# Vortex-Induced Vibration of Deep-Sea Mining Pipes: Analysis Using the Slicing Method
## 3 Construction and Verification of Numerical Model
### Physical Model Selection and Model Verification  
Since there are few research studies on physical experiments of deep-sea mining pipes, and deep-sea mining pipes and traditional risers have many similarities, the meth  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Grid No.**} & **Total Foreground** & **Outermost Thickness of** & **Near-Wall Grid** & **Total Background** & \multirow{2}{*}{**C\({}_{\text{LRMS}}\)**} & \multirow{2}{*}{**C\({}_{\text{Dmean}}\)**} \\  & **Grid Cells** & **Foreground Grid** & **Thickness** & **Grid Cells** & & \\ \hline I & 30,820 & 0.01D & 0.001D & 251,835 & 1.581 & 1.039 \\ II & 43,152 & 0.008D & 0.001D & 359,676 & 1.584 & 1.042 \\ III & 58,310 & 0.006D & 0.001D & 486,822 & 1.577 & 1.046 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Grid convergence test (Re = 3000).  
Figure 5: The numerical solution process of slicing method.  
ods adopted in this paper are basically the same for the model establishment and fluid-structure coupling solution of deep-sea mining pipes and traditional risers. In this section, model tests with fixed boundary conditions at both the top and bottom are used for numerical verification.  
To validate the fidelity of the numerical model in this research, the experimental setup designed by [PERSON] [24] is utilized as a benchmark for conventional riser simulation analyses discussed in this section. The experimental configuration features the riser's bottom end coupled to an adjustment module via precision universal joints, while its top end is linked to the upper motion module, integrating tension sensors and tensioning devices. A schematic representation of this experimental arrangement is depicted in Figure 6. For the purpose of assessing the vibration response characteristics of the riser, a total of 12 detection points are strategically positioned along its axial direction. The position of the 12 two-dimensional flow-field slices divided in this paper is the same as that of the above experimental monitoring points. The numerical simulation method used is the same as that described above. Other experimental parameters are shown in Table 2.  
Five groups of homogeneous flow conditions were taken to conduct our numerical simulation of the vortex-induced vibration of the riser, and the \(y_{\text{RMS}}\) results at slice 06 of the riser were compared with the experimental results of [PERSON] et al., as shown in Table 3.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Correlation Parameter** & **Numerical Value** & **Unit** \\ \hline External diameter (d) & 0.02 & m \\ Length (L) & 5 & m \\ Top tension (T) & 80 & N \\ Bending stiffness (EI) & 42.62 & Nm\({}^{2}\) \\ Tensile stiffness (EA) & \(1.47\times 10^{6}\) & N \\ Mass ratio (m*) & 1.96 & - \\ First-order inherent frequency (f\({}_{1}\)) & 0.99 & Hz \\ Second-order inherent frequency (f\({}_{2}\)) & 2.34 & Hz \\ Third-order inherent frequency (f\({}_{3}\)) & 4.64 & Hz \\ Fourth-order inherent frequency (f\({}_{4}\)) & 7.67 & Hz \\ \hline \hline \end{tabular}
\end{table}
Table 2: Model parameters of the riser.  
Figure 6: Test device diagram.  
According to the above data, we found that in the five working conditions we selected, the dimensionless value of the transverse flow displacement of the riser obtained by the numerical simulation method in this study was slightly higher than the result of the reference test, but these deviations were all lower than 8%, which was within a certain range, so we could confirm that the numerical model we established had high accuracy.