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A Semi-Empirical Prediction Method for Broadband Hull-Pressure Fluctuations and Underwater Radiated Noise by Propeller Tip Vortex Cavitation ^{†}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Prediction of the Maximum Source Level

#### 2.1. Vortex Models

#### 2.2. Prediction of Cavity Size

#### 2.3. Prediction of Source Levels

_{p}-values according to Equation (8), where $\Delta f$ corresponds to the resolution bandwidth of the amplitude spectrum and ${f}_{bpf}$ to the blade passage frequency. The levels were converted to decibel values according to Equation (9). The frequencies were made non-dimensional with ${f}_{bpf}$:

## 3. Shape of the Spectrum

#### 3.1. Source Level

#### 3.2. Hull-Pressure and URN Spectra

## 4. Comparison of Predicted and Measured Hull Pressures and URN

## 5. Discussion

## 6. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Flow chart of the Empirical Tip Vortex cavity (ETV) model for broadband hull pressure fluctuations and underwater radiated noise.

**Figure 2.**Comparison between various vortex models. The reference values are taken from the values for the inviscid vortex at $r={r}_{v}$.

**Figure 3.**Measured and fitted azimuthal velocity distribution and cavity size variation for a wing of elliptical planform at 7 deg angle of attack. Experiments by Pennings et al. [29].

**Figure 4.**Measured and fitted cavity size variation for a propeller at two advance ratios. Experiments by Kuiper [30], ${\mathrm{Re}}_{n1}=1.38\times {10}^{6},\hspace{0.17em}\hspace{0.17em}{\mathrm{Re}}_{n2}=2.76\times {10}^{6}$.

**Figure 5.**Example of a non-dimensional hull pressure power density spectrum of a two-bladed research propeller. The solid line is the 1/6 octave band smoothened spectrum.

**Figure 7.**Comparison between measured and predicted levels and frequency of the centre of the hump for the cases used in the development of the method.

**Figure 8.**Comparison between measured and predicted maximum level of the hump for a two-bladed research propeller tested at various advance ratios and cavitation numbers. The cavitation pattern corresponding to the encircled symbol is shown on the right.

**Figure 11.**Example of the measured and predicted non-dimensional hull pressure spectrum for a two-bladed research propeller.

**Figure 12.**Example of the measured and predicted non-dimensional hull pressure spectrum for a ship propeller of the database tested at model scale.

**Figure 13.**Example of the measured and predicted non-dimensional hull pressure spectrum for a ship propeller of the database tested at full scale.

**Figure 14.**Measured and predicted non-dimensional hull pressure spectrum for the combi-freighter at a ship speed of 10 knots. P1 corresponds to the centre transducer and P2 is located closer to the cavity collapse. Experimental data measured by DAMEN and MARIN.

**Figure 15.**Measured and predicted radiated noise spectrum in one-third octave band levels for the combi-freighter at a ship speed of 10 knots. Experimental data by DNV-GL.

**Figure 16.**Measured and predicted radiated noise spectrum in one-third octave band levels for the cruise vessel at a ship speed of 18 knots. Experimental data by Kipple [45].

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**MDPI and ACS Style**

Bosschers, J. A Semi-Empirical Prediction Method for Broadband Hull-Pressure Fluctuations and Underwater Radiated Noise by Propeller Tip Vortex Cavitation ^{†}. *J. Mar. Sci. Eng.* **2018**, *6*, 49.
https://doi.org/10.3390/jmse6020049

**AMA Style**

Bosschers J. A Semi-Empirical Prediction Method for Broadband Hull-Pressure Fluctuations and Underwater Radiated Noise by Propeller Tip Vortex Cavitation ^{†}. *Journal of Marine Science and Engineering*. 2018; 6(2):49.
https://doi.org/10.3390/jmse6020049

**Chicago/Turabian Style**

Bosschers, Johan. 2018. "A Semi-Empirical Prediction Method for Broadband Hull-Pressure Fluctuations and Underwater Radiated Noise by Propeller Tip Vortex Cavitation ^{†}" *Journal of Marine Science and Engineering* 6, no. 2: 49.
https://doi.org/10.3390/jmse6020049