#
Effects of Intercooling and Inter-Stage Heat Recovery on the Performance of Two-Stage Transcritical CO_{2} Cycles for Residential Heating Applications

^{*}

## Abstract

**:**

_{2}) have been attracting great interest. The higher inter-stage superheating of CO

_{2}makes it difficult to predict the effects of the intercooling on heating performance of a two-stage transcritical CO

_{2}cycle. In addition, very little is known about the potential of inter-stage heat rejection recovery in the heating performance enhancement of this cycle. In order to explore the effects of intercooling and inter-stage heat rejection recovery potential, three “sub-cycles”—(1) a sub-cycle with heat recovery, (2) a sub-cycle without heat recovery, and (3) a sub-cycle without intercooling—were modeled in Engineering Equation Solver (EES) software for three commonly-used two-stage transcritical cycles: (1) an intercooler cycle, (2) a flash cycle, and (3) a split cycle. Then, the discharge pressure and intermediate pressure were simultaneously optimized. Based on the optimization results, the heating performance of the sub-cycles for each cycle were compared. The results demonstrate that the incorporation of intercooling without heat recovery was detrimental to the heating performance in comparison to the absence of intercooling. It is also clear that there is a great potential for heating performance improvement through inter-stage heat recovery.

## 1. Introduction

_{2}) is considered especially attractive because it is nonflammable, nontoxic, free from mutagens and carcinogens, and very low in cost [1]. However, the major disadvantage of the CO

_{2}cycle that influences its acceptance in the market is its lower performance [2,3,4].

_{2}, in most areas of application, cycles are operated in transcritical conditions, and the existence of an “optimum” discharge pressure has received significant attention in the research community. In terms of the two-stage transcritical CO

_{2}cycle, both the intermediate pressure and discharge pressure influence system performance, with each having an optimum value. Due to this unusual nature, many researchers have conducted studies on the optimization of the discharge pressure and intermediate pressure for two-stage transcritical CO

_{2}cycles.

_{2}cooling cycles. They reported that the ideal intermediate pressure has frequently been found to differ from the classical estimation of the geometric mean of the evaporator and discharge pressure. The formula for the classical estimation is $\sqrt{Pev\times Pd}$, where $Pev$ is the pressure in the evaporator and $Pd$ is the discharge pressure of the second-stage compressor. Additionally, an optimum discharge pressure has generally been found to exist, with a higher gas cooler temperature leading to a higher optimum discharge pressure. Hwang et al. [7] measured the experimental performance of intercooler and split cycles, and found that every cycle displayed an optimum discharge pressure. Cavallini et al. [8] performed a theoretical analysis on a split cycle and an experimental analysis on an intercooler cycle. They investigated the effect of the second-stage pressure ratio on performance. Manole [9] found that the optimum intermediate pressure differed from the classical estimate also. Agrawal et al. [10] simultaneously optimized the discharge pressure and inter-stage pressure for flash and intercooler cycles, and found an optimum intermediate pressure and optimum discharge pressure for each cycle. Ozgur [11] performed a theoretical simulation of an intercooler cycle and determined the optimum discharge pressure for various gas cooler outlet temperatures. Ozgur and Bayrakci [12] studied the effect of the intermediate pressure on performance and concluded that there was an optimum intermediate pressure that maximized both first-law and second-law efficiencies. Cecchinato et al. [13] studied the split, flash, and intercooler systems experimentally, and confirmed that the optimum intermediate pressure deviated from the classical estimate by examining different intermediate pressures at specific discharge pressures. Srinivasan [14] studied an intercooler system and also found that the optimal intermediate pressure differed from the classical estimate. Almeida and Barbosa [15] simulated transcritical CO

_{2}cycles with and without intercooling. They found that intercooling provided a significant increase in the coefficient of performance (COP). Ozgur and Tosun [16] simulated flash and intercooler cycles and noted that the intermediate pressure had a greater effect on flash cycles. Zhang et al. [17] examined the effect of the discharge pressure, intermediate pressure, and mass flow rate on various flash and intercooler systems, and found an optimum value for all parameters investigated. Bush et al. [3] tested a lab-scale two-stage system to explore the effects of the mechanical subcooling on the system performance. A steady-state model for the system was developed and presented. To improve the performance of the transcritical CO

_{2}system, different combinations of a liquid suction heat exchanger after-cooler and two-stage compression were embedded into the system configuration by Mohammadi [4]. The modified configurations were modeled in detail using Engineering Equation Solver (EES) software, and energy and exergy analyses were performed for each configuration.

_{2}cycles with and without an expander-compressor, which used an expander as an expansion device and served as an assistant compressor or the main compressor. Several different expander-compressor arrangements, including the two-stage cycle, were investigated. Bayrakci et al. [20] also analyzed the expander usage in a two-stage transcritical CO

_{2}cooling system. Variable parameters in this study were the gas cooler pressure, inter-stage pressure, and evaporation temperature of the refrigerant. Xing et al. [21] proposed a cycle with two ejectors as expansion devices. The performance of the improved two-stage cycles were evaluated and then compared with those of the basic two-stage cycle with a flash tank. Nemati et al. [22] compared the performance of a two-stage ejector-expansion transcritical refrigeration cycle using ethane and CO

_{2}as refrigerants. The theoretical analysis of the cycle performance characteristics was carried out for both refrigerants according to the first and second laws of thermodynamics. Zhang et al. [23] conducted a sensitivity study for three typical expander-based transcritical CO

_{2}cycles, including a two-stage cycle. The sensitivities of the maximum COP to the key operating parameters, including the inlet pressure of the gas cooler, the temperatures at evaporator inlet and gas cooler outlet, the inter-stage pressure, and the isentropic efficiency of expander, were obtained.

_{2}cycle for heating applications regarding COP in terms of the discharge pressure. The classical estimate of the intermediate pressure was employed in this analysis. This finding differs from cooling cycle in that the heating COP decreases as the refrigerant is cooled down at the intercooler.

_{2}system for cooling applications while few paid attention to cycles for heating applications. In fact, the inter-stage superheating of compressed CO

_{2}vapor is far higher than that of traditional refrigerants [13]. For example, when R134a, R410a, and CO

_{2}are compressed between an evaporating temperature of 270 K and a condensing temperature of 290 K, R134a is superheated by only 2.88 K and R410a is superheated by 8.89 K, while CO

_{2}is superheated by 16.57 K. This feature leads to the difficulty in predicting whether the intercooling has a beneficial effect on the heating performance of the two-stage cycle. This is because the removal of heat decreases the second-stage work but it also reduces the amount of heat that can be released from the gas cooler. As a result, it is not apparent which of these opposing effects has a greater influence on heating COP. In addition, it would be a waste of energy if the inter-stage heat is rejected to the ambient environment. However, very little is known about the potential of inter-stage heat rejection recovery in the heating performance enhancement of two-stage transcritical CO

_{2}cycles.

_{2}cycles for heating applications, three “sub-cycles” have been optimized and compared based on the models developed in EES 10.0 software (University of Wisconsin, WI, USA) for two-stage transcritical CO

_{2}cycles. Because both the two pressures could affect the performance, unlike using classical estimate of intermediate pressure in Pitarch et al. [25], the two optimal pressures for each sub-cycle were identified simultaneously in this study. The three sub-cycles were: (1) a sub-cycle with heat recovery (with HR), (2) a sub-cycle without heat recovery (without HR), and (3) a sub-cycle without intercooling (without IC). In terms of two-stage cycle selection for investigation, due to the unavailability of advanced expansion technology in the market and the findings that the throttling valve heating cycles are able to be applied to the advanced expansion cycles, in this study, the three commonly-used cycles with a throttling valve were investigated: (1) a basic two-stage compression intercooler cycle, (2) a flash cycle, and (3) a split cycle.

## 2. Cycles and Sub-Cycles under Analysis

_{2}expanding after the gas cooler enters a flash tank at the inter-stage pressure, where the vapor will be drawn by the HP compressor and the liquid will be throttled to the evaporator pressure. (3) Split Cycle: The cycle incorporates an LP and HP compressor in series, and two expansion valves. The mass flow splits after the gas cooler, where one part expands through the valve and enters the evaporator, and the other part expands and is injected with the outgoing stream of the low-pressure compressor.

_{2}(kg/s);$h$ is the specific enthalpy of CO

_{2}(kJ/kg).

## 3. Mathematical Modelling

#### 3.1. Thermodynamic Analysis

_{2}and water, which are presented as follows from the former research results.

_{2}pressure at the outlet of the compressor (MPa), and ${P}_{c,i}$ is the CO

_{2}pressure at the inlet of the compressor (MPa). For the split cycle, the temperatures for the high-pressure IHX could be given by [25]:

_{2}enthalpy at the outlet of the expansion valve (kJ/kg) and ${h}_{\mathrm{inlet}}$ is the CO

_{2}enthalpy at the inlet of the expansion valve (kJ/kg).

_{2}transcritical refrigeration plant, where the difference between the gas cooler outlet CO

_{2}temperature and inlet water temperature was reported to be less than 5 °C. Hence, the temperature difference between the inlet water and outlet CO

_{2}was taken as 5 °C in this study.

_{2}cycle, the pressure drop in the pipes and heat exchanger is very small. Hence, the pressure drop in the pipes and heat exchangers were considered to be negligible. This assumption has little influence on the thermodynamic state parameters and thus the optimization results.

#### 3.2. Optimization Conditions

_{2}are 31.1 °C and 7.39 MPa, this means the heat is rejected in a supercritical process in residential heating applications. Hence, the lower bound of the P

_{D}for the second stage compressor was taken to be 7.4 MPa and the upper bound of the P

_{M}, namely the discharge pressure of the first stage compressor, was taken to be 6.8 MPa. The manufacturer could provide a CO

_{2}compressor capable of operating at the maximum of 14 MPa; therefore, the upper bound of the P

_{D}was taken to be 14 MPa.

_{2}temperature (discussed in Section 3.1), the lower bound of P

_{M}for these two sub-cycles was set to be 5.1 MPa, where 5.1 MPa is the corresponding saturated pressure of CO

_{2}at 15 °C. Table 2 presents the optimization conditions.

## 4. Results and Discussion

_{D}and P

_{M}. The performance was evaluated over an evaporator temperature range of −20 °C to 0 °C. The heat rejected from gas cooler was used for space heating, so the gas cooler outlet temperature of CO

_{2}was fixed at 40 °C to meet the requirements of space heating. This temperature could be achieved by adjusting the inlet water flow rate according to the heat demand. The performance parameters and their optimum values are displayed graphically and elucidated below.

#### 4.1. Optimization Results

#### 4.1.1. Intercooler Cycle

_{D}and P

_{M}for each sub-cycle with the change of T

_{ev}from −20 °C to 0 °C for the intercooler cycle. It was found that for the sub-cycle without heat recovery, the optimum P

_{M}was calculated to have an optimum value of 5.1 MPa for all operating conditions. This means the that sub-cycle without heat recovery had a maximum COP when P

_{M}was operating at its minimum limit. The sub-cycle without intercooling had an optimum P

_{M}of 5.1 MPa when the T

_{ev}was less than −15 °C. It was also observed that the optimum P

_{D}of each sub-cycle decreased linearly with T

_{ev}. For the sub-cycle with heat recovery, the optimal P

_{D}decreased linearly with T

_{ev}, while P

_{M}increased with T

_{ev}.

#### 4.1.2. Flash Cycle

_{D}and P

_{M}for each sub-cycle with the change of T

_{ev}from −20 °C to 0 °C for the flash cycle. With the similarity of the intercooler cycle, the sub-cycle without heat recovery had an optimum P

_{M}of 5.1 MPa. The sub-cycle without intercooling had an optimum P

_{M}of 5.1 MPa at T

_{ev}equals −20 °C. It was also observed that the optimum P

_{D}decreased almost linearly with T

_{ev}for all the sub-cycles while P

_{M}increased with T

_{ev}for the sub-cycle with heat recovery. The optimum P

_{D}of the sub-cycle without HR showed a significant decrease, while the optimum P

_{D}had a slight decrease for the other two sub-cycles.

