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

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## Abstract

**:**

_{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 efficiency 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 affected by the ambient temperature and the turbine exhaust temperature.

## 1. Introduction

_{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.

_{2}mixed with other fluids has been proposed as the working fluid to expand the application of tCO

_{2}[14]. Notably, the CO

_{2}-based mixtures can integrate the advantages of each individual pure fluid and exhibit environmental properties as well as efficiency, which have thereby attracted increasing attention in recent years [15,16]. Furthermore, applying CO

_{2}mixtures in TRC can also lead to superior temperature matching with heat source over that of the CO

_{2}Brayton cycle. At present, the reported working fluids of CO

_{2}mixtures are mainly CO

_{2}blends with hydrocarbons, hydrofluorocarbons, and hydrofluoroolefins [17]. For instance, Dai et al. [18] investigated the thermodynamic performance of TRC using the zeotropic mixtures of CO

_{2}mixed with seven working fluids possessing low global warming potentials (GWP). Their results denoted that the thermal efficiency of the TRC was enhanced by the zeotropic mixtures; besides, the operation pressure of the investigated TRC was decreased. Moreover, Yang [19] examined the improvements of the economic performance of TRC with CO

_{2}mixtures, and discovered that, the TRC with CO

_{2}/fluoroethane (R161) mixtures displayed better economic performance than those in other TRCs with CO

_{2}/difluoromethane, CO

_{2}/tetrafluoropropene, CO

_{2}/tetrafluoroethane, CO

_{2}/propane, and pure CO

_{2}. Moreover, Shu et al. [20] explored the improvements in the thermodynamic and economic performance of TRC using a CO

_{2}-based mixture to recover the engine waste heat. Their findings suggested that TRCs with CO

_{2}/R152a, CO

_{2}/R161, and CO

_{2}/R32 mixtures could achieve the optimal performances, along with a low operation pressure and the optimal total heat transfer area. Thus, TRC with CO

_{2}/R161 mixture is promising to be used to recover the low-grade energy.

_{2}/R161 mixture is associated with the superiorities of fine thermostability, as well as optimal thermodynamic and economic performances in TRC, which can thereby be utilized for low-grade energy recovery at a high ambient temperature. Nonetheless, few existing studies [13,14,15,16,17,18,19,20] have examined the cooling process of TRC with CO

_{2}/R161 mixture. Usually, water cooling is employed for analysis, but the water resource issue [21] has drawn growing attention, since water is a kind of valuable natural resource. On this account, the direct air cooling technique will be an ideal approach for thermodynamic cycles in arid areas with water shortage.

_{2}/R161 mixture with the direct air cooling system had been proposed and investigated in this paper. Firstly, the thermodynamic model of the TRC system was 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].

## 2. Model and Considerations

_{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.

_{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.

#### 2.1. Calculation Assumptions

#### 2.2. Mathematical Model

_{2}/R161 mixture.

_{2}mixture and air was as follows,

_{Ct}is the heat emission of the cooling tower (W), h

_{CO2}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}).

^{−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 $\Delta {T}_{LMTD}$ represents the logarithmic mean temperature (K), which can be calculated as follows,

_{2}mixture, the Krasnoshchekov–Petukhov correlation [30,31] was employed,

_{2}mixture.

_{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.

_{3}represents the distance between the heat exchanger bundles bottom and the ground (m), H

_{4}indicates the distance between the top of the heat exchanger bundles and the ground (m), H

_{5}is the distance between the tower outlet and the ground (m), ${T}_{a4}$ stands for the air temperature at state 4 (K), m

_{a}is indicative of the air flow (kg·s

^{−1}), ${A}_{fr}$ is the face area of the heat exchanger bundle bottom (m

^{2}), ${\rho}_{a34}$ signifies the average air density of the heat exchanger bundles (kg·m

^{−3}), A

_{5}denotes the outlet area of the cooling tower (m

^{2}), ${\rho}_{a5}$ represents the outlet air density of cooling tower (kg·m

^{−3}), and K indicates the coefficients of air loss in the NDDCT. More details are presented in Table 2.

## 3. Results and Discussion

#### 3.1. Thermodynamic Analysis

_{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.

_{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.

_{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.

#### 3.2. Design Parameters and Performance Analysis of Cooling Tower

_{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.

_{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 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 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.

_{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 Figure 13, Figure 14 and Figure 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.

_{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.

