Refrigeration and heat pump systems are closely linked, using the same working fluid developed for refrigeration, a study by Chanson et al. presents a review of this technology [26] . Carbon dioxide was among the first refrigerants used in vapor compression refrigeration systems, the detailed history of the role of CO₂ in the development of refrigeration has been compiled by Pearson [27] . The CO₂ transcritical cycle technology, unlike the conventional refrigeration cycle, works with a compressor discharge pressure higher than the critical pressure, which prevents any condensation of the CO₂ which is used as refrigerant. In this zone, there is no longer any relationship between pressure and temperature, so no condensation. The condenser used in the conventional vapor compression cycle is replaced by a gas cooler called a “gas cooler”. However, cold occurs by heat absorption and evaporation after expansion of low pressure refrigerant such as similar in conventional subcritical cycle [28] . Figure 3 presents the basic transcritical CO₂ cycle as well as its lg p-h diagram which was established on the basis of the assumptions presented in Table 2 . Theoretically compared to a classic vapor compression cycle, the transcritical CO₂ cycle is less efficient under the same conditions. Its basic characteristics define a significantly higher operating pressure than conventional refrigerant systems; The absence of phase change during the transfer of sensible heat from the high pressure side prevents a continuous drop in temperature of the CO₂ fluid and therefore can be heated to a very high temperature continuously. Due to the better flow and heat transfer properties of CO₂ [29] , the volume and size of CO₂ heat exchangers can be reduced compared to other refrigeration systems. Even taking into account these advantages, the transcritical cycle presents less efficient performance at high outdoor ambient temperatures as presented by a drop in COP of 10% on a study carried out on the CO₂ air conditioning system [30] [31] .

CO₂ used as working fluid in transcritical cycle technology to compete with conventional cycle is a major challenge. Efficiency remains the disadvantage of the transcritical system as the vapor produced at the outlet of the gas cooler must be compressed, not to mention the high compression ratio to be achieved. This phenomenon is all the more important as the outside temperature is high. The implementation of more complex cycles by researchers on transcritical systems allowing an improvement in efficiency similar to that of conventional fluids is presented and analyzed in the following sections.

Figure 3. Basic transcritical CO₂ cycle (a) and lg p-h diagram (b) [27] .

In view of the results obtained in the comparison of the systems with conventional fluid and with CO₂ [32] , it is noted that the efficiency of the basic system of the refrigeration cycle with transcritical CO₂ is lower. However, technological advances as illustrated in Figure 4 promise to improve or even make this technology superior to conventional subcritical cycles.

To raise the level of performance of the transcritical refrigeration system, the internal heat exchanger (IHX) comes into play as shown in Figure 5 , it is used to transfer heat between the base and high pressure circuits. It has been shown that it can both improve or decrease system performance due to the trade-off between increased capacity and discharge temperature depending on working fluids and operating conditions. [33] [34] . In improving the performance of the system, the IHX having a larger exchange surface is beneficial for the increase of the COP as well as the reduction of the optimal pressure to the value of the maximum COP by respecting the size limit to prevent the compressor discharge temperature to exceed its design limit [35] [36] . This COP value has undergone a 10% increase obtained in a transcritical CO₂ cycle for residential air conditioning [37] . In order to obtain the energy and exegetical performance of a transcritical CO₂ chiller with and without internal heat exchanger, Purohit et al. [38] carried out an experimental study in a hot climate situation (45˚C), the improvements obtained with the use of IHX were 5.71% and 5.05% in energy and exegetical efficiency respectively at an evaporation temperature of −5˚C.

Several other IHX configurations different from the one presented in Figure 5 have been studied by Sanchez et al. [39] namely: cooler outlet, liquid reservoir outlet and in both positions at the same time. The best configuration was that of the coupling of the two positions from which an increase in the COP of 13% was obtained.

A study carried out by Mohammed Tarawne on this cycle with a porous internal heat exchanger makes it possible to obtain an increase in the refrigerating capacity and the coefficient of performance of 49.7% and 93%, respectively and electrical consumption of the compressor per kW of refrigeration reduced by approximately 29.6% [40] .

In the transcritical CO₂ refrigeration cycle, the proportion of fluid in the gaseous state coming from the gas cooler in the liquid receiver is greater compared to the conventional subcritical system where the condenser transforms the gaseous fluid partially or completely into liquid, and therefore the performance of the system is reduced when it ends up in the evaporator.

