# Sound Radiation of Aerodynamically Excited Flat Plates into Cavities

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## Abstract

**:**

## 1. Introduction

## 2. Theory

**Power Law**[6,9]

**Reichardt’s Formula**[14]

## 3. Materials and Methods

#### 3.1. Experimental Setup

#### 3.1.1. Flow Field

#### 3.1.2. Sound Field

#### 3.2. Measurement Technology and Methods

- Cavity volume: minimum and maximum
- Microphone arrangement: left, top and rear
- Flow velocity: $45\text{}\mathrm{m}{\mathrm{s}}^{-1}$
- Plate thickness: $1\text{}\mathrm{m}\mathrm{m}$, $3\text{}\mathrm{m}\mathrm{m}$ and $5\text{}\mathrm{m}\mathrm{m}$

## 4. Experimental Results

#### 4.1. Flow Characterization

#### 4.1.1. Flow Parameters

#### 4.1.2. Boundary Layer

#### 4.2. Flow-Induced Sound Radiation into the Cavity

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

APSD | Auto Power Spectral Density |

CAD | Computer Aided Design |

CTA | Constant Temperature Anemometry |

DTC | Digital Temperature Compensation |

LSV | Laser Scanning Vibrometry |

SPL | Sound Pressure Level |

## References

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**Figure 6.**Velocity profile at $45\text{}\mathrm{m}\text{}{\mathrm{s}}^{-1}$ with distances x = 100, 350 and $520\text{}\mathrm{m}\mathrm{m}$ from the nozzle outlet.

**Figure 7.**Turbulence intensity at $45\text{}\mathrm{m}\text{}{\mathrm{s}}^{-1}$ with a distance x = 100, 350 and $520\text{}\mathrm{m}\mathrm{m}$ from the nozzle outlet.

**Figure 8.**Dimensionless velocity profiles at $45\text{}\mathrm{m}\text{}{\mathrm{s}}^{-1}$ with a distance of x = $350\text{}\mathrm{m}\mathrm{m}$ from the nozzle outlet. (

**a**) Turbulent presumed boundary layer in case of shear stress 1; (

**b**) Laminar presumed boundary layer.

**Figure 9.**Dimensionless velocity profiles of the turbulent presumed boundary layer at $45\text{}\mathrm{m}\text{}{\mathrm{s}}^{-1}$ in case of shear stress 1 with a distance of x = $350\text{}\mathrm{m}\mathrm{m}$ from the nozzle outlet.

**Figure 11.**Sound Pressure Level at variation of the microphone position (plate thickness $t=1\text{}\mathrm{m}\mathrm{m}$). (

**a**) Different measuring surfaces; (

**b**) On the cover panel in z-direction; (

**c**) On the rear panel in x-direction (minimum volume).

**Figure 15.**Plate vibration forms (plate thickness $t=1\text{}\mathrm{m}\mathrm{m}$). (

**a**) Plate vibration at $f=11.875\text{}\mathrm{Hz}$; (

**b**) Plate vibration at $f=45\text{}\mathrm{Hz}$; (

**c**) Plate vibration at $f=164.375\text{}\mathrm{Hz}$; (

**d**) First shape mode at $f=353.125\text{}\mathrm{Hz}$; (

**e**) Plate vibration at $f=396.875\text{}\mathrm{Hz}$; (

**f**) Second shape mode at $f=736.25\text{}\mathrm{Hz}$; (

**g**) Third shape mode at $f=1111.875\text{}\mathrm{Hz}$; (

**h**) Forth shape mode at $f=1356.875\text{}\mathrm{Hz}$; (

**i**) Fifth shape mode at $f=1718.125\text{}\mathrm{Hz}$.

$\mathit{x}-\mathbf{pos}.$ | ${\mathit{x}}_{\mathbf{new}}$ | ${\mathit{u}}_{\mathbf{\infty}}$ | ${\mathit{u}}_{{\mathit{\tau}}_{1}}$ | ${\mathit{\delta}}_{100}$ | ${\mathit{\delta}}_{1}$ | ${\mathit{\delta}}_{2}$ | ${\mathit{H}}_{12}$ | ${\mathit{R}\mathit{e}}_{\mathit{x}}=$ | ${\mathit{R}\mathit{e}}_{{\mathit{\tau}}_{1}}=$ | ${\mathit{R}\mathit{e}}_{{\mathit{\delta}}_{2}}=$ |
---|---|---|---|---|---|---|---|---|---|---|

