## 2 Risers' Geometries and Materials and FE Modeling
### FE Modeling
Reynolds numbers are calculated by Equation (8), where \(U\) is the flow velocity, \(D\) is the outside diameter of the riser, and \(v\) is kinematic viscosity coefficient. \[Re=\frac{UD}{v} \tag{8}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Flow Parameters** & **Riser Type** & \(Re\) & **Tension Force (N)** \\ \hline density (kg/m\({}^{3}\)) & 1024 & Riser 1 & 101,887 & 31,145 \\ velocity (m/s) & 0.36 & Riser 2 & 110,716 & 12,838 \\ \(v\) & 1.06 \(\times\) 10\({}^{-6}\) & Riser 3 & 105,283 & 9776 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Flow parameters and Re and top tensions of the risers. Figure 3: FE models of flow and riser. To ensure the accuracy of the simulation for vortex shedding phenomenon, the fluid grid for the 5D \(\times\) 5D area around the riser was refined to take the data exchange between the riser and flow into account. The dynamic mesh was employed in the refined zone. The dynamic mesh zones involved seven faces, i.e. the six surrounding planes of the refined zone (set as stationary) and the contact surface between fluid and riser (set as system coupling). Smoothing and remeshing were utilized as the dynamic mesh methods. For smoothing method, 0.6 and 0.8 were used for spring constant factor and Laplace node relaxation, respectively. Remeshing method included local cell, local face and region face; also, the sizing function is turned on. In terms of the flow surface (\(XY\)-direction), 4478 elements were employed (including the refined area) for both 2D and 3D simulation; in the depth of the flow (\(Z\)-direction), 150 elements were applied for 3D simulation. In total, 671,700 elements, which balanced the accuracy and computational cost, were utilized in the flow zone (3D simulation). The number of the elements for the fluid zone was decided based on convergence study, i.e., reducing the number might lead to the loss of accuracy while increasing the number could not change the result obviously. For the steel riser, the traditional modeling method was utilized with isotropic steel. For the composite risers (Risers 2 and 3), two different methods, effective modulus method and layered-structure method, were established. In effective modulus method, composite riser is regarded as an anisotropic monolithic structure rather than layered-structure using Equations (1)-(6), i.e., only the effective properties for the entire riser in Table 3 is required. In the layered-structure method, the properties for the liner and each composite lamina (Table 2) are required as well as the lamination configuration of the riser (Table 1) to create the real structure of the composite riser. Comparatively speaking, EMM is easier during the modeling process and needs less computational resource to obtain the global results, while LSM can be used to get the response of each composite lamina at the expense of larger computational resource and longer calculation time. The risers are modeled by Solid185; 240 elements in length direction and 20 elements in hoop direction were employed. In total, 4800 elements were utilized in the riser based on convergence study. Compared to the element number in the fluid zone, the number of elements for risers would not lead to significant difference in the requirement of computational resource and calculation time. All the risers were fixed at the bottom and simple supported at the top. Top tension force was also employed at the top end of the risers, which equals to 1.5 times the weight for the steel riser and 2 times the weight for the composite riser (Table 4). In the two-way FSI, the riser deformation, the flow data variation and the influence between them were considered. Figure 3 shows the FE model of the flow and riser.