Thermodynamic Analysis of the Air-Cooled Transcritical Rankine Cycle Using CO 2 / R161 Mixture Based on Natural Draft Dry Cooling Towers

: Heat rejection in the hot-arid area is of concern to power cycles, especially for the transcritical Rankine cycle using CO 2 as the working ﬂuid in harvesting the low-grade energy. Usually, water is employed as the cooling substance in Rankine cycles. In this paper, the transcritical Rankine cycle with CO 2 / R161 mixture and dry air cooling systems had been proposed to be used in arid areas with water shortage. A design and rating model for mixture-air cooling process were developed based on small-scale natural draft dry cooling towers. The inﬂuence of key parameters on the system’s thermodynamic performance was tested. The results suggested that the thermal e ﬃ ciency of the proposed system was decreased with the increases in the turbine inlet pressure and the ambient temperature, with the given thermal power as the heat source. Additionally, the cooling performance of natural draft dry cooling tower was found to be a ﬀ ected by the ambient temperature and the turbine exhaust temperature.


Introduction
The energy crisis and environmental pollution have become barriers for the sustainable development of the human society, which can be ascribed to the massive consumption of fossil fuels since the industrial revolution [1]. Scientists and technicians worldwide have employed a variety of methods to deal with these issues. Typically, harvesting the low-grade energies, such as solar energy, geothermal energy, and industrial waste heat, has been recognized as one of the effective approaches to alleviate the energy and environmental issues [2][3][4].
Generally, thermodynamic cycles, including the organic Rankine cycle (ORC) [5,6], Kalina cycle [7,8], and transcritical Rankine cycle (TRC) [9], which have used the low-boiling-point working fluid, are adopted to recover the low-grade energy. Of them, the TRC, which adopts the natural non-flammable and non-toxic CO 2 as the working fluid (hereinafter referred as "tCO 2 ") [10][11][12], has more compact equipment than the Kalina cycle, and it can lead to a higher output power than ORC, thus displaying great application prospects in the field of low-grade energy utilization. However, the normal operation pressure of the tCO 2 system is about 10 MPa due to the high critical pressure of CO 2 (about 7.38 MPa), which will give rise to safety concerns. Another challenge is CO 2 condensation in the tCO 2 system as a result of the low critical temperature of CO 2 (about 304 K) [13]. It is difficult to use tCO 2 in areas with high surrounding temperature, especially, in arid areas with water shortage. constructed and verified. Subsequently, the natural draft dry cooling tower (NDDCT) model was established based on the experimental data from Li et al. [22]. Afterward, the performance of the NDDCT was analyzed under different ambient temperatures and thermal loads of turbine exhaust. Moreover, this work was expected to shed valuable light on the mixture working fluids [23][24][25] and ORC using the direct air cooling system [26]. The schematic diagram of the power plant is presented in Figure 1. As can be observed, the power plant consisted of four basic components, including the heater, the turbine, the cooling tower, and the pump. Moreover, there were four processes regarding the thermodynamic cycle of the working fluid in the system, among which, in process 1-2, the condensed fluid was pumped into the high pressure state; in process 2-3, the working fluid experienced phase transition and changed into the high temperature and high pressure supercritical state in the heater; in process 3-4, the Additionally, the temperature-entropy (T-s) diagram of the corresponding power plant system using CO 2 /R161 (50/50 wt.%) is plotted in Figure 2. Noteworthily, the working fluid had experienced the single-and two-phase condensation processes in the NDDCT, during which temperature glide had occurred. supercritical fluid was expanded to produce power in the turbine; and in process 4-1, the working fluid was cooled in the cooling tower. Here, the NDDCT was selected as the condenser, which could cool the working fluid with no water loss and almost no parasitic power consumption [27]. Additionally, the temperature-entropy (T-s) diagram of the corresponding power plant system using CO2/R161 (50/50 wt.%) is plotted in Figure 2. Noteworthily, the working fluid had experienced the single-and two-phase condensation processes in the NDDCT, during which temperature glide had occurred.   Figure 3 presents the critical pressure and critical temperature for the CO 2 /R161 mixtures with various mass fractions [28]. Clearly, the critical temperature of the mixtures was increased with the increase in the mass fraction of R161. Meanwhile, the critical pressure of the mixtures was decreased, which rendered a lower TRC operation pressure than that of tCO 2 , and laid the foundation for the practical application of TRC using CO 2 mixtures.  Additionally, the temperature-entropy (T-s) diagram of the corresponding power plant system using CO2/R161 (50/50 wt.%) is plotted in Figure 2. Noteworthily, the working fluid had experienced the single-and two-phase condensation processes in the NDDCT, during which temperature glide had occurred.  Figure 3 presents the critical pressure and critical temperature for the CO2/R161 mixtures with various mass fractions [28]. Clearly, the critical temperature of the mixtures was increased with the increase in the mass fraction of R161. Meanwhile, the critical pressure of the mixtures was decreased, which rendered a lower TRC operation pressure than that of tCO2, and laid the foundation for the practical application of TRC using CO2 mixtures.

