# The Effect of Porous Media on Wave-Induced Sloshing in a Floating Tank
## 4 Results and Discussion
### Sloshing in a Tank Filled with Porous Media: EL Method vs. Mechanical Model  
In this example, the configuration of a rectangular body in the wave channel is the same as described in Section 3. The piston-type wavemaker was set on the left side of the channel to generate harmonic waves that propagated along the x direction to the right side. The wave frequency was 0.58 Hz, which was resonant with the floating body. Two cases were tested. The large wave had its wave height = 0.05 m, so the demand stroke of the wavemaker was 2.64 cm, while the small wave had its wave height = 0.03 m, so the demand stroke of the wavemaker was 1.58 cm [45]. The water tank was installed in a way in which the bottom was aligned with the centerline of the floating body. The tank length was 0.64 m and the water depth was 0.047 m, hence the fundamental sloshing frequency was 0.53 Hz. The masses of the tank and porous media were neglected. The porosity of the porous media = 0.96. Assume the first modal damping ratio was 18.4%, which results in \(\alpha_{1}\) = 1.28 s\({}^{-1}\) and \(\alpha_{2}\) = 5.0 m\({}^{-1}\) being used in the EL method [26]. A total of 80 two-node linear elements were distributed on the boundary of the sloshing fluid. When the mechanical model was applied, both the single-degree-of-freedom (SDOF) (namely, only the fundamental sloshing mode was considered) and five-degree-of-freedom (5-DOF) (namely, the first five sloshing modes were considered) systems were tested. The numerical configurations for the EL method and mechanical model are shown in Figure 7.  
Figure 6: The response spectra of the floating body under free vibration at an initial 5\({}^{\circ}\) pitch. The surge motion responses of the floating body undergoing large wave excitation are shown in Figure 8. The body drifted along the x direction due to the continuous incoming waves. The numerical displacements were slightly different but the accelerations and velocities were very close. Since the dynamic responses depended on the external forces, their correlation will be explained via the horizontal forces as shown in Figure 9. The sloshing force cancels out the wave load due to phase cancellation. The EL method had a larger sloshing reaction, hence a smaller total force and a smaller acceleration were obtained. It is noticeable that in past experiments [25], the mechanical model overestimated the sloshing force. However, in our case, the external excitations to the water tank were different as the coupling effect was involved. Therefore, one may not always expect an over-predicted value from the mechanical model. Figure 8: The surge motion responses of the floating body, configured with a water tank installed with porous media, undergoing large wave excitation. Figure 7: The numerical configurations for (**a**) EL method; (**b**) mechanical model, in the FSI problem (not to scale). The heavy motion responses of the floating body and the vertical resultant forces to the body are shown in Figures 10 and 11, respectively. The mean value of the steady-state displacement was \(-0.0043\) m, which was the same as the static displacement. The responses by both methods were identical except for the sloshing force. The mechanical model assumes the vertical sloshing force as a dead load, while the EL method takes the dynamic force due to the momentum change and convective acceleration into account. However, this effect was not significant in the vertical direction. It only caused a 3% (10 N) deviation from the dead load. Therefore, the heave response remained the same. Figure 10: The heave motion responses of the floating body, configured with a water tank installed with porous media, undergoing large wave excitation. Figure 9: The horizontal forces acting on the floating body for the large-wave case. The pitch motion responses of the floating body and the overturning moments to the body are shown in Figures 12 and 13, respectively. The sloshing overturning moment by the EL method was nonlinear, while that by the mechanical model was linear.