Application and discussion on entransy analysis of ammonia/salt absorption heat pump systems

This study investigates the application of the entransy analysis in ammonia/salt absorption heat pump (AHP) systems. The results of the entransy analysis are compared with those of energy analysis and exergy analysis under typical and various operating conditions. Entransy dissipation and exergy loss in each component, as well as coefficient of performance (COP), exergy efficiency and entransy efficiency of systems, are discussed. The changing trends of entransy dissipation in each component are similar under various operating conditions. However, the entransy analysis performs better than the exergy analysis in evaluating the irreversible loss of each component. Moreover, the differences between the exergy analysis and entransy analysis are mainly in absorber, generator and SHE. Especially in the NH 3 /NaSCN system, the proportion of entransy dissipation in generator is 60.8%, which is almost twice of the proportion of exergy loss (34.9%). In addition, under various operating conditions, entransy efficiency and COP have roughly the same changing trend. Meanwhile, entransy efficiency is more reasonable than exergy efficiency in evaluating the performance of systems under the absorption temperature, which varies from 30 ◦ C to 50 ◦ C. These comparison results demonstrate that the entransy analysis is appropriate to evaluate the performance of ammonia/salt AHP systems and suitable for analyzing the irreversibility of each component.


INTRODUCTION
In recent years, absorption heat pump (AHP) has gained great interest. Compared with the conventional vapor compression heat pumps, the AHPs consume less electricity power and can utilize low-grade thermal energy from geothermal, solar and biomass energy sources [1,2]. In addition, AHP has the advantage of better-friendly economy and environment [3].
The H 2 O/LiBr and NH 3 /H 2 O are the most common used solutions in AHPs; however, some drawbacks of the solutions limit the application of absorption systems [4][5][6]. For example, the crystallization possibility and high freezing point of the H 2 O/LiBr solution, as well as the complex and costly rectifier of the NH 3 /H 2 O system. Besides, NH 3 /LiNO 3 and NH 3 /NaSCN are considered as substitutes for NH 3 /H 2 O [7,8]. Compared to NH 3 /H 2 O absorption system, NH 3 /LiNO 3 and NH 3 /NaSCN absorption systems avoid rectification equipment and have relatively high coefficient of performance (COP) [9].
Many efforts have been devoted to investigate on the NH 3 /LiNO 3 and NH 3 /NaSCN absorption systems using the energy analysis and exergy analysis. Sun [9] performed the energy analysis for NH 3 /H 2 O, NH 3 /LiNO 3 and NH 3 /NaSCN single-effect absorption systems and concluded that NH 3 /salt systems perform better than the NH 3 /H 2 O system. Zhu and Gu [10,11] carried out the energy analysis and exergy analysis on the NH 3 /NaSCN absorption system. Farshi et al. [7] presented the energy analysis and exergy analysis of NH 3 /LiNO 3 and NH 3 /NaSCN absorption systems, concluding that the possibility of crystallization will be increased by higher generation temperatures. Cai et al. [12,13] improved the exergy analysis method for the NH 3 /LiNO 3 and NH 3 /NaSCN absorption refrigeration systems. Pandya et al. [14] evaluated the thermodynamic performance and optimal parameters of ammonia/salt absorption cooling system. However, the exergy analysis is used to analyze the irreversibility of AHP system from the perspective of heat-work conversion [15]. In the AHP system, the central irreversible loss is caused by the heat and mass transfer process between the internal working solution and external fluid. The concept of entransy dissipation proposed by Guo et al. [16] can represent the irreversibility, which is caused by the heat and mass transfer process. Chen et al. [17] confirmed that entransy dissipation is appropriate for measuring the irreversibility of the system in the heat transfer process. Zhang et al. [18] carried out the entransy analysis in the optimization of HVAC systems. Moreover, Wang et al. [19] used the entransy analysis to propose the optimization design of an absorption temperature transformer. Li [20] introduced the entransy dissipation method into the analysis of the internal heat and mass transfer of the absorber and obtained the approach and guiding principles for optimizing the thermodynamic performance of the absorber. Zhang et al. [21] conducted the concept of concentration entransy in the entransy analysis of absorption systems and established entransy dissipation calculation model of the H 2 O/LiBr absorption system. Above all, compared to the energy analysis and exergy analysis, the entransy analysis method can accurately identify the irreversibility caused by heat and mass transfer of each component in absorption systems. Thus, the information of the entransy analysis indicates the effective direction to improve the performance of absorption systems.
In reviewing the literature, it can be found that the previous studies on NH 3 /LiNO 3 and NH 3 /NaSCN absorption systems mainly used the methods of the energy analysis and exergy analysis. However, few studies have focused on utilizing the method of the entransy analysis in NH 3 /salt AHP systems. Thus, in this study, the entransy analysis is proposed to investigate and evaluate the performance of the NH 3 /salt AHP systems under typical and various operating conditions. Moreover, the results of the entransy analysis are compared with those of the energy analysis and exergy analysis. In detail, exergy loss and entransy dissipation of each component, as well as COP, exergy efficiency and entransy efficiency of systems under typical and various operating conditions, are evaluated.

