# Numerical Simulation of a Submerged Floating Tunnel: Validation and Analysis
## 2 CEL Method for One- and Two-Way Fluid-Structure Coupling Validation
### Verification of Round-Rod Dragging Results  
The CEL method was applied in a two-way fluid-structure coupling analysis to verify that it can be applied for studying SFTs. To achieve this, a circular rod was given an initial velocity in a body of water that remained stationary. To validate the CEL method in a two-way fluid-structure coupling calculation, the drag force obtained from the numerical simulation was compared with the drag force calculated using the Morison equation (Equation (5)) as follows:  
\[F=C_{D}\frac{1}{2}\rho V^{2}D \tag{5}\]  
where \(C_{D}\) is the drag force coefficient and \(F\) is the drag force. In the hypothetical model [32], the circular rod had a diameter of 0.02 m, and 0.14 m of its length was submerged in the water body. The water body was simulated using Eulerian elements, with a density of 1000 kg/m\({}^{3}\), a viscosity of 0.001 Pa-s, and a speed of sound of 1480 m/s. The upper surface of the water body was a free boundary, while the bottom and the four sides were smooth boundaries, with the velocity set to zero. The horizontal degree of freedom was relaxed at the top of the circular rod, while the degrees of freedom in the other directions were constrained. The contact between the cylinder and the fluid was defined as a smooth hard contact, allowing no mutual intrusion in the normal direction and setting the tangential friction to zero. \(V_{x}\) was set to the top of the cylinder for calculation, with different horizontal velocities. Figure 3 illustrates the velocity field clouds of the circular rod at different stages during its motion through the fluid. The results demonstrate that when the circular rod moved through the fluid at a certain speed, the velocity fields of both the rod and its surrounding fluid underwent significant changes. During the motion, a bulge formed in front of the circular rod, which led to the separation of the boundary layer at the maximum point of the column section width. This resulted in the formation of a free shear layer that extended to the back of both sides of the column. Within this shear layer, the outer part had a lower flow rate than the inner part, leading to a rotational tendency in the fluid and the formation of a vortex. The empirical curve of \(C_{D}\) vs. \(Re\) is shown in Figure 4.  
In this study, the drag force on a circular rod was simulated at various \(Re\) values by changing the horizontal velocity of the rod. The empirical values of the drag force, \(F\), were calculated using Equations (4) and (5), with the joint calculation of the motion velocity, \(V\). The simulated drag force was calculated as the drag force in the horizontal direction between the contact surface of the circular rod and the fluid, consisting primarily of frictional resistance and differential pressure resistance. The drag force under each  
Figure 3: Velocity field clouds at different stages in a model of two-way fluid–solid coupling. velocity condition was plotted as a fluctuating temporal curve, and the average value was taken as the simulated solution for the drag force on the circular rod. Table 2 shows the simulated and empirical solutions for the drag force of the cylinder at various \(Re\) values. At low \(Re\) values, the effect of fluid viscosity was prominent, resulting in vortex dissipation. The gradual dissipation of the momentum and energy of the fluid resulted in a relatively stable flow. However, at high \(Re\) values, complex turbulence phenomena occurred. Generally, \(Re\) values needed to be controlled within the range of \(10^{4}\) to \(10^{5}\), such that the fluid formed a complex flow field on the surface of the structure, generating nonlinear effects such as vortices and turbulence, which caused significant friction and drag. Due to the large inertial force of the fluid, its vibration response was also significant at high \(Re\) values, causing noticeable dynamic responses within the structure.