## 4 Fluid-Structure Interaction  
The fluid-structure interaction (FSI) responses to the water hammer effect using numerical simulations are determined in this research to assess the safety and design of the high-pressure pipelines in NPPs. The FSI response on the dynamic behavior of the CEA model pipe is studied by coupling Ansys CFD and Transient Structural modules. The one-way FSI approach is used in this simulation where the fluidic forces influence the structural deformation of the pipe. The cyclic disturbance to the fluid flow due to the structural response is neglected in this research owing to the very short duration of the entire event. The fluid to structural coupling is automatically generated in the Ansys workbench module to facilitate ease of data transfer, although both the domains are independent of each other. A strongly implicit coupling algorithm is used in this research through the applications of Ansys workbench, where the solver pertains to a sub-iterative approach to attain convergence at the end of the time step. The sub-iterative approach helps to balance the fluidic forces at the end of each consecutive time steps where the applied time steps should satisfy the Courant-Friedrichs-Lewy (CFL) conditions [3; 36]. The structural response to  
Figure 6: Pressure (**a**) and velocity (**b**) distribution from the CFD simulations. the fluidic forces can be obtained on the common boundary interface \(\Gamma\). The governing equation for the structure is given in the following Equation (5):  
\[\rho^{s}\frac{D^{2}d}{Dt^{2}}-\
abla(F\cdot S(d))=\rho^{s}b^{s} \tag{5}\]  
where \(\rho^{s}\) and \(b^{s}\) represent the density and the body forces applied on the structure, with \(F\), \(d\), and \(S\) being the deformation gradient tensor, structural displacement, and the second Piola-Kirchhoff stress tensor, respectively. [PERSON] et al. reported that the influence of the FSI on their component initiates a non-uniform distribution of dynamic loads [37]. Another study attempted a numerical simulation on the comparison of the dynamic behavior of the crack under blast loading conditions of the coupled (FSI) and uncoupled models. The numerical simulations proved to be a validatory backdrop to evaluate its prediction with the experimental results [38]. [PERSON] et al. solved a k-\(\epsilon\) turbulence model to determine the Reynolds stress through an implicit FEM to obtain the structural behavior of the pipe due to the whipping effect on high energy pipelines, and the governing equations are given by Equation (6), based on the effects of external time-dependent fluidic pressure [39; 40]. Equation (6) is as follows:  
\[[M]\big{\{}\ddot{u}(t)\big{\}}+[C]\big{\{}\dot{u}(t)\big{\}}+[K]\big{\{}u(t) \big{\}}+\big{\{}\dot{\rm G}\cdot\rm{Ap}(t)\big{\}}=\big{\{}F(t)\big{\}} \tag{6}\]  
where \([M]\), \([C]\), and \([K]\) are the mass, damping, and stiffness matrices of the system with \(\ddot{u}\), \(\dot{u}\), and \(u\) acceleration, velocity, and displacement vectors, respectively, and \(F(t)\) is the thrust and fluid force on the pipe with G being the rectangular transformation matrix of the forces in the normal direction in the fluid area and A as the diagonal matrix in the fluid area, with p as the total fluidic pressure on the pipe. The classical Hooke's stress-strain relationship is applied to the FSI response in the pipe's longitudinal direction, and the continuity equation can be derived by Equation (7), as follows:  
\[\varepsilon_{x}=\frac{\partial w_{x}}{\partial x}=\frac{1}{E}[\sigma_{x}-\
u( \overline{\sigma_{r}}+\overline{\sigma_{\theta}})] \tag{7}\]  
where \(w_{x}\) is the axial displacement of the pipe wall due to the motion of the fluid, with \(\sigma_{x}\) being the pipe stress along the direction [35].