System description
Before discussion on the entransy analysis of the NH 3 /salt AHP systems, it is important to address detailed information on the components and working pairs of the single-effect AHP system. As given in Figure 1, the single-effect AHP system is mainly consisted by a generator, condenser, evaporator, absorber, solution heat exchange (SHE), refrigerant throttle valve (RTV), pump and solution throttle valves (STV). The generator is driven by the high-temperature heat source, where the NH 3 vapor (state 7) is generated from the weak solution (state 3). The strong solution (state 4) passes the SHE (state 5), gets throttled by the STV (state 6) and then enters the absorber absorbing the NH 3 vapor (state 10) from the evaporator. The weak solution (state 1) is pumped by the pump (state 2) and passes the SHE (state 3) before entering the generator. The NH 3 vapor (state 7) generated in the generator goes through the condenser to be condensed into liquid NH 3 (state 8) and subsequently gets throttled by the RTV (state 9). Then, the refrigerant vaporizes in the evaporator (state 10).
Additionally, as depicted by state 1 to state 6 in Figure 1, the AHP system also includes the solution circle. For the NH 3 /salt AHP systems, the solution circle employs two different working pairs, which are NH 3 /LiNO 3 and NH 3 /NaSCN. The thermophysical properties of the two working pairs are obtained from Libotean et al. [22,23], Chaudhari et al. [24] and Farshi et al. [7,25]. Meanwhile, in this work, the crystallization concentrations of NH 3 /LiNO 3 and NH 3 /NaSCN in different operating conditions have also been considered. Detailed crystallization concentration equations can be found in Wu et al. [6] and Ferreira [26].

Thermodynamic analysis
In the following section, the equations of the energy analysis, exergy analysis and entransy analysis are applied to the overall components of the system. Moreover, in order to simplify the thermodynamic analysis, some reasonable assumptions are made as follow [27,28]: (1) The whole system is operated under steady state conditions.
(2) The heat loss and pressure loss are neglected.
(3) The refrigerants are saturated at the outlet of the condenser and evaporator.
(4) The solutions are under the phase equilibrium condition at the outlet of the generator and absorber.

Energy analysis and exergy analysis
The energy analysis of the single-effect AHP system is based on the first law of thermodynamics. The basic principles of the first law of thermodynamics are the conservation of mass and energy, as given in equations (1) to (3) The COP of the single-effect AHP system is defined as follows: The solution circulation ratio is defined as follows: where the subscripts w and s represent the weak and strong refrigerant solutions, respectively. The energy analysis detailed above provides quantitative results of the single-effect AHP system. However, the exergy analysis is capable of identifying and quantifying the exergy and exergy loss of components in the single-effect AHP system. Exergy is the maximum theoretical useful work received from energy under the environment. The specific exergy of each stream and the exergy loss of each component are given in equations (6) and (7), respectively.
The exergy loss of each component can be written as The overall exergy loss of the single-effect AHP system is the sum of all components, as given in equation (8): The efficiency of the second law of thermodynamics for the single-effect AHP system can be evaluated by the exergy efficiency. The exergy efficiency (η e ) indicates the ratio of the output hot water exergy in absorber and condenser to the input driving exergy in generator, which is detailed in equation (9):

