#
Investigation of the Impact Factors on the Optimal Intermediate Temperature in a Dual Transcritical CO_{2} System with a Dedicated Transcritical CO_{2} Subcooler

^{*}

## Abstract

**:**

_{2}is used to constitute a dual transcritical system to reduce performance deterioration under high gas-cooler outlet temperature. Aiming at the system configuration, improvement potential, and optimization, the proposed system is deeply analyzed, and corresponding coupling models are presented in detail. First, the veracity of simulation models is completely verified by comparing with previous measurements. Then, the existence of the optimal intermediate temperature is validated, while the optimal values are found to increase with the augmentation in ambient and water-feed temperatures. Moreover, the negative effects of the pinch point on the heat transfer inside the gas cooler could be greatly reduced by using the dual gas cooler. Finally, a predictive correlation for optimal intermediate temperature determination with ambient and water-feed temperature as independent variables is proposed, which provides a theoretical basis for the proposed system to realize efficient control in the industrialization process.

## 1. Introduction

_{2}in this study) has come back into researchers’ views since its transcritical operating mode was proposed by Lorentzen [1,2]. In recent years, the transcritical CO

_{2}system was further introduced into space-heating applications [3,4] due to its characteristics that can be employed to provide a hot recirculating medium at extremely high temperature [5]. In cold regions with a heating season of more than 4 months, especially in northern China, coal-fired boilers, gas-fired boilers, and even electric boilers (and coal-fired electricity in general) are still the most widely used type of space heating, which has doubtlessly brought about great environmental pollution. By contrast, air-source heat-pump heating technology is a cleaner solution since the only consumption is electric power and most of the energy source is heat energy from the atmosphere. Thus, as natural refrigeration with the ability for high-temperature water supply in a transcritical mode, the import of a transcritical CO

_{2}system into space-cooling/heating applications suggests a revolution in the heating/cooling energy-supply fields because of the environmental friendliness and higher performance coefficient (ratio of heating capacity and power consumption).

_{2}system would deteriorate sharply with the increase in the gas-cooler outlet CO

_{2}temperature that is limited by the working medium (water in general) inlet temperature is always the biggest problem blocking its popularization within the space-heating industries. Researchers have been devoted to performance improvement studies of the transcritical CO

_{2}system for decades.

_{2}system, the flash tank/economizer and multi-compression (which are called “parallel cycles” in this article) were introduced into the transcritical cycles. Although a quite mature technology for conventional refrigeration cycles [10,11,12], the parallel cycles not only enhanced the system performance, but also improved system properties such as the reduction of discharge temperature [13]. Additionally, various research has been carried out around vapor injection techniques in transcritical cycles, and three kinds of modifications were compared [14,15,16]. Similarly, with the expander-based system, the vapor ejector benefits from energy recovery from the expanding process into the compression process [17,18]. Considering the very high-pressure difference between cooling and evaporating pressures in the transcritical cycle, the potential for energy recovery could be remarkable.

_{2}temperature directly, the subcooling technology has developed considerably over recent years. Sarkar proposed a combined configuration of the transcritical CO

_{2}system with an auxiliary thermoelectric module as the subcooler, which is sandwiched between the gas cooler and expansion valve [21], by which the optimal discharge pressure could be reduced by more than 15% while the system COP could be increased up to 20% under certain conditions. Furthermore, considering the inconvenience of the thermoelectric module, Llopis et al. proposed a similar system with a conventional vapor-compression cycle as the subcooler [22,23], by which better subcooling effects could be achieved. In addition, as the working fluid in the subcooler, several kinds of refrigerants are comprehensively compared regarding their subcooling performance, where it is found that no obvious difference in system performance occurred with a change of working refrigerants. Aiming for a similar subcooler-based transcritical CO

_{2}system, Dai et al. studied energetic performance by using zeotropic mixture refrigerant as the working fluid in the subcooler [24], and the corresponding exergy and economic analyses were carried out in detail [25].

