An application of conventional and advanced exergy approaches on a R41/R1233ZD(E) cascade refrigeration system under optimum conditions

Painstaking adjustment of an optimum low-temperature cycle (LTC) condenser temperature allows cascade refrigeration system (CRS) to operate at maximum performance. This study exhibits an original approach because, for the first time, advanced exergy analysis is implemented under an optimum LTC condenser temperature of CRS operating with R41/R1233zd(E) as an environmentally-friendly refrigerant pair. Under the auspices of advanced exergy analysis, there is endogenous exergy destruction of 50.43% and exogenous exergy destruction of 49.57% within total exergy destruction. It is pointed out that the interactions between the CRS components (external irreversibilities) are partly less than exergy destruction that occurs within components (internal irreversibilities). The avoidable part within total exergy destruction, which is greater than the unavoidable part, indicates that components have a high improvement potential with a value of 56.31%. Furthermore, LTC compressor depends significantly on other components, as it has the largest exogenous part of exergy destruction with 75.82%. The results indicate that the CRS’s exergy efficiency, which can be determined based on conventional exergy analysis, is only 36%. However, this increases to 68% with the improvements needed for the components. Cite this article as: Cenker A, Servet G H. An application of conventional and advanced exergy approaches on a R41/R1233ZD(E) cascade refrigeration system under optimum conditions. J Ther Eng 2022;8(2):182–201. Journal of Thermal Engineering Web page info: https://jten.yildiz.edu.tr DOI: 10.18186/thermal.1080196


INTRODUCTION
Refrigeration is a prerequisite for human comfort, peace and health, and it is also vital to industrial processes, electronic devices and applications in food preservation [1]. Refrigeration systems are increasingly demanding more energy, a situation that introduces numerous ecological challenges, such as global warming [2]. The use of refrigerants with high Global Warming Potential (GWP) and Ozone Depletion Potential (ODP), which contribute cardinally to global warming and thereby affect people's health, has become an attention-grabbing issue. Some restrictions and prohibitions on the use of refrigerants have been introduced through decisions made due to international agreements and policies, such as the F-gas Regulation, the Kyoto Protocol, the Montreal Protocol and the Paris Agreement [3]. Chlorofluorocarbons (CFCs), a part of the most common first-generation refrigerant group and among the substances that destroy the ozone layer, were the first prohibited refrigerants [4,5]. Hydrochlorofluorocarbons (HCFCs), which are identified as second-generation refrigerants, have a wide range of uses. Still, since they contain chlorine atoms (as do the CFCs), they destroy the stratospheric ozone due to a high GWP and an ODP higher than zero [6]. It is intended to completely ban the use, production and import of all the refrigerants in this class by 2030 [7]. Hydrofluorocarbons (HFCs), which are categorised as third-generation refrigerants and cause less environmental anxiety than the previous generations of refrigerants, currently have an extensive range of utilisation. Nevertheless, the Kigali amendment to the Montreal Protocol has led to the gradual reduction of traditional HFC refrigerants with high GWP [8]. Hydrofluoro-olefins (HFOs), which have emerged as the fourth-or next-generation refrigerants, have very low GWP and zero ODP values and therefore have little or no undesirable impact on the environment [9,10]. With these considerations in mind, new studies are examining refrigerants in the HFO-class to promote environmental sustainability [11][12][13][14][15].
Five different approaches in reliance on the application of advanced exergy analysis have been reported by Ref. [16]. These five approaches include: (1) the engineering method, (2) the thermodynamic cycle method, (3) the structural theory method, (4) the exergy balance method and (5) the equivalent components method. The thermodynamic cycle method for advanced exergy analysis is the most convenient and produces the best results for different cases (ideal, real and unavoidable) where a thermodynamic cycle can be defined [17]. Despite numerous papers considering the advantages of conventional exergy analysis, the mutual interdependencies present in the system components are beyond the scope of conventional exergy analysis; such methods are unable to evaluate the real potential for improving the components. In the thermodynamic cycle method for advanced exergy analysis, it is possible to do this because the destruction of each component's exergy is split into avoidable/unavoidable and endogenous/exogenous parts [18]. Such splitting approaches enable the designer and operator of an energy conversion system to identify efficiency optimisation strategies. Not only is the accuracy of exergy analysis promoted by this splitting, but this method also enhances the understanding of how thermodynamic inefficiencies occur, as well as offering opportunities to analyse exergybased performance concerning exergo-economic and exergo-environmental factors [19,20].
Looking deeply into the open literature, the adoption of advanced exergy approach, particularly in the analysis of ejector -based refrigeration systems and absorption refrigeration systems, has attracted a great deal of attention. A summary of the studies carried out in the field of refrigeration is given in Table 1.
In this study, R41, which is considered appropriate for use at low temperatures and recommended, is used. R1233zd (E), which is one of the new generation refrigerants, is recommended for HTC. This refrigerant has no explosive and flammable properties. Thus, the combination of R41/R1233zd(E) is proposed to perform advanced exergy analysis of the CRS. There is only one study in the literature on advanced exergy analysis of the CRS conducted by Gholamian et al. [35]. They used R744 in the lowtemperature cycle (LTC) and R717 in the high-temperature cycle (HTC). However, they did not care about optimum LTC temperatures. Determining a LTC condenser temperature, which is a crucial indicator for achieving the best performance from the standpoint of energy-and exergybased parameters is necessary because it plays a pivotal role in the operation of the CRSs. This study is the first which focuses on finding an optimum LTC condenser temperature for ideal, real and unavoidable thermodynamic cycles before splitting the exergy destruction into avoidable/ unavoidable and endogenous/exogenous parts of the CRS. The main aim of using the advanced exergy approach by splitting exergy destruction into various parts is to procure more detailed knowledge regarding the levels of interaction (endogenous/exogenous) among the components, to identify the improving potential of the system (avoidable/ unavoidable), and to give conceivable suggestions aimed at enhancing the system efficiency.