A possible approach to solve this problem is the implementation of a flash gas bypass (FGB), the purpose of this method is to have this vapor sucked directly by the compressor while avoiding its passage into the evaporator. Figure 6 shows the FGB configuration. Coming from the gas cooler, the fluid is throttled by the HP valve in a two-phase state and ends up in the liquid receiver where there is phase separation. Thus, the liquid found in the lower part of the tank is directed to the evaporator through the expansion device or expansion valve, while the vapor found in the upper part is led directly to the suction of the compressor through the MT valve. This valve plays an important role in controlling the evaporator outlet conditions in superheat regulation [41] . As part of the improvement of cycle performance by the FGB method, a parametric model of the CO₂ FGB system was established using an engineering equation solver, thus proving a COP improvement of 7% compared to the basic transcritical cycle [42] , while an experimental comparison was carried out with a classic conventional system which presents an increase in the cooling capacity and the COP of 9 and 7% respectively thanks to the FGB [43] .

The purpose of this technology is almost similar to that of the FGB discussed above, which is to avoid expanding the vapor coming out of the reservoir and then recompressing it. From the moment when the outside temperatures begin to increase (more than 15˚C), we will have inside the CO₂ tank a proportion of flash gas vapor which becomes very high and therefore this vapor must be eliminated not to disturb the operation of the MT compression stage. In addition to producing cold, this stage must also devote itself to eliminating gas flashes which increase with the increase in the outside temperature and therefore reduce the efficiency of the system. To compensate for these losses in efficiency, the setting up of a parallel compression stage which sucks from the reservoir is integrated into the transcritical cycle as illustrated in Figure 7 , the concept being to reduce the losses of bottlenecks [44] . One method is to pass the flash gas through a vent in the main compressor compression chamber [45] . This design can also be made with a twin T-shaft compressor [46] . Another type uses a number of cylinders from the main compressor to do parallel compression [47] . The advantage of this technology is that there is less flash gas which disturbs the production of cold. Since this compression stage draws directly above the receiver, the required compression power is reduced and the system efficiency reaches at least or more the same level as refrigeration systems using FGB [48] .

Some studies of the performance of this system have been carried out, including a theoretical and experimental study, which stipulates that an ideal cycle can achieve improvements in COP of more than 30% and cooling capacity of more than 65% compared to the basic CO₂ system [49] . Lui and coll [46] also compared parallel CO₂ compression to the base cycle and found up to 21% increase in COP and 5.3 bar reduction in discharge pressure at high outdoor ambient temperature although the improvement in COP is generally less than 10% under subcritical conditions. A study carried out by Tao et al. evaluates the thermodynamic performances of the CO₂ refrigeration cycle with ejector and parallel compression [50] .

With respect to the fundamental system of the transcritical CO₂ refrigeration cycle, the two-stage compression as shown in Figure 8 , is used for extremely low temperature cycles which cannot be produced economically through the use of a single-stage system. Indeed, the compression rate is too high to reach the temperatures necessary for the evaporation and condensation of the steam. Thus, the compression efficiency is reduced, the refrigerant vapor in the compressor increases in temperature and so does the energy consumption. Therefore, multi-stage compression with intercooling method can be used to improve system reliability. Various studies indicate that the heat rejection pressure alone is not enough to determine the optimal COP. In the case of the two-stage CO₂ refrigeration system, the other parameters such as the intermediate pressure and the intermediate temperature must be coupled and therefore require simultaneous optimization [9] .

The vortex tube is an energy splitting device in which one airflow rises and the other descends, both rotating in the same direction with the same angular velocity. The speed of the internal vortex inside the vortex tube is conserved, which means that the torque of the internal vortex is lost. The lost energy manifests as heat in the outer vortex, which is why the outer vortex becomes hot and the inner one becomes cool as shown in Figure 9 . The application of the vortex tube in the refrigeration system can reduce the loss of throttling process. CO₂ was used as the working fluid to simulate the energy splitting effect of the vortex tube [52] . In a study of the performance of two countercurrent vortex tubes, CO₂ provides greater thermal separation capacity than air [53] . Li et al. [54] studied a configuration of the transcrack CO₂ refrigeration system as shown in Figure 10 . Assuming 100% gas-liquid separation efficiency, this system could provide up to 37% increase in cycle efficiency. A theoretical analysis of the transcritical CO₂ refrigeration cycle with vortex tube expansion was performed by Lui et al. [55] . The system with vortex tube was found to have a higher COP than the traditional system with expander.

