# Temperature-Activated Change of Permeable Material Properties for Low-Noise Trailing Edge Applications

^{*}

## Abstract

**:**

^{5}and 3.14 × 10

^{5}and no incidence. A microphone array is used to determine far-field sound pressure level changes upon trailing edge heating. It is found that broadband noise emission can be actively controlled by varying the temperature of the porous trailing edge inserts. Specifically, the electrically heated inserts yield a noise level variation of up to 2.5 dB with the heated one being noisier compared to a baseline, unheated material with similar micro-structure. Resistivity measurements of permeable samples with varying temperature show that flow resistivity increases with the fluid temperature which is in agreement with the reported trailing edge noise increase.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Flow Resistivity

#### 2.2. Aeroacoustic Measurements

^{2}. TBL-TE noise is evaluated for a NACA0018 airfoil with chord length $c=20\mathrm{c}\mathrm{m}$. An interchangeable trailing edge with a length of $4\mathrm{c}\mathrm{m}$ allows for the use of different solid and porous inserts. The airfoil is placed between two wooden side plates with a height of $1.2\mathrm{m}$ and a distance between the contraction outlet and the leading edge of $0.5\mathrm{m}$. All experiments are carried out for a geometrical angle of attack of $0{}^{\circ}$ adjusted based on a digital inclination measuring device.

## 3. Results and Discussion

#### 3.1. Heated Flow through Porous Materials

#### 3.2. Far-Field Noise

## 4. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CSM | Cross Spectral Matrix |

EDM | Electrical Discharge Machining |

FS | Full Scale |

IR | Infrared |

P800 | Porous metal foam with nominal pore size of ${d}_{p}=800\mathsf{\mu}\mathrm{m}$ |

SPI | Source Power Integration |

SPL | Sound Pressure Level |

TBL-TE noise | Turbulent Boundary Layer Trailing Edge noise |

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**Figure 1.**Experimental test rig used for specifying porous material properties at varying temperatures (

**a**). Pressurized air is forced through a cylindrical material sample (

**b**) and the static pressure drop is recorded. The porous material is metallic foam with a nominal pore diameter of ${d}_{p}=800\mathsf{\mu}\mathrm{m}$ (

**c**).

**Figure 2.**Aeroacoustic measurement setup in the vertical, anechoic wind tunnel of TU Delft (

**a**). The airfoil can be equipped with exchangeable trailing edge inserts (

**c**) and heating of the porous metal foam is achieved by means of electrical heating wires (

**b**).

**Figure 5.**Change in normalized pressure drop along porous samples with $t=6\mathrm{c}\mathrm{m}$ due to changing fluid temperatures. Quadratic curve fitting is indicated by the dashed lines and a magnification of the linear flow region is provided.

**Figure 6.**Change of material constants $C/{C}_{0}$, $K/{K}_{0}$ and $R/{R}_{0}$ with temperature for $t=6\mathrm{c}\mathrm{m}$. Black dashed line indicates the constant coefficient ratio as expected for the geometrical constants C and K. The theoretical relation for R according to Equation (2) with $n=0.6$ is indicated in red. Error bars represent regions which contain 68% of simulated values.

**Figure 7.**Comparison of far-field noise spectra of different heated and unheated trailing edge cases for $U=15\mathrm{m}{\mathrm{s}}^{-1}$ and $U=25\mathrm{m}{\mathrm{s}}^{-1}$. SPLs as observed at a distance of $1\mathrm{m}$ from the airfoil are depicted (

**a**) as well as a comparison between selected measurement cases (

**b**).

**Table 1.**Characterizing properties of the porous metal foam P800 for a sample thickness of $6\mathrm{c}\mathrm{m}$ as characterized by Rubio Carpio et al. [16].

Nominal Pore Size ${\mathit{d}}_{\mathit{p},0}$ | Porosity $\mathit{\phi}$ | Resistivity R | Permeability K | form Coefficient C |
---|---|---|---|---|

$800\mathsf{\mu}\mathrm{m}$ | $91.65\%$ | $6728\mathrm{N}\mathrm{s}{\mathrm{m}}^{-4}$ | $27.1\times {10}^{-10}{\mathrm{m}}^{2}$ | $2612.54{\mathrm{m}}^{-1}$ |

$\mathit{T}=22{}^{\circ}\mathbf{C}$ | $\mathit{T}=50{}^{\circ}\mathbf{C}$ | $\mathit{T}=90{}^{\circ}\mathbf{C}$ | |
---|---|---|---|

$R={C}_{a}$ [$\mathrm{N}\mathrm{s}/{\mathrm{m}}^{4}$] | 6274 | 6511 | 7003 |

$K=\mu /R$ [${\mathrm{m}}^{2}$] | $2.92\times {10}^{-9}$ | $3.00\times {10}^{-9}$ | $3.05\times {10}^{-9}$ |

$C={C}_{b}/\rho $ [${\mathrm{m}}^{-1}$] | 2242 | 2202 | 2124 |

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**MDPI and ACS Style**

Mayer, J.; Rubio Carpio, A.; Ragni, D. Temperature-Activated Change of Permeable Material Properties for Low-Noise Trailing Edge Applications. *Appl. Sci.* **2019**, *9*, 3119.
https://doi.org/10.3390/app9153119

**AMA Style**

Mayer J, Rubio Carpio A, Ragni D. Temperature-Activated Change of Permeable Material Properties for Low-Noise Trailing Edge Applications. *Applied Sciences*. 2019; 9(15):3119.
https://doi.org/10.3390/app9153119

**Chicago/Turabian Style**

Mayer, Jonathan, Alejandro Rubio Carpio, and Daniele Ragni. 2019. "Temperature-Activated Change of Permeable Material Properties for Low-Noise Trailing Edge Applications" *Applied Sciences* 9, no. 15: 3119.
https://doi.org/10.3390/app9153119