_{2}system as the expansion device instead of the expander, and the benefit of the vortex tube lies not only in the transformation from isenthalpic throttling to isentropic expansion, but also in the additional heating capacity caused by the hot side of the vortex tube. Theoretical results showed that the vortex tube-based transcritical CO

_{2}system performs significantly better over the baseline cycle [26]; however, no experimental validation could be found to support the theoretical conclusions.

_{2}system is employed to be the auxiliary subcooler. With the help of a transcritical CO

_{2}subcooler proposed in our study, this combined system has finally, and for the first time, achieved the goal of energy-saving and environmental protection. Similar to the HFC subcooler-based systems, the auxiliary transcritical CO

_{2}cycle is also installed between the main cycle’s gas cooler and electrical expansion valve (EEV), while the operating mechanism and corresponding dynamic response rules of the whole system might be different because the operating mode of the auxiliary cycle is transformed from the subcritical to the transcritical. In this study, the whole system (i.e., an upgraded heat-pump system) is theoretically discussed in depth and the inherent characteristics of the system are well established.

_{2}system, subcooling technology has already become one of the most popular topics in both cooling and heating applications. Much significant research has been carried out regarding performance prediction, simulation procedure, and parameter optimization works of the subcooler-based system, although there still are some specific points to be mentioned in this study. First, our work is one of the few that use pure natural refrigerant (CO

_{2}) replacing HFCs and hydrocarbon (HCs) (R134a, R600a etc.) as the working fluid in the subcooler cycle, which manifested the lower GWP of our system, because R744 (CO

_{2}) GWP = 1, R600a GWP = 3, and R134a GWP = 1300. Second, in this study, the main points of the research on the dual system are the establishment and validation of the simulation models, as well as the prediction of the optimal intermediate temperature. Moreover, most content in this paper is occupied by the discussion of the effective factors seeking the optimal intermediate temperature, and a predictive correlation is finally obtained based on the operating conditions as variables.

## 2. System Description

#### 2.1. System Configuration

_{2}flows from both auxiliary and main cycles are located on the right side of the gas cooler, where the exit of the recirculating water loop is also located. As a whole, the proposed dual CO

_{2}system could realize the intended target: absorbing thermal energy from the ambient environment via the main cycle evaporator (i.e., a fine-tube heat exchanger) and exhausting thermal energy to the recirculating water via the dual gas cooler, which results in space-heating effects through the heating terminals during the heating season (more than 4 months in northern China). With the assistance of 6 pressure transmitters and 12 thermocouples (including the ambient temperature sensor, which does not appear in Figure 1a), all the refrigerant state points could be measured and thermodynamic research could be continued.

#### 2.2. Theoretical Analysis

_{2}at the main cycle’s gas-cooler outlet could be further cooled down from state point 9 to state point 3. Having been subcooled, the CO

_{2}temperature before the main cycle’s EEV could be reduced to lower than the water-feed temperature (i.e., 40 °C in Figure 1b), which causes a lower discharge pressure in the main cycle. Comparatively, the discharge pressure of the auxiliary cycle must be much higher than that of the main cycle because the CO

_{2}temperature before the auxiliary cycle’s EEV should be no less than the water-feed temperature. Moreover, in general, the discharge temperature increases with increase in discharge pressure. However, due to higher evaporating pressure and lower pressure ratio in this cycle, the discharge temperature of the auxiliary cycle might be remarkably lower than that of the main cycle (see Figure 1b) although the auxiliary cycle’s discharge pressure is far higher. As a coupled system, the displacement ratio of the two compressors is strictly constrained by the heating capacity coupling condition: the cooling capacity of the auxiliary cycle should be identical to the subcooling capacity of the main cycle, i.e., the regulation of the intermediate temperature (achieved by regulating the auxiliary compressor speed) can be only realized by adjusting the compressor displacement ratio or frequency ratio.