This technology allows expansion work recovery for the transcritical CO₂ cycle to reduce the throttling loss which is much higher due to the physical properties of CO₂. Figure 11 shows the configuration of the expansion system in which the regulator is replaced by an expander. A few studies involving expanders in the CO₂ cycle have been elaborated among which Yang et al. [57] performed a thermodynamic analysis of the system and found that the efficiency of the transcritical CO₂ cycle with expander was more efficient, preventing a decrease of 50% exergy loss and a 30% improvement in overall system exergy efficiency. A recovery of about 37% of the compressor work can be observed with a marked improvement if the inlet temperature of the expander increases [58] .

In the operation of the basic transcritical CO₂ cycle in a situation of high outside temperature, the temperature of the refrigerant at the outlet of the gas cooler is much higher than that of the ambient temperature, hence a high proportion of vapor which is unfavorable to the proper operation of the system. To overcome this restriction, the use of a subcooler as shown in Figure 12 is one of the techniques to improve cycle performance to reach that of conventional systems at high ambient temperatures.

The objective is therefore to reduce the outlet temperature of the gas cooler to a value lower than that of the ambient temperature, thus producing a lower quantity of vapor in the expansion and consequently reducing the work of the parallel compressor. The researchers presented different subcooling technologies at the outlet of the gas cooler such as: the method of dedicated mechanical subcooling (DMS) including a study of the performance compared to the parallel compression scheme and under cooling via gas cooler dedicated water was carried out by D’Agaro. For the thermoelectric subcooling (TES) method, a thermoelectric module based on the Peltier effect is used. This concept has been used in transcritical CO₂ refrigeration by Schoenfield et al. [60] who evaluated the effects of the input current on the overall cooling capacity of the system and the COP.

As mentioned in the previous section, the efficiency of the basic transcritical CO₂ system weakens under high outdoor ambient operating conditions. The adiabatic gas cooler is an evaporative cooling method which consists of pre-cooling the air before it enters the gas cooler as shown in Figure 13 . This method of spraying water to the condenser is also applied in refrigeration facing temperature peaks [61] . However, there is a trade-off between balancing water consumption and improving COP for practical application in CO₂ system. Girotto et al. [62] [63] analyzed both solutions and found an improvement in COP of 17% for a 30% precooling solution and a COP of 27% for a 100% precooling solution. However, the ideal choice should refer to the actual climate, the area where the equipment will be installed, and the availability of water.

Specifically used as a vacuum pump in steam installations, the ejector is a device known since antiquity. Its technology has been widely studied over time of which a comprehensive review was presented by Besagni et al. in 2016 [65] . In transcritical CO₂ installations, it is used to increase the pressure of another refrigeration line completely free of charge by exploiting the expansion at the outlet of the gas cooler as shown in Figure 14(a) . Thereby, it can improve system efficiency and reduce exhaust pressure appropriately [66] as well as improve COP by up to 28% [67] [68] . The ejector is a simple, low-cost system with no moving parts, so it is widely used in the prospect of improving the efficiency of the transcritical CO₂ system. Figure 14(b) shows its integration into the modified cycle [69] which, thanks to its mechanism, makes it possible to exploit the depression created by the venturi effect and makes it possible, using first a pressurized fluid, to compress a second fluid by mixing them while transmitting energy to the fluids. This technology has undergone several studies in its process of improvement and optimization in the applications of mobile air conditioning [70] , multi-ejector system in the refrigeration of supermarkets [71] , dairy, sea water chiller [72] , residential CO₂ air conditioning [73] and several other improvement studies as presented in Table 3 [74] . Zheng et al. present a review of modeling, optimization and experimental studies of ejectors for CO₂ refrigeration [75] .

Figure 14. (a). Diagram of the ejection [76] ; (b). Integration ejector in the CO₂ refrigeration cycle [77] .

