# Self Noise Reduction and Aerodynamics of Airfoils with Porous Trailing Edges

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Airfoils

^{2}and Damtec SBM K 20, r = 12,900 Pa·s/m

^{2}) as well as an airfoil made of a metal foam with a high airflow resistivity (Siperm R200, r = 150,000 Pa·s/m

^{2}). An overview of all airfoils of the present study is given in Table 1, while Figure 1 shows samples of the porous materials.

^{2}) has an unexpectedly low airflow resistance, which might be due to small slits between adjacent slices of the material. As expected, it seems that the airflow resistance of the airfoil made of Siperm R200 might be higher than expected based on the airflow resistivity r of the material. Still, in the remainder of this paper the airflow resistivity r will be used to characterize the porous airfoils.

#### 2.2. Wind Tunnel

#### 2.3. Microphone Array and Data Processing

#### 2.4. Aerodynamic Measurements

## 3. Results and Discussion

#### 3.1. Aerodynamic Results

^{2}(second to Porex with r = 315,500 Pa·s/m

^{2}), it achieves the highest lift and the lowest drag of the porous airfoils. This can be assumed to be due to the change of the surface as a result of the water cutting, as described in Section 2.1. It seems that the water cutting, although not resulting in a much higher airflow resistance R (see Figure 3b), does improve the aerodynamic properties, maybe by making the surface smoother. In addition, as expected Figure 9 shows that the airfoil made of Damtec estra, which has a nominal airflow resistivity of 86,100 Pa·s/m

^{2}, generates less lift and more drag than the other porous airfoil made of a rubber granulate, Damtec SBM K 20 with r = 12,900 Pa·s/m

^{2}. This is due to the differences in the airflow resistance R, as shown in Figure 3b.

^{2}). As would be expected, the lift coefficient increases with decreasing extent of the porous material, while the drag coefficient decreases with decreasing s. When the porous extent is only 5% of the total chord length, a lift coefficient of about 85% to 95% of the value for the non-porous reference value can be reached, while the increase in drag is about 3% to 22%.

#### 3.2. Acoustic Results

^{2}, and Damtec SBM K 20, r = 12,900 Pa·s/m

^{2}). With the exception of a small range of low frequencies, those airfoils generate considerably more noise than the non-porous reference airfoil. This may be caused by the surface of the two materials, which seem to exhibit a higher roughness than that of the airfoils made of metal foams. Another possible reason is that these materials have a very low porosity, which was already found to be disadvantageous regarding a potential trailing edge noise reduction [22]. In addition, the airfoils are not rigid, which may lead to vibrations of the trailing edge and thus to additional noise. The airfoil made of Recemat (r = 8200 Pa·s/m

^{2}) leads to a strong noise increase compared to the non-porous reference airfoil at low to medium frequencies, while the spectra for the airfoil made of Porex (r = 315,500 Pa·s/m

^{2}) feature a noticeable hump around the 3 kHz third octave band. The reason for this increased noise is not fully clear yet. However, when compared with previous results [4,5] on fully porous airfoils it is reasonable to assume that the noise generated at the aft end of the impermeable foil at $x=b-s$ (as observed in the sound maps in Figure 11) is an important contribution. As mentioned above, noise from this source could be avoided by adding serrations to the trailing edges of the foil. However, many of the porous materials lead to a visible noise reduction compared to the non-porous reference airfoil at a large range of geometric angles of attack. Basically, judging by the data shown in Figure 12 for only a subset of the airfoils, no clear trend can be derived for the dependence of the noise reduction on the angle of attack.

^{2}) lead to a broad hump in the sound pressure level spectra in a range of Strouhal numbers between 10 and 20.

^{2}) generates a higher overall sound pressure level than the reference airfoil especially for porous extents of $s/b$ = 0.3 and $s/b$ = 0.5 and at high Reynolds numbers. This is due to the increased noise generation of these airfoils at low and medium frequencies, which was already observed in Figure 12. In general, it can be seen from Figure 16 that materials with medium to high airflow resistivities result in the highest reduction of the overall sound pressure level, which is in good agreement with the results from previous studies on fully porous airfoils [4,5,22]. Regarding the porous extent, it can be concluded that, on average, the reduction of the OSPL increases with increasing extent. However, it has to be kept in mind that a large porous extent s also leads to a notable aerodynamic penalty (see Figure 8 and Figure 10).