Calculation Assumptions
The assumptions of the power plant system are exhibited in Table 1. Typically, the heat source of the system could be solar energy, geothermal energy, or waste heat. Therefore, the thermal power of 500.00 kW was given as the heat source for the universality of the system, while the range of the

Calculation Assumptions
The assumptions of the power plant system are exhibited in Table 1. Typically, the heat source of the system could be solar energy, geothermal energy, or waste heat. Therefore, the thermal power of 500.00 kW was given as the heat source for the universality of the system, while the range of the turbine inlet temperature was 423.15-473.15 K. In addition, the mass flow of the working fluid was calculated according to the heat balance equation. The annual average air temperature was 298.15 K, and, in this paper, the air temperature fluctuated within the range of 293.15-303.15 K. Furthermore, there was no pressure loss in the pipeline and heat exchanger, and the whole power plant system operated at the steady state.

Mathematical Model
The equations for the system components were based on the first law of thermodynamics. The National Institute of Standards and Technology (NIST) REFPROP program [29] was used for physical properties of CO 2 /R161 mixture.
As for the turbine: For the pump: For the heater: For cooling tower: Energies 2019, 12, 3342

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The heat exchanger in the cooling tower was made up of bundles with the same structural and functional characteristics. It can be seen in Figure 4 that each bundle was composed of 10 finned tubes arranged in five rows. Meanwhile, the working fluid would enter the bundle through the left side of the fifth row in the finned tubes and leave the bundle at the right side of the first row in the finned tubes. Then, the air would cool the working fluid by flowing from the bottom to the top of the bundle. The calculation for the heat exchanger model is also presented in Figure 4. Generally, the traditional method of heat exchanger modeling is only valid for a working fluid with constant properties. In this study, the nodal approach was adopted in designing the heat exchanger, in which each row of the heat exchanger bundles was divided into 24 sections, as if a number of small heat exchangers were connected in series.
where QCt is the heat emission of the cooling tower (W), hco2 represents the enthalpy of CO2 (J·kg -1 ), while i and o stand for the inlet and outlet of the working fluid, respectively, and C p,air indicates the average heat capacity of air (J·kg -1 ·K -1 ). Additionally, the product of the heat transfer area and the overall heat transfer coefficient (UA) of the heat exchanger could be obtained through the logarithmic mean temperature difference (LMTD), as displayed below.
where U is the thermal conductivity of the system (W·m -2 ·K −1 ), A stands for the area of heat transfer (m 2 ), FT indicates the correction factor of LMTD (which amends the counter current flow as the cross-flow), and T LMTD Δ represents the logarithmic mean temperature (K), which can be calculated as follows, when the working fluid experienced counter current flow in the heat exchanger, The heat balance equation between CO 2 mixture and air was as follows, where Q Ct is the heat emission of the cooling tower (W), h CO 2 represents the enthalpy of CO 2 (J·kg −1 ), while i and o stand for the inlet and outlet of the working fluid, respectively, and C p,air indicates the average heat capacity of air (J·kg −1 ·K −1 ). Additionally, the product of the heat transfer area and the overall heat transfer coefficient (UA) of the heat exchanger could be obtained through the logarithmic mean temperature difference (LMTD), as displayed below.
where U is the thermal conductivity of the system (W·m −2 ·K −1 ), A stands for the area of heat transfer (m 2 ), F T indicates the correction factor of LMTD (which amends the counter current flow as the cross-flow), and ∆T LMTD represents the logarithmic mean temperature (K), which can be calculated as follows, Energies 2019, 12, 3342 6 of 17 when the working fluid experienced counter current flow in the heat exchanger, On the other hand, the condenser could be divided into the superheated single-phase region and the two-phase region based on the working fluid state at the turbine outlet. For the single-phase region of the CO 2 mixture, the Krasnoshchekov-Petukhov correlation [30,31] was employed, where U represents the heat transfer coefficient and D suggests the inner diameter of the tube. The following correlation [32] was used for the two-phase region of the CO 2 mixture.
where g represents acceleration due to gravity, ρ f and ρ g are the densities of liquid and vapor working fluid, and i f g is the modified latent heat of vaporization. The heat transfer coefficient at the air side [22] was calculated as follows, where h a is the air side heat transfer coefficient, A a stands for the air side heat transfer area, and Re a indicates the Reynolds number of air. Moreover, the characteristic length of Re a was deemed as the equivalent circular diameter of the air flow passage, which was 1.7 × 10 −2 m for this particular heat exchanger.
The structure chart of the NDDCT and the distribution diagram of air side resistance are displayed in Figures 5 and 6, respectively. Clearly, the NDDCT consisted of the tower support columns, the heat exchanger bundles, the hyperbolic-type tower shell, and the sensors.
where U represents the heat transfer coefficient and D suggests the inner diameter of the tube.
The following correlation [32] was used for the two-phase region of the CO2 mixture.
where g represents acceleration due to gravity, f ρ and g ρ are the densities of liquid and vapor working fluid, and i fg ′ is the modified latent heat of vaporization.
The heat transfer coefficient at the air side [22] was calculated as follows, where ha is the air side heat transfer coefficient, Aa stands for the air side heat transfer area, and Rea indicates the Reynolds number of air. Moreover, the characteristic length of Rea was deemed as the equivalent circular diameter of the air flow passage, which was 1.7 × 10 −2 m for this particular heat exchanger.
The structure chart of the NDDCT and the distribution diagram of air side resistance are displayed in Figures 5 and 6, respectively. Clearly, the NDDCT consisted of the tower support columns, the heat exchanger bundles, the hyperbolic-type tower shell, and the sensors.
where 1 p a is the air pressure at state 1 in Figure 1 Table 2.

Loss coefficient Equation
The tower support loss coefficient, Kts  The ventilation equation represents the balance equation between the buoyancy with the result of air heating and the air pressure loss in the NDDCT, as shown below: where p a1 is the air pressure at state 1 in Figure 1 Table 2.

Loss Coefficient Equation
The tower support loss coefficient, Cooling tower inlet loss coefficient, K ct he Cooling tower outlet loss coefficient, K to Heat exchanger loss coefficient, K he Characteristic Reynolds number, Ry = ma The specified parameters for the design of the NDDCT are listed in Table 3. The design flow of the NDDCT was built on the parameter iteration according to the energy conservation equation and the ventilation equation. Typically, the minimum ∆T LMTD was 5.00 K. The detailed data for the heat exchanger are listed in Table 4.

