## 5 Analysis of the VIV Model Test Data of Flexible Riser with Staggered Buoyancy Elements
### Prediction with Default Parameters  
The numerical model to predict the response of the flexible riser with staggered buoyancy elements is constructed in VIVANA. The structural damping is set to be 1% of the critical damping.  
The default excitation coefficient parameters from VIVANA are used to predict the VIV response. The predicted response frequencies from the default set of excitation coefficients and the measured responses are presented as a function of towing speed in Figure 8. The non-dimensional frequency (\(f=\frac{f_{\infty}\cdot U}{U}\)) corresponding to the bare riser's excitation frequency typically ranges 0.125-0.155 for different configurations in the model test [16]. The non-dimensional frequency for the buoyancy element was generally lower than that for the bare riser section. Significantly lower non-dimensional frequency (\(f_{CF}\approx 0.1\)) could be found in model tests for shorter buoyancy element (L\({}_{\text{B}}\)/D\({}_{\text{B}}=1\)) configuration [18]. When comparing with the measured responses, the response frequencies are, in general, over-predicted  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Bare Riser** & **Buoyancy Element** \\ \hline Total length between pinned ends (m) & 38.00 & 38.00 \\ Outer diameter (mm) & 30.00 & 80.00 \\ Outer/inner diameter of fiberglass rod/pipe (mm) & 27/21 & 27/21 \\ The length of one buoyancy element (m) & – & 0.4086 \\ Bending stiffness, EI (N-m\({}^{2}\)) & 572.3 & 572.3 \\ [PERSON]’s modulus, E (N/m\({}^{2}\)) & \(3.46\times 10^{10}\) & \(3.46\times 10^{10}\) \\ Mass in the air (kg/m) & 1.088 & 5.708 \\ Weight in water (kg/m) & 0.579 & 0.937 \\ Mass ratio (-) & 1.54 & 1.14 \\  & \(1.32\times 10^{5}\) & \(3.51\times 10^{5}\) \\ Reynolds number (-) & - & - \\  & \(3.16\times 10^{5}\) & \(8.42\times 10^{5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: The material properties of the bare riser section and the buoyancy element.  
Figure 6: Definitions of LC, LB, DC, and DB.  
Figure 7: Staggered buoyancy configurations over the riser.  
by the VIVANA model with the default set of excitation coefficients. This suggests the over-prediction of the excited modes, hence, higher stress and fatigue damage.  
Figure 9 shows the curvature RMS values for the default set of parameters for different configurations. It is observed from the test data that 1/1 configuration has the lowest curvature, whereas L\({}_{\text{C}}\)/L\({}_{\text{B}}\) = 3/1 configuration has the highest curvature. It can also be noted that the configuration L\({}_{\text{C}}\)/L\({}_{\text{B}}\) = 2/2 has higher curvature even the percentage of buoyancy element coverage is the same as the 1/1 configuration. The maximum RMS curvature using the default set of parameters is in general over-predicted than the measurements.  
The predicted A/D for 2/2 configuration at U = 1.0 m/s are presented in Figure 10. It shows that the riser is excited at two response frequencies and modes due to excitations from the bare sections and the buoyancy sections of the riser. The predicted vortex shedding frequency of the buoyancy section is 2.1 Hz and the 5 th mode of the riser system is excited. The vortex shedding frequency of the bare riser section is 5.8 Hz, which corresponds to the 14 th mode.  
Figure 8: Excited response frequencies for five configurations at flow speeds between 0.5–1.2 m/s. (**Left**): prediction using the default set of excitation coefficients from VIVANA; (**Right**): measured response frequencies from Shell Test.  
Figure 9: Curvature RMS values for five configurations at flow speeds between 0.5–1.2 m/s. (**Left**): prediction using the default set of excitation coefficients from VIVANA; (**Right**): measured curvature from Shell Test.  
Identification of an Optimal Dataset of Excitation Coefficient Parameters for the Flexible Riser with Staggered Buoyancy Elements