## 4. Summary

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A | [m^{2}] | cross sectional area of porous sample |

b | [m] | airfoil chord length |

c | [m/s] | speed of sound |

${c}_{D}$ | [-] | drag coefficient |

${c}_{L}$ | [-] | lift coefficient |

${f}_{c}$ | [Hz] | (third octave band) center frequency |

${F}_{D}$ | [N] | drag force |

${F}_{L}$ | [N] | lift force |

h | [m] | thickness of a porous sample |

M | [-] | Mach number |

${L}_{p}$ | [dB] | sound pressure level |

${p}_{0}$ | [Pa] | ambient pressure |

q | [m^{3}/s] | volume flow rate |

r | [Pa·s/m^{2}] | airflow resistivity |

R | [Pa·s/m^{3}] | airflow resistance |

$Re$ | [-] | chord based Reynolds number |

s | [m] | chordwise extent of porous material |

S | [m^{2}] | “wetted” area of the airfoil |

$Sr$ | [-] | chord based Strouhal number |

U | [m/s] | free stream velocity (flow speed) |

w | [m] | airfoil span width |

x, y, z | [m] | cartesian coordinates |

$\alpha $ | [${}^{\xb0}$] | geometric angle of attack |

$\mathrm{\Delta}p$ | [Pa] | pressure difference across porous sample |

$\mathrm{\Delta}{L}_{p}$ | [dB] | sound pressure level difference |

$\mathrm{\Lambda}$ | [m] | viscous characteristic length |

${\mathrm{\Lambda}}^{\prime}$ | [m] | thermal characteristic length |

$\nu $ | [m^{2}/s] | kinematic viscosity of air |

$\rho $ | [kg/m^{3}] | density of air |

${\rho}_{s}$ | [kg/m^{3}] | density of skeletal material |

${\rho}_{t}$ | [kg/m^{3}] | total density |

$\sigma $ | [-] | porosity |

$\tau $ | [-] | tortuosity |

## References

- Herr, M. Design criteria for low-noise trailing edges. In Proceedings of the 13th AIAA/CEAS Aeroacoustics Conference, Rome, Italy, 21–23 May 2007. [Google Scholar]
- Finez, A.; Jondeau, E.; Roger, M.; Jacob, M.C. Broadband noise reduction with trailing edge brushes. In Proceedings of the 16th AIAA/CEAS Aeroacoustics Conference, Stockholm, Sweden, 7–9 June 2010. [Google Scholar]
- Sudhakaran, R.; Mimani, A.; Porteous, R.; Doolan, C.J. An experimental investigation of the flow-induced noise generated by a porous trailing edge of a flat plate. In Proceedings of the Acoustics, Australian Acoustical Society, Hunter Valley, Australia, 15–18 November 2015. [Google Scholar]
- Geyer, T.F.; Sarradj, E.; Fritzsche, C. Measurement of the noise generation at the trailing edge of porous airfoils. Exp. Fluids
**2010**, 48, 291–308. [Google Scholar] [CrossRef] - Geyer, T.F.; Sarradj, E.; Fritzsche, C. Porous airfoils: noise reduction and boundary layer effects. Int. J. Aeroacoust.
**2010**, 9, 787–820. [Google Scholar] [CrossRef] - Herr, M.; Reichenberger, J. In search of airworthy trailing-edge noise reduction means. In Proceedings of the 17th AIAA/CEAS Aeroacoustics Conference, Portland, OR, USA, 5–8 June 2011. [Google Scholar]
- Herr, M.; Rossignol, K.S.; Delfs, J.; Lippitz, N.; Mößner, M. Specification of porous materials for low-noise trailing-edge applications. In Proceedings of the 20th AIAA/CEAS Aeroacoustics Conference, Atlanta, GA, USA, 16–20 June 2014. [Google Scholar]
- Carpio, A.R.; Martínez, R.M.; Avallone, F.; Ragni, D.; Snellen, M.; van der Zwaag, S. Experimental characterization of the turbulent boundary layer over a porous trailing edge for noise abatement. J. Sound Vib.
**2019**, 443, 537–558. [Google Scholar] [CrossRef] - Ali, S.A.S.; Azarpeyvand, M.; da Silva, C.R.I. Trailing-edge flow and noise control using porous treatments. J. Fluid Mech.
**2018**, 850, 83–119. [Google Scholar] - Jiang, C.; Moreau, D.J.; Yauwenas, Y.; Fischer, J.R.; Doolan, C.J.; Gao, J.; Kingan, M. