# Design of Quadruple Offset Butterfly Valve Used in Power Plants
## 3 Finite Element Analysis
### Design of Number of Laminated Seal Layers
#### 3.1.3 Result of the Thermal-Structural Coupled Analysis  
In this present study, the contact pressure is calculated by Equation (20) [16], and a leakage criterion was used, which is contact pressure compared with the working pressure and estimated leakage by Equation (21) [12], shown in Figure 14.  
\[P_{contact}=0.798\sqrt{\frac{F}{l\left(\frac{1-p_{1}^{2}}{E_{1}}\right)+(\frac{1 -p_{2}^{2}}{E_{2}})}},\;\mathrm{F}=P_{working}\times cos\varphi \tag{20}\]  
When contact stress is higher than the working pressure, it could guarantee airtightness. \[P_{contact}>P_{working}\;:\;\mathrm{no\ leakage}P_{contact}<P_{working}\;:\; \mathrm{leakage} \tag{21}\]  
The proper contact pressure generated by the seal provides good sealing performance and does not affect the disc's opening and closing. Therefore, a trade-off between smooth driving and sealing is conducted. If contact pressure is a little higher than the working pressure (1 MPa), it ensures both the sealing performance and smooth driving of disc. Table 3 represents the contact pressures results at the angles of 88.1\({}^{\circ}\)and 66.1\({}^{\circ}\) and maximum values for the different numbers of laminated seal layers (one-layer, three-layers, five-layers, seven-layers) and temperatures (25 \({}^{\circ}\)C and 350 \({}^{\circ}\)C). The contact pressures of the one-layer model at 25 \({}^{\circ}\)C were 17.46 MPa at 86.1\({}^{\circ}\) and 12.51 MPa at the angle of 66.1\({}^{\circ}\), respectively, whereas some regions showed 0 MPa, so leakage may occur near the shaft. At 350 \({}^{\circ}\)C, the contact pressures were 98.2 MPa and 0.039 MPa at the angles of 86.1\({}^{\circ}\) and 66.1\({}^{\circ}\), respectively. The maximum value at 350 \({}^{\circ}\)C was 282.5 MPa, but the leakage was produced near the shaft, as shown in Figure 15.  
Figure 14: The criterion for leakage. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Angle 86.1\({}^{\circ}\)**} & \multicolumn{2}{c}{**Angle 66.1\({}^{\circ}\)**} & \multicolumn{2}{c}{**Max Contact-**} \\  & **(MPa)** & & **(MPa)** & & **Pressure (MPa)** \\ \hline  & 25 \({}^{\circ}\)C & 350 \({}^{\circ}\)C & 25 \({}^{\circ}\)C & 350 \({}^{\circ}\)C & 25 \({}^{\circ}\)C & 350 \({}^{\circ}\)C \\
1-layers & 17.46 & 98.2 & 12.51 & 0.04 & 27.78 & 282.5 \\
3-layers & 2.92 & 42.48 & 8.51 & 154.25 & 24.23 & 154.25 \\
5-layers & 2.87 & 14.37 & 8.25 & 89.8 & 24.16 & 114 \\
7-layers & 1.59 & 74.4 & 13.9 & 64.5 & 13.9 & 93.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The contact pressure of the laminated seal. The contact pressures of the three-layers at the angles of 86.1\({}^{\circ}\) and 66.1\({}^{\circ}\) were 2.92 MPa and 8.51 MPa at 25 \({}^{\circ}\)C, and 42.9 MPa and 154.25 MPa at 350 \({}^{\circ}\)C, as shown in Figure 16. Leakage did not occur, and compared with the one-layer model at 350 \({}^{\circ}\)C, the contact pressures were reduced compared with one-way, but they were still too much larger than the working pressure (1 MPa). The contact pressures of the five-layers at the angles of 86.1\({}^{\circ}\) and 66.1 were 2.87 MPa and 8.25 MPa at 25 \({}^{\circ}\)C, and 14.37 MPa and 89.8 MPa at 350 \({}^{\circ}\)C, as shown in Figure 17. The maximum contact pressure was 114 MPa at 350 \({}^{\circ}\)C, leakage was not found, and compared with the three-layer model at 350 \({}^{\circ}\)C, the max contact pressures were reduced by 40 MPa. Figure 16: The contact pressure distribution of the three-layers model. Figure 15: The contact pressure distribution of the one-layer model. The contact pressures of the seven-layers at the angles of 86.1\({}^{\circ}\) and 66.1\({}^{\circ}\) were 13.9 MPa and 1.59 MPa at 25 \({}^{\circ}\)C, and 93.5 MPa (maximum) and 27.184 MPa at 350 \({}^{\circ}\)C, respectively. The maximum contact stress (93.5 MPa) of the seven-layers at 350 \({}^{\circ}\)C was lower than that of one-layer (282.5 MPa), three-layers (154.25 MPa), and five-layers (114 MPa).