# Green Shipping--Multifunctional Marine Scrubbers for Emission Control: Silencing Effect
## 3 Results and Discussion
### Model-Scale Scrubber  
The simple FEM model was extended to simulate the TL of the model-scale scrubber. Considering the model of the scrubber with the tube discontinuity, a perusal of Figure 13 shows a good fit between the FEM-simulated and experimental TL curves in the frequency range up to 1500 Hz, where the discrepancy between \(f_{min}\) is less than 3%, and where between amplitudes, it is less than 5 dB (Tables 7 and 8). At higher frequencies, the discrepancy between the TL amplitudes becomes higher. This inaccuracy is caused by a non-plane wave propagation of the sound at higher frequencies in the model-scale scrubber due to a change of the wave propagation direction caused by the angle between the inlet pipe and scrubber body [35]. In this regard, it should be remembered that the hypothesis of plane wave propagation was adopted both in the experimental measurements and in the numerical model. However, the FEM model shows appreciable accuracy (Tables 7 and 8) [34] in the frequency range 20-1000 Hz, the range in which human hearing is the most sensitive [36] and the range that is taken as a reference by industry [34]. Therefore, the assessed FEM model can be employed to analyse the effects of scrubber modifications (e.g., water presence or geometry modifications) on the TL. For this purpose, a model-scale scrubber without tube discontinuity was first modelled in order to avoid the influence of such discontinuity on the TL. Indeed, the scrubber is usually connected to the exhaust line without tube discontinuity. A perusal of Figure 14 shows that the discontinuity influences the TL amplitudes in the frequency range of interest (20-1000 Hz) and the \(f_{min}\) and \(f_{max}\) at higher frequencies. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(n\)} & \multicolumn{2}{c}{**FEM**} & \multirow{2}{*}{**Delta**} & \multicolumn{2}{c}{**FEM**} & \multirow{2}{*}{**Delta**} & \multicolumn{2}{c}{**FEM**} & \multirow{2}{*}{**Delta**} \\  & \(f_{min}\) & & \(f_{min}\) & & \(f_{max}\) & & \(f_{max}\) \\  & **(Hz)** & & **(\%)** & **(Hz)** & **(\%)** & **(Hz)** & **(\%)** \\ \hline
0 & 0 & 0.0 & 220 & 0.0 & 16.3 & \(-\)0.3 \\
1 & 348 & 0.0 & 510 & +0.4 & 19.3 & \(+\)0.3 \\
2 & 680 & \(-\)0.7 & 860 & \(-\)5.7 & 12.0 & \(-\)0.8 \\
3 & 1040 & \(-\)0.9 & 1220 & \(-\)0.5 & 19.5 & \(-\)0.7 \\
4 & 1370 & \(-\)0.9 & 1510 & \(-\)0.7 & 16.4 & \(+\)0.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison between experimental and FEM with discontinuity data of simple expansion chamber. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(n\)} & \multicolumn{2}{c}{**Experimental**} & \multirow{2}{*}{**FEM**} & \multirow{2}{*}{**Delta**} & \multirow{2}{*}{**Experimental**} & \multirow{2}{*}{**FEM**} & \multirow{2}{*}{**Delta**} \\  & \(f_{min}\) & & \(f_{min}\) & & \(f_{max}\) & & \(f_{max}\) \\  & **(Hz)** & & **(Hz)** & & **(Hz)** & **(Hz)** & **(\%)** \\ \hline
0 & 0 & 0 & 0.0 & 119 & 120 & +0.8 \\
1 & 195 & 190 & \(-\)2.6 & 288 & 290 & +0.7 \\
2 & 351 & 350 & \(-\)0.3 & 448 & 460 & +2.7 \\
3 & 511 & 510 & \(-\)0.2 & 584 & 570 & \(-\)2.4 \\
4 & 668 &Figure 14: Comparison between experimental and FEM-simulated TL of the model-scale scrubber with and without discontinuity and with water. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(n\) & \begin{tabular}{c} **Experimental Amplitudes** \\ **(dB)** \\ \end{tabular} & \
\begin{tabular}{c} **FEM Amplitudes** \\ **(dB)** \\ \end{tabular} &
\begin{tabular}{c} **Delta Amplitudes** \\ **(dB)** \\ \end{tabular} \\ \hline
0 & 9.4 & 6.3 & \(-\)3.1 \\
1 & 14.8 & 12.2 & \(-\)2.6 \\
2 & 23.0 & 21.2 & \(-\)1.8 \\
3 & 67.3 & 62.5 & \(-\)4.8 \\
4 & 18.0 & 16.2 & \(-\)1.8 \\
5 & 9.0 & 7.4 & +1.6 \\
6 & 5.2 & 5.3 & +0.1 \\
7 & 8.6 & 7.2 & \(-\)1.4 \\
8 & 9.4 & 13.4 & +4.0 \\
9 & 13.7 & 23.1 & +9.4 \\
10 & 49.9 & 48.8 & \(-\)1.1 \\
11 & 15.0 & 10.2 & \(-\)4.8 \\
12 & 10.2 & 7.3 & \(-\)2.9 \\
13 & 6.1 & 9.2 & +3.1 \\ \hline \hline \end{tabular}
\end{table}