## 4. Conclusions

_{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 CO

_{2}/R161 is decreased with increases in the turbine inlet pressure and ambient temperature, with thermal power being used as the heat source.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

h | enthalpy (kJ/kg) |

Q | heat transfer rate (kW) |

m | mass flow rate (kg/s) |

U | heat transfer coefficient (W·m^{−2}·K^{−1}) |

c_{p} | specific heat capacity (kJ/kg·K) |

T | temperature (K) |

A | heat exchanger area (m^{2}) |

D | inner diameter (m) |

K | coefficient of loss of air |

H | height (m) |

L | length (m) |

Greek symbols | |

$\Delta T$ | temperature difference (K) |

$\rho $ | density (kg/m^{3}) |

Acronyms | |

ORC | organic Rankine cycle |

TRC | transcritical Rankine cycle |

LMTD | logarithmic mean temperature difference |

NDDCT | natural draft dry cooling tower |

Subscripts | |

p | pump |

t | turbine |

cool | cool water |

a | air |

i | inlet |

o | outlet |

## Appendix A

## References

- Vélez, F.; Segovia, J.J.; Martín, M.C.; Antolín, G.; Chejne, F.; Quijano, A. A technical, economical and market review of organic Rankine cycles for the conversion of low-grade heat for power generation. Renew. Sustain. Energy Rev.
**2012**, 16, 4175–4189. [Google Scholar] - Yamamoto, T.; Furuhata, T.; Arai, N.; Mori, K. Design and testing of the Organic Rankine Cycle. Energy
**2001**, 26, 239–251. [Google Scholar] [CrossRef] - Wang, S.; Liu, C.; Zhang, C.; Xu, X.; Li, Q. Thermo-economic evaluations of dual pressure organic Rankine cycle (DPORC) driven by geothermal heat source. J. Renew. Sustain. Energy
**2018**, 10, 063901. [Google Scholar] [CrossRef] - Ding, Y.; Liu, C.; Zhang, C.; Xu, X.; Li, Q.; Mao, L. Exergoenvironmental model of Organic Rankine Cycle system including the manufacture and leakage of working fluid. Energy
**2018**, 145, 52–64. [Google Scholar] [CrossRef] - Zhang, C.; Liu, C.; Xu, X.; Li, Q.; Wang, S.; Chen, X. Effects of superheat and internal heat exchanger on thermo-economic performance of organic Rankine cycle based on fluid type and heat sources. Energy
**2018**, 159, 482–495. [Google Scholar] [CrossRef] - Gao, H.; Liu, C.; He, C.; Xu, X.; Wu, S.; Li, Y. Performance analysis and working fluid selection of a supercritical Organic Rankine Cycle for low grade waste heat recovery. Energies
**2012**, 5, 3233–3247. [Google Scholar] [CrossRef] - Marston, C.H. Parametric analysis of the Kalina cycle. J. Eng. Gas Turb. Power
**1990**, 112, 107–116. [Google Scholar] [CrossRef] - Gao, H.; Chen, F. Thermo-economic analysis of a bottoming Kalina cycle for internal combustion engine exhaust heat recovery. Energies
**2018**, 11, 3044. [Google Scholar] [CrossRef] - Zhang, C.; Liu, C.; Xu, X.; Li, Q.; Wang, S. Energetic, exergetic, economic and environmental (4E) analysis and multi-factor evaluation method of low GWP fluids in trans-critical organic Rankine cycles. Energy
**2019**, 168, 332–345. [Google Scholar] [CrossRef] - Sadreddini, A.; Ashjari, M.A.; Fani, M.; Mohammadi, A. Thermodynamic analysis of a new cascade ORC and transcritical CO
_{2}cycle to recover energy from medium temperature heat source and liquefied natural gas. Energy Convers. Manag.**2018**, 167, 9–20. [Google Scholar] [CrossRef] - Rony, R.U.; Yang, H.; Krishnan, S.; Song, J. Recent advances in transcritical CO
_{2}(R744) heat pump system: A review. Energies**2019**, 12, 457. [Google Scholar] [CrossRef] - Omar, A.; Saghafifar, M.; Mohammadi, K.; Alashkar, A.; Gadalla, M. A review of unconventional bottoming cycles for waste heat recovery: Part II—Applications. Energy Convers. Manag.
**2019**, 180, 559–583. [Google Scholar] [CrossRef] - Yari, M.; Mahmoudi, S.M.S. Thermodynamic analysis and optimization of novel ejector-expansion TRCC (transcritical CO
_{2}) cascade refrigeration cycles (Novel transcritical CO_{2}cycle). Energy**2011**, 36, 6839–6850. [Google Scholar] [CrossRef] - Xia, J.; Wang, J.; Zhang, G.; Lou, J.; Zhao, P.; Dai, Y. Thermo-economic analysis and comparative study of transcritical power cycles using CO