CYCLE DESCRIPTION
The CRS is a refrigeration system that is widely used in applications where low temperature is required, consisting of two vapour-compression refrigeration systems connected with a cascade heat exchanger or cascade condenser, where R41 (fluoromethane) [53] is used in LTC for cooling, and R1233zd(E) (trans-1-Chloro-3,3,3-trifluoropropene) [54]

R744
The dominantly endogenous part of the system's exergy destruction should be recognised, and it is possible to improve the system components to avoid 43.44% of total exergy destruction.

Chen et al. [47]
Ejector refrigeration R245fa Ejector, generator and condenser should be taken into consideration to increase the performance of the overall system.

Morosuk and
Tsatsaronis [48] Vapor-compression refrigeration is utilised in the high-temperature cycle (HTC) to condense the refrigerant circulating in LTC. The working principle of the CRSs is the same with single-stage vapour compression refrigeration systems except for one difference. This difference is the cascade heat exchanger, a compact component that acts as an evaporator in LTC and a condenser in HTC. It is assumed that the cascade heat exchanger is well-insulated [55]; therefore, the heat delivered by the R41 in LTC is equal to the heat received by the R1233zd(E) in HTC. A schematic diagram represented by the subcritical CRS  is depicted in Figure 1. The thermo-physical, environmental and safety properties of the refrigerants, as mentioned above, are listed in Table 2 [12,27,34,56].

ASSUMPTIONS MADE IN THE ANALYSIS
The analysis of the CRS can be simplified based on suppositions found in the literature [14,21,27,34,35]. These simplifications are as follows: • Heat losses and pressure drops in connection pipes and system components are not taken into account. • All components of the CRS are considered to be a steady-state and steady-flow process. • The reference state (dead state) is the ambient temperature (T 0 ) of 25 o C and pressure (P 0 ) of 101.325 kPa.

DETERMINATION OF THE CRS PARAMETERS
Advanced exergy analysis requires assumptions for real, ideal and unavoidable cycles. The operating parameters of the real cycle are given in Table 3 [12,[34][35][36]. Table 4 presents the real, ideal and unavoidable conditions for each CRS component, as suggested by Ref. [35,61]. The real and unavoidable conditions are used to find the avoidable/ unavoidable parts in the advanced exergy analysis. The real and ideal conditions are used to find the endogenous/exogenous parts. The unavoidable cycle conditions are between real and ideal conditions.

METHODOLOGY
Conventional and advanced exergy analyses are undertaken to assess the CRS under an optimum LTC condenser temperature for thermodynamic analysis. The equations used for these computations are presented in the following sub-sections.

ENERGY TERMS
The input and output conditions underpinning many engineering systems' operation stay unchanged for lengthy intervals. This is exemplified by the elements of a refrigeration system (e.g. condenser, evaporator, throttle valve, compressor), which are operational for extensive periods before system maintenance.  The temperature difference in CHX, ΔT 5°C P r refers to compressor compression ratios in LTC and HTC.  A throttling process is always irreversible for real and unavoidable cycles; consequently, a throttling valve is assumed to be replaced by an isentropic expander for an ideal cycle [17,18,20]. and its components, the mass and energy balance equations are also illustrated in Table 5 [58].