Thermodynamic Analysis
Firstly, the calculated thermal efficiency of CO 2 /R161 TRC was compared with that of Dai et al. [18]. As shown in Figure 7, the simulation results were consistent with those previously reported, which verified the correctness of our calculation. Moreover, those results also suggested that the thermal efficiency of CO 2 /R161 TRC was enhanced with the decrease in the CO 2 mass fraction in CO 2 /R161 mixtures.  On the other hand, Figure 8 plots the changes in thermal efficiency depending on the variation of turbine inlet pressure at various turbine inlet temperatures using CO2/R161 (mass fraction of 0.5/0.5). As can be observed, the thermal efficiency was first increased and then decreased as the turbine inlet pressure was elevated. In other words, there was an optimal turbine inlet pressure to obtain the maximal thermal efficiency of the system. In addition, the optimal turbine inlet pressure was boosted with the increase in turbine inlet temperature. In our study, the optimal turbine inlet  On the other hand, Figure 8 plots the changes in thermal efficiency depending on the variation of turbine inlet pressure at various turbine inlet temperatures using CO 2 /R161 (mass fraction of 0.5/0.5). As can be observed, the thermal efficiency was first increased and then decreased as the turbine inlet pressure was elevated. In other words, there was an optimal turbine inlet pressure to obtain the maximal thermal efficiency of the system. In addition, the optimal turbine inlet pressure was boosted with the increase in turbine inlet temperature. In our study, the optimal turbine inlet pressure was determined to be about 8.00 MPa at the turbine inlet temperature of 373.15 K, which was changed to about 18.00 MPa at the turbine inlet temperature of 473.15 K. On the other hand, Figure 8 plots the changes in thermal efficiency depending on the variation of turbine inlet pressure at various turbine inlet temperatures using CO2/R161 (mass fraction of 0.5/0.5). As can be observed, the thermal efficiency was first increased and then decreased as the turbine inlet pressure was elevated. In other words, there was an optimal turbine inlet pressure to obtain the maximal thermal efficiency of the system. In addition, the optimal turbine inlet pressure was boosted with the increase in turbine inlet temperature. In our study, the optimal turbine inlet pressure was determined to be about 8.00 MPa at the turbine inlet temperature of 373.15 K, which was changed to about 18.00 MPa at the turbine inlet temperature of 473.15 K. The evolution of the thermal efficiency with the variations in mass fraction and turbine inlet pressure at different minimum circulation temperatures is exhibited in Figure 9. Obviously, the thermal efficiency increased with the increase in turbine inlet pressure in the presence of low R161 mass fraction. In the meantime, the maximum thermal efficiency appear as the R161 mass fraction was increased. However, the thermal efficiency was gradually decreased with the increase in turbine inlet pressure at the high R161 mass fraction. Besides, the minimum circulation temperature would also affect the thermal efficiency of the system. The evolution of the thermal efficiency with the variations in mass fraction and turbine inlet pressure at different minimum circulation temperatures is exhibited in Figure 9. Obviously, the thermal efficiency increased with the increase in turbine inlet pressure in the presence of low R161 mass fraction. In the meantime, the maximum thermal efficiency appear as the R161 mass fraction was increased. However, the thermal efficiency was gradually decreased with the increase in turbine inlet pressure at the high R161 mass fraction. Besides, the minimum circulation temperature would also affect the thermal efficiency of the system. Table 5 lists the optimal operation parameters of CO 2 /R161 TRC at the condensing temperature of 308.15 K and the turbine inlet temperature of 423.15 K. As can be seen, the optimal thermal efficiency was about 7.40%, the optimal output work was about 37.00 kW, the optimal working medium flow was 1.60 kg/s, and the heat rejection of the condenser was about 463.00 kW.   Table 5 lists the optimal operation parameters of CO2/R161 TRC at the condensing temperature of 308.15 K and the turbine inlet temperature of 423.15 K. As can be seen, the optimal thermal efficiency was about 7.40%, the optimal output work was about 37.00 kW, the optimal working medium flow was 1.60 kg/s, and the heat rejection of the condenser was about 463.00 kW.

Design Parameters and Performance Analysis of Cooling Tower
Notably, the as-prepared TRC with CO2 blends was more sensitive to the environment temperature, since the CO2 mixtures could directly exchange heat with air in the NDDCT, which was different from the conventional indirect cooling system. Therefore, the effects of the environment temperature and temperature variation of CO2 mixtures on the system were also investigated.