_{2}temperature before the main cycle’s EEV and the increase in the auxiliary cycle’s evaporating pressure would definitely occur in pairs, as the red dashed lines show in Figure 1b. The variation mentioned above causes changes to the internal heat-transfer capacity ($\mathsf{\Delta}{\mathrm{Q}}_{inter}$) and the main cycle’s quality after the EEV ($\mathsf{\Delta}{\mathrm{x}}_{evap,in}$) in Figure 1b.

## 3. Mathematical Model

#### 3.1. The Seeking Process of Optimal Discharge Pressures

#### 3.2. The Simulation Process of the Dual System’s Thermodynamic Performance

_{2}compression process [27], the heat transfer in the internal heat exchanger [3,28], the supercritical CO

_{2}cooling process in the gas cooler [29,30], the subcritical CO

_{2}evaporating process [31], and the heat-transfer correlations of air and water sides [32]. The main equations and correlations of those components’ simulation models are summarized in Table 1. In the whole simulation process, because our creative works are embodied not in the mathematical models of the components but in the coupling model of the overall system, the simulation flow charts are clearly shown in this section.

## 4. Results Discussion

#### 4.1. The Verification of the Simulation Model

_{2}system with a dedicated transcritical CO

_{2}subcooler is carefully built, and plentiful measurements are carried out in the enthalpy difference laboratory. The detailed parameters of the prototype can be found in our previous publication [33], and the intermediate temperature can be achieved by regulating the auxiliary compressor speed. After comparing the simulation results with our previous tests, the veracity of the simulation models can be verified, which gives us the convenience to carry on the discussion that is shown below based only on the simulation results. The relative errors between the tested data and simulation results are no more than 5% across the operating range, and the comparison is shown in Figure 3. The working condition is −12°C in ambient temperature, and 50 °C/70 °C in water-feed/supply temperature, respectively.

#### 4.2. Discussion about the Intermediate Temperature

_{2}gas-cooler outlet temperatures of both main and auxiliary cycles, and the water-feed temperature. The theoretical data shown by the full lines in Figure 4, Figure 7 and Figure 9 are simulated results considering the discharge pressure optimizations in both main and auxiliary cycles. However, the observed optimal discharge pressures of one or both sub-cycles are not high enough to bring about the expected discharge temperatures in some cases, which causes a deficiency of the heat-transfer temperature difference between the CO

_{2}flows and the recirculating water, if the water-supply temperature is high. Because of the low temperature difference following the deficiency of the heating capacity, the CO

_{2}gas-cooler outlet temperature could not be completely cooled down to the level of the water-feed temperature any further. It is conceivable that the settled discharge pressures should be further increased to overcome the deterioration caused by the much higher gas-cooler outlet temperatures, which brings about the irreversible decline of the overall system performance, as shown by the dashed lines in Figure 4. In contrast to the full lines that represent the ideal cases, these situations are defined by “real cases” in this study to show that those cases represented by the dashed lines are real results considering the fixed heat exchanger in practice. The above-mentioned deterioration would be sharper with the decline in water-feed temperature, the rise in ambient temperature, and the increase in water-supply temperature, because lower water-feed temperature corresponds to lower optimal discharge pressures, and higher ambient temperature represents lower compression ratio, which would definitely cause a decline in discharge temperature. Moreover, higher water-supply temperature is adverse for the establishment of temperature difference inside the gas cooler.

_{2}refrigerant the lower the refrigerant temperature is after the main EEV, the further the refrigerant state point deviates from the saturated liquid line.

_{2}cycle: the discharge pressure of the main cycle does not increase with the increasing refrigerant temperature before EEV, while that of the auxiliary cycle does not rise with the increase in evaporating temperature. The conclusion that the discharge pressure would increase with evaporating temperature is proposed under the premise of certain water-supply temperature or certain heat-transfer temperature differences inside the gas cooler. However, the discharge temperature of the auxiliary cycle is very free in most cases in this study, which causes a declining optimal discharge pressure with rising evaporating temperature [34]. The simulation evidence has indicated that great increase in power dissipation and little increase in heating capacity could be achieved by a further rise in the auxiliary cycle’s discharge pressure.

