# Visualization of Underwater Radiated Noise in the Near- and Far-Field of a Propeller-Hull Configuration Using CFD Simulation Results

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## Abstract

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## 1. Introduction

## 2. Simulation Methods

- RANS;
- RANS with activated cavitation;
- LES with activated cavitation.

- Average residuals of the velocity equations;
- Time mean integral forces and moments data on the propeller and the hull boundaries;
- Angular phase locked time evolution of the Q-criterion $Q=50\cdot {10}^{3}{\mathrm{s}}^{-2}$ isosurface of trailing vortices and the volume phase fraction $\alpha =0.5$ isosurface;
- Periodic behavior over time of two pressure probes located one cell upstream of the outlet downstream of the propeller and at the lowest z-coordinate of the mesh, where positive z is pointing in opposite direction to the gravity vector.
- With the last criterion, it is ensured that the propeller slipstream and all pressure disturbances have propagated through the complete simulation domain and that no pressure reflections occur at the inlet or outlet.

## 3. Visual Interpretation of Acoustic Fields

#### 3.1. Pressure

#### 3.2. Turbulence and Vortices

#### 3.3. Proudman Acoustic Sources

#### 3.4. Lighthill Stress Tensor

#### 3.5. Frequency Domain Analysis

#### 3.6. POD

## 4. Noise of a Propeller-Hull Combination

#### 4.1. Test Case

#### 4.2. Interaction with Structure

#### 4.2.1. Pressure Pulses

#### 4.2.2. Phase

#### 4.2.3. POD

#### 4.3. Emission into the Fluid Domain

#### 4.3.1. Isosurfaces of Acoustic Sources

#### 4.3.2. Lighthill Stresses

#### 4.3.3. Directivity

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**First 4 harmonic propeller blade frequencies incompressible hull pressure above propeller, comparison of domain extent, RANS without cavitation.

**Figure 4.**First 4 harmonic propeller blade frequencies incompressible hull pressure above propeller, comparison of domain extent, RANS with cavitation.

**Figure 5.**First 4 harmonic propeller blade frequencies incompressible hull pressure above propeller, comparison of domain extent, LES with cavitation.

**Figure 7.**Phase information on hull at the first 4 harmonic propeller blade harmonic frequencies, comparison of domain extent, and RANS.

**Figure 8.**Phase information on hull at the first 4 harmonic propeller blade harmonic frequencies, comparison of domain extent, RANS with cavitation.

**Figure 9.**Phase information on hull at the first 4 harmonic propeller blade harmonic frequencies, comparison of domain extent, LES with cavitation.

**Figure 10.**First 4 POD modes of pressure time data set on hull above propeller, comparison of domain extent, RANS.

**Figure 11.**First 4 POD modes of pressure time data set on hull above propeller, comparison of domain extent, RANS with cavitation.

**Figure 12.**First 4 POD modes of pressure time data set on hull above propeller, comparison of domain extent, LES with cavitation.

**Figure 16.**Near Wall Q-criterion $Q=5\cdot {10}^{4}{\text{}\mathrm{s}}^{-2}$ isosurface on shaft brackets, propeller, and rudder.

**Figure 17.**Comparison of isosurfaces of turbulent kinetic energy $k=1.5{\text{}\mathrm{m}}^{2}/{\mathrm{s}}^{2}$ (purple), second order statistical moments of pressure time history ${\overline{{p}^{\prime}}}^{2}=1\cdot {10}^{6}{\text{}\mathrm{Pa}}^{2}\text{}$ (orange), and Q-criterion $Q=5\cdot {10}^{4}{\text{}\mathrm{s}}^{-2}$ (green) around rotating mesh region and sliding mesh interface.

**Figure 18.**Instantaneous pressure pulses ${p}^{\prime}$ in $\left[\mathrm{Pa}\right]$ at arbitrary converged timestep on the midplane.

**Figure 19.**Instantaneous pressure $p$ in $\left[\mathrm{Pa}\right]$ at arbitrary converged timestep on midplane through the propeller and corresponding Lighthill stress tensor magnitude $\left|{T}_{ij}\right|$ in $[\mathrm{Kg}/{\mathrm{ms}}^{2}$ ].

**Figure 22.**Perturbation stress tensor ${P}_{ij}^{\prime}$ magnitude (

**a**) and magnitude of off-diagonal components (

**b**,

**c**) on midplane in $[\mathrm{Kg}/{\mathrm{ms}}^{2}$ ].

**Figure 24.**Lighthill stress tensor ${T}_{ij}$ magnitude of off-diagonal components in $[\mathrm{Kg}/{\mathrm{ms}}^{2}$ ].

**Figure 27.**Directivity of harmonic frequencies on the passive rectangular box around propeller-hull combination.

**Figure 28.**Complex phase angle information on the passive sphere from Figure 26.

**Figure 29.**Complex phase angle information at ${f}_{Z=1}$ on the passive rectangular box shown in Figure 27.

Stage | $\mathbf{Time}\text{}\mathbf{Until}\text{}\mathbf{Convergence}\text{}\left[\mathbf{h}\right]$ | $\mathbf{Time}\text{}\mathbf{for}\text{}\mathbf{FFT}\text{}\mathbf{Data}\text{}\mathbf{Acquisition}\text{}\left[\mathbf{h}\right]$ | $\mathbf{Physical}\text{}\mathbf{Simulation}\text{}\mathbf{Time}\text{}[{\mathbf{f}}_{1}^{-1}]$ |
---|---|---|---|

RANS | $1.7\cdot {10}^{4}$ | $2.4\cdot {10}^{3}$ | 320 |

RANS + Cav | $4.8\cdot {10}^{3}$ | $7.2\cdot {10}^{3}$ | 29 |

LES + Cav | $7.2\cdot {10}^{3}$ | $3.4\cdot {10}^{4}$ | 28 |

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**MDPI and ACS Style**

Kimmerl, J.; Abdel-Maksoud, M.
Visualization of Underwater Radiated Noise in the Near- and Far-Field of a Propeller-Hull Configuration Using CFD Simulation Results. *J. Mar. Sci. Eng.* **2023**, *11*, 834.
https://doi.org/10.3390/jmse11040834

**AMA Style**

Kimmerl J, Abdel-Maksoud M.
Visualization of Underwater Radiated Noise in the Near- and Far-Field of a Propeller-Hull Configuration Using CFD Simulation Results. *Journal of Marine Science and Engineering*. 2023; 11(4):834.
https://doi.org/10.3390/jmse11040834

**Chicago/Turabian Style**

Kimmerl, Julian, and Moustafa Abdel-Maksoud.
2023. "Visualization of Underwater Radiated Noise in the Near- and Far-Field of a Propeller-Hull Configuration Using CFD Simulation Results" *Journal of Marine Science and Engineering* 11, no. 4: 834.
https://doi.org/10.3390/jmse11040834