Design Parameters and Performance Analysis of Cooling Tower
Notably, the as-prepared TRC with CO 2 blends was more sensitive to the environment temperature, since the CO 2 mixtures could directly exchange heat with air in the NDDCT, which was different from the conventional indirect cooling system. Therefore, the effects of the environment temperature and temperature variation of CO 2 mixtures on the system were also investigated.
The design parameters of the NDDCT at the condenser heat rejection of about 463.00 kW (as discussed in Table 5) are listed in Table 6. As can be seen, the height of the cooling tower was 10.00 m; the diameters of the inlet and the outlet of the cooling tower were 7.14 and 5 m, respectively; the number of heat exchanger bundles was seven; the working fluid outlet temperature was 307.98 K; and the air mean outlet temperature was about 318.85 K.
The temperature profiles of CO 2 mixture and air in the cooling tower are presented in Figure 10. As can be figured out, the CO 2 mixture had experienced transition from the single-phase vapor state to the vapor-liquid two-phase state in the fifth row of the finned tubes. Afterward, the CO2 mixture was slowly condensed into the saturated liquid during cooling from the fourth to the first row of the finned tubes. It is noted that the air temperature was plotted between every layer of finned tubes in the air-cooled heat exchangers. The discontinuity in the air temperature trends during phase change of the CO 2 /R161 mixture is due to an abrupt decrease in mixture heat transfer coefficient, which results in a high temperature difference in the vapor phase. However, the smaller rejection heat in the vapor phase reduced the air temperature difference. Moreover, the air temperature through the overall length of the cooling tower is shown in Appendix A Figure A1. The heat transfer coefficient of CO 2 mixture variation in the heat exchanger is presented in Figure 11. Clearly, the heat transfer coefficient of the CO 2 mixture was about 200 W/m 2 ·K at the single-phase vapor state, while that was increased to Energies 2019, 12, 3342 11 of 17 3000 W/m 2 ·K at the vapor-liquid two-phase state. The temperature difference in each row was about 3.00 K, and the outlet temperature of air at the fifth row of the finned tubes was about 318.15-320.15 K.   The air velocity through the heat exchanger bundles is calculated and presented in Figure 12. It is noted that the discontinuity in the air velocity trend is due to data selection, which are ones between every layer of finned tubes. Actually, air flows across tubes with a continuous velocity. The air velocity through the overall length of the cooling tower is shown in Appendix Figure A2. As can be seen, the air velocity was about 0.63 m/s at the first row of finned tubes, which was increased to 0.67 m/s at the fifth row of finned tubes. This was because air heating would result in a decrease in density and an increase in buoyancy, thus, giving rise to the increased air velocity through the heat exchanger bundles.  The air velocity through the heat exchanger bundles is calculated and presented in Figure 12. It is noted that the discontinuity in the air velocity trend is due to data selection, which are ones between every layer of finned tubes. Actually, air flows across tubes with a continuous velocity. The air velocity through the overall length of the cooling tower is shown in Appendix Figure A2. As can be seen, the air velocity was about 0.63 m/s at the first row of finned tubes, which was increased to 0.67 m/s at the fifth row of finned tubes. This was because air heating would result in a decrease in density and an increase in buoyancy, thus, giving rise to the increased air velocity through the heat exchanger bundles. The air velocity through the heat exchanger bundles is calculated and presented in Figure 12. It is noted that the discontinuity in the air velocity trend is due to data selection, which are ones between every layer of finned tubes. Actually, air flows across tubes with a continuous velocity. The air velocity through the overall length of the cooling tower is shown in Appendix A Figure A2. As can be seen, the air velocity was about 0.63 m/s at the first row of finned tubes, which was increased to 0.67 m/s at the fifth row of finned tubes. This was because air heating would result in a decrease in density and an increase in buoyancy, thus, giving rise to the increased air velocity through the heat exchanger bundles. Figure 11. Heat transfer coefficient of CO2 mixture variation in the heat exchanger.
