# Performance Analysis of the Supercritical Carbon Dioxide Re-compression Brayton Cycle
###### Abstract  
This paper presents performance analysis results on supercritical carbon dioxide (\(sCO_{2}\)) re-compression Brayton cycle. Monthly exergy destruction analysis was conducted to find the effects of different ambient and water temperatures on the performance of the system. The results reveal that the gas cooler is the major source of exergy destruction in the system. The total exergy destruction has the lowest value of 390.1 kW when the compressor inlet temperature is near the critical point (at 35 \({}^{\circ}\)C) and the compressor outlet pressure is comparatively low (24 MPa). The optimum mass fraction (\(x\)) and efficiency of the cycle increase with turbine inlet temperature. The highest  
The Rankine cycle and the air-standard Brayton cycle are well-known thermodynamic cycles. The benefit of the Rankine cycle is that high efficiency can be achieved because the pump consumes a very small amount of work, since compression is carried out when the working fluid is in the liquid state [8]. The advantage of the Brayton cycle is that the turbine inlet temperature is high; thus, it can achieve high efficiency, but the disadvantage is that the work consumed by the compressor is very large. Due to this, the air-standard Brayton cycle's efficiency is not significantly higher than that of the steam-based Rankine cycle. The primary advantage of the supercritical \(CO_{2}\) (\(sCO_{2}\)) Brayton cycle is that the positive points of the steam-based Rankine cycle and air-standard Brayton cycle are both combined. The turbine inlet temperature in the \(sCO_{2}\) Brayton cycle is high. Moreover, since the compressor operates near the \(CO_{2}\) critical point at very high pressure at which the density is significantly high and the compressibility factor is small, the work that is consumed by the compressor is significantly low. The \(sCO_{2}\) Brayton cycle operates above the critical point, so the need for condensing the system is removed and the system has a simple layout. Since the \(sCO_{2}\) re-compression Brayton cycle has very high operating pressures compared to the steam-based Rankine cycle, the size of the \(sCO_{2}\)-based power system's components is considerably smaller [9].  
Currently, extensive research is being conducted on \(sCO_{2}\)-based power systems, and the \(sCO_{2}\) Brayton cycle can be found in a variety of arrangements in the literature, such as in reheated and intercooled re-compression layouts [10]. [PERSON] et al. [11] reviewed the different single and combined layouts of \(sCO_{2}\) Brayton cycle power systems with efficiencies of 40%-50% and 50%-60%, respectively, while [PERSON] and [PERSON] [8] analyzed a re-compression \(sCO_{2}\) Brayton cycle power system with an integrated turbine design and optimization algorithm. In their study, they proposed that the cycle performs best when the inlet temperature of the compressor is set near the \(CO_{2}\) critical temperature (i.e., 32-37 \({}^{\circ}\)C) and the compressor inlet pressure is set slightly above the \(CO_{2}\) critical pressure (i.e., 7.8-8.1 MPa) along with a moderate pressure ratio (i.e., 2.9-3.1). [PERSON] et al. [12] carried out a design optimization and performance analysis of the \(sCO_{2}\) re-compression Brayton cycle. They developed detailed mathematical models of the cycle components and simulation codes for the turbine, compressor and heat exchanger. These codes were used to analyze the performance of the cycle under the design conditions as well as off-design conditions.  
To analyze the performances of thermal power systems, researchers have used different performance parameters, including thermal efficiency (\(\eta_{th}\)) and exergy efficiency (\(\eta_{ex}\)). Moreover, to indicate the cost and size of the thermodynamic system, parameters such as the total heat transfer area coefficient (\(