Refrigeration plays a central role in the process of preserving and transporting perishable goods. Applied in commercial supermarkets, it includes refrigerated display cases, refrigerators and cold stores. Traditional supermarket refrigeration equipment consumes a huge percentage of kilowatts compared to other commercial establishments [87] [88] . In addition, these traditional systems use conventional refrigerants as the working fluid, which represents a danger to the environment. The CO₂ used as a refrigerant in these systems is a much better solution in the field of food refrigeration [89] .

In order to improve the CO₂ transcritical cycle technologies of supermarkets, researchers have developed the indirect CO₂ refrigeration system, the refrigeration system using CO₂ as a low temperature cascade configuration refrigerant and the refrigeration system using CO₂ as the main refrigerant [90] . Sun et al. [91] designed a partial cascade CO₂ two-stage commercial supermarket compression refrigeration system, then compared it to the traditional R134a system.

The once natural ice and snow fields have gradually been replaced by artificial fields, which makes ice/snow sports one of the most popular activities. Artificial ice rinks generally use mechanical refrigeration systems to provide cooling. Early artificial ice rinks primarily used R22 as a refrigerant and brine as a secondary loop medium [92] . At the end of the 20th century, CO₂ began to be applied to the refrigeration systems of artificial ice rinks and the results obtained were remarkable [93] . For the first time in the field of winter sports, transcritical CO₂ technology has been used in the 2022 Winter Games in China, which not only meets the concept of “green Olympic science and technology”, but also encourages the research and development of the application of transcritical CO₂ engineering technology in ice and snow sites [94] .

Conventional refrigerants such as R134a and R407c are often used for the air conditioning of passenger and commercial vehicles respectively. The use of transcritical CO₂ refrigeration system in automotive air conditioning has the advantages of high cooling capacity, low pressure ratio, high working efficiency and environmental protection [95] .

Transcritical CO₂ technology in automotive air conditioning seems to be better suited but however exhibits very high operating pressures. A system configuration with indirect heating or cooling has been proposed as illustrated in Figure 15 by Carrie et al. [96] . In order to meet the global cooling and heating demand of electric vehicles, Chen et al. [97] developed a CO₂ heat pump system with intercooling. Wang et al. [98] compared the performance characteristics of R134a and CO₂ heat pump systems in electric vehicles.

A bibliographic study carried out by Hongzeng et al. presents progress on transcritical CO₂ heat pumps and refrigeration cycles in the field of vehicles [99] .

Heat pump heating has become an increasingly popular technology due to its performance and ability to reduce energy costs [100] . The heat pump using CO₂ as the working fluid is an innovative and eco-responsible dual-use technology (heating and DHW) that offers superior performance to conventional systems [101] . The use of R744 in the heat pump cycle is accompanied by the high operating pressures in low and high pressure. In order to improve the efficiency of the system, a sub-cooler is used, but the expansion operated on the gas for this exchange also allows reinjection into the intermediate stage of the compressor. Thus, the overall pressure of the discharged gases decreases, and the power absorbed by the compressor is reduced. Ghazizade-Ahsaee et al. [102] introduced as presented in Figure 16 , the thermoelectric subcooling and the ejector in the transcritical CO₂ direct expansion geothermal heat pump system, and found an increase in the COP and system stability. Feng et al. [103] built an experimental platform for a transcritical CO₂ heat pump water heater system. An experimental study on the performance of a compact, water-cooled CO₂ heat pump assisted by a subcooler presents a significantly increased cooling capacity and coefficient of performance of 40.7% and 37.7% respectively. Additionally, the optimum discharge pressure is lowered by 0.5 MPa [104] .

Carbon dioxide used as a working fluid in refrigeration systems has proven its potential in this field. However, it is clear that standard CO₂ systems were very well suited to cold (<8˚C) or even temperate (≤15˚C) climates. From the moment the external temperatures begin to increase, we find inside the CO₂ tank a proportion of flash gas vapor which becomes greater and disrupts the operation of the medium temperature compression stage; Which makes the standard base CO₂ system less effective for hot climates. To compensate for these losses in efficiency, researchers integrated “a parallel compression stage”. This technological advancement makes it possible to equip the standard system with one or more compressors which suck from the upper level of the CO₂ tank and therefore reduce the proportion of flash gas which disrupts the production of cold. Thus, the consumption of electrical energy is reduced compared to the compressor which sucks at the level of the evaporator.

