## 1 Introduction  
The supercritical carbon dioxide (SCO\({}_{2}\)) Brayton cycle has been considered one of the most promising alternatives to existing power generation systems, such as the steam Rankine and gas Brayton cycles. The steam Rankine cycle can achieve high thermal efficiency due to the low pumping power, but the overall size of the system is large because the steam density of the low pressure side is lower than the atmospheric pressure. The turbine inlet temperature (TIT) of the gas Brayton cycle is higher than in the steam Rankine cycle. It can achieve a high thermal power output, but material integrity and high compression work problems still remain. The SCO\({}_{2}\) cycle has the advantages of both the steam Rankine and gas Brayton cycles because of its fluid characteristics. First of all, the supercritical region of the SCO\({}_{2}\) is readily accessible (T\({}_{\rm c}\) = 31.1 \({}^{\circ}\)C, P\({}_{\rm c}\) = 73.8 bar); thus, the system can be controlled easily compared to other critical state fluids. Because the SCO\({}_{2}\) cycle operates near the critical point, the fluid reflects both liquid and gas properties. The compression work of the SCO\({}_{2}\) consumes less than the conventional gas Brayton cycle. In addition, the density difference between the hot and cold sides are small. This means that the overall size of the SCO\({}_{2}\) power generation system can be minimized compared to the conventional power generation systems. Based on the advantages, the SCO\({}_{2}\) cycle can be applied to various technologies, such as concentrating power, fossil fuel, geothermal, nuclear, ship-board propulsion, waste heat recovery, etc. Therefore, the development of the SCO\({}_{2}\) power cycle has been extensively studied. Studies on the SCO\({}_{2}\) cycle have taken place since the 1960s, but its development did not occur due to these technological advances [1,2]. In the 2000s, [PERSON] et al. [3] studied the SCO\({}_{2}\) cycle as the next power generation system for Generation IV nuclear reactors because the TIT for advanced nuclear reactors is about 550 \({}^{\circ}\)C, a system operating condition which is between the steam Rankine and gas Brayton cycles. Because the SCO\({}_{2}\) cycle can be designed in a wide range of the TIT, the SCO\({}_{2}\) system has received more attention as the next power generation system. In addition, the SCO\({}_{2}\) cycle can also be used in various heat sources, such as fossil fuel, concentrating solar power, shipboard propulsion, waste heat recovery, and geothermal. After validating the SCO\({}_{2}\) cycle as a new power generation system, numerous studies have been conducted to verify the cycle. Sandia National Laboratories designed a recompression configuration, and various experimental facilities have been developed, such as turbine and compressor performance characterizations [4; 5; 6]. The Naval Nuclear Laboratory designed and built an integrated system test (IST) for the SCO\({}_{2}\) Brayton cycle. The IST is a simple recuperated Brayton cycle for variable turbomachinery tests. The system demonstrated that the SCO\({}_{2}\) Brayton cycle was controlled throughout the entire system operation, but inherent problems related to the SCO\({}_{2}\) Brayton cycle were identified [7; 8; 9]. Ecogen Power Systems designed a SCO\({}_{2}\) power cycle (EPS-100) for exhaust heat recovery applications. The EPS-100 is the first commercial-scale SCO\({}_{2}\) system, and it has a 7 MWe scale with multiple stages of recuperation and extraction from the heat source. The validation test of the EPS-100 was completed, and commercialization took place [10; 11]. The SunShot program, which develops the SCO\({}_{2}\) Brayton cycle for a concentrating solar power (CSP) system, was initiated with a simple recuperated cycle [12]. The target demonstration of the SCO\({}_{2}\) system is 10 MWe with a 50% net thermal efficiency.