# Simulating Slosh Induced Damping, with Application to Aircraft Wing-like Structures
## 4 Results and Discussion
### Impact of Compartment Numbers
If we take \(t/T=5.5\) as an example (Figure 21c), the direction of motion for the water is to move to the rear of the compartment and then rush along the rear baffle to impact the ceiling of the tank. It should be noted that these directional flows for the sloshing tank with \(N_{c}=4\) do not happen at every time instant. For example, at \(t/T=5.0\), disordered turbulent motions are observed in the very front compartment, as shown in Figure 19c. For the sloshing tank with \(N_{c}=8\) and \(D_{i}=0.5\), a clear sloshing pattern, which is similar to that of \(N_{c}=8\) and \(D_{i}=0.25\), can be observed in Figures 19d and 20d. Figure 19: Snapshots for the sloshing tank with \(D_{i}=0.5\) 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 22 shows the normalised force-velocity diagram of the tank for the last five cycles with \(D_{i}=0.5\) and four different compartment numbers. Similar to that of \(D_{i}=0.25\), with the strong impact on the ceiling of the tank by the sloshing waves during the second half of the down stroke and the interaction between the splashing water and the floor of the tank during the second half of the upstroke, the fluid force for \(N_{c}=8\) and \(D_{i}=0.5\)  
Figure 12:0 Snapshots for the sloshing tank with \(D_{i}=0.5\) 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. is smaller with other cases in the third and first quadrants. This brings more damping to the system. For \(N_{c}=4\), it can be observed that the vertical fluid force is marginally smaller than that of the \(N_{c}=1\) in the second and third quadrant, with the existence of the directional flow as shown in Figures 21c and 20c. Figure 12:1 Snapshots for the sloshing tank with \(D_{i}=0.5\) 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. We further plotted the instantaneous non-dimensional tip vertical displacement of the system over ten cycles for \(D_{i}=1.0\) in Figure 12:2 There is no significant difference that can be observed in the decay process of the beam-tank system for different compartment numbers. As observed in Figures 8 and 11, the sloshing pattern at \(D_{i}=1.0\) and \(N_{c}=1\) are dominated by the violent vertical motion from the third cycle onwards. As shown in Figure 24a-d, by placing baffles inside the water tank, the sloshing motion is also dominated by the violent vertical motion. Figure 12:3 Time history of non-dimensional tip vertical displacement of the system normalised by the initial excitation amplitude over ten cycles for \(D_{i}=1.0\). Figure 12:4 Normalised force–velocity diagram for the last five oscillation cycles with \(D_{i}=0.5\). Figure 25 shows the normalised force-velocity diagram of the tank for the last five oscillation cycles with \(D_{i}=1.0\) and four different compartment numbers. The force-velocity loops for different compartment numbers are very close to each other, with no significant difference that can be observed at \(D_{i}=1.0\) compared with that at \(D_{i}=0.5\) and  
Figure 12:5 Snapshots for the sloshing tank with \(D_{i}=1.0\) 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. \(D_{i}=0.25\), which indicates that the damping provided by these sloshing tanks are similar. This is consistent with the results shown in Figure 12:6