## 4 Results and Discussion
### Hydrodynamic Forces on the Semi-Submerged Cylinder  
As shown in Figure 4, the time history of the hydrodynamic loads on a semi-submerged cylinder under the steady flow velocity of U = 0.8 m/s was presented. The blue and red solid lines respectively represent the hydrodynamic forces in the IL and CF directions. The mean force in the IL direction \(F_{X\text{M}}\) and mean lift force in the CF direction \(F_{Y\text{M}}\) are 27.6 N and 178.9 N, respectively. A novel phenomenon of an obvious mean downward lift force is witnessed for semi-submerged cylinder and reported by [PERSON] et al. (2019) [PERSON] et al. (2019). This mean lift force is greater than the drag force and should be considered in the real engineering projects. For the hydrodynamic force on semi-submerged cylinder in an oscillatory flow, the time history of these forces in both IL and CF directions for KC = 18.8 and \(\beta\) = 111,364 is shown in Figure 5. Similar to hydrodynamic force on semi-submerged cylinder in steady flow, the mean downward force in the CF direction \(F_{Y\text{M}}\) can be obviously witnessed. The values of \(F_{Y\text{M}}\) were 162.3 N for KC = 18.8 at \(\beta\) = 111,364, while no mean values of the force in the IL direction can be observed. The mean lift force in the CF direction can reach and even exceed the fluctuating force amplitude of hydrodynamic force in the IL direction (\(F_{X}\)). The fluctuating components of two forces are in the same magnitudes. Figure 4: Time history of the hydrodynamic forces for semi-submerged cylinder under a flow velocity of U = 0.8 m/s. Figure 5: Time history of the hydrodynamic forces for semi-submerged cylinder under Keulegan-Carpenter (KC) = 18.8 at \(\beta\) = 111,364. (**a**) Time history of forced motion; (**b**) Time history of the hydrodynamic forces on semi-submerged cylinder; (**c**) The spectrum of the hydrodynamic loads. From the spectrum of the hydrodynamic forces in both IL and CF directions as shown in Figure 5c, the dominant frequency of force in the IL direction is the same as expected for the forced motion frequency (\(f_{\circ}\)) of 0.18 Hz and the response frequency in the CF direction is found to be always dominated by twice the value of \(f_{\circ}\) (\(f\) = 0.36 Hz) under KC = 18.8 and \(\beta\) = 111,364. It indicates that this lift force with higher frequency could cause more severe damage to related structures and cannot be neglected. To understand the background mechanics of the mean lift downward force in an oscillatory flow, a camera is placed on the apparatus to record the surface waveforms. Figure 6a clearly shows the recorded local surface distortions. According to the phenomenon recorded by the camera, we infer that the mean downward lift force can be attributed to the asymmetric flow field and the pressure difference between the top and bottom of the cylinder [19; 23] as shown in Figure 7c. Furthermore, Figure 7 presents the time history of hydrodynamic force and sketches of flow field around cylinder in one period to give more detailed features. Combining with forced motion velocity, we observed that the lift force reaches its amplitude value at around time points I, III, V. From Figure 7c, the top-sided flow velocity is more significant when the forced motion velocity reach its maximum (\(U_{max}\)). Thus, the maximum lift force value appears near the time points of \(U_{max}\). Figure 6: The pictures of slamming and its developing process sketch. (**a**) Pictures of slamming phenomenon; (**b**) Sketch of slamming developing process. Figure 7: Time history of forced motion, hydrodynamic force and sketches of flow field around cylinder in one period under KC = 18.8 at \(\beta\) = 111,364. (**a**) Time histories of forced motion displacement and velocity; (**b**) The hydrodynamic loads on semi-submerged cylinder; (**c**) Sketches of flow filed change. However, there is a phase difference between \(F_{Ymax}\) and \(U_{max}\). These two maximum values do not reach at the same time. The maximum of force \(F_{Ymax}\) is reached before the \(U_{max}\).