$\mathbf{mm}$ | $\mathbf{mm}$ | $\mathbf{m}\text{}{\mathbf{s}}^{-\mathbf{1}}$ | $\mathbf{m}\text{}{\mathbf{s}}^{-\mathbf{1}}$ | $\mathbf{mm}$ | - | - | - | ${\mathit{u}}_{\infty}{\mathit{x}}_{\mathbf{new}}/\mathit{\nu}$ | ${\mathit{u}}_{\mathit{\tau}}{\mathit{\delta}}_{\mathbf{100}}/\mathit{\nu}$ | ${\mathit{u}}_{\infty}{\mathit{\delta}}_{\mathbf{2}}/\mathit{\nu}$ |

350.0 | 702.2 | 45.00 | 1.80 | 14.44 | 1.80 | 1.38 | 1.30 | 1.91 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{6}$ | 1571 | 3.76 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{6}$ |

392.5 | 721.7 | 45.01 | 1.79 | 14.77 | 1.89 | 1.45 | 1.31 | 1.96 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{6}$ | 1598 | 3.93 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{6}$ |

435.0 | 807.7 | 45.01 | 1.78 | 16.18 | 2.07 | 1.58 | 1.31 | 2.18 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{6}$ | 1722 | 4.26 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{6}$ |

477.5 | 859.4 | 45.01 | 1.77 | 17.01 | 2.22 | 1.70 | 1.31 | 2.31 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{6}$ | 1796 | 4.58 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{6}$ |

520.0 | 977.8 | 45.01 | 1.74 | 18.87 | 2.41 | 1.83 | 1.31 | 2.63 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{6}$ | 1963 | 4.92 $\times \phantom{\rule{0.166667em}{0ex}}{10}^{6}$ |

**Table 2.**Comparison of the boundary layer parameters to analytical approaches and to the curve fitting beyond the approach of Golliard.

$\mathit{x}-\mathbf{pos}.$ | ${\mathit{u}}_{0}$ | ${\mathit{u}}_{{\mathit{\tau}}_{1}}$ | ${\mathit{u}}_{{\mathit{\tau}}_{2}}$ | ${\mathit{u}}_{{\mathit{\tau}}_{\mathbf{Go}}}$ | ${\mathit{u}}_{{\mathit{\tau}}_{{\mathbf{Go}}_{2}}}$ | $\frac{{\mathit{u}}_{{\mathit{\tau}}_{1}}}{{\mathit{u}}_{\infty}}$ | $\frac{{\mathit{u}}_{{\mathit{\tau}}_{2}}}{{\mathit{u}}_{\infty}}$ | $\frac{{\mathit{u}}_{{\mathit{\tau}}_{\mathbf{Go}}}}{{\mathit{u}}_{0}}$ | $\frac{{\mathit{u}}_{{\mathit{\tau}}_{{\mathbf{Go}}_{2}}}}{{\mathit{u}}_{0}}$ |
---|---|---|---|---|---|---|---|---|---|

$\mathbf{mm}$ | $\mathbf{m}\text{}{\mathbf{s}}^{-\mathbf{1}}$ | $\mathbf{m}\text{}{\mathbf{s}}^{-\mathbf{1}}$ | $\mathbf{m}\text{}{\mathbf{s}}^{-\mathbf{1}}$ | $\mathbf{m}\text{}{\mathbf{s}}^{-\mathbf{1}}$ | $\mathbf{m}\text{}{\mathbf{s}}^{-\mathbf{1}}$ | - | - | - | - |

350.0 | 44.11 | 1.799 | 1.823 | 1.758 | 1.792 | 0.040 | 0.041 | 0.040 | 0.041 |

392.5 | 43.87 | 1.795 | 1.819 | 1.733 | 1.763 | 0.040 | 0.040 | 0.039 | 0.040 |

435.0 | 44.44 | 1.776 | 1.799 | 1.730 | 1.767 | 0.039 | 0.040 | 0.039 | 0.040 |

477.5 | 43.99 | 1.765 | 1.789 | 1.704 | 1.739 | 0.039 | 0.040 | 0.039 | 0.040 |

520.0 | 43.78 | 1.743 | 1.766 | 1.664 | 1.707 | 0.039 | 0.039 | 0.038 | 0.039 |

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**MDPI and ACS Style**

Osterziel, J.; Zenger, F.J.; Becker, S.
Sound Radiation of Aerodynamically Excited Flat Plates into Cavities. *Appl. Sci.* **2017**, *7*, 1062.
https://doi.org/10.3390/app7101062

**AMA Style**

Osterziel J, Zenger FJ, Becker S.
Sound Radiation of Aerodynamically Excited Flat Plates into Cavities. *Applied Sciences*. 2017; 7(10):1062.
https://doi.org/10.3390/app7101062

**Chicago/Turabian Style**

Osterziel, Johannes, Florian J. Zenger, and Stefan Becker.
2017. "Sound Radiation of Aerodynamically Excited Flat Plates into Cavities" *Applied Sciences* 7, no. 10: 1062.
https://doi.org/10.3390/app7101062