## 4 Fluid-Structure Interaction
The refined plot of the displacements after the impact is shown in Figure 11b. The velocity distribution plots of all three models show similar values of the velocity at impact, with negligible deviations. Figure 11: (**a**) Displacement vs. time plot and (**b**) refined plot region after impact. Figure 10: Imported pressure from the CFD analysis to the corresponding pipe surfaces (**a**) fully 3D, (**b**) 550 mm and (**c**) 150 mm models. The stresses associated with each model vary in time from the start till the impact but show similar stress fields at the impact location. This is due to the absence of solid elements along the deformable bend of the pipe during the whip phenomenon where the stress distribution is not calculated for the one-dimensional elements. The stress distribution contours on the lateral section of the fully 3D model is shown in Figure 13, depicting the impact location, which helps in further simplifying the model by considering the region around the impact for solid modeling and neglecting the other regions. Figure 14 shows the stress fields around the impact location for all three model pipes where no significant changes could be seen. Since this research is dedicated to the behavior at the impact location, the differences in the stress distribution along the length of the pipe can be deemed negligible. Figure 12: (**a**) Stress vs. time and (**b**) velocity vs. time plots. Figure 13: Stress distribution of the fully 3D model at impact. From Table 2, it is evident that all three models possess similarity in the time taken to impact after fluid flow initiation, while negligible differences can be observed in the impact velocity comparable with the experimental results [4]. The comparison of the models with the results of the ABAQUS-EPGEN and TEDEL codes are in close agreement with the impact time. These results show that the simplified coupled models can be substituted for the solid models where the kink locations are being majorly considered to estimate the mechanical behaviour under impact conditions. All three models show similar deformable behaviour, as shown in Figure 12, even with the simplified approach of reducing the solid model to 5% of its original length. However, the fluid modeling parameters can be developed for the FSI models by taking into consideration the two-way FSI approach and solving under controlled water hammer conditions. The comparison of the model parameters is shown in Table 3 and their independent displacement contours are shown in Figure 15a-c which predicts similar mechanical displacements for all three models, suggesting that a localized solid modeling technique can generate equal and optimal results with significant differences in their computational time and effort. The maximum values of total displacement and the equivalent von Mises stress are almost similar to the pipe-to-wall impact model for both the simplified model cases. However, the computational time is significantly reduced for the localized 150 mm model, which contains less than half the number of finite elements when compared to the 550 mm model, and all three models behave similarly under the dynamic structural conditions. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{3}{c}{**Pipe-to-Wall Impact Testing Method**} \\ \hline
**Model Type** & **Time to Impact** & **Velocity at Impact** \\  & **(ms)** & **(m/s)** \\ \hline CEA Experiment [2] & 13.2 & - \\ \hline ANSI 58.2 Standard [4] & 10.1 & 13.42 \\ \hline ABAQUS-EPGEN (V4.5) Code [4] & 7.1 & 13.51 \\  (beam-shell formulation) & 8.4 & - \\ \hline Fully 3D model (Ansys R2) & 18 & 16.26 \\ \hline
550 mm Solid Pipe model (Extended) & 18 & 15.97 \\  (beam-solid formulation) & 18 & 16.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Validation of the 1D/3D modeling approach with the experimental results. Figure 14: Stress distribution and mechanical behaviour at the point of impact of the (**a**) fully 3D model, (**b**) 550 mm model, and (**c**) 150 mm model.