EXERGY TERMS
The term exergy denotes the potential that an available amount of energy can be converted into work [59]. The computation of this potential depends on environmental and energy conditions and is an expression of the highest amount of work that can be obtained. The lost work potential during a process change is defined as irreversibility or exergy destruction. The less the exergy destruction during a process change, the more the work produced or, the less the work consumed [60]. Analysis of conventional exergy denotes a thermodynamic analysis whose foundation is the second law, facilitating a significant and realistic assessment and comparison of state changes and energy systems. Exergy balance for any control volume at steady state is obtained by Eq. (3) [61].
The total exergy of a system without magnetic, electrical, nuclear and surface tension effects is expressed by Ė. Exergy is divided into four groups as chemical exergy Ė CH , physical exergy Ė PH , kinetic exergy Ė KE and potential exergy Ė PE , as indicated in Eq. (4) [61]. The total exergy of the refrigerant flow for the unit mass can be obtained by Eq. (5) [61]. In this study, chemical exergy has a null value in the present work because the modelled CRS system is free of a chemical reaction. The assumption is that there are insignificant changes in the system kinetic and potential exergy. Consequently, Eq. (6) [35] helps to determine the flow of physical exergy associated with the unit mass. The exergy balance equations of components of the CRS are also illustrated in Table 6 [34,58], while the other performance parameters are found by Eqs. (4)-(6) [17,19,36,39,40,47,62].
The conventional exergy efficiency of the overall system is obtained by Eq. (7).  to improve an overall system relying on combining these parts, and advanced exergy analysis offers a more robust foundation for exergo-environmental and exergo-economic investigations [48]. It is possible to introduce specific enhancements to safeguard against structural modifications from a component of the exergy destruction of a system or the components' efficiency. The exergy destruction can be avoided via either operational enhancements or technical designs (or a combination of the two). It is regarded as an avoidable part of the exergy destruction (Ė AV D,k ). The amount of Ė AV D,k for the k th the component plays a significant role in determining the improvement steps and predicting the improvement potential of a system. The exergy destruction associated with physical, economic and technological constraints is considered as an unavoidable part of the exergy destruction of the k th component (Ė UN D,k ), even if the best technology is applied. Thus, the exergy destruction can be split into avoidable and unavoidable parts, as seen in Eq. (10) [18,39,64].
The formation of the exergy destruction caused by the component itself is called endogenous part of the exergy destruction (Ė EN D,k ), whereas exogenous part of the exergy destruction is the exergy destruction that results from the relationship of the examined component with the other components (Ė EX D,k ). Total of Ė EN D,k and Ė EX D,k gives the exergy destruction of the real process, as indicated in Eq. (11) [18, 19,36,39,65].
Division of exergy destruction by the overall fuel exergy associated with the system, on the whole, is calculated by Eq. (8).
The exergy destruction proportion in the k th components in the overall exergy destruction is found by Eq. (9).

ADVANCED EXERGY ANALYSIS
Even though conventional exergy analysis is a productive approach in pinpointing the causes, locations, and magnitudes of particular types of irreversibility [63], key limitations include the inability to identify confounding effects (e.g., the impact of interactions between components in a system), the failure to identify root causes of exergy destructions that take place in equipment, and the absence of improvement possibilities for equipment. In complex systems, particularly those containing multiple interacting elements, these interactions must often be considered to facilitate system optimisation under conventional exergy analysis [36]. Contrastingly, advanced exergy analysis accounts for these limitations, thus illuminating thermodynamic systems from a novel vantage point. This procedure splits exergy destruction into multiple parts, comprising avoidable-unavoidable and endogenous-exogenous exergy destructions. Designers can determine how In comparison to conventional energy analysis, advanced energy analysis is a more complicated process. This can be facilitated by creating a solution procedure flow chart in Figure 2 to make it possible to follow the CRS analysis, as inspired by Ref. [40].

SIMULATION RESULTS AND DISCUSSION
In this study, a CRS, a system capable of meeting lowtemperature refrigeration requirements with a refrigeration capacity of 1 kW, is used to conduct advanced exergy analysis. Referring to Table 2, R41 in LTC and R1233zd(E) in HTC are selected because both refrigerants cause minimum environmental damage and do not contribute to ozone destruction. Before the advanced exergy analysis approach, energy and exergy-based thermodynamic analyses are conducted to obtain prior knowledge regarding the system investigated. For all the computations, Thermopy library is used in Python programming platform (version 3.7.4).

