parameters viz. compressor work, COP, exergetic efficiency, total exergy destruction rate and exergy destruction ratio have been explored for different variables viz. degree of sub-cooling, evaporator temperature, effectiveness of subcooler, isentropic efficiency of compressor and condenser temperature. A set of computer code has been formulated in Engineering Equation Solver (EES) (Klein and Alvarado [22]) to perform the analysis. The steady state governing equations, based on first and second law of thermodynamics have been developed. Energy Analysis The first law based work, energy and mass conservation principles are presented in equations (1)-(2).

where 𝑄̇ , Ẇ and 𝑚̇ are the rate of heat, work and mass transfer crossing the boundary of the system respectively. The coefficient of performance (COP) of simple, dedicated mechanically subcooled, subcooler and overall VCR cycles are given by the equation (3)-(9). 𝑄̇

where Q̇ e is the net refrigeration effect produced and Ẇcomp is the actual work of the compressor. 𝑄̇

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𝑊̇𝑐𝑜𝑚𝑝2 = ṁ r, SC (ℎ6 − ℎ5 ) 𝑄̇𝑒,𝐷𝑆𝐶 𝑐𝑜𝑚𝑝1 +𝑊̇𝑐𝑜𝑚𝑝2

where Q̇ e,DSC , Q̇ e,SC , Ẇcomp1 , Ẇcomp2 , ṁ r, DSC and ṁ r, SC are net refrigerant effect, net compressor work and mass flow rate of dedicated mechanically subcooled and subcooler VCR cycles respectively. The effectiveness of subcooler 𝜀𝑆𝐶 is the ratio of minimum heat transfer to the maximum heat transfer. T -T

where 𝜀𝑆𝐶 is the effectiveness of subcooler and T3 ,T5 and T8 are temperatures at respective state points. The energy balance in the subcooler is given by equation (11)

Exergy Analysis The second law of thermodynamics expresses the concept of exergy. The exergy is defined as the degree measure of quality or usefulness of energy to impact the environment. The maximum useful work which can be extracted from a system as it reversibly comes into equilibrium with its environment. (Bejan et al. (1996), Arora and Kaushik [12]). For the refrigerant flowing in a refrigerating system, the exergy is defined as follows (Bejan et al. [20]):

where h0 and s0 are the enthalpy and entropy values of the refrigerant at dead state pressure P 0 and temperature T0. Exergy destruction(ĖD ) or internal exergy destruction losses which are caused by irreversibilites of the system is the algebric sum of total exergy at the inlet and outlet of the system. General exergy balance is given by (Dincer and Kanoglu [21]):

where ĖD is the rate of exergy destruction and Ėin and Ėout are the total exergy transferred by heat, work and mass. Exergy Destruction (𝐄̇D) in the Components of Dedicated Mechanically Subcooled Vapour Compression Refrigeration Cycle (DSC) The exergy destruction in each component of the dedicated mechanically subcooled vapour compression refrigeration cycle is given by the following equations: Evaporator 1

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(𝐸̇𝐷 )𝑐𝑜𝑚𝑝1 = 𝐸̇𝑋 1 + 𝑊̇𝑐𝑜𝑚𝑝1 − 𝐸̇𝑋 2 = 𝑚̇𝑟,𝐷𝑆𝐶 (h1 − 𝑇0 𝑠1 ) +𝑊̇𝑐𝑜𝑚𝑝1 − 𝑚̇𝑟,𝐷𝑆𝐶 (h2 − 𝑇0 𝑠2 )

where Ė𝐷 , Ė𝑋 , ṁr and Tb are the exergy destruction rate, exergy rate, mass flow rate and temperature of space to be cooled for the dedicated mechanically subcooled and subcooler cycle respectively. T0 , h0 and s0 are the temperature, enthalpy and entropy of dead state.