The air velocity through the heat exchanger bundles is calculated and presented in Figure 12. It is noted that the discontinuity in the air velocity trend is due to data selection, which are ones between every layer of finned tubes. Actually, air flows across tubes with a continuous velocity. The air velocity through the overall length of the cooling tower is shown in Appendix Figure A2. As can be seen, the air velocity was about 0.63 m/s at the first row of finned tubes, which was increased to 0.67 m/s at the fifth row of finned tubes. This was because air heating would result in a decrease in density and an increase in buoyancy, thus, giving rise to the increased air velocity through the heat exchanger bundles. The effects of ambient temperature on the CO 2 outlet temperature in the condenser, the heat rejection of cooling tower, and the mass flow rate of air through the cooling tower are calculated, as presented in Figures 13-15, respectively. Specifically, the increase in ambient temperature would reduce the mass flow rate of air and decrease the heat rejection of the NDDCT, thus, deteriorating the cooling of CO 2 mixtures. For instance, the turbine exhaust temperature of the CO 2 mixture was 345.00 K, the heat rejection of the cooling tower was 450.00 kW, and the outlet temperature of CO 2 in the condenser was 312.15 K at the ambient temperature of 303.15 K. Importantly, the performance of the NDDCT was enhanced with the increases in ambient temperature and the heat rejection of cooling tower coupled with the decrease in CO 2 outlet temperature in the condenser. Noteworthily, the pressure of the CO 2 mixture was changed with the alteration in the condensation temperature of CO 2 mixture. The effects of ambient temperature on the CO2 outlet temperature in the condenser, the heat rejection of cooling tower, and the mass flow rate of air through the cooling tower are calculated, as presented in Figures 13-15, respectively. Specifically, the increase in ambient temperature would reduce the mass flow rate of air and decrease the heat rejection of the NDDCT, thus, deteriorating the cooling of CO2 mixtures. For instance, the turbine exhaust temperature of the CO2 mixture was 345.00 K, the heat rejection of the cooling tower was 450.00 kW, and the outlet temperature of CO2 in the condenser was 312.15 K at the ambient temperature of 303.15 K. Importantly, the performance of the NDDCT was enhanced with the increases in ambient temperature and the heat rejection of cooling tower coupled with the decrease in CO2 outlet temperature in the condenser. Noteworthily, the pressure of the CO2 mixture was changed with the alteration in the condensation temperature of CO2 mixture.    In addition, as presented in Figure 14, the heat rejection of cooling tower was increased as the turbine exhaust temperature was elevated ( Figure 13) at the same ambient temperature, while the CO2 outlet temperature in the condenser remained largely unchanged. Typically, the driving force of air flow in the NDDCT was the density difference between the hot air in the cooling tower and the cool air out of the cooling tower. Additionally, the heat exchange was driven by the temperature difference between the air and the CO2 mixture. Thus, the density difference between air in and out of the cooling tower was enlarged as the turbine exhaust temperature was elevated, which would result in the increased mass flow rate of air and air velocity, finally boosting the heat rejection of the cooling tower.

