# The Effect of Porous Media on Wave-Induced Sloshing in a Floating Tank
## 4 Results and Discussion
### Floating Body in Resonant Waves: Controlled vs. Uncontrolled  
The uncontrolled body means that no water tank was installed on the platform, otherwise, it is called a controlled body. For the controlled body, an additional case is considered where the tank was only filled with water and no porous media, which suggests the porosity \(\gamma\) = 1 and the coefficients \(\alpha_{1}\) = 0.1 s\({}^{-1}\) and \(\alpha_{2}\) = 0 m\({}^{-1}\) were used in the EL method [46]. When the large wave was applied, the body motions and the resultant forces along the horizontal direction are shown in Figures 23 and 24, respectively. The uncontrolled case stopped at 17.3 s due to the numerical instability induced by the high velocity of a wave jet on the body. The water tank was prone to keep the floating body oscillating around the original position, hence it could slow down the lateral drift. Although the force cancellation was weak, it still reduced the surge motion. However, the floating body was free to surge in our case, and the effectiveness of the surge mitigation by the porous media in the sloshing fluid was not obvious. Figure 23: The surge responses of the controlled and uncontrolled floating bodies subject to large wave excitation. Figure 24: The horizontal forces act on the controlled and uncontrolled floating bodies for the large-wave case. The body motions and the resultant forces along the vertical direction are shown in Figures 25 and 26, respectively. The mean values of the steady-state displacement were different for the controlled and uncontrolled cases because their total weights were different. The uncontrolled body was lighter, so it had a larger initial acceleration. As their transient response vanished, they oscillated in the same way but had different equilibrium points. This implies that the sloshing fluid did not change the heave motion of the body. Besides, the difference between the vertical sloshing forces from the tanks with and without porous media equaled their difference in water weight. The porous media did not affect the vertical sloshing force. The body motions and the resultant forces about the angular axis are shown in Figures 27 and 28, respectively. For the uncontrolled case, the responses were greatly amplified due to resonance. The maximum angular displacement was 11.3\({}^{\circ}\). In the controlled cases, the maximum angular displacements were significantly reduced to 2.2\({}^{\circ}\) (without porous media) and 1.6\({}^{\circ}\) (with porous media). Moreover, their transient responses decayed very fast and the steady-state responses were suppressed. This can be explained later by the energy exchange in the body-tank system. The force cancellation between the sloshing reaction and wave loading was strong, showing that the tuning condition may have been satisfied. The tank with porous media had better performance in reducing pitch vibration than the other tank, but the overall performance should be validated through other near-resonance tests in the next example. Figure 28: The overturning moments act on the controlled and uncontrolled floating bodies for the large-wave case. Figure 27: The pitch responses of the controlled and uncontrolled floating bodies subject to large wave excitation. The response spectra of the controlled and uncontrolled floating bodies subject to large wave excitation are shown in Figure 29. The major oscillatory frequency does not shift (still 0.58 Hz), while a small local peak shows up at the frequency of 0.53 Hz, which is equal to the natural frequency of the sloshing fluid in the tank. The dynamic characteristic of the entire system was not affected because the water tank was not heavy enough (the mass ratio was 13%). The maximum amplitudes of the angular responses of the floating body were greatly decreased. Compared to the tank without porous media, the porous media could further reduce the peak response of the surge and pitch motions.