## 3 Design of Supercritical CO2 Heat Exchanger  
Figure 1 illustrates a schematic of the SCO2 heat exchanger tube bundle. The tube specification was based on commercial availability and cost. The available tube diameter and the thickness of the S34709 material were 21.7 mm and 4.9 mm, respectively. The basic configuration of the SCO2 heat exchanger had a rectangular duct fed by a flue gas. The heat transfer from the hot flue gas to the cold SCO2 occurred in the rectangular duct. A staggered tube array with a counter-crossflow arrangement was considered. The tube length pitch (S\({}_{\text{L}}\)) and tube height pitch (S\({}_{\text{T}}\)) were 35 mm and 60 mm, respectively. The selection of the tube length pitch was based on the minimum thickness for pipe bends for induction and incrementing bending [24]. The straight line of the heat exchanger tube was 800 mm. The height and length of the tube were 471.7 mm and 2086.7 mm, respectively. Figure 2 shows the heat exchanger nozzle, header, and tube supporting structure. The total length of the SCO2 heat exchanger was estimated as 5132 mm, and the lengths of the SCO2 heat exchanger combustor and SCO2 heat exchanger chamber were 1577 mm and 2765 mm, respectively. As a concept for the tube-supporting structure, rectangular plates made by the welding method were considered.  
Preliminary simulation of the SCO2 heat exchanger was performed using an in-house heat exchanger analysis code. Figure 3 shows a program flow chart for the analysis of the SCO2 heat exchanger. An effective number of the transfer unit method was used for the simulation code. The thermo-properties of the flue gas and SCO2 were obtained from the NIST REFPROP Database 23, Version 9.1 [25]. The fluid properties, such as Reynolds number, heat transfer coefficient, and friction factor, were calculated based on the thermal properties of the working fluids. Then, the heat transfer characteristics, such as overall heat transfer coefficient, number of transfer units, and effectiveness, were computed to obtain the outlet temperature of the working fluid. The pressure drop of each fluid was then obtained when the calculation of the outlet temperature was converged. For the shell side, the heat transfer correlation proposed by [PERSON] [26] was used. The pressure drop correlation for the staggered tube banks was employed [27]. For the tube side, the heat transfer correlation proposed by [PERSON] [28] was used, and the pressure drop was calculated by considering the entrance, momentum, core friction, and exit effects [29]. The validation of the developed code was verified with other commercially available heat exchanger code. The simulation results showed that the outlet temperature (600.6 \({}^{\circ}\)C) can be obtained with the present design considerations of the SCO2 heat exchanger. In addition, the pressure drop on the SCO2 side satisfied the design constraints (<1.5 bar). However, there is a limitation in using the in-house heat exchanger code because it only represents the outlet conditions. This means that it is difficult to find local heat transfer characteristics along the heat exchanger tubes as well as thermal stress along the tubes. Therefore, the analysis of thermal characteristics was conducted using commercial three-dimensional CFD codes.