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Total Exergy Destruction Total exergy destruction of the system is the sum of exergy destruction in each component of the system. The total exergy destruction in dedicated mechanically subcooled vapour compression refrigeration cycle (DSC) is given by:

Exergetic Efficiency The exergetic efficiency is the ratio of total exergy recovered to the total exery supplied and is given by (Dincer and Kanoglu (2010)): ∑ 𝐸̇

where ηex is the exergetic efficiency of the cycle. ∑ Ėout , ∑ Ėin and ∑ ĖD are the total exergy recovered, supplied and destructed respectively. The exergetic efficiency of vapour compression refrigeration system is defined as the ratio of the exergy of heat absorbed in the evaporator from the space to be cooled at temperature T b to the actual compressor work input (Ẇcomp ) (Arora and Kaushik [12]). Exergy efficiency can also be defined as The exergetic efficiency is the ratio of exery in products to the exergy of fuel. The exergetic efficiency of dedicated mechanically subcooled, subcooler and overall VCR cycles are given by the equations (27)-(29).

Figure 3. Exergy balance in evaporator of DSC and the space to be cooled [23]

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Exergy Destruction Ratio (EDR) The EDR is the total exergy destruction in the system to the exergy in the products (Arora and Kaushik [12]) and is given by equation (30).

The exergy destruction ratio for the dedicated mechanically subcooled, subcooler and overall VCR cycles are given in following (31)-(33).

Mathematical Modelling The present work investigates the performance of dedicated mechanically subcooled vapour compression refrigeration cycle (DSC) on the bassis of first and second law of thermodynamics. The mathematical fomulation of thermodynamic relations have been carried out considering mass, energy and work conservation principles for system and system components. Table 1. Input variable considered except where the variation of these system variables involved (Arora and Kaushik [12]) S.No. 1. 2. 3. 4. 5. 6. 7.

Input variables Evaporator1 temperature (T e, DSC) Degree of subcooling ((∆T)sc )(3-3a) Condenser1,2 temperature (Tc,DSC and Tc,SC), assuming summer conditions in a country near the equator line. Isentropic efficiency of compressor (𝜂𝑐𝑜𝑚𝑝1 , 𝜂𝑐𝑜𝑚𝑝2 ) Effectiveness of subcooler (εSC ) Net refrigerating effect (Q̇ e,DSC ) Ambient or dead state temperature (T 0) and pressure (P0)

Values -100C 50C 500C 80% 0.8 3.5167 kW 250C and 101.325 kPa

The following assumptions have been considered to formulate the complex thermodynamic model of dedicated mechanically subcooled vapour compression refrigeration cycle (DSC) except where the variation of physical parameters involved.    

It is assumed that the state of refrigerant is dry and saturated at the entry of compressor at state points 1 and 5. Difference between evaporator temperature and the temperature of space to be cooled (T b, DSC -Te, DSC, Tb,SC -Te,SC ) is 5 0C. The range of variation of evaportor1 temperature (T e, DSC) is -20 0C to 10 0C. The range of variation of condenser1 temperature (T e, SC) is 30 0C to 50 0C.

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The heat losses and pressure losses from the system and system components are negligible. The whole system operates in steady state condition. The range of degree of subcooling (ΔT)SC is 5 to 30 0C. The pressure drop in evaporator (δe ) and condenser (δc ) is assumed to be zero.

Results And Discussion

Energy and exergy analysis of dedicated mechanically subcooled vapour compression refrigeration cycle (DSC) have been performed using a computer software based program in Engineering Equation Solver (EES) (Klein and Alvarado [22]) which has been shown in Figure 1(a) and 2(b). The considered refrigerants for the analysis are R134a, R1234yf and R1234ze. The computation of the various performance parameters viz. compressor work, COP, exergetic efficiency, total exergy destruction rate and exergy destruction ratio (EDR) have been done by calling builtin functions (i.e. specific entropy, specific enthalpy, temperature and pressure etc.) of the EES library. The results from the present analysis have been compared with the results of Arora et al. [12]. It is observed that the difference in the value of COP and exergetic efficiency is within a range of ±1%. The difference in results may be due to the pressure drop in evaporator and condenser is assumed to be zero. Effect of Subcooling The effect of degree of sub-cooling (ΔT)sc on various performance parameters viz. compressor work (𝑊̇𝐶 ), COP, exergetic efficiency (𝜂𝑒𝑥 ), total exergy destruction rate (𝐸̇𝐷, 𝑇𝑜𝑡𝑎𝑙 ) and exergy destruction ratio (EDR) has been illustrated in Figure 4(a) to 4(d).