#### 4.1.3. Split Cycle

_{D}and P

_{M}for each sub-cycle with the change of T

_{ev}from −20 °C to 0 °C for the split cycle. It can be observed that, regarding the optimal P

_{M}of the sub-cycle without heat recovery, the split cycle resembled the other two cycles investigated above. The sub-cycle without heat recovery had an optimum P

_{M}of 5.1 MPa until T

_{ev}was around −5 °C. Like the flash cycle, the optimum P

_{D}decreased almost linearly with the increase of the T

_{ev}for all the sub-cycles and the P

_{M}increased with the increase of the T

_{ev}for the sub-cycle with heat recovery and the sub-cycle without intercooling. This might be because the sub-cycle without heat recovery had the maximum COP at the lower bound of the P

_{M}when the T

_{ev}was less than −5 °C. Therefore, the P

_{D}without HR was larger than the P

_{D}with HR when the T

_{ev}was less than −5 °C and lower than the P

_{D}with HR when T

_{ev}was 0 °C and −5 °C.

_{D}and P

_{M}values of the three cycle types, it can be concluded that the optimal P

_{D}decreased with T

_{ev}and the optimal P

_{M}increased with T

_{ev}for two-stage heating operations. These findings agree with the results of Agrawal et al. [10] for cooling operations.

#### 4.2. Effects on Performance

#### 4.2.1. Intercooler Cycle

_{ev}varied from −20 °C to 0 °C, the sub-cycle with heat recovery experienced an increase in COP from 2.4 to 3.3. The COP of the sub-cycle with heat recovery was greater than that of the sub-cycle without intercooling by 11.2% to 14.1%, and greater than that of the sub-cycle without heat recovery by 24.2% to 50.3%.

_{2}mass for the sub-cycles operating at optimum conditions in the intercooler cycle.

_{ev}= −20 °C, the heating capacity of the sub-cycle without intercooling was greater than that of the sub-cycle with heat recovery by 5.3%. Meanwhile, the compression work of the sub-cycle without intercooling was greater than that of the sub-cycle with heat recovery by 17.3%. As a result, the sub-cycle with heat recovery outperformed the sub-cycle without intercooling.

#### 4.2.2. Flash Cycle

_{ev}from 2.7 to 3.7, and was greater than that of the sub-cycle without intercooling by 9.8% to 10.4%. It was also greater than that of the sub-cycle without heat recovery by 34.3% to 19.7% as the evaporator temperature increased. In addition, the COP of the sub-cycle without heat recovery was less than that of the sub-cycle without intercooling by 17.7% to 7.8% as T

_{ev}increased.

_{ev}increased. The compression work of the sub-cycle without intercooling was more than that of the sub-cycle without heat recovery by 11.3% to 8.7% as T

_{ev}increased. Obviously, the greater heating capacity of the sub-cycle without intercooling was a more significant factor that its better performance. Hence, the sub-cycle without intercooling yielded a higher COP than the sub-cycle without heat recovery.

#### 4.2.3. Split Cycle

_{ev}.

_{M}at the lower bound until T

_{ev}was around −5 °C. Consequently, the heating capacity slope of the sub-cycle without HR changed at around −5 °C. This led to the heating capacity of the sub-cycle without HR being greater than the sub-cycle with HR when T

_{ev}was more than −5 °C.

## 5. Conclusions

_{2}cycle and inter-stage heat rejection recovery potential were explored for three commonly used two-stage cycles—intercooler, flash, and split cycles—through a performance comparison of three sub-cycles. When the sub-cycles operated at optimal conditions, the main findings were as follows:

