## 2 Materials and Methods
### Finite Element Analysis
#### 2.2.1 Geometry and Analysis Conditions
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**(a) Thermal Conductivity**} \\ \hline \multirow{2}{*}{**Temperature (\({}^{\circ}\)C)**} & \multicolumn{3}{c}{**Thermal Conductivity (W/m-\({}^{\circ}\)C)**} \\ \cline{2-4}  & **A240–316** & **A216 WCB** & **Graphite** \\ \hline
25 & 14.1 & 11.5 & 108.4 \\
100 & 15.4 & 12.7 & 106.5 \\
200 & 16.8 & 13.8 & 102.5 \\
250 & 17.6 & 14.3 & 100.3 \\
300 & 18.3 & 14.9 & 98.3 \\
350 & 19.0 & 15.4 & 88.9 \\ \hline \hline \multicolumn{4}{c}{**(b) Thermal Expansion**} \\ \hline \multirow{2}{*}{**Temperature (\({}^{\circ}\)C)**} & \multicolumn{3}{c}{**Thermal Expansion (10\({}^{\text{-6}}\) m/m-\({}^{\circ}\)C)**} \\ \cline{2-4}  & **A240–316** & **A216 WCB** & **Graphite** \\ \hline
25 & 0 & 0 & 0 \\
100 & 1.3 & 1.0 & 0.8 \\
200 & 3.1 & 2.3 & 1.8 \\
250 & 4.0 & 3.0 & 1.8 \\
300 & 4.9 & 3.7 & 1.8 \\
350 & 5.9 & 4.5 & 1.8 \\ \hline \hline \multicolumn{4}{c}{**(c) Mechanical Property**} \\ \hline \multirow{2}{*}{**Temperature (\({}^{\circ}\)C)**} & \multicolumn{3}{c}{**Elastic Modulus (GPa)**} & \multicolumn{3}{c}{**Poisson’s Ratio**} \\ \cline{2-4}  & **A240–316** & **A216 WCB** & **Graphite** & **A240–316** \\ \hline
25 & 195 & 202 & 9.83 & \\
100 & 189 & 198 & 9.53 & \\
200 & 183 & 192 & 9.53 & \\
250 & 179 & 189 & 9.53 & \\
300 & 176 & 185 & 9.53 & \\
350 & 172 & 179 & 6.619 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Nonlinear material properties according to temperature. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**1-Layer Model**} & \multicolumn{2}{c}{**3-Layer Model**} & \multicolumn{2}{c}{**5-Layer Model**} & \multicolumn{2}{c}{**7-Layer Model**} \\ \hline \multirow{2}{*}{**Stainless Steel**} & \multirow{2}{*}{**Graphite**} & **Stainless Steel** & \multirow{2}{*}{**Graphite**} & **Stainless Steel** & \multirow{2}{*}{**Graphite**} & **Stainless Steel** \\ \cline{3-3} \cline{5-8}  & & 0.6 & 3.20 & 0.6 & 2.13 & 0.6 & 1.45 \\ Thickness & & 0.8 & 3.10 & 0.8 & 2.07 & 0.8 & 1.39 \\ (mm) & & 1.0 & 3.00 & 1.0 & 2.00 & 1.0 & 1.55 \\  & & 1.2 & 2.90 & 1.2 & 1.93 & 1.2 & 1.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Thicknesses of graphite and stainless steel according to the number of layers. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{Carbon} & \(\leq\)0.08\% & Silicon & \(\leq\)1.0\% & Manganese & \(\leq\)2.0\% \\ Phosphorous & \(\leq\)0.045\% & Sulphur & \(\leq\)0.030\% & Nickel & 10–14\% \\ Chromium & 16\%\(\sim\)18\% & Molybdenum & 2\%\(\sim\)3\% & Iron & 61.8\%\(\sim\)72\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Chemical composition of (American Society for Testing and Materials) ASTM A240 Grade 316 Stainless Steel. Thermal-structural coupled analysis was conducted to calculate contact stress considering deformation caused by the thermal loads and the working pressure (1 MPa). In the thermal analysis, the convective heat transfer coefficient, \(3.675\times 10^{-3}\) W/mm\({}^{2.\circ}\)C, was employed to the edges of the body, the retainer and the seal, which was exposed to the room temperature, and the thermal load of 350 \({}^{\circ}\)C was imposed on the edges, where contact with the working fluid occurred, as shown in Figure 12(a). Friction coefficients between the disc and the seal were 0.3 for stainless steel and 0.21 for graphite, respectively, as shown in Figure 12(b) [19]. The global hexagonal grid size of the disc, the body, and the retainer was 1 mm, and that of the seal was 0.5 mm. The denser sizing of 0.1 mm was set up to the edges of the seal and the body at which contact stress occurs as shown in Figure 13(a), and the number of nodes was 555,953 and that of elements was 182,554. The orthogonal quality of 98.9% was close to 1, and skewness of 92.8% was close to 0 as shown in Figure 13(b), which verifies the FE model. Figure 14: Generation of mesh. Figure 13: Analysis condition of thermal simulation. (**a**) Temperature and convection, (**b**) friction coefficient. SS, stainless steel; G, graphite.