Figure 4. (a) Variation in compressor work (𝑊̇𝐶 ) with degree of subcooling (∆𝑇𝑠𝑐 ), (b) effect of degree of subcooling (∆𝑇𝑠𝑐 ) on COP, (c) Effect of degree of subcooling (∆𝑇𝑠𝑐 ) on exergetic efficiency (ηex), (d) variation in total exergy destruction rate (E ̇_(D,Total) ) and exergy destruction ratio (EDR) with subcooling (∆𝑇𝑠𝑐 ) of OC

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Figure 4(a) represents the effect of sub-cooling (ΔT)sc on compressor work (𝑊̇𝐶 ). For 1 Ton refrigeration, compressor work of dedicated mechanically subcooled (DSC) (𝑊̇𝐶𝑜𝑚𝑝1 ) decreases with increase in degree of subcooling (DOS) because the mass flow rate of refrigerant decreases with increase in degree of subcooling for constant refrigeration load of 3.5167kW. However, the compressor work first decreases and then increases for overall cycle (OC) with increase in degree of sub-cooling for the considered refrigerants. This is due to that the compressor work of OC (𝑊̇𝐶𝑜𝑚𝑝1 + 𝑊̇𝐶𝑜𝑚𝑝2 ) decreases for low values of DOS as the value of 𝑊̇𝐶𝑜𝑚𝑝1 decreases and the values of 𝑊̇𝐶𝑜𝑚𝑝2 are very small. For the higher values of DOS, the compressor work of subcooler cycle (𝑊̇𝐶𝑜𝑚𝑝2 ) increases while 𝑊̇𝐶𝑜𝑚𝑝1 decreases. However the compressor work for the simple VCR cycle is is higher than that of the DSC. The optimize value of degree of sub-cooling lies within 20-250C for overall cycle. It has been observed that the compressor work is minimum for R1234ze and maximum for R1234yf for DSC and OC. Figure 4(b) shows the variation of COP with degree of sub-cooling for the considered refrigerants R134a, R1234yf and R1234ze. The COP of the dedicated mechanically subcooled cycle increases and the COP of subcooler cycle decreases with increase in DOS for the considered refrigerants. However, the COP of the overall cycle first increases, maximise for optimum value of DOS which lies within 20-250C and then decreases with increase in DOS. In order to increase DOS, The temperature and pressure of evaporator of subcooler cycle has to achieved lower values which reduces the COP of the subcooler cycle while for the constant refrigerating load of Q̇ e,DSC = 3.5167kW, the compressor work (𝑊̇𝐶𝑜𝑚𝑝1 ) of DSC decreases linearly and the COP of DSC is Q̇e,DSC (“Eq.(4)”). Thus the COP of the DSC increases linearly with increase in DOS. The COP of OC is Ẇcomp1 Q̇e,DSC (“Eq.(9)”) which increases with increase in COP of DSC and decreases with decrease in COP of Ẇcomp1 +Ẇcomp2

subcooler cycle due to increase in compressor work of SC with increase in DOS. Thus the COP of OC first increases (as COP of DSC increases faster) reaches to maximum value and then decreases (as COP of SC cycle decreases faster) for the refrigerant considered. It is observed that the COP is maximum for R1234ze and minimum for R1234yf. The COP of simple VCR cycle is lower than the DSC and OC. Figure 4(c) illustrates the effect of degree of sub-cooling (∆𝑇𝑠𝑐 ) on exergetic efficiency (ηex (OC)) of overall cycle. The exergetic efficiency of the overall cycle first increases reaches to a maximum value and then decreases with increase in DOS for the considered refrigerants. The optimum value of degree of sub-cooling lies between 20 to 250C for which the value of exergetic efficiency is maximum. The exergetic efficiency of overall cycle is given by ηex (OC) =

first increases, reaches to a maximum value and then decreases with increase in DOS (Figure 4(b)) and the term |(1 −