After the text edit has been completed, the paper is ready for the template. Improving energy efficiency and reducing greenhouse gas emissions are key to the technological progress of electrical systems. Various engine cycles and CO₂ power have been proposed for various applications. However, their potentials for waste heat recovery are still largely unexplored. For low temperature heat applications, transcritical cycles, in particular the organic Rankine cycle (ORC) can compete with other existing technologies. While supercritical CO₂ cycles, in particular the supercritical Brayton cycle, are more attractive for medium and high temperature sources to replace Rankine vapor cycles. As a working fluid, the environmentally friendly fluid CO₂ has interesting thermophysical properties (density, isobaric specific heat capacity, thermal conductivity and viscosity), represented by the curves in Figure 17 .

CO₂ can be used as an alternative to organic working fluids in small to medium sized electrical systems for low quality heat sources. It is considered a promising fluid for closed Brayton and Rankine cycles, but its unique property calls for new thinking in the design of cycle components.

Using low-grade heat as an energy source and recovering waste heat from various processes offers opportunities for sustainable energy in the future with fewer environmental issues. The fundamental technologies for converting this low quality heat into electricity using CO₂ as the working fluid, including transcritical organic Rankine cycle technology and supercritical Brayton cycle technology are elaborated in the following sections along with advances in engine cycle technology and CO₂ power.

Power conversion systems include organic Rankine cycle (ORC), steam Rankine cycle (steam turbine), air Brayton cycle (gas turbine), combined cycle gas turbine (CCGT) and the direct and indirect cycles SCO₂. The Brayton cycle SCO₂ is the power conversion system which combines the advantages of the steam Rankine cycle and the gas turbine system as schematically shown in Figure 18 . Due to this, the fluid is compressed in the incompressible region and higher turbine inlet temperature can be operated with fewer material issues compared to steam Rankine cycle. System performance is affected by temperature and supercritical CO₂ pressure at the high pressure turbine inlet, as this temperature increases, system efficiency also increases, especially at low turbine inlet temperature pressure. For a simple CO₂ engine cycle, the efficiency of the system increases proportionally with the improvement in the efficiency of the turbine.

As indicated in the previous section, many potential advantages exist for the SCO₂ engine cycle. It can be applied to various heat sources such as: nuclear and coal-fired power plants, waste heat recovery, concentrating solar systems and geothermal energy devices. The following sections discuss recent progress of the various applications of supercritical CO₂ cycles.

The SCO₂ power cycle is being researched for application to sodium-cooled fast reactors [107] [108] . This cycle is often used in high-temperature gas-cooled reactors, which have high thermal efficiency, relatively low turbine inlet temperature, compact size and simple layout [109] . However, the rate of heat transfer in the recuperator is limited by the pinch point [110] . To improve system performance, a recompression cycle as shown in Figure 19 has been proposed, and the split-flow arrangement can effectively alleviate this problem. This SCO₂ recompression cycle can be applied to a fourth generation sodium-cooled fast reactor, it is also promising for fusion reactors whose estimated efficiency is 42.44% [111] . Although this cycle has a higher efficiency than other configurations, research indicates that it is difficult to improve it further [112] .

SCO₂ power cycle can be used as lower cycle for waste or exhaust/waste heat recovery, which can be gas turbine or internal combustion engine with overall energy efficiency improvement. Hou et al. [113] designed a combined cycle consisting of a gas turbine, a SCO₂ recompression cycle, a steam Rankine cycle and an ORC with an azeotropic working fluid, they found a 2.33% efficiency increase compared to traditional gas-steam combined system.

In the marine application, a CO₂ power system was integrated with a compression refrigeration cycle using CO₂ as the working fluid; the exhaust heat from the gas turbine was used to drive the regenerative cycle of SCO₂, resulting in an 18% increase in system power output [114] . A mixture based on CO₂ in the combined cooling and power cycle for the recovery of residual heat from the engine was studied [115] [116] and an optimization was carried out by Ligeng et al [117] . Zhenchang et al. carried out a study on supercritical CO₂ power cycles for energy cascade use of natural gas engines, the thermal efficiency was increased from 42.4% to 48.94% [118] . Improving the performance of the combined CO₂ refrigeration and electricity cycle driven by engine exhaust gases is carried out by Elattar et al. [119] .