Entransy analysis
In addition to the energy analysis and exergy analysis, the entransy analysis is also employed to evaluate the performance of absorption systems. Entransy is a physical quantity that represents the heat transfer ability of an object [16]. The entransy dissipation can be expressed as follows: In absorption system, the entransy dissipation can also be expressed as follows: (11)where G w is the variation in the external water entransy, G x is the variation in the solution concentration entransy, G s is the variation in the solution heat entransy and G v is the variation in the vapor entransy.
It is worth noting that the changes in solution concentration entransy and solution heat entransy are not included in condenser and evaporator. Meanwhile, the solution heat entransy is the only parameter considered in SHE. The entransy dissipation calculation model of the single-effect absorption system can be found in the previous investigation [21].
The overall entransy dissipation of the single-effect AHP system is the sum of all components: The entransy efficiency of the single-effect AHP system is defined as follows: where T a , T c and T g are the absorption temperature, condensation temperature and generation temperature during system operation, respectively.

Model validation
For the purpose of verifying the accuracy of the single-effect NH 3 /salt AHP model, the simulation results are validated by comparing with the results reported by Farshi et al. [7], as shown in Table 1. It can be seen that, under the same operating conditions, the simulation results of the proposed model show good International Journal of Low-Carbon Technologies 2021, 00, 1-10 3 Table 1. Comparison between simulation results from Farshi et al. [ 7 ] and this work.

RESULTS AND DISCUSSIONS
In this section, the entransy analysis in NH 3 /salt AHP systems has been investigated and evaluated under typical and various operating conditions. Meanwhile, the obtained results of entransy analysis have been compared with those of the energy analysis and exergy analysis. Detailed results and discussions are given in Sections 3.1 and 3.2.

Typical operating conditions
Under typical operating conditions, the operating parameters of the systems are listed in Table 2. The inlet/outlet temperatures of the high-temperature water used in generator are 125/115 • C. The returned water from the users flowing through absorber and condenser in series and the low-temperature water used in evaporator are 35/45 • C and 17/12 • C, respectively. The operating parameters are specified according to the application in floor heating [8]. By employing the parameters listed in Table 1, the simulated results of NH 3 /salt AHP systems have been given in Table 3. The concentration difference between the weak and strong solutions demonstrates that the solution circulation ratio of the NH 3 /LiNO 3 system is lower than that of the NH 3 /NaSCN system. However, COP of the NH 3 /NaSCN system (1.592) is higher than that of the NH 3 /LiNO 3 system (1.544). This result can be explained by the fact that exergy loss and entransy dissipation of the NH 3 /NaSCN system are lower than those of the NH 3 /LiNO 3 system. Meanwhile, exergy efficiency and entransy efficiency of the NH 3 /NaSCN system are also higher than those of the NH 3 /LiNO 3 system.
For the purpose of comparing the exergy analysis and entransy analysis under typical operating conditions, the statistic results of exergy loss and entransy dissipation for each component have been shown in Figure 2. The column figure indicates that the generator plays a main role in irreversible losses of NH 3 /salt AHP systems, either for exergy loss or entransy dissipation. Meanwhile, the proportions of exergy loss and entransy dissipation in evaporator are the lowest in the overall system, as can be observed from Figure 2. The proportions of exergy loss in absorber and condenser are almost equal to those of the entransy dissipation. The similar results of the NH 3 /LiNO 3 system and NH 3 /NaSCN system further verify the reliability of the entransy analysis in NH 3 /salt AHP systems. However, the differences between exergy loss and entransy dissipation can also be found. Specifically, for NH 3 /NaSCN system, exergy loss in SHE is as large as 29.7%, while entransy dissipation is only 15.8%. Although the proportions of exergy loss and entransy dissipation in generator are the largest, the dramatic distinctions between the values of exergy loss and entransy dissipation still exist. In the NH 3 /NaSCN system, the proportion of entransy dissipation (60.8%) in the generator is almost twice that of exergy loss (34.9%).
The entransy dissipation analysis can distinguish the irreversible losses caused by heat and mass transfer in each component of absorption systems. Table 4 lists the specific irreversible losses in each component of NH 3 /salt AHP systems using entransy dissipation analysis. As can be seen in Table 4, the  variations in the external water entransy and solution concentration entransy are greatly in absorber. In generator, the variation of external water entransy is the greatest (−7731.3 kW·K for NH 3 /LiNO 3 system, −7469.6 kW·K for NH 3 /NaSCN system) due to the large temperature difference between the inlet and outlet of driving hot water. Moreover, entransy dissipation in SHE is large than that in absorber and condenser. In general, larger entransy dissipation means larger irreversible loss. Reducing entransy dissipation of component can improve its performance. Therefore, the information from the entransy dissipation analysis indicates the most effective direction to improve performance of absorption systems. Additionally, it can be seen that the significant difference between the NH 3 /LiNO 3 system and NH 3 /NaSCN system is the variation in the solution heat entransy of absorber (−412.9 kW·K for NH 3 /LiNO 3 system, −131.0 kW·K for NH 3 /NaSCN system). It can be therefore concluded that, under typical operating conditions, the entransy analysis is appropriate in the NH 3 /salt AHP systems. The entransy dissipation method performs better than the exergy loss method in investigating and evaluating the irreversible loss of each component in absorption systems.