_{2}would never during the heat-transfer process reach inside the gas cooler of a transcritical CO

_{2}cycle, the pinch point of the heat transfer can also be observed in many cases due to the huge increase of specific heat near the critical point [35]. As shown in Figure 10b, the curve of the water temperature displays almost a linear growth, while the cooling rate curve of the refrigerant CO

_{2}is much more complicated with the change of the complex heat capacity variation near the critical point. It is well known that a steep rise of specific heat capacity of refrigerant CO

_{2}could be observed nearby the critical point, which causes a slow process of temperature change to be seen during the heat-rejection process from point 1 to 3 in Figure 1b. That trend is clearly shown in Figure 10b as a blue line. By contrast, the specific heat capacity of water keeps almost constant during the heating process, which causes linear growth of the black line in Figure 10b. As a result, the temperature distribution inside the gas cooler must experience a certain process with lower temperature difference between water and CO

_{2}. Moreover, it could be found that the heating rate curve of the recirculating water would be slowed down gradually before the pinch point if the flow path geometry of the gas cooler is settled as the abscissa, because the heat-transfer temperature difference declines gradually. However, as shown in Figure 10a, the inflection points of both the cooling rate curves are located in different places, which consequently makes the heating rate curve of the recirculating water rise smoothly and the average heat-transfer temperature difference remain almost constant along the main region of the gas cooler. Through such a clever design, a preferable configuration of the dual system with better compactness and higher heat-transfer efficiency inside the gas cooler could be finally achieved.

#### 4.3. Predictive Correlation

#### 4.4. Regulation of the Intermediate Temperature

## 5. Conclusions

_{2}system is discussed in a wide range of operating conditions. Based on the economic analyses in the literature [24,25], a conclusion is drawn that the dual system is advantageous in in an economic respect if it could be popularized, because higher heating performance and COP result in lower operating costs. Moreover, the optimal intermediate temperature of the dual system is studied based on theoretical simulation and corresponding results, and the main conclusions are as follows:

- (i)
- After comparison with the measurement data from our previous works, the veracity of the simulation models could be verified, which gives us the convenience to carry on the most discussion based on only the simulation results.
- (ii)
- The existence of optimal intermediate temperature is validated, while optimal values of the intermediate temperature increase with an increase in ambient temperature and water-feed temperature. Subsequently, the system COP also increases with an increase in ambient temperature, but decreases with the water-feed temperature.
- (iii)
- Due to the existence of the optimal intermediate temperature, the system performance rises first and then declines, while the auxiliary cycle’s performance rises gradually with the increase in intermediate temperature. As for the main cycle’s performance, no obvious rule could be observed.
- (iv)
- By using the dual gas cooler (the heat rejection of the auxiliary and main cycles is installed inside a same gas cooler), the negative effects of the pinch point on the heat transfer inside the heat exchanger could be greatly reduced.
- (v)
- A predictive correlation for the optimal intermediate temperature determination, with the ambient and water-feed temperature as the independent variables, is proposed, while the relative prediction errors are no more than 5% across 18 working conditions.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

