# Pressure Fluctuation and Flow-Induced Noise of the Fin and Rudder in a Water Tunnel
## 6 Conclusions  
In this study, LES was used to predict pressure fluctuation on the surface of a fin and rudder in a water tunnel experiment, and the noise generated by the turbulent flow was analyzed. The height of the rudder and fin model was 1.225 m, and the flow velocity discussed ranged from 3 m/s to 8 m/s. The following can be concluded:  
1. The pressure fluctuation at the monitoring points tested in the experiments decreased with an increase in frequency. The average rate of decrease in the pressure fluctuation was around 9.7 dB/Oct for frequencies of up to 5.0 kHz.
2. As the flow velocity increases, the magnitude of pressure fluctuations also increases, indicating that the variation in flow velocity significantly affects the flow conditions around the fin and rudder region. The pressure fluctuations at the rudder are more pronounced compared to the pressure fluctuations at the fin.
3. Flow-induced noise is mainly generated at the two sides of the fin and rudder and the wake region. As the flow velocity increases, the overall sound pressure level of flow-induced noise also increases. The relationship between the sound power radiated by the fin and rudder and the flow velocity corresponds to a power of about seven.
4. The flow-induced noise basically maintains a symmetrical radiative directivity on both sides of the flap and rudder, and the noise radiated on both sides is greater than that radiated in the flow direction. On the symmetrical radiant surface, i.e., the XY plane in the present work, the noise presents high values around 120\({}^{\circ}\) and 240\({}^{\circ}\).  
By delving into the intricacies of pressure fluctuations and flow-induced noise, engineers are empowered to refine the contours and arrangements of the control surfaces of fins and rudders with the purpose of minimizing acoustic emissions and enhancing hydrodynamic performance. This deepened understanding also serves to guide the design of control surfaces capable of withstanding diverse hydrodynamic environments, constituting a vital step in augmenting maritime safety and reliability. The comparative use of experimental data and simulation results can enhance the accuracy of prediction results in the design stage. Furthermore, by optimizing the form and placement of fins and rudders in accordance with pressure variation data, engineers can improve propulsion systems and steering mechanisms for heightened efficiency, leading to more agile navigation and thriftier fuel consumption. Lastly, insights from the study have led to the development of noise reduction designs, thereby decreasing the noise level of underwater vehicles.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Velocity of Flow** & **Overall RNL (20–1000 Hz)/dB** & **SWL/dB** \\ \hline
3 m/s & 76.34 & 87.33 \\
5 m/s & 100.08 & 111.07 \\
8 m/s & 107.56 & 118.55 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Comparison of overall RNL values at different flow velocities.  
**Author Contributions:** Conceptualization, all authors; methodology, D.Q. and Y.L.; software, D.Q. and Y.C.; validation, D.Q. and R.L.; formal analysis, D.Q. and Y.Z.; investigation, Y.L.; resources, D.Q. and Y.L.; data curation, D.Q. and Y.C.; writing--original draft preparation, D.Q. and Y.C.; writing--review and editing, Y.L. and Y.Z.; visualization, D.Q. and R.L.; supervision, Y.L.; project administration, Y.L. and Y.Z.; funding acquisition, Y.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (No. 52301393) and the Research and Development Fund of Naval University of Engineering (No. 42531T01D).  
Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
The authors declare no conflicts of interest.