Conclusions
A transcritical Rankine cycle system with natural draft dry cooling tower using CO2/R161 blends has been established in this paper. The thermodynamic performance and optimal operation parameters of the system, together with the cooling performance of natural draft dry cooling tower, are discussed. In addition, the design procedures of the natural draft dry cooling tower in a transcritical Rankine cycle using a CO2/R161 mixture are provided. The conclusions can be drawn that the CO2/R161 mixture has the potential to be used in arid areas, using dry air cooling methods with great thermodynamic performance. The decrease in ambient temperature will lead to the increase in the mass flow rate of air and the heat rejection of cooling tower, which will result in the lower inlet temperature of CO2/mixture in the pump. Moreover, the thermal efficiency of transcritical Rankine cycle using CO2/R161 is decreased with increases in the turbine inlet pressure and ambient temperature, with thermal power being used as the heat source.  In addition, as presented in Figure 14, the heat rejection of cooling tower was increased as the turbine exhaust temperature was elevated ( Figure 13) at the same ambient temperature, while the CO 2 outlet temperature in the condenser remained largely unchanged. Typically, the driving force of air flow in the NDDCT was the density difference between the hot air in the cooling tower and the cool air out of the cooling tower. Additionally, the heat exchange was driven by the temperature difference between the air and the CO 2 mixture. Thus, the density difference between air in and out of the cooling tower was enlarged as the turbine exhaust temperature was elevated, which would result in the increased mass flow rate of air and air velocity, finally boosting the heat rejection of the cooling tower.

Conclusions
A transcritical Rankine cycle system with natural draft dry cooling tower using CO 2 /R161 blends has been established in this paper. The thermodynamic performance and optimal operation parameters of the system, together with the cooling performance of natural draft dry cooling tower, are discussed. In addition, the design procedures of the natural draft dry cooling tower in a transcritical Rankine cycle using a CO 2 /R161 mixture are provided. The conclusions can be drawn that the CO 2 /R161 mixture has the potential to be used in arid areas, using dry air cooling methods with great thermodynamic performance. The decrease in ambient temperature will lead to the increase in the mass flow rate of air and the heat rejection of cooling tower, which will result in the lower inlet temperature of CO 2 /mixture in the pump. Moreover, the thermal efficiency of transcritical Rankine cycle using  Figure A1. The air temperature through the overall length of the cooling tower. Figure A1. The air temperature through the overall length of the cooling tower.