_{2}-based mixtures as working fluids. Appl. Therm. Eng.**2018**, 144, 31–44. [Google Scholar] [CrossRef] - Guo, J.; Li, M.; Xu, J.; Yan, J.; Wang, K. Thermodynamic performance analysis of different supercritical Brayton cycles using CO
_{2}-based binary mixtures in the molten salt solar power tower systems. Energy**2019**, 173, 785–798. [Google Scholar] [CrossRef] - Manzolini, G.; Binotti, M.; Bonalumi, D.; Invernizzi, C.; Iora, P. CO
_{2}mixtures as innovative working fluid in power cycles applied to solar plants. Techno-economic assessment. Sol. Energy**2019**, 181, 530–544. [Google Scholar] [CrossRef] - Baik, W.; Lee, W.; Yun, R. Heat transfer and pressure drop characteristics of CO
_{2}mixtures in a pipeline under the seawater condition. Int. J. Heat Mass Transf.**2019**, 136, 627–634. [Google Scholar] [CrossRef] - Dai, B.; Li, M.; Ma, Y. Thermodynamic analysis of carbon dioxide blends with low GWP (global warming potential) working fluids-based transcritical Rankine cycles for low-grade heat energy recovery. Energy
**2014**, 64, 942–952. [Google Scholar] [CrossRef] - Yang, M.H. The performance analysis of the transcritical Rankine cycle using carbon dioxide mixtures as the working fluids for waste heat recovery. Energy Convers. Manag.
**2017**, 151, 86–97. [Google Scholar] [CrossRef] - Shu, G.; Yu, Z.; Tian, H.; Liu, P.; Xu, Z. Potential of the transcritical Rankine cycle using CO
_{2}-based binary zeotropic mixtures for engine’s waste heat recovery. Energy Convers. Manag.**2018**, 174, 668–685. [Google Scholar] [CrossRef] - Sun, Z.; Liu, C.; Xu, X.; Li, Q.; Wang, X.; Wang, S.; Chen, X. Comparative carbon and water footprint analysis and optimization of Organic Rankine Cycle. Appl. Therm. Eng.
**2019**, 158, 113769. [Google Scholar] [CrossRef] - Li, X.; Duniam, S.; Gurgenci, H.; Guan, Z.; Veeraragavan, A. Full scale experimental study of a small natural draft dry cooling tower for concentrating solar thermal power plant. Appl. Energy
**2017**, 193, 15–27. [Google Scholar] [CrossRef] - Hu, J.; Liu, C.; Li, Q.; Shi, X. Molecular simulation of thermal energy storage of mixed CO
_{2}/IRMOF-1 nanoparticle nanofluid. Int. J. Heat Mass Transf.**2018**, 125, 1345–1348. [Google Scholar] [CrossRef] - Chen, X.; Liu, C.; Li, Q.; Wang, X.; Xu, X. Dynamic analysis and control strategies of Organic Rankine Cycle system for waste heat recovery using zeotropic mixture as working fluid. Energy Convers. Manag.
**2019**, 192, 321–334. [Google Scholar] [CrossRef] - Zhou, Y.; Li, Q.; Wang, Q. Energy storage analysis of UIO-66 and water mixed nanofluids: An experimental and theoretical study. Energies
**2019**, 12, 2521. [Google Scholar] [CrossRef] - Usman, M.; Imran, M.; Yang, Y.; Lee, D.H.; Park, B. Thermo-economic comparison of air-cooled and cooling tower based Organic Rankine Cycle (ORC) with R245fa and R1233zde as candidate working fluids for different geographical climate conditions. Energy
**2017**, 123, 353–366. [Google Scholar] [CrossRef] - Hooman, K. Dry cooling towers as condensers for geothermal power plants. Int. Commun. Heat Mass
**2010**, 37, 1215–1220. [Google Scholar] [CrossRef] - NIST Webbook. Available online: http://webbook.nist.gov/chemistry/fluid/ (accessed on 1 June 2019).
- Lemmon, E.W.; Huber, M.L.; McLinden, M.O. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties Refprop; Version 9.1; NIST: Gaithersburg, MD, USA, 2007. [Google Scholar]
- Pioro, I.L.; Khartabil, H.F.; Duffey, R.B. Heat transfer to supercritical fluids flowing in channels—Empirical correlations (survey). Nucl. Eng. Des.
**2004**, 230, 69–91. [Google Scholar] [CrossRef] - Petukhov, B.S. Heat Transfer and Friction in Turbulent Pipe Flow with Variable Physical Properties. In Advances in Heat Transfer; Hartnett, J.P., Irvine, T.F., Eds.; Elsevier: Amsterdam, The Netherlands, 1970; pp. 503–564. [Google Scholar]
- Cengel, Y.A.; Klein, S.; Beckman, W. Heat Transfer: A Practical Approach; McGraw-Hill: New York, NY, USA, 1998; Volume 141. [Google Scholar]
- Kröger, D.G. Air-Cooled Heat Exchangers and Cooling Towers; PennWell Books: Tulsa, OK, USA, 2004; Volume 1. [Google Scholar]