MODEL VALIDATION OF THE SIMULATION
The present model of this study is compared with the existing models in the literature. This is carried out to test how accurate the computer code that is developed for simulations of analyses. Figure 3 shows that the analysis results of R170-R161 CRS by Ref. [34] are compared with those of this study under the same working conditions (T cond = 40°C, T ev = −40°C, ΔT = 5°C). The results show that the COP values found by Ref. [34] and by this study are in good agreement, with a difference of approximately 0.003%. Figure  4 presents that comparison of this study's model with the reference model of Ref. [27] is made in terms of exergy efficiency with varying evaporator temperatures for R41/ R404A under the same working conditions (T ev = −45°C, T cond = 40°C, ΔT = 5°C). The deviation between the two compared models is at a minimum level, a difference of only 0.02%.

IDENTIFICATION OF AN OPTIMAL LTC CONDENSER TEMPERATURE FOR EACH CYCLE
An optimum LTC condenser temperature is perhaps the most crucial operating parameter. The determination of an optimum LTC condenser temperature under all ideal, real and unavoidable conditions indicates that the CRS can operate at maximum performance. Therefore, Figure   Technological and economic limitations determine the minimum value of the exergy destruction. The unavoidable part of the exergy destruction of the k th component is calculated by considering each component separated from the system. The exergy destruction rate per unit product exergy (Ė D /Ė P ) UN k is calculated by assuming that the component of a system operates under high efficiency and low losses. The unavoidable part of the exergy destruction of the k th component can be explained in Eq. (12), including the product exergy rate of the real process [18, 19,36,39].
If the unavoidable part of the exergy destruction of the k th component is well-known, the avoidable part of the exergy destruction is obtained by Eq. (13) [40].
The unavoidable part of the exergy destruction of the k th component calculated by the advanced exergy analysis method is split into endogenous and exogenous parts, which are then split into unavoidable-endogenous in Eq. (14), unavoidable-exogenous in Eq. (15), avoidableendogenous in Eq. (16) and avoidable-exogenous in Eq. (17) of the exergy destruction of the k th component [16]. ,EX ) part of the exergy destruction of the k th component can be reduced by improving the structure of the overall system, the efficiency of the other components and the efficiency of the k th component [16, 19, 36, Figure 5a) and 56.57% (Figure 5b) at an LTC condenser temperature of -12 o C, respectively. The efficiency based on the CRS's energy and exergy cannot theoretically exceed COP of 2.165 ( Figure 5a) and exergy efficiency of 76.07% (Figure 5b), respectively, at a LTC condenser temperature of -21.

RESULTS OF THE ENERGY AND CONVENTIONAL EXERGY ANALYSIS
Energy (the first law of thermodynamics) and conventional exergy analyses, which have been widely adopted before applying the advanced exergy approach, are considered first. In this regard, the thermodynamic performance values of the CRS, which operate under ideal, real and unavoidable conditions, are computed based on energy and conventional exergy approaches. Tables 7-9 outlines each stage's thermodynamic properties in the CRS for real, ideal and unavoidable operating conditions, respectively. In the light of the main data required for the CRS specified in Table 4, real, ideal and unavoidable conditions are     The condenser is supposed here to be a productive component. The condensation process heat is released into the environment for each cycle (Tables 10-12), then Ė L,tot = Ė P,cond (Table 6). However, the condenser is a dissipative component without exergy of product or exergy efficiency. The product value is determined to make it easier to conduct advanced exergy analysis [36]. Tables 7-9 depict the exergy values at each CRS point. Advanced exergy analysis is mediated by ideal, real, and unavoidable cycles, so the calculation of exergy destruction in each of these cycles is conducted for all CRS components. The values at points 11 and 12 in Tables 7-9, the overall system exergy of the product (Ė P,tot = Ė P,ev ) does not fluctuate, so the mass flow rates associated with the secondary working fluid for the evaporator are identical, which can also be derived from the fixed refrigeration capacity, as reported by Ref.

