## 4 Results and Discussion
### Drag and Added Mass Coefficients for Semi-Submerged Cylinder  
Combining measured hydrodynamic force and forced motion in the IL direction, we can calculate the drag coefficient (\(C_{D}\)) and added mass coefficient (\(C_{m}\)) using the method proposed in Section 3. To verify the identified method of hydrodynamic coefficients, the hydrodynamic force is recalculated through Equation (8) by identified drag and added mass coefficient as shown in Figure 10. The blue dashed line and red solid line represent the measured force and calculated force, respectively. The good consistency is witnessed between measured and calculated value. This demonstrates the validity of the identification method for hydrodynamics of semi-submerged cylinder under an oscillatory flow. Figure 11 shows the drag and added mass coefficients distribution with KC number under different Stokes number \(\beta\). The relationship between C\({}_{D}\) and \(\beta\) is indistinct as shown in Figure 11a. When the KC number is less than 20, the discrete distribution features is very obvious. Therefore, the Stokes number would more greatly affect the drag coefficient at this condition (KC \(<\) 20) but does not show a significant influence on drag coefficient under KC \(>\) 20. As the value of \(\beta\) increase, the drag coefficient increases under smaller KC number (KC \(<\) 20) but decreases under larger KC number (KC \(>\) 20). Different from the results of drag coefficients, the distinctive features is found that C  
Figure 10: Time history of the measured and calculated hydrodynamic forces for semi-submerged cylinder in the in-line (IL) direction under KC = 18.8 at \(\beta\) = 11,364 (A = 0.75 m, T = 5.5 s). Figure 9: Time history of the measured and calculated hydrodynamic forces for semi-submerged cylinder in the cross-flow (CF) direction under KC = 18.8 at \(\beta\) = 11,364 (A = 0.75 m, T = 5.5 s). increase with KC and \(\beta\) number as shown in Figure 11b. For the semi-submerged cylinder, the free surface effects cannot be ignored. Thus, the Froude number will be an important parameter to describe the hydrodynamic coefficients [14,19]. Further, Figure 12 present the drag and added mass coefficient changing with Froude number under the same Stokes number. The drag coefficient in Figure 12a shows the disorderly and irregular characteristics. The relationship between \(C_{D}\) and Fr cannot be directly concluded under the same Stokes number. As for the added mass coefficient of semi-submerged cylinder, the positive correlation between \(C_{m}\) versus Fr is also obviously seen under the same \(\beta\) value as shown in Figure 12b. Under the same KC number, it is clear that hydrodynamic coefficients are significantly related to the Froude number as illustrated in Figure 13. When KC < 20, the drag coefficient decreases as Froude number increases. An unexpected phenomenon is observed that the drag coefficient increase linearly with Froude number as KC > 20 as shown in Figure 13a. With the increase of KC number, the relationship of drag coefficient has a significant evolution trend with Froude number, nonlinear decay changing to linear increase. Additionally, the added mass coefficients show a nonlinear (KC < 20) and a linear (KC > 20) increase trend similar to the trend of drag coefficient under KC > 20. The evolution trend from nonlinear to linear uptrend of the added mass coefficient can also be witnessed. From above observation, it can be inferred that using the Froude number and KC number to predict the hydrodynamic coefficient of semi-submerged cylinder in an oscillatory flow is a promising way in engineering project, especially for larger KC number (KC > 20). Figure 11: Drag and added mass coefficients changing with KC number under different Stokes number ((a) drag coefficients; (b) added mass coefficient). Figure 12: Drag and added mass coefficients changing with Froude number under different Stokes number ((a) drag coefficients; (b) added mass coefficient).