**Figure 2.**Temperature–entropy (T–s) diagram (CO

_{2}/R161: 50/50 wt.%) of the transcritical Rankine cycle (TRC).

**Figure 5.**The distribution of heat exchangers in natural draft dry cooling tower (NDDCT).*DALR: Dry adiabatic lapse rate.

**Figure 8.**The relationships between thermal efficiency and turbine inlet pressure under various turbine inlet temperatures.

**Figure 9.**Contours of thermal efficiency with variation of mass fraction and turbine inlet pressure at different circulation minimum temperatures.

Parameter | Value |
---|---|

Thermal power of heat source (kW) | 500.00 |

Annual average air temperature (K) | 298.15 |

Isentropic turbine efficiency | 0.70 |

Isentropic pump efficiency | 0.80 |

Turbine inlet temperature (K) | 423.15 |

Turbine inlet pressure (MPa) | 15.00 |

Pressure losses | 0.00 |

**Table 2.**The coefficients of loss of air in NDDCT [33].

Loss Coefficient | Equation |
---|---|

The tower support loss coefficient, K_{ts} | ${K}_{ts}=\frac{2\Delta {p}_{ats}{\rho}_{a34}}{{(\frac{{m}_{a}}{{A}_{fr}})}^{2}}=\frac{{C}_{Dts}{L}_{ts}{d}_{ts}{n}_{ts}{A}_{fr}{}^{2}}{{(\pi {d}_{3}{H}_{3})}^{3}}(\frac{{\rho}_{a34}}{{\rho}_{a1}})$ |

Contraction loss coefficient, K_{ctc} | ${K}_{ctc}=(1-\frac{2}{{\sigma}_{c}}+\frac{1}{{\sigma}_{c}{}^{2}})(\frac{{\rho}_{a34}}{{\rho}_{a1}})(\frac{{A}_{fr}}{{A}_{e3}}{)}^{2}$ |

Expansion loss coefficient, K_{cte} | ${K}_{cte}={(1-\frac{{A}_{e3}}{{A}_{3}})}^{2}(\frac{{\rho}_{a34}}{{\rho}_{a1}})(\frac{{A}_{fr}}{{A}_{e3}}{)}^{2}$ |

Cooling tower inlet loss coefficient, K_{ct} | ${K}_{ct}={K}_{cthe}({\rho}_{a34}/{\rho}_{a1}){({A}_{fr}/{A}_{e3})}^{2}$ Terblanche and Kroger correlation ${K}_{cthe}=[100-18(\frac{{d}_{3}}{{H}_{3}})+0.94(\frac{{d}_{3}}{{H}_{3}}{)}^{2}]\chi {K}_{he}^{[-1.28+0.183(\frac{{d}_{3}}{{H}_{3}})-7.769\times {10}^{-3}(\frac{{d}_{3}}{{H}_{3}}{)}^{2}]}$ |

Cooling tower outlet loss coefficient, K_{to} | ${K}_{to}=\frac{\Delta {p}_{a56}}{\frac{{\rho}_{a5}{v}_{a5}^{2}}{2}}=\frac{2{\rho}_{a5}\Delta {p}_{a56}}{{(\frac{{m}_{a}}{{A}_{5}})}^{2}}=-0.28F{r}_{D}^{-1}+0.04F{r}_{D}^{-1.5}$ $F{r}_{D}={(\frac{{m}_{a}}{{A}_{5}})}^{2}/[{\rho}_{a5}({\rho}_{a6}-{\rho}_{a5})g{d}_{5}]s$ |

