# Numerical Investigation into Effects of Viscous Flux Vectors on Hydrofoil Cavitation Flow and Its Radiated Flow Noise

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Target Problem Description

## 3. Governing Equations and Numerical Implementations

#### 3.1. Governing Equations

#### 3.2. Turbulence Modeling

#### 3.3. Numerical Implementations

#### 3.4. Viscous Flux Treatements

#### 3.4.1. Viscous Lagging Approach

#### 3.4.2. Full Viscous Approach

#### 3.4.3. Thin-Layer Approximation

#### 3.5. Acoustic Analogy for Cavitation Noise Prediction

## 4. Results and Discussion

#### 4.1. Verification Tests

#### 4.2. Viscous Effects on Flow Field Prediction

#### 4.3. Viscous Effects on Hydro-Acoustic Field Prediction

^{−5}s.) and total three-cycle data are used. The predicted acoustic wave directivity for each case is presented in Figure 15.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Comparison of predicted pressure coefficient distribution with large eddy simulation (LES) data by Roohi et al. [40].

**Figure 3.**Comparison of time-averaged x-directional velocity distribution with experimental results by Huang et al. [41]: (

**a**) $x/C=0.2$; (

**b**) $x/C=0.4$; (

**c**) $x/C=0.6$; (

**d**) $x/C=0.8$; and (

**e**) $x/C=1.0$.

**Figure 4.**Predicted time-variation and power spectral density of non-dimensional hydrodynamic forces: (

**a**) lift force; (

**b**) drag force.

**Figure 5.**Time-variations of predicted cavity volume of three different viscous flux vector treatment methods.

**Figure 10.**Time-averaged vapor volume fraction distribution at five stream-wise locations: (

**a**) viscous lagging; (

**b**) full viscous; and (

**c**) thin-layer cases.

**Figure 11.**Comparison of zoomed time-averaged vapor volume fraction distribution for three different viscous flux treatment methods at five stream-wise locations: (

**a**) $x/C=0.2$; (

**b**) $x/C=0.4$; (

**c**) $x/C=0.6$; (

**d**) $x/C=0.8$; and (

**e**) $x/C=1.0$.

**Figure 15.**Time-averaged x-directional velocity distribution at five stream-wise locations: (

**a**) viscous lagging; (

**b**) full viscous; and (

**c**) thin-layer cases.

**Figure 16.**Comparison of zoomed time-averaged x-directional velocity distribution with experimental results by Huang et al. [40]: (

**a**) x/C = 0.4; and (

**b**) x/C = 0.6.

**Figure 18.**Predicted directivity of radiated hydro-acoustic noise: (

**a**) viscous lagging; (

**b**) fill viscous; and (

**c**) thin-layer cases.

**Figure 19.**Predicted hydro-acoustic pressure due to monopole source: (

**a**) directivity, spectrum at three azimuth angles of (

**b**) 350°; (

**c**) 40°; and (

**d**) 80°.

**Figure 20.**Predicted hydro-acoustic pressure due to dipole source: (

**a**) directivity, spectrum at three azimuth angles of (

**b**) 350°; (

**c**) 40°; and (

**d**) 80°.

Parameters | $\mathbf{R}{\mathbf{e}}_{\mathit{c}}$ | $\mathit{\sigma}$ | ${\mathit{U}}_{\infty}$ (m/s) | $\mathit{C}$ (m) | Angle of Attack (°) |
---|---|---|---|---|---|

Values | $7.0\times {10}^{5}$ | 0.8 | 10 | 0.07 | 8 |

**Table 2.**Comparison of time-averaged non-dimensional cavity thickness with experimental results by Wang et al. [3].

Location | Experiments | Viscous Lagging | Full Viscous | Thin-Layer |
---|---|---|---|---|

$x/C=0.2$ | 0.0195 | 0.0285 | 0.0280 | 0.0286 |

$x/C=0.4$ | 0.0658 | 0.0811 | 0.0738 | 0.0748 |

$x/C=0.6$ | 0.1166 | 0.1529 | 0.1245 | 0.1234 |

$x/C=0.8$ | 0.1834 | 0.2161 | 0.1798 | 0.1737 |

$x/C=1.0$ | 0.2339 | 0.2637 | 0.2324 | 0.2198 |

**Table 3.**Estimated acoustic power levels (dB) for three different viscous flux models according to source types. PWL: predicted acoustic power level.

Viscous Flux Treatment | Viscous Lagging | Full Viscous | Thin-Layer |
---|---|---|---|

PWL (dB) | 168.8 | 177.1 | 177.4 |

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**MDPI and ACS Style**

Kim, S.; Cheong, C.; Park, W.-G.
Numerical Investigation into Effects of Viscous Flux Vectors on Hydrofoil Cavitation Flow and Its Radiated Flow Noise. *Appl. Sci.* **2018**, *8*, 289.
https://doi.org/10.3390/app8020289

**AMA Style**

Kim S, Cheong C, Park W-G.
Numerical Investigation into Effects of Viscous Flux Vectors on Hydrofoil Cavitation Flow and Its Radiated Flow Noise. *Applied Sciences*. 2018; 8(2):289.
https://doi.org/10.3390/app8020289

**Chicago/Turabian Style**

Kim, Sanghyeon, Cheolung Cheong, and Warn-Gyu Park.
2018. "Numerical Investigation into Effects of Viscous Flux Vectors on Hydrofoil Cavitation Flow and Its Radiated Flow Noise" *Applied Sciences* 8, no. 2: 289.
https://doi.org/10.3390/app8020289