)|remains constant with increase in DOS because the value of T0 and Tb,DSC remains constant with

increase in DOS. Hence the value of ηex (OC) first increases, reaches to a maximum value and then decreases. The optimum value of DOS lies between 20 to 250C for the considered refrigerants. Hence the exergetic efficiency of the OC follows the trend of COP. It can be observed that ηex (OC) is maximum for R134a and minimum for R1234yf. Figure 4(d) shows the variation in total exergy destruction rate (𝐸̇𝐷, 𝑇𝑜𝑡𝑎𝑙 ) and exergy destruction ratio (EDR) with degree of subcooling (∆𝑇𝑠𝑐 ) for overall cycle. The value of 𝐸̇𝐷, 𝑇𝑜𝑡𝑎𝑙 and EDR first decreases, reaches to a minimum value and then increases with increase in DOS for the refrigerants considered. The value of Q̇ e,OC first increases reaches to a maximum value and then decreases with increase in DOS (Figure 4(b)). Therefore, the exergy recovered from the system and system components first increases, reaches to a maximum value and then decreases with increase in DOS. Consequently, the 𝐸̇𝐷, 𝑇𝑜𝑡𝑎𝑙 first decreases, reaches to a ∑(ĖD )OC

)|. Hence EDR first decreases, reaches to a minimum value and

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then increases with increase in DOS (∆𝑇𝑠𝑐 ). It can also be observed that the values of 𝐸̇𝐷, 𝑇𝑜𝑡𝑎𝑙 and EDR are minimum for R134a and maximum for R1234yf. Effect of Evaporator Temperature The effect of evaporator1 temperature (Te, DSC) on various performance parameters viz. compressor work (𝑊̇𝐶 ), degree of subcooling (ΔT)sc, COP, exergetic efficiency (𝜂𝑒𝑥 ), total exergy destruction rate (𝐸̇𝐷, 𝑇𝑜𝑡𝑎𝑙 ) and exergy destruction ratio (EDR) has been shown in Figure 5(a) to 5(d).

Figure 5. (a) Variation in compressor work(𝑊̇𝐶 ) with evaporator1 Temperature (T e, DSC), (b) effect of evaporator1 temperature (T e,DSC) on degree of subcooling (∆𝑇𝑠𝑐 ) and COP, (c) effect of evaporator1 temperature (Te,DCS) on exergetic efficiency ( ηex) of overall cycle, (d) variation in total exergy destruction rate (𝐸̇𝐷,𝑇𝑜𝑡𝑎𝑙 ) and exergy destruction ratio (EDR) with evaporator1 temperature (Te,DCS) of overall cycle Figure 5(a) shows the varition in compressor work (𝑊̇𝐶 ) with evaporator1 temperature (Te, DSC) for dedicated mechanically subcooled and overall VCR cycle. The compressor work of DSC (𝑊̇𝐶𝑜𝑚𝑝1 ) and OC (𝑊̇𝐶𝑜𝑚𝑝1 + 𝑊̇𝐶𝑜𝑚𝑝2 ) decreases with increase in evaporator1 temperature (T e, DSC) for considered refrigerants. As the evaporator1 temperature increases, the pressure ratio between evaporator and condenser decreases and for constant refrigeration load of 3.5167kW, the mass flow rate of refrigerant also decreases. Moreover, the evaporator2 temperature of sub-cooler cycle also increases. Hence the compressor work of DSC and OC decreases with increase in evaporator1 temperature. It is observed that the value of compressor work is minimum for R1234ze and maximum for R1234yf. Figure 5(b) illustrates the effect of evaporator1 temperature (T e, DSC) on DOS (ΔT)sc and COP for OC. The value of DOS decreases and COP increases with increase in evaporator1 temperature for the refrigerant considered. For the constant refrigeration load of 3.5167kW, lower amount of sub-cooling is required in the sub-

