# Simulating Slosh Induced Damping, with Application to Aircraft Wing-like Structures
## 4 Results and Discussion
### Impact of Compartment Numbers
From the snapshots in Figures 14 and 16, the sloshing behaviour with eight compartments shows strong impacts with the ceiling and floor of the tank for all compartments in every oscillation cycle. This is reflected in Figure 17, which shows the normalised force-velocity diagram for the last five cycles with \(D_{i}=0.25\). It can be seen that the vertical fluid force for \(N_{c}=8\) is smaller than that with smaller compartment numbers in the third quadrant, likely due to the strong impact to the ceiling of the tank by the sloshing waves during the second half of the down stroke. A larger overall vertical fluid force in the fourth quadrant is also observed in the tank with \(N_{c}=8\) compared with others, which is due to the interaction between the splash water and the floor of the tank during the first half of the upstroke. Figure 14: Snapshots for the sloshing tank with \(D_{i}=0.25\) at \(t/T=5.0\) for (**a**) \(N_{c}=1\), (**b**) \(N_{c}=2\), (**c**) \(N_{c}=4\) and (**d**) \(N_{c}=8\). Water phase is shown as transparent red with dark red representing the free surface. Blue arrows show the general direction of motion of the sloshing water. Figure 15: Snapshots for the sloshing tank with \(D_{l}=0.25\) at \(t/T=5.5\) for (**a**) \(N_{c}=1\), (**b**) \(N_{c}=2\), (**c**) \(N_{c}=4\) and (**d**) \(N_{c}=8\). Water phase is shown as transparent red with dark red representing the free surface. Blue arrows show the general direction of motion of the sloshing water. It is also observed that the water tank with \(N_{c}=4\) has larger vertical fluid force in the first and third quadrant compared with other cases. As discussed, this larger vertical fluid force is due to the lack of interaction between sloshing waves and the top/bottom walls of the tank of the misaligned sloshing frequencies and the oscillation frequency. A larger vertical fluid force in the first and third quadrant will bring less damping to the system. Figure 16: Snapshots for the sloshing tank with \(D_{i}=0.25\) at \(t/T=6.0\) for (**a**) \(N_{c}=1\), (**b**) \(N_{c}=2\), (**c**) \(N_{c}=4\) and (**d**) \(N_{c}=8\). Water phase is shown as transparent red with dark red representing the free surface. Blue arrows show the general direction of motion of the sloshing water. Less impact between the sloshing wave and the ceiling also makes the sloshing tank with \(N_{c}=2\) have larger fluid force in both the first and third quadrant compared with that of \(N_{c}=1\) and provide less damping to the system. Figure 18 shows the instantaneous non-dimensional tip vertical displacement of the system over ten oscillation cycles for \(D_{i}=0.5\). From the fifth oscillation cycle onwards, a clear decay in the tip displacement can be observed with \(N_{c}=8\) and \(N_{c}=4\), compared with \(N_{c}=1\) and \(N_{c}=2\). Figures 19 and 20 present snapshots of the sloshing tank with \(D_{i}=0.5\) with different compartment numbers during the sixth cycle (from \(t/T=5.0\) to \(t/T=6.0\)). Similar to  
Figure 17: Normalised force–velocity diagram for the last five oscillation cycles with \(D_{i}=0.25\). Figure 18: Time history of non-dimensional tip vertical displacement of the system normalised by the initial excitation amplitude over ten cycles for \(D_{i}=0.5\). findings in Figures 10 and 11, the front half of the tank for \(D_{i}=0.5\) and \(N_{c}=1\) is dominated by the violent vertical motion. This agrees with observations from Figures 19a and 20a at \(t/T=5.0\) to \(t/T=6.0\). By involving a baffle in the middle of the tank, as shown in Figures 19b and 20b, the sloshing pattern is different from that with \(N_{c}=1\), but the front half of the tank is also characterised by the turbulent vertical impacting motion, while in the rear half appears some waveform. By increasing the compartment number to four, although still highly turbulent, the water starts to display directional flow in all the compartments, instead of violent disordered turbulent behaviour. This is especially true for the front compartment.