## 4 CFD Analysis of a Supercritical CO2 Heat Exchanger
### Thermal Stress Analysis  
To show the integrity of the SCO\({}_{2}\) heat exchanger tube, thermal stress analysis was conducted using a commercial CFD code, ABAQUS [31]. High-temperature regions of the heat exchanger tube  
Figure 7: CFD results around the heat exchanger tube: (**a**) temperature distributions on the outer tube surface, (**b**) heat transfer coefficient distributions on the outer tube surface, (**c**) temperature distributions on the inner tube surface, (**d**) heat transfer coefficient distributions on the inner tube surface. located near the SCO\({}_{2}\) outlet region (flue inlet region) were analyzed. Therefore, 10 straight lines with 10 bending flow paths were modeled for the thermal stress simulation. With consideration of the symmetrical structure of the heat exchanger tube, a half scale of the heat exchanger tube was analyzed. 1,114,135 elements were used for the thermo-mechanical analysis. Three-dimensional continuum element DCC3D8 was used to obtain the temperature distribution, and the stress analysis was carried out using the C3D8 continuum solid element. In order to obtain temperature distributions for the heat exchanger tube, temperature and heat transfer coefficient profiles obtained from the thermal analysis were used as the input for thermal stress analysis. Because the pressure drop in the heat exchanger and heat exchange chamber was negligible compared to the operating condition, the pressures in the SCO\({}_{2}\) heat exchanger tube and the chamber were assumed to be 200 bar and atmospheric pressure, respectively. Figure 8 illustrates the temperature distribution in the scaled heat exchanger tube. A solid temperature of the heat exchanger tube is closer to the SCO\({}_{2}\) temperature because the SCO\({}_{2}\) heat transfer coefficient is higher than that of the flue gas. The evaluation of thermal stress analysis was based on the allowable stress value of S34709. The allowable stress value at a temperature of 650 \({}^{\circ}\)C is 539 bar, which is based on ASME Sec. II [23]. The finite element stress analysis was performed with three cases separately: (1) thermal loading, (2) pressure loading, and (3) thermal and pressure loading. Figure 8: Heat exchanger tube temperature distributions used in the thermal stress analysis. Figure 9 shows the tube displacement due to the temperature distribution in the heat exchanger tube. Figure 9a,b represent the tube displacement shape and the principal strain distributions, respectively. The high-temperature area near the exit of the SCO\({}_{2}\) had a large tube expansion, and it gradually decreased. The principal strain distributions showed similar distributions compared to the tube displacement. The maximum principal strain value was discovered to be 0.017. If the deformation of the heat exchanger tube is not considered, thermal buckling due to excessive pressure stress can occur. In the present SCO\({}_{2}\) heat exchanger design, empty space in the chamber was considered, which maintained the integrity of the tube even when the tube displacement appeared. Figure 9: Tube displacements on the tube: (**a**) tube displacement shape, (**b**) the maximum principal strain distributions. Von-Mises stress distributions are shown in Figure 10 along the scaled heat exchanger tube. Figure 10a,b are the results of the thermal and pressure loading cases, respectively. In the case of thermal loading, the maximum stress was found near the tube bending area. On the other hand, the maximum stress was located at the tube bending area for the pressure loading condition. The maximum local von-Mises stress values were 35.5 bar and 516 bar for the thermal and pressure loading cases, respectively. It was confirmed that these stress values were lower than the allowable stress value. Figure 10c is the result of thermal stress analysis considering both the thermal and pressure loading cases. The stress distributions in the tube were similar to the combination of the thermal and pressure loading cases.