A | Heat-transfer area (m^{2}) |

${c}_{p}$ | Specific heat capacity (kJ∙kg^{−1}∙K^{−1}) |

d | Diameter (m) |

f | Friction factor |

h | Enthalpy (kJ∙kg^{−1}) |

m | Mass flow rate (kg∙s^{−1}) |

p | Pressure (MPa) |

Pr | Prandtl number |

Q | Heat-transfer rate (kW) |

R | Fouling resistance (K∙m^{2}∙W^{−1}) |

Re | Reynolds number |

T | Temperature (℃) |

$\dot{W}$ | Power consumption (kW) |

$\alpha $ | Convective heat-transfer coefficient (W∙K^{-1}∙m^{-2}) |

$\delta $ | Thickness of the fin (m) |

γ | heat leakage coefficient |

$\eta $ | Efficiency |

$\lambda $ | Conductivity (W∙K^{-1}∙m^{-2}) |

$\rho $ | Density (kg∙m^{-3}) |

$\xi $ | Dehumidification coefficient |

Subscripts | |

av | Average |

air | air |

comp | Compressor |

eq | Equivalent |

eva | Evaporator |

f | feed |

gc | Gas cooler |

h | Heating |

i | Inner |

in | System inlet |

is | Isentropic |

out | System outlet |

o | Outer |

r | Refrigerant |

single | Single phase |

tube | tube |

v | Volumetric |

w | Water |

wall | Tube wall |

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**Figure 1.**(

**a**) The sketch map of the dual CO

_{2}system; (

**b**) the p-h diagram of the dual CO

_{2}system; (

**c**) the sketch map of the dual gas cooler.

**Figure 2.**(

**a**) The process of the dual optimal discharge pressure-seeking; (

**b**) the process of the dual system’s thermodynamic simulation.

**Figure 5.**(

**a**) The optimal intermediate temperature versus the operating conditions (water-feed temperature and ambient temperature); (

**b**) the maximum system COP versus the operating conditions (water-feed temperature and ambient temperature).

**Figure 6.**The thermodynamic parameters of the auxiliary cycle, main cycle and whole system under 50 °C/70 °C in water-feed/supply temperatures.

**Figure 7.**The refrigerant mass flow rates in both auxiliary and main cycles versus the intermediate temperature.

**Figure 8.**The evaporator entrance quality and evaporating pressure in main cycle versus the intermediate temperature.

**Figure 9.**The discharge pressure/temperature in both cycles versus the intermediate temperature at 40 °C/60 °C in water-feed/supply temperatures.

**Figure 10.**(

**a**) The temperature distribution of the combined gas cooler; (

**b**) the pinch point location inside the gas cooler [35].

Components | Detailed Models | |
---|---|---|

CO_{2} compression model [27] | Each time step was divided into: 1) the isentropic process with constant mass (1-2*); 2) the inner change with constant volume (2*-2). | |

$\left(\right)open="\{">\begin{array}{c}{s}_{2}^{*}={s}_{1}\\ {m}_{2}^{*}={m}_{1}\\ {\rho}_{2}^{*}={m}_{2}^{*}/{V}_{2}\\ {u}_{2}^{*}=u\left({s}_{2}^{*},{\rho}_{2}^{*}\right)\end{array}$$\left(\right)open="\{">\begin{array}{c}{m}_{2}={m}_{2}^{*}+\sum {m}_{valve}+\sum {m}_{leak}\\ {U}_{2}={u}_{2}^{*}\xb7{m}_{2}^{*}+\sum {H}_{valve}+\sum {H}_{leak}+\sum Q\\ {u}_{2}={U}_{2}/{m}_{2}\\ {\rho}_{2}={m}_{2}/{V}_{2}\\ {s}_{2}=s\left({u}_{2},{\rho}_{2}\right)\end{array}$ | (1) | |

${m}_{valve}\left(t\right)={C}_{d}\xb7{A}_{valve}\xb7\sqrt{\frac{2{\rho}_{up}\mathsf{\Delta}P}{1-{\beta}^{4}}}$ | (2) | |

$Q\left(t\right)=\alpha \left(t\right)\xb7A\left(t\right)\xb7\left[{T}_{wall}-T\left(t\right)\right]$ | (3) | |

$x=\frac{S}{2}\left[\left(1-cos\theta \right)+\frac{1}{\lambda}\left(1-\sqrt{1-{\lambda}^{2}si{n}^{2}\theta}\right)\right]$ | (4) | |

${V}_{c}=\frac{\mathsf{\pi}{D}^{2}S}{8}\left[\left(1-cos\theta \right)+\frac{1}{\lambda}\left(1-\sqrt{1-{\lambda}^{2}si{n}^{2}\theta}\right)\right]+{V}_{0}$ | (5) | |