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cooler to the refrigerant of DSC. Thus the DOS decreases with increase in Te, DSC. However, the compressor work decreases as shown in Figure 5(a), the value of COP increases. It has been observed that the value of DOS and COP are maximum for R1234ze and minimum for R1234yf. Figure 5(c) depicts the effect of evaporator1 temperature (Te, DSC) on exergetic efficiency (𝜂𝑒𝑥 ) of OC for considered refrigerants. The exergetic efficiency is given by COP(OC) × |(1 − COP(OC) increases (Figure 5(b)) and the value of term |(1 −

temperatue as (Tb, DSC -Te, DSC =50C). `Hence, the value of 𝜂𝑒𝑥 (𝑂𝐶) decreases with increase in evaporator1 temperature. It can be observed that the value of 𝜂𝑒𝑥 (𝑂𝐶) is maximum for R134a and minimum for R1234yf. Figure 5(d) illustrates the variation in total exergy destruction rate (𝐸̇𝐷, 𝑇𝑜𝑡𝑎𝑙 ) and exergy destruction ratio (EDR) with evaporator1 temperature (Te, DSC) of OC. The decreases with increase in Te, DSC. It is observed that the value of 𝐸̇𝐷, 𝑇𝑜𝑡𝑎𝑙 and EDR are minimum for R1234ze and maximum for R1234yf. 𝐸̇𝐷, 𝑇𝑜𝑡𝑎𝑙 increases and EDR decreases with increase in Te, DSC for refrigerant considered. As the exergetic efficiency decreases with increase in evaporator1 temperature (Figure 5(c)), the rate of exergy recovered of system component decreases. By which the 𝐸̇𝐷, 𝑇𝑜𝑡𝑎𝑙 decreases with increase in Te, DSC. However, the exergy of product decreases with increase in Te, DSC because the term |(1 −

Effect of Condenser Temperature The effect of degree of condenser1,2 temperature (Tc, DSC = Tc, SC) on various performance parameters viz. compressor work (𝑊̇𝐶 ), COP, exergetic efficiency (𝜂𝑒𝑥 ), total exergy destruction rate (𝐸̇𝐷, 𝑇𝑜𝑡𝑎𝑙 ) and exergy destruction ratio (EDR) has been depicted in Figure 6(a) to 6(d). Figure 6(a) illustrates the effect of condenser1,2 temperature (Tc, DSC = Tc, SC) on compressor work ̇ (WC,SVCR , ẆComp1 , ẆComp2 and(ẆComp1 + ẆComp2 )) of simple vapour compression refrigeration cycle (SVCR), DSC, SC and OC for refrigerants considered. The values of compressor work increases with increase in condenser temperature. As the condenser temperature increases, the pressure ratio between evaporator and condenser increases for which more work has been done by the compressor. Therefore, the value of 𝑊̇𝐶 increases with increase in Tc. It is also observed that the value of 𝑊̇𝐶 is minimum for R1234ze and maximum for R1234yf in DSC, OC and SVCR. Figure 6(b) shows the effect of condenser1,2 temperature (Tc, DSC = Tc, SC) on COP of DSC, OC, SC and SVCR for considered refrigerants. The COP of DSC, OC and SVCR decreases with increase in Tc, DSC = Tc, SC. This is due to that for constant refrigeration load of 3.5167kW, the compressor work increases with increase in condenser temperature. Thus the COP of DSC, OC and SVCR decreases with increase in condenser temperature. However, the COP of sub-cooler VCR cycle (SC) increases with increase in condenser temperature. The rate of heat of heat transfer to evaporator2 increases in the sub-cooler, consequently the refrigeration load of sub-cooler cycle increases and hence COP of sub-cooler cycle increases with increase in condenser temperature. It has also been observed that the COP is maximum for R1234ze and minimum for R1234yf. Figure 6(c) presents the variation in exergetic efficiency (𝜂𝑒𝑥 ) with condenser temperature (T c, DSC = Tc, SC) of DSC, OC and SVCR cycles for considered refrigerants. The value of 𝜂𝑒𝑥 decreases with increase in T c, DSC = Tc, SC. Exergetic efficiency is given by the relation, ηex = COP × |(1 −

remains constant and the value of COP decreases with increase in condenser temperature. Hence the value of 𝜂𝑒𝑥 decreases with increase in Tc, DSC = Tc, SC. It can also be observed that the value of 𝜂𝑒𝑥 is maximum for R1234ze and minimum for R1234yf.