- There was a great potential for performance improvement via the recovery of heat from the intercooler. The COP of the sub-cycle with heat recovery was greater than that of the sub-cycle without intercooling by around 13.1% for the basic intercooler cycle, 10.2% for the flash cycle, and 10.9% for the split cycle; furthermore, it was greater than that of the sub-cycle without heat recovery by around 37.5% for the basic intercooler cycle, 26.0% for the flash cycle, and 25.4% for the split cycle.
- Incorporating an intercooler without heat recovery reduced the COP compared to the sub-cycle without intercooling for all cycle types. The COP of the sub-cycle without heat recovery was less than that of the sub-cycle without intercooling by around 17.4% for the basic intercooler cycle, 12.4% for the flash cycle, and 11.4% for the split cycle.
- The sub-cycle with heat recovery had a better COP than the sub-cycle without intercooling for all three cycle types examined; this was because the sub-cycle with heat recovery had lower compression work and lower heating capacity. However, the lowered compression work was a more significant factor, which led to a better performance. Similarly, the lower COP of the sub-cycle without heat recovery compared to the sub-cycle without intercooling was attributed to the fact that the decrease in heating capacity was more significant than the difference in compression work.
- It was found that the optimum discharge pressure, P
_{D}, decreased with the evaporating temperature, T_{ev}, and the optimum intermediate pressure, P_{M}, increased with T_{ev}. This result was consistent with the results for cooling operations in the literature.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