Various operating conditions
For the purpose of further evaluating the performance of entransy analysis method in NH 3 /salt AHP systems, it is critical to investigate the entransy dissipation in each component and entransy efficiency of systems under various operating conditions. Therefore, the changes in generation temperature (T g ), absorption (T a ) and condensation (T c = T a + 5) temperatures, as well as evaporation temperature (T e ), are considered. The comparison results among COP, exergy efficiency and entransy efficiency of systems are discussed in this section.

Generation temperature
In order to investigate the performance of the entransy analysis method in NH 3 /salt AHP systems under different generation temperature conditions, the exergy loss analysis and entransy dissipation analysis of NH 3 /salt AHP systems are given in Figures 3  and 4, respectively. As shown in Figure 3, the total exergy loss and total entransy dissipation in NH 3 /LiNO 3 system increase with the increasing of generation temperature. Moreover, the changing trends of exergy loss and entransy dissipation in each component are similar. Specifically, as the generation temperature increases, the growth of exergy loss and entransy dissipation in generator and absorber are faster than those in condenser. The exergy loss and entransy dissipation in evaporator remain almost consistent. However, there are some discrepancies between the values of exergy loss and entransy dissipation in SHE, as can be seen from Figure 3a and b. The exergy loss in SHE in Figure 3a is always higher than that in absorber, but the entransy dissipation in SHE in Figure 3b is gradually lower than that in absorber. Figure 4 shows the exergy loss and entransy dissipation in the NH 3 /NaSCN system under various generation temperature conditions. Similarly, the total exergy loss and total entransy dissipation in the NH 3 /NaSCN system keep rising with the increasing of generation temperature. The changing trends of exergy loss and entransy dissipation in each component are similar. However, the exergy loss in SHE in Figure 4a is larger than that in generator under low generation temperature conditions. The entransy dissipation in SHE in Figure 4b is much lower than that in generator under various generation temperature conditions. The simulation results from Figures 3 and 4 demonstrate that the variations of entransy dissipation and exergy loss in NH 3 /salt AHP systems have the same trend under various generation temperature conditions. However, the values of entransy dissipation and exergy loss have some discrepancies in analyzing the irreversible losses in SHE, especially in the NH 3 /NaSCN system. These results may be related to the selection of the reference state in the exergy loss analysis, which leading to excessive exergy loss in SHX. The entransy dissipation is not related to the reference state and is proportional to local temperature difference [21]. Above all, the entransy analysis based on the transport phenomena is suitable for analyzing the irreversibility of each component in NH 3 /salt AHP systems under various generation temperature conditions. Another aspect, COP, exergy efficiency and entransy efficiency are the key factors in analyzing the performance of NH 3 /salt AHP systems. As can be seen in Figure 5, with the increasing of generation temperature, COP, exergy efficiency and entransy efficiency of both systems increase first and then decrease. Specifically, entransy efficiency and exergy efficiency have the same changing trend. After reaching their maximum values, entransy efficiency and exergy efficiency continue to decrease. However, the value of COP slightly decreases after reaching the maximum. The results can be explained by the fact that the higher generation temperature causes the generator to produce more NH 3 vapor, which increases the concentration difference between the weak and strong solutions and improves the performance of system. This contributes positively to COP, exergy efficiency and entransy efficiency. However, a too high generation temperature may lead to more irreversible losses (shown in Figures 3 and 4), which has a negative impact on COP, exergy efficiency and entransy efficiency. Moreover, the values of COP, exergy efficiency and entransy efficiency reach the maximum when the generation temperature are 117 • C, 96 • C and 102 • C for the NH 3 /LiNO 3 system and 126 • C, 100 • C and 108 • C for the NH 3 /NaSCN system.
It is evident that COP, exergy efficiency and entransy efficiency of the NH 3 /LiNO 3 system are higher than those of the NH 3 /NaSCN system under the generation temperatures lower than 100 • C. Moreover, the possibility of crystallization is also an important problem for NH 3 /salt AHP systems. The mark of 'X' indicates that crystallization may occur here. In general, the crystallization of the working solution is most likely to occur at the entrance of the absorber [6,7]. It can be seen that solution crystallization in the NH 3 /NaSCN system is likely to take place under the generation temperature higher than 136 • C, as shown in Figure 5. The NH 3 /LiNO 3 system will not crystallize under various generation temperature conditions.