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(c) (d) Figure 6. (a) Variation in compressor work (𝑊̇𝐶 ) with condenser temperature (T c), (b) effect of condenser temperature (Te,DSC) on COP, (c) Effect of condenser temperature (Tc) on exergetic efficiency (ηex), (d) Variation in total exergy destruction rate (𝐸̇𝐷,𝑇𝑜𝑡𝑎𝑙 ) and exergy destruction ratio (EDR) with condenser temperature (Tc) Figure 6(d) depicts the effect of condenser temperature (T c, DSC = Tc, SC) on total exergy destruction rate ̇ (𝐸𝐷,𝑇𝑜𝑡𝑎𝑙 ) and exergy destruction ratio (EDR) of DSC, OC and SVCR cycles. The value of 𝐸̇𝐷, 𝑇𝑜𝑡𝑎𝑙 and EDR increases with increase in Tc, DSC = Tc, SC. As the condenser temperature increases, the exergy destruction rate in system components increases as well as the exergy of products (|Q̇ e,DSC (1 −

value of COP decreases (Figure 6(b)). Hence the total exergy destruction rate and EDR increase with increase in Tc, DSC = Tc, SC. It has been seen that the value of 𝐸̇𝐷, 𝑇𝑜𝑡𝑎𝑙 and EDR is minimum for R134a and maximum for R1234yf.

Conclusions

The current work presents the energy and exergy analysis of dedicated mechanically sub-cooled vapour compression refrigeration cycle (DSC). The comparison of DSC, overall cycle (OC), sub-cooler cycle (SC) and simple vapour compression refrigeration cycle (SVCR) has also been considered for R134a, R1234ya and R1234ze using a computer software based program in EES. The theoretical performance analysis involves the variation of DOS, evaporator temperature and condenser temperature to check the performance parameters viz. compressor work, COP, exergetic efficiency, and total exergy destruction rate and exergy destruction ratio. The main concluding points of the current work are as follows:  The COP of dedicated mechanically sub-cooled VCR cycle (DSC) and overall cycle (OC) is higher than the simple VCR cycle.

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 The optimum value of DOS lies between 20 0C to 250C for which 𝑊̇𝐶 , COP and 𝜂𝑒𝑥 are maximum in OC.  The COP of OC improves while 𝜂𝑒𝑥 goes down with increase in evaporator temperature.  The high condenser temperature reduces the performance (COP and𝜂𝑒𝑥 ) of the cycle.  Higher condenser temperature promotes exergy destruction while exergy destruction reduces for lower values of evaporator temperature. The optimum value of DOS lies between 20 0C to 250C.  The performance of R1234ze is better than R1234yf and comparable to R134a.  Finally, it is inferred that the dedicated mechanically sub-cooled VCR cycle performs better than that of simple VCR cycle and the performance of HFO R1234ze is better than R1234yf.

Nomenclature

COMP Compressor Cond Condenser COP Coefficient of performance DOS Degree of sub-cooling DSC Dedicated mechanically sub-cooled VCR cycle (∆T)sc Degree of subcooling ĖD Exergy destruction rate (kW) ED Exergy destruction EDR Exergy destruction ratio EES Energy equation solver Ė Rate of exergy (kW) E.V. Expansion valve GWP Global warming potential h Specific enthalpy (kJ/kg) HFC Hydrofluorocarbon HFO Hydrofluoroolefin 𝑚̇𝑟 Mass flow rate of refrigerant (kg/s) ODP Ozone depleting potential P Pressure (kappa) SVCR Simple vapour compression refrigeration 𝑄̇𝑒 Rate of net refrigerating effect (kW) s Specific entropy (kJ/kg0C) T Temperature (0C) Tb Boundary temperature (0C) Te Evaporator temperature (0C) T0 Dead state temperature (0C) VCR Vapour compression refrigeration ̇ 𝑊 Work rate (kW) ε Effectiveness 𝜂 Efficiency Ʃ represents summation 0 Dead state C Condenser Comp Compressor Cond Condenser e Evaporator ex Exergetic SC Su-cooling cycle OC Overall cycle i Input o Output

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