${P}_{c,o}$ | Pressure at the outlet of the compressor (MPa) |

${P}_{c,i}$ | Pressure at the inlet of the compressor (MPa) |

${P}_{D}$ | Discharge pressure of the second-stage compressor (MPa) |

${P}_{M}$ | Inter-stage pressure (MPa) |

$\dot{W}$ | Compression work (kJ/s) |

$\dot{Q}$ | Heating capacity (kJ/s) |

$\eta $ | Compressor efficiency (-) |

${\dot{m}}_{1}$ | Mass flowrate (kg/s) |

$h$ | Specific enthalpy (kJ/kg) |

## References

- Kim, M.H.; Pettersen, J.; Bullard, C.W. Fundamental process and system design issues in CO
_{2}vapor compression systems. Prog. Energy Combust. Sci.**2004**, 30, 119–174. [Google Scholar] [CrossRef] - Sarkar, J. Review on Cycle Modifications of Transcritical CO
_{2}Refrigeration and Heat Pump Systems. J. Adv. Res. Mech. Eng.**2010**, 1, 22–29. [Google Scholar] - Bush, J.; Beshr, M.; Aute, V.; Radermacher, R. Experimental evaluation of transcritical CO
_{2}refrigeration with mechanical subcooling. Sci. Technol. Built Environ.**2017**, 23, 1013–1025. [Google Scholar] [CrossRef] - Mohammadi, S.M.H. Theoretical investigation on performance improvement of a low-temperature transcritical carbon dioxide compression refrigeration system by means of an absorption chiller after-cooler. Appl. Therm. Eng.
**2018**, 138, 264–279. [Google Scholar] [CrossRef] - Dincer, I.; Kanoglu, M. Refrigeration Systems and Applications, 2nd ed.; John Wiley & Son: Hoboken, NJ, USA, 2010; p. 119. [Google Scholar]
- Groll, E.A.; Kim, J.H. Review of recent advances toward transcritical CO
_{2}cycle technology. HVAC R Res.**2007**, 13, 499–520. [Google Scholar] [CrossRef] - Hwang, Y.H.; Celik, A.; Radermacher, R. Performance of CO
_{2}cycles with a two stage compressor. In Proceedings of the International Refrigeration and Air Conditioning Conference, West Lafayette, IN, USA, 12–15 July 2004. [Google Scholar] - Cavallini, A.; Cecchinato, L.; Corradi, M.; Fornasieri, E.; Zilio, C. Two-stage transcritical carbon dioxide cycle optimisation: A theoretical and experimental analysis. Int. J. Refrig.
**2005**, 28, 1274–1283. [Google Scholar] [CrossRef] - Manole, D. On the optimum inter-stage pressure parameters for CO
_{2}trans-critical systems. In Proceedings of the 7th Gustav Lorentzen Conference on Natural Working Fluids, Trondheim, Norway, 29–31 May 2006. [Google Scholar] - Agrawal, N.; Bhattacharyya, S.; Sarkar, J. Optimization of two-stage transcritical carbon dioxide heat pump cycles. Int. J. Therm. Sci.
**2007**, 46, 180–187. [Google Scholar] [CrossRef] - Ozgur, A.E. The performance analysis of a two-stage transcritical CO
_{2}cooling cycle with various gas cooler pressures. Int. J. Energy Res.**2008**, 32, 1309–1315. [Google Scholar] [CrossRef] - Ozgur, A.E.; Bayrakci, H.C. Second law analysis of two-stage compression transcritical CO
_{2}heat pump cycle. Int. J. Energy Res.**2008**, 32, 1202–1209. [Google Scholar] [CrossRef] - Cecchinato, L.; Chiarello, M.; Corradi, M.; Fornasieri, E.; Minetto, S.; Stringari, P.; Zilio, C. Thermodynamic analysis of different two-stage transcritical carbon dioxide cycles. Int. J. Refrig.
**2009**, 32, 1058–1067. [Google Scholar] [CrossRef] - Srinivasan, K. Identification of optimum inter-stage pressure for two-stage transcritical carbon dioxide refrigeration cycles. J. Supercrit. Fluids
**2011**, 58, 26–30. [Google Scholar] [CrossRef] - Almeida, I.M.G.; Barbosa, C.R.F.; Int Inst, R. Influence factors in performance of the two-stage compression transcritical R744 cycle. In Iir International Congress of Refrigeration, 23rd ed.; Int Inst Refrigeration: Paris, France, 2011; Volume 23, p. 782. [Google Scholar]
- Ozgur, A.E.; Tosun, C. Thermodynamic analysis of two-stage transcritical CO
_{2}cycle using flash gas by-pass. Int. J. Exergy**2015**, 16, 127–138. [Google Scholar] [CrossRef] - Zhang, Z.Y.; Wang, H.L.; Tian, L.L.; Huang, C.S. Thermodynamic analysis of double-compression flash intercooling transcritical CO
_{2}refrigeration cycle. J. Supercrit. Fluids**2016**, 109, 100–108. [Google Scholar] [CrossRef] - Manjili, F.E.; Yavari, M.A. Performance of a new two-stage multi-intercooling transcritical CO
_{2}ejector refrigeration cycle. Appl. Therm. Eng.**2012**, 40, 202–209. [Google Scholar] [CrossRef] - Sun, Z.L.; Li, M.X.; Han, G.M.; Ma, Y.T. Performance study of a transcritical carbon dioxide cycle with an expressor. Energy
**2013**, 60, 77–86. [Google Scholar] - Bayrakci, H.C.; Ozgur, A.E.; Alan, A. Thermodynamic analysis of expander usage in two stage transctitical R744 cooling systems. ISI Bilim. Tek. Derg.
**2014**, 34, 91–97. [Google Scholar] - Xing, M.B.; Yu, J.L.; Liu, X.Q. Thermodynamic analysis on a two-stage transcritical CO
_{2}heat pump cycle with double ejectors. Energy Conv. Manag.**2014**, 88, 677–683. [Google Scholar] [CrossRef] - Nemati, A.; Mohseni, R.; Yari, M. A comprehensive comparison between CO
_{2}and Ethane as a refrigerant in a two-stage ejector-expansion transcritical refrigeration cycle integrated with an organic Rankine cycle (ORC). J. Supercrit. Fluids**2018**, 133, 494–502. [Google Scholar] [CrossRef] - Zhang, B.; Chen, L.; Liu, L.; Zhang, X.Y.; Wang, M.; Ji, C.F.; Song, K.I. Parameter Sensitivity Study for Typical Expander-Based Transcritical CO
_{2}Refrigeration Cycles. Energies**2018**, 11, 1279. [Google Scholar] [CrossRef][Green Version] - Wang, H.L.; Ma, Y.T.; Tian, J.R.; Li, M.X. Theoretical analysis and experimental research on transcritical CO
_{2}two stage compression cycle with two gas coolers (TSCC plus TG) and the cycle with intercooler (TSCC plus IC). Energy Conv. Manag.**2011**, 52, 2819–2828. [Google Scholar] [CrossRef] - Pitarch, M.; Navarro-Peris, E.; Gonzalvez, J.; Corberan, J.M. Analysis and optimisation of different two-stage transcritical carbon dioxide cycles for heating applications. Int. J. Refrig.
**2016**, 70, 235–242. [Google Scholar] [CrossRef] - EES Manual. Available online: Fchartsoftware.com/assets/downloads/ees_manual.pdf (accessed on 1 December 2019).
- Ortiz, T.M.; Li, D.; Groll, E.A. Evaluation of the Performance Potential of CO
_{2}as a Refrigerant in Air-to-Air Air Conditioners and Heat Pumps: System Modelling and Analysis. In ARTI Final Report; No. 21CR/610-10030; Research Centre, Purdue University: West Lafayette, IN, USA, 2003. [Google Scholar] - Llopis, R.; Nebot-Andrés, L.; Cabello, R.; Sánchez, D.; Catalán-Gil, J. Experimental evaluation of a CO
_{2}transcritical refrigeration plant with dedicated mechanical subcooling. Int. J. Refrig.**2016**, 69, 361–368. [Google Scholar] [CrossRef]