Figure 19 shows the modified SCO₂ recompression cycle in which two heat exchangers have been installed to recover in series the waste heat which can be on an internal combustion engine, the heat of the coolant and that of the exhaust gases. Under the design conditions, the waste heat recovery efficiency was 17.86% higher than that of the recompression cycle for an efficiency of 74.83% [121] . In order to recover these two heat sources simultaneously, Song et al. [122] designed an SCO₂ cycle with two-stage regeneration and the maximum engine power output was increased by 6.9%. A modified SCO₂ Brayton recompression cycle which combines the advantages of the preheated Brayton SCO₂ cycle is being studied to recover waste heat from gas turbines [123] . An optimization study of the organic Rankine cycle powered by the residual heat of a multi-ejector CO₂ refrigeration cycle was carried out by Dimitrios et al. [124] .

The performances of the SCO₂ cycles were studied for high temperature solar thermal energy systems whose thermal efficiency was about 32% for a source of temperature 600˚C and a compressor inlet pressure of 85 bar [125] . Al Sulaiman et al. [126] evaluated five different SCO₂ cycle configurations for a solar power plant with a heliostat field, the best efficiency of 40% was obtained with the regenerative cycle whose performance Singh et al. [127] analyzed direct-fired regenerative CO₂ cycle dynamics for large-scale solar power generation. To cope with variations in solar radiation, a CSP system with heat storage has been studied [128] . When power output fluctuates frequently, turbine and compressor performance degrades significantly for every 1% reduction in turbine efficiency, system efficiency and relative power output could be reduced by 0.431 and 1.713% respectively [129] . Therefore, variations in turbine and compressor efficiencies should be assessed during the system design phase to improve the robustness of the SCO₂ cycle. A radial turbine can be used in an SCO₂ cycle thanks to its low expansion rate. El Samad et al. [130] designed a single-stage radial turbine for a 100 MW SCO₂ cycle. For solar power plants, a thermodynamic analysis of the CO₂ -SF6 mixture Brayton cycle is more effective than SCO₂ [131] .

Rankine’s transcritical CO₂ cycle is more suitable for this technology because it has much lower temperatures than nuclear reactors and coal-fired power plants. Few studies have assessed the feasibility of the SCO₂ cycle for the use of geothermal energy. Ruiz-Casanova et al. [132] compared four different configurations and reported that intercooling could reduce CO₂ mass flow as well as compressor work.

Compared with conventional Rankine steam cycle, SCO₂ cycle has low critical pressure, high density, high heat transfer rate, high specific power and small size which makes it suitable for various heat sources.

Rankine’s transcritical CO₂ cycle is suitable for low-grade energy use. Chen et al. [133] found that this cycle is suitable for energy recovery from low quality heat sources. In the transcritical Rankine cycle, the working fluid is heated directly from the liquid state to the supercritical state. CO₂ with a critical temperature (31.4˚C) and a relatively low pressure (7.38 MPa), can be compressed directly to its supercritical pressure and heated to its supercritical state before expansion in order to obtain a better thermal match with the heat source [134] . The temperature curves between the CO₂ and the heat source are approximately parallel due to the excellent temperature glide match, which can effectively avoid pinch point limitations as shown in Figure 20 hence less loss of exergy [135] .

Recent research has also shown that the SCO₂ power cycle has excellent performance in utilizing solar energy and geothermal heat which has low power generation cost [136] , compact system size and superior thermal efficiency [137] [138] . Experimental studies on a transcritical solar CO₂ cycle using a solar collector field, a microturbine, a condenser, a feed pump and CO₂ as the working fluid have been carried out [139] - [142] .

More importantly, the transcritical CO₂ Rankine cycle can efficiently utilize a lower temperature heat source than organic working fluids due to the low critical temperature of CO₂. In order to improve the performance of the CO₂ Rankine cycle for different heat sources and purposes, the following changes have been made: 1) an internal heat exchanger is introduced into the CO₂ Rankine cycle at high temperature of the heat source whose temperature range generates the optimum pressure is higher and the optimum pressure can be reduced by using an internal heat exchanger [143] . 2) Solar-based transcritical CO₂ Rankine cycle for heat and power cogeneration has two heat recovery systems whose efficiency Zhang et al. [139] [144] reported electrical, thermal and heat recovery efficiency of their Rankine transcritical CO₂ system could reach up to 20%, 36.2% and 68.0% respectively. 3) The transcritical CO₂ Rankine system with multiple heat sources should realize cascading use of energy. Farzaneh et al. [145] found that an additional heat source would increase the net power output and the thermal efficiency of the system. Rankine’s CO₂ cycle with multiple heat sources reduces cooling water requirements. 4) Rankine transcritical CO₂ cycle with an ejector can improve maximum net power output by up to 10.2% but decrease thermal efficiency by 23.9% [146] .