CO_{2} cooling model [29,30] | ${q}_{r}^{i}={m}_{r,l}\left({h}_{r,in}^{i}-{h}_{r,out}^{i}\right)={\alpha}_{r}^{i}{A}_{l}\left({T}_{r,in}^{i}-{T}_{wall,i}\right)$ | (6) |

${\alpha}_{r}=\frac{{\lambda}_{b}}{{d}_{i,j}}\xb7N{u}_{r}=\frac{{\lambda}_{b}}{{d}_{i,j}}\xb7\frac{\left({f}_{r,H}/8\right)\left(R{e}_{b}-1000\right)Pr}{1.07+12.7\sqrt{{f}_{r,H}/8}\left(P{r}^{\frac{2}{3}}-1\right)}$ | (7) | |

${f}_{r,H}={f}_{r,s}{\left[R{e}_{f}{\left(\frac{{d}_{i,i}}{{D}_{H}}\right)}^{2}\right]}^{0.05}$ | (8) | |

${f}_{r,s}={\left[1.82\mathrm{log}\left(R{e}_{f}\right)-1.64\right]}^{-2}$ | (9) | |

CO_{2} evaporating model [31] | ${q}_{r}^{i}={m}_{r,l}\left({h}_{r,out}^{i}-{h}_{r,in}^{i}\right)={\alpha}_{r}^{i}{A}_{l}\left({T}_{wall,i}-{T}_{r,in}^{i}\right)$ | (10) |

${\alpha}_{IorA}={\alpha}_{wet}={\left[{\left(S{\alpha}_{nb}\right)}^{3}+{\alpha}_{cb}^{3}\right]}^{1/3}$ | (11) | |

${\alpha}_{nb}=131{p}_{r}^{-0.0063}{\left(-lo{g}_{10}{P}_{r}\right)}^{-0.55}{M}^{-0.5}{q}^{0.58}$ | (12) | |

${\alpha}_{cb}=0.0133R{e}_{\delta}^{0.69}P{r}_{L}^{0.4}\frac{{\lambda}_{L}}{\delta}$ | (13) | |

${\alpha}_{single}=0.023R{e}_{r}^{0.8}P{r}_{r}^{0.4}\frac{{\lambda}_{r}}{{d}_{i}}$ | (14) | |

$\mathsf{\Delta}{p}_{m}={G}^{2}\left\{{\left[\frac{{\left(1-x\right)}^{2}}{{\rho}_{L}\left(1-\epsilon \right)}+\frac{{x}^{2}}{{\rho}_{V}\epsilon}\right]}_{out}-{\left[\frac{{\left(1-x\right)}^{2}}{{\rho}_{L}\left(1-\epsilon \right)}+\frac{{x}^{2}}{{\rho}_{V}\epsilon}\right]}_{in}\right\}$ | (15) | |

$\mathsf{\Delta}{p}_{A}=4{f}_{A}\frac{\mathsf{\Delta}l}{{d}_{i}}\frac{{\rho}_{V}{u}_{V}^{2}}{2}$ | (16) | |

Air flow through the fine-tube heat exchanger [32] | ${q}_{air}^{i}={\alpha}_{air}^{i}{\xi}^{i}{A}_{of}\left({T}_{air,av}^{i}-{T}_{wall}^{i}\right)$ | (17) |

${\alpha}_{air}=\frac{{\lambda}_{air}}{{d}_{of}}\xb7N{u}_{air}=\frac{{\lambda}_{air}}{{d}_{of}}\xb70.982R{e}_{{d}_{of}}^{0.424}{\left(\frac{{P}_{f}}{{d}_{of}}\right)}^{-0.0887}{\left(\frac{N{P}_{t}}{{d}_{of}}\right)}^{-0.159}$ | (18) | |

Circulating water through the gas cooler [32] | ${q}_{w}^{i}={\alpha}_{w}^{i}{A}_{l}\left({T}_{w,out}^{i}-{T}_{wall}^{i}\right)$ | (19) |

