## 2 FPAPr Design and Fabrication
### Simulation  
In this study, before fabricating the FPAPr, we verified their applicability through a simulation of a weld zone with an irregular shape. The simulation was performed using CIVA, which is mainly used for ultrasonic propagation behavior [38]. The four types of commonly used, irregularly shaped pipes were modeled to perform the simulation, as shown in Figure 6. Table 2 summarizes the data and material properties of the used specimens.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Probe Type** & **FPAPr(P/E)** & **FPAPr(T/R)** \\ \hline Total Elements (ch) & 32 & 32 \(\times\) 2 \\ Nominal frequency & 5 & 5 \\ (MHz) & 16 & 12.8 \\ Elevation (mm) & 10 & 5 \\ Pitch (mm) & 0.5 & 0.4 \\ Gap (mm) & 0.1 & 0.1 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Specifications of the two types of FPAPr.  
Figure 5: Images of phased array probe with a flexible structure geometry excluding solid wedge: (a) 32 channel(ch), P/E, pitch 0.5 mm; (b) 32 ch \(\times\) 2, T/R, pitch 0.4 mm.  
Figure 7 illustrates the scan plans for the simulation. Transverse waves were used for the inspection wave mode, and the 1-skip technique was used to detect defects by reflecting once on the bottom surface for defect detection. Flaws (notch, side drilled hole (SDH), etc.) that could be generated in reality at the irregularly shaped weld zones were modeled by reflecting actual experimental conditions. The probe modeling parameters were identical to the FPAPr fabrication specifications, and the sweep angle was maintained between 35 and 75\({}^{\circ}\) to allow the control volume to encompass the entire weld zone [39, 40, 41, 42, 43, 44, 45].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & \begin{tabular}{c} **Elbow–Flange–** \\ **Reducer** \\ \end{tabular} & \
\begin{tabular}{c} **Tapered Elbow** \\ **to Pipe** \\ \end{tabular} &
\begin{tabular}{c} **Upper-Tapered Pipe** \\ **Upper-Tapered Pipe** \\ \end{tabular} \\ \hline Material & Carbon Steel & Carbon Steel & Carbon Steel \\ Longitudinal Velocity & 5900 m/s & 5900 m/s & 5900 m/s \\ Transverse & 3230 m/s & 3230 m/s & 3230 m/s \\ Velocity & 7.8 \(\times\) 10\({}^{3}\) kg/m\({}^{3}\) & 7.8 \(\times\) 10\({}^{3}\) kg/m\({}^{3}\) & 7.8 \(\times\) 10\({}^{3}\) kg/m\({}^{3}\) \\ A diameter & 100 mm & 150 mm & 300, 350 mm \\ Thickness & 8 mm & 14.8, 20.0 mm & 36.5, 51 mm \\ \hline \hline \end{tabular}
\end{table}
Table 2: Specifications of the curved pipes used in the simulation.  
Figure 6: Actual specimens applied to the simulation; (**a**) a pipe with 100 mm diameter flange–elbow structure; (**b**) a pipe with 150 mm diameter tapered elbow structure; (**c**) a pipe with 300 mm diameter tapered upper structure.  
Figure 7: _Cont_.  
Figure 8 shows the simulation results of applying the FPAPr on the flange-elbow, tapered elbow, and branch pipe. The signal sensitivity was a factor that could be used to examine the FPAPr contact wherein the contact and signal sensitivity are proportional to each other. A relatively adequate signal sensitivity was observed from the overall simulation result, which indicated reliable FPAPr contact. Additionally, the location and size of the flaw could be assessed by calculating and applying a suitable focal law.