Heat exchanger loss coefficient, K_{he} | Characteristic Reynolds number, $Ry=\frac{{m}_{a}}{{\mu}_{a34}{A}_{fr}T}$ ${K}_{he}=31383.8475R{y}^{-0.332458}+\frac{2}{{\sigma}_{a}{}^{2}}(\frac{{\rho}_{a3}-{\rho}_{a4}}{{\rho}_{a3}+{\rho}_{a4}})$ |

Parameter | Unit | Value |
---|---|---|

Aspect ratio of cooling tower, H_{5}/d_{3} | - | 1.40 |

Tower inlet height, H_{3} | m | 5.00 |

Tower diameter ratio, d_{5}/d_{3} | - | 0.70 |

Heat exchanger coverage of tower inlet, A_{fr}/A_{3} | - | 0.65 |

Number of tower supports, n_{ts} | - | d_{3}/(82.96/60) |

Length of tower support, L_{ts} | m | H_{3} × (15.78/13.67) |

Heat Exchanger Parameter | Unit | Value |
---|---|---|

Hydraulic diameter of tube | m | 9.00 × 10^{−3} |

Inside area of tube per unit length | m^{2} | 2.85 × 10^{−2} |

Inside cross-sectional flow area | m^{2} | 6.40 × 10^{−5} |

Length of finned tube | m | 3.84 |

Effective length of tube | m | 3.79 |

Number of tube rows | - | 5 |

Number of tubes per bundles | - | 220 |

Number of water passes | - | 10 |

Number of bundles | - | 18 |

Total effective frontal area | m^{2} | 76.60 |

Fin root diameter | m | 9.50 × 10^{−3} |

Fin pitch | m | 2.10 × 10^{−3} |

Plant Solution | Value |
---|---|

Turbine inlet temperature (K) | 423.15 |

Turbine inlet pressure (MPa) | 12.45 |

Cycle efficiency (%) | 7.42 |

Plant power output (kW) | 37.11 |

Condensing temperature (K) | 308.15 |

CO_{2}/R161 mass fraction ratio | 0.5/0.5 |

Vapor fraction at turbine outlet (%) | 100.00 |

Turbine outlet temperature (K) | 345.00 |

Mass flow rate of the working fluid (kg·s^{−1}) | 1.62 |

Heat rejection (kW) | 462.89 |

Parameters | Cooling Tower System |
---|---|

Tower height (m) | 10.00 |

Tower outlet diameter (m) | 5.00 |

Tower inlet diameter (m) | 7.14 |

Tower inlet height (m) | 4.00 |

Number of heat exchanger bundles | 7 |

Frontal area (m^{2}) | 29.80 |

Working fluid inlet temperature (K) | 345.00 |

Working fluid outlet temperature (K) | 307.98 |

Working fluid inlet pressure (MPa) | 3.89 |

Working fluid mass flow (kg·s^{−1}) | 1.62 |

Heat rejection (kW) | 463.00 |

Air mass flow (kg·s^{−1}) | 22.20 |

Air mean outlet temperature (K) | 318.85 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zhou, Y.; Tang, J.; Zhang, C.; Li, Q.
Thermodynamic Analysis of the Air-Cooled Transcritical Rankine Cycle Using CO_{2}/R161 Mixture Based on Natural Draft Dry Cooling Towers. *Energies* **2019**, *12*, 3342.
https://doi.org/10.3390/en12173342

**AMA Style**

Zhou Y, Tang J, Zhang C, Li Q.
Thermodynamic Analysis of the Air-Cooled Transcritical Rankine Cycle Using CO_{2}/R161 Mixture Based on Natural Draft Dry Cooling Towers. *Energies*. 2019; 12(17):3342.
https://doi.org/10.3390/en12173342

**Chicago/Turabian Style**

Zhou, Yingjie, Junrong Tang, Cheng Zhang, and Qibin Li.
2019. "Thermodynamic Analysis of the Air-Cooled Transcritical Rankine Cycle Using CO_{2}/R161 Mixture Based on Natural Draft Dry Cooling Towers" *Energies* 12, no. 17: 3342.
https://doi.org/10.3390/en12173342