calculated. The last two columns in
[47]. The conventional exergy analysis results for each component are given in Tables 10-12. The exergy destruction  to boost the performance of the CRS. However, it is impossible to determine whether irreversibilities originate from other components or the components themselves because conventional exergy destruction cannot give us an idea of what these irreversibilities cause. The reason is that elimination of these restrictive factors can only be achieved through an advanced exergy approach. ,EX ) for advanced exergy analysis. Information can be obtained about how much of the exergy destruction that occurs from the component's internal irreversibility and/or the component's interaction as the external irreversibility can be avoided or unavoided. As can be seen from both Table 13 and Figures 6-12, the Ė EN D,k of the evaporator (0.0480 kW or 100%), HTC throttle valve (0.0536 kW or 88%), and condenser (0.0574 kW or 70.82%) and cascade condenser (0.0538 kW or 51.26%) is greater than the Ė EX D,k of the other components of the CRS (Ė EN D,k > Ė EX D,k ). All of the evaporator's exergy destruction takes place in the endogenous part so that the irreversibility for this component only results from the component itself; therefore, there is no exergy destruction in the exogenous part of this component. It should be pointed out that in Table 13 that Ė EX D,k of the LTC compressor (0.09 kW or 75.81%), LTC throttle valve (0.045 kW or 67.19%) and HTC compressor (0.0843 kW or 66.02%) are much greater than the Ė EN D,k , so the exergy destruction of these components is dependent to a great extent on other components of the CRS, which means that improvements in the other system components can reduce the Ė EX D,k of the mentioned components, increasing the efficiency of the CRS.

RESULTS OF THE ADVANCED EXERGY ANALYSIS
It is worth noting from both  [61]. It can be inferred from Table 13 and          Table   13 is the modified exergy efficiency calculated by Eq. (22). Consequently, the exergy efficiency of the CRS leaps from 36 to 68% with necessary improvements required to the components of the CRS.

CONCLUSION
Conventional exergy analysis can quantitatively identify inefficiencies in an energy system. Although it is a newer approach, advanced exergy analysis can specify the origins of irreversibilities and real improvement potential. In this paper, an advanced exergy approach is applied in conjunction with a conventional exergy analysis to examine the exergy performance of the R41/R1233zd(E) CRS analysed in line with an optimum LTC condenser temperature. The far-reaching implications obtained are listed as follows: 1. The most critical CRS components in the conventional exergy analysis are the HTC compressor, followed by the LTC compressor and cascade condenser, suggesting that the three components should be given the highest priority in optimising the CRS performance. Conversely, the advanced exergy analysis suggests that LTC compressor, HTC compressor, and cascade condenser prioritise improvement due to their high avoidable exergy destruction rates.
2. The CRS's total exergy destruction accounts for the endogenous part of 50.43% and the exogenous part of 49.57%, meaning that interactions between the CRS components remain somewhat lower.

The LTC compressor is the most dependent on
other components of the CRS since it is the component with the most significant exogenous part of the exergy destruction (0.09 kW or 75.82%).

5.
The avoidable part of the total exergy destruction is 56.31%, which is slightly more significant than the unavoidable part, meaning that component improvements have high potential to improve the CRS performance.
6. The maximum improvement potentials of LTC compressor and HTC compressor are more significant compared to other components of the CRS because their avoidable exergy destruction rates are 0.0992 kW (83.57%) and 0.0989 kW (77.45%). In contrast, their endogenous-avoidable exergy destruction rates are 0.0240 kW (20.22%) and 0.0336 kW (26.31%), respectively.

7.
The HTC throttle valve's inefficiencies, condenser and evaporator are mainly stemmed from the components themselves (internal irreversibility), thereby possessing the high endogenous exergy destruction.
8. The exergy efficiency of the CRS, which is calculated in the conventional exergy analysis, remains at only 36%, while the improvements required for the components soar the exergy efficiency of the CRS to approximately 68%.

9.
Advanced exergy approach exhibits a more robust foundation than the conventional exergy approach for exergo-environmental and exergo-economic investigations; therefore, it is vital to make such investigations for the future studies using the refrigerants that harm the least environment.

ACKNOWLEDGEMENT
Cenker Aktemur is a PhD scholarship holder from the Council of Higher Education (YÖK) in the field of Renewable Energy and Energy Storage, which is one of the 100 national priority areas determined by YÖK within the scope of the 100/2000 Program.

AUTHORSHIP CONTRIBUTIONS
Authors equally contributed to this work.

DATA AVAILABILITY STATEMENT
The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

CONFLICT OF INTEREST
The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

ETHICS
There are no ethical issues with the publication of this manuscript.