${\alpha}_{w}=\frac{{\lambda}_{w}}{{D}_{eq}}\xb7N{u}_{w}=\frac{{\lambda}_{w}}{{D}_{eq}}\xb70.023R{e}_{w}^{0.8}P{r}_{w}^{0.4}$ | (20) |

Main Components | Type | Characteristics | |
---|---|---|---|

Main cycle’s compressor | (Panasonic) DC-inventor rotary compressor | Displacement: 8.0 ml/rev | |

Auxiliary cycle’s compressor | (Haili) DC-inverter rotary compressor | Displacement: 3.26 ml/rev | |

Dual gas cooler | Tube-in-tube | Outside tube | Φ22 × 2.45 mm |

Galvanized steel tube | |||

Inside tube | Φ6.35 × 0.7 mm × 2 tubes | ||

Φ7 × 1 mm × 1 tubes | |||

Copper tube | |||

Length | 17.6 m | ||

Main cycle’s evaporator | Wavy-finned tube | Tube | Φ7 × 1 mm |

Number of rows | 2 | ||

Number of tubes per row | 40 | ||

Tube length | 1.5 m | ||

Internal heat exchanger | Plate heat exchanger | Primary channel volume | 0.549 L |

Secondary channel volume | 0.610 L | ||

Material | Channel plate: stainless steel | ||

Brazing: Copper |

**Table 3.**The prediction errors between the sought optimal intermediate temperatures and the predictive values.

Water-Feed Temperature/°C | Water-Supply Temperature/°C | Ambient Temperature/°C | Sought Value of Optimal Intermediate Temperature/°C | Calculated Value of Optimal Intermediate Temperature/°C | Relative Error/% |
---|---|---|---|---|---|

40 | 50 | −20 | 14.74 | 15.30 | 3.65 |

40 | 50 | −10 | 19.55 | 19.65 | 0.51 |

40 | 50 | 0 | 23.53 | 24.00 | 1.97 |

45 | 55 | −20 | 16.99 | 16.70 | −1.72 |

45 | 55 | −10 | 20.84 | 21.05 | 1.01 |

45 | 55 | 0 | 26.41 | 25.40 | −3.97 |

50 | 60 | −20 | 18.65 | 18.10 | −3.07 |

50 | 60 | −10 | 22.79 | 22.45 | −1.51 |

50 | 60 | 0 | 26.78 | 26.80 | 0.07 |

40 | 60 | −20 | 15.87 | 15.30 | −3.71 |

40 | 60 | −10 | 20.07 | 19.65 | −2.12 |

40 | 60 | 0 | 24.31 | 24.00 | −1.29 |

45 | 65 | −20 | 17.09 | 16.70 | −2.33 |

45 | 65 | −10 | 21.02 | 21.05 | 0.16 |

45 | 65 | 0 | 26.36 | 25.40 | −3.80 |

50 | 70 | −20 | 18.72 | 18.10 | −3.42 |

50 | 70 | −10 | 22.73 | 22.45 | −1.24 |

50 | 70 | 0 | 25.56 | 26.80 | 4.65 |

© 2020 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**

Song, Y.; Wang, H.; Cao, F.
Investigation of the Impact Factors on the Optimal Intermediate Temperature in a Dual Transcritical CO_{2} System with a Dedicated Transcritical CO_{2} Subcooler. *Energies* **2020**, *13*, 309.
https://doi.org/10.3390/en13020309

**AMA Style**

Song Y, Wang H, Cao F.
Investigation of the Impact Factors on the Optimal Intermediate Temperature in a Dual Transcritical CO_{2} System with a Dedicated Transcritical CO_{2} Subcooler. *Energies*. 2020; 13(2):309.
https://doi.org/10.3390/en13020309

**Chicago/Turabian Style**

Song, Yulong, Haidan Wang, and Feng Cao.
2020. "Investigation of the Impact Factors on the Optimal Intermediate Temperature in a Dual Transcritical CO_{2} System with a Dedicated Transcritical CO_{2} Subcooler" *Energies* 13, no. 2: 309.
https://doi.org/10.3390/en13020309