# A Comparative Study on Violent Sloshing with Complex Baffles Using the ISPH Method
## 4 Configurations of Different Complex Baffles  
To evaluate the influence of sloshing dampening by using different configurations of the complex baffle, a series of practical designs are illustrated in this section. For generality, the length scale of the sloshing tank, the internal baffles, and their installation positions have been normalized by the length of the sloshing tank; i.e., \(L=1.2\) m, as used in the previous section of model validation. In total, five different baffle configurations are investigated in the present study and the schematic view of each design scenario is shown in Figure 5a-f. These include a reference sloshing tank without any internal baffle, one vertical baffle, two horizontal baffles, one vertical and two horizontal baffles, and one T-shaped baffle. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Models** & **Grid/Particle No.** & **Grid/Particle Size (m)** & **CPU Time (h)** & \(Er\) (P1)** & \(Er\) (P2) \\ \hline \multirow{3}{*}{STAR-CCM+} & 11,589 & 0.01 & 11.1 & 2.42\% & 3.32\% \\  & 45,376 & 0.004 & 32.2 & 0.92\% & 1.69\% \\  & 88,463 & 0.002 & 72.5 & 0.82\% & 1.52\% \\ \hline \multirow{3}{*}{ISPH} & 9000 & 0.004 & 1.3 & 1.77\% & 1.35\% \\  & 16,000 & 0.003 & 2.8 & 0.97\% & 0.93\% \\ \cline{1-1}  & 49,000 & 0.002 & 7.2 & 0.40\% & 0.36\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Numerical error and CPU analyses of ISPH and STAR-CCM+. To further evaluate the performance of each baffle configuration, either simple or complex, the length and installation height of these baffles are also altered to examine the collective effect on the sloshing pressure. A summary on the relevant key parameters of change is provided in Table 2. Inside the Table, \(\Omega\) is the external excitation frequency and \(\Omega_{0}\) is the natural frequency of the sloshing tank without any baffle, calculated by  
\[\Omega_{0}=\sqrt{(g\pi/L)\text{tanh}(\pi d)/L} \tag{13}\]  
where \(g\) is the gravitational acceleration, \(L\) is the length of the tank, and \(d\) is the depth of water. During the design of the external excitation conditions as shown in Table 2, \(\Omega\) values have been selected in such a way that the maximum impact pressure for each baffle scenario can be captured, and also the normalized frequencies \(\Omega/\Omega_{0}\) are more or less within a consistent range for all the design cases. In ISPH computations, the tank experiences a forced harmonic rolling motion with an amplitude of 10\({}^{\circ}\) and an excitation frequency as listed in Table 2. The tank is rotated at the geometric center, where P1 and P2 are the two locations of pressure monitoring. A particle size of \(dx=0.004\) m and a time step of \(dt=0.00032\) s are used for all the tests. The model is run for a sufficiently long time of 16 s to extract the stable numerical data and the repeatability of the sloshing flow condition is well achieved within the first 2-4 s, depending on the different baffle systems. The impact pressure on the tank wall due to the sloshing liquids is the main focus of the present study for the evaluation of the efficiency of various complex baffles. The computed particle snapshots with pressure contours for the selected two cases in Figure 5d,e are shown in Figure 6, to illustrate the violent sloshing flow and strong fluid-structure interactions with  
Figure 5: Different configurations of the baffles for sloshing tank: (**a**) reference case without baffle; (**b**) one vertical baffle; (**c**) two horizontal baffles; (**d**) one vertical and one horizontal baffle; (**e**) one vertical and two horizontal baffles; (**f**) one T-shaped baffle. the installed baffles for half of the sloshing period \(T\). This qualitatively demonstrates the important role the baffles have played in the sloshing mitigation process, through which strong jet collisions and fluid-baffle actions dampened the flow energy. The smooth and noise-free stable pressure fields indicate the robustness of ISPH pressure solution scheme, which will support the following analyses of the impact pressures.