**Figure 1.**Intercooler cycle: (

**a**) schematic and (

**b**) P–h diagram. HP: high pressure, LP: low pressure. (The numbers (1, 2, 3, 4, 5, 6) in (

**a**) refer to the position of the working fluid; The numbers (1, 2, 3, 4, 5, 6) in (

**b**) refer to the thermodynamic state point of the working fluid in P–h diagram.).

**Figure 2.**Flash cycle: (

**a**) schematic and (

**b**) P–h diagram. (The numbers (1, 2, 3, 4, 5, 6) in (

**a**) refer to the position of the working fluid; The numbers (1, 2, 3, 4, 5, 6) in (

**b**) refer to the thermodynamic state point of the working fluid in P–h diagram.).

**Figure 3.**Split cycle: (

**a**) schematic and (

**b**) P–h diagram. (The numbers (1, 2, 3, 4, 5, 6) in (

**a**) refer to the position of the working fluid; The numbers (1, 2, 3, 4, 5, 6) in (

**b**) refer to the thermodynamic state point of the working fluid in P–h diagram.).

**Figure 7.**Heating coefficient of performance (COP) for the intercooler cycle at an optimum discharge and intermediate pressure.

**Figure 8.**Heating capacity and compression work for intercooler cycle at an optimum discharge and intermediate pressure.

**Figure 10.**Heating capacity and compression work for the flash cycle at an optimum discharge and intermediate pressure.

**Figure 12.**Heating capacity and compression work for split cycle at optimum discharge and intermediate pressure.

Name of the Sub-Cycle | Feature | Abbreviation |
---|---|---|

Sub-cycle with heat recovery | With both intercooling and heat recovery | with HR |

Sub-cycle without intercooling | With neither intercooling or heat recovery | without IC |

Sub-cycle without heat recovery | With only intercooling | without HR |

Name of the Sub-Cycles | P_{D} | P_{M} | ||
---|---|---|---|---|

Lower bound | Upper bound | Lower bound | Upper bound | |

Sub-cycle with heat recovery | 7.4 MPa | 14 MPa | 5.1 MPa | 6.8 MPa |

Sub-cycle without intercooling | 7.4 MPa | 14 MPa | 2.5 MPa | 6.8 MPa |

Sub-cycle without heat recovery | 7.4 MPa | 14 MPa | 5.1 MPa | 6.8 MPa |

© 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/).

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**MDPI and ACS Style**

Ma, J.; Mhanna, A.; Juan, N.; Brands, M.; Fung, A.S. Effects of Intercooling and Inter-Stage Heat Recovery on the Performance of Two-Stage Transcritical CO_{2} Cycles for Residential Heating Applications. *Energies* **2019**, *12*, 4763.
https://doi.org/10.3390/en12244763

**AMA Style**

Ma J, Mhanna A, Juan N, Brands M, Fung AS. Effects of Intercooling and Inter-Stage Heat Recovery on the Performance of Two-Stage Transcritical CO_{2} Cycles for Residential Heating Applications. *Energies*. 2019; 12(24):4763.
https://doi.org/10.3390/en12244763

**Chicago/Turabian Style**

Ma, Juanli, Ahmad Mhanna, Neil Juan, Monica Brands, and Alan S. Fung. 2019. "Effects of Intercooling and Inter-Stage Heat Recovery on the Performance of Two-Stage Transcritical CO_{2} Cycles for Residential Heating Applications" *Energies* 12, no. 24: 4763.
https://doi.org/10.3390/en12244763