Principle and advantage of the Brayton cycle

The basic Brayton cycle consists of at least five main components namely: heater, turbine, pre-cooler, compressor and working fluid. The different basic processes are adiabatic compression, isobaric heating, adiabatic expansion and isobaric heat release. Figure 21 presents the cycle and the T.S. diagram in which the actual process is represented by the red dotted line due to the loss of energy during the cyclic process.

1) Due to the low work of compression, the supercritical CO₂ Brayton system exhibits high thermal efficiency when applied at moderate temperatures. Figure 22 presents the curves of variations of the thermal efficiency of the cycle with different forms of system varying with the temperature of the heat source under the typical operating conditions, including water-Rankine, helium Brayton (a turbine and a compressor), helium Brayton (three turbine, six compressors, intermediate heating and cooling).

2) Critical pressure is one-third that of water, allowing it to operate under relatively low pressure.

3) The high density of the supercritical CO₂ fluid allows smaller equipment such as: fairly compact turbomachines and more compact heat exchangers.

4) The pressure ratio decreases the number of stages in the turbine.

However, the supercritical CO₂ Brayton cycle still has some disadvantages such as the corrosive material with temperatures above 500˚C and the requirement of high pressure to achieve high efficiency. The following sections present the different modifications of the cycle carried out by the researchers.

The work capacity of the turbine for several cycle configurations can be increased by adding a reheat process. Comparative performance studies for these different cycle configurations (SRBC, RCBC, pre-compression and expansion cycle) have been conducted by several researchers. Liao et al. [150] performed analyzes and comparison of the performance of these new configurations, the results showed that the RCBC has the highest efficiency up to 45%.

Although the Brayton SCO₂ cycle has proven to be a promising motor cycle for providing high efficiency in excess of 50%, it can still be improved by adding a suitable bottom cycle using its own waste heat, such as the Brayton CO₂ transcritical cycle (TCBC) [151] , ORC [152] - [154] , KC [155] and the organic flash cycle (OFC) [156] . This cycle can be applied to solar energy, nuclear energy, high temperature fuel cells, waste heat sources and CO₂ capture and storage in coal-fired power plants.

The Brayton cycle uses concentrated solar energy to directly heat supercritical CO₂ to power a turbine. Singh et al. [127] developed a control-oriented direct heating SRBC model varying with ambient temperature. Since the value of solar heat input varies with temperature, an extremum-seeking control strategy by regulating the CO₂ mass flow rate has been proposed to maximize the power output of a direct-fired SRBC system [157] which was also studied by Singh et al. [158] with dry cooling and a softer response.

SCBC replacement of other electrical or working fluid cycles applied to solar energy is competitive. Turchi [159] found that RCBC had higher thermal efficiency among helium BC. Muto et al. compared performance between PCBC (650˚C, 20 MPa) and Brayton subcritical cycle with two intercoolers (650˚C, 10 MPa), where each cycle was integrated with a 100 Mw centralized solar system. The thermal efficiency of PCBC was found to be around 48.9% compared to 45.3% for other cycles. Enriquez [160] revealed that the gross efficiency of the SRBC with reheating of two double loop solar fields was 44.4%, while the gross efficiency of the Rankine subcritical water power cycle was 41.8%. Saboora et al. evaluated the performance of a concentrated solar power plant using Brayton cycles with supercritical carbon dioxide [161] , an optimization study was carried out on a solar tower energy production system with supercritical CO₂ integrated into the cycle Steam Rankine [162] . Thermodynamic optimization of supercritical carbon dioxide Brayton cycles for combined heat and power production is studied by Ruiqiang et al. [163] . For the application of the solar thermal power plant integrated into the air-cooled supercritical CO₂ Brayton cycle with concentrator, the GHG emissions of the s CO₂ cycle are 21% to 41% lower than those of the steam Rankine cycle [164] .