Absorption and condensation temperatures
The exergy loss analysis and entransy dissipation analysis of NH 3 /salt AHP systems under various absorption (T a ) and condensation (T c = T a + 5) temperature conditions are given in Figures 6 and 7, respectively. Figure 6 shows that the total exergy loss and total entransy dissipation in NH 3 /LiNO 3 system decrease with the increasing of absorption and condensation temperatures. In addition, the changing trends of exergy loss and entransy dissipation in each component are similar. With the absorption temperature increases from 32 • C to 46 • C, the exergy loss and entransy dissipation in absorber, condenser and evaporator show a downward trend. Exergy loss in generator decreases by 31.3%, while entransy dissipation in generator drops by 16.4%. Exergy loss in SHE increases by 41.4% and entransy dissipation in SHE rises by 51.7%. As shown in Figure 7, the total exergy loss and total entransy dissipation in the NH 3 /NaSCN system decrease with the increasing of absorption and condensation temperatures. The changing trends of exergy loss and entransy dissipation in each component of NH 3 /NaSCN system and NH 3 /LiNO 3 system are similar. However, exergy loss in SHE in Figure 7a is larger than that in generator under high absorption and condensation temperature conditions. Entransy dissipation in SHE in Figure 7b is much lower than that in generator under various absorption and condensation temperature conditions. Those comparison results in Figures 6 and 7 indicate that the total entransy dissipation of NH 3 /salt AHP systems decrease with the increasing of absorption and condensation temperatures. There are some differences between the values of exergy loss and entransy dissipation in generator and SHE under various absorption and condensation temperature conditions, especially in the NH 3 /NaSCN system. Figure 8 shows the variations of COP, exergy efficiency and entransy efficiency with the absorption and condensation temperatures of NH 3 /salt AHP systems. The simulation results reveal that, with the increasing of absorption and condensation temperatures, COP continues to decrease, while exergy efficiency keeps growing. Meanwhile, entransy efficiency slightly increases first and then decrease with the increase of these temperatures. But actually, excessive absorption and condensation temperatures will reduce the performance of absorption systems. As the absorption and condensation temperatures increase, the absorption and condensation pressures become higher, resulting in the deterioration of the separation process in generator and absorption processes in absorber. Under various absorption and condensation temperature conditions, the changing trends of COP, exergy efficiency and entransy efficiency based on different analysis methods have some differences. In addition, the simulation results from Figure 8 also demonstrate that COP and entransy of NH 3 /NaSCN system are higher than those of the NH 3 /LiNO 3 system when the absorption temperature below 48 • C. At the same time, exergy efficiency of NH 3 /NaSCN system is slightly higher than that of the NH 3 /LiNO 3 system. These comparison results in Figure 8 manifest that entransy efficiency is more reasonable than exergy  efficiency in analyzing the performance of NH 3 /salt AHP systems under various absorption and condensation temperature conditions.

Evaporation temperature
The exergy loss analysis and entransy dissipation analysis of NH 3 /salt AHP systems under various evaporation temperature conditions are shown in Figures 9 and 10, respectively. The simulation results of NH 3 /LiNO 3 system in Figure 9 show the total exergy loss increases from 8.65 kW to 9.39 kW and the total entransy dissipation slightly decreases first and then increases with the evaporation temperature increases from 6 • C to 20 • C. Additionally, in Figure 9a, the exergy loss in absorber rises rapidly by 1772.3%. The exergy loss in SHE decreases dramatically by 57.8%. The exergy losses in condenser and generator increase by 12.7% and 5.6%, respectively. In Figure 9b, the entransy dissipation in absorber only increases by 16.5%. Entransy dissipation in SHE decreases by 44.0%. Entransy dissipation in condenser and generator increases by 12.5% and 11.9%, respectively. Furthermore, as shown in Figure 10, the differences between exergy loss and entransy dissipation in NH 3 /NaSCN system can also be found. Specifically, in Figure 10a, exergy loss in generator rises sharply by 55.7%. Exergy loss in SHE is larger than that in generator under low evaporation temperature conditions. In Figure 10b, entransy dissipation in generator only increases by 16.3%, while entransy dissipation in SHE is much lower than that in generator. Moreover, in absorber, with the evaporation temperature increases from 6 • C to 20 • C, exergy loss increases dramatically by 236%, while the entransy dissipation only rises by 25.7%. Above all, we can draw the conclusion that the total entransy dissipation of NH 3 /salt AHP systems decrease with the increasing of evaporation temperature. The changing trends of exergy loss and entransy dissipation in absorber are quite different under various evaporation temperature conditions. Additionally, there are some differences between the values of exergy loss and entransy dissipation in generator and SHE of NH 3 /salt AHP systems.
The variations of COP, exergy efficiency and entransy efficiency with the evaporation temperature of NH 3 /salt AHP systems are given in Figure 11. It can be seen that, with the increase of evaporation temperature, the values of COP, exergy efficiency and entransy efficiency have a tendency to grow slowly. As the evaporation temperature increases, the evaporation pressure becomes higher. Therefore, the absorption process is strengthened, and the solution concentration difference is enlarged. The circulation ratio becomes smaller, which helps to improve performance of absorption systems. In addition, the values of three indicators of the NH 3 /NaSCN system are greater than those of the NH 3 /LiNO 3 system under various evaporation temperature conditions. Hence, it is noted that from the comparison results the entransy efficiency is suitable for investigating the performance of NH 3 /salt AHP systems under various evaporation temperature conditions.

CONCLUSIONS
In this study, the application of entransy analysis in NH 3 /salt AHP systems under typical and various operating conditions is discussed. Moreover, the results of entransy analysis are compared and verified with those of energy analysis and exergy analysis. The main conclusions can be drawn as follows: (1) The entransy dissipation method performs better than the exergy loss method in investigating and evaluating the irreversible loss of each component in NH 3 /salt AHP systems. The differences between the exergy loss analysis and entransy dissipation analysis are mainly in absorber, generator and SHE. Especially in NH 3 /NaSCN system, the proportion of entransy dissipation in generator is 60.8%, while the proportion of exergy loss is only 34.9%. In addition, the changing trends of entransy dissipation in each component of NH 3 /NaSCN and NH 3 /LiNO 3 systems are similar under various operating conditions. (2) Under various operating conditions, entransy efficiency and COP of NH 3 /salt AHP systems have roughly the same changing trend. Moreover, entransy efficiency is more reasonable than exergy efficiency in evaluating the performance of systems under the absorption temperature varies from 30 • C to 50 • C. Under various evaporation temperature conditions, the value of entransy efficiency of the NH 3 /NaSCN system is higher than that of the NH 3 /LiNO 3 system. Similar results can also be obtained at higher generation temperature, as well as lower absorption and condensation temperatures.
(3) To summarize, the entransy analysis is appropriate to evaluate the performance of NH 3 /salt AHP systems and suitable for analyzing the irreversibility of each component in the systems.
Further work should be focused on reducing the irreversible loss of each component and improving the performance of NH 3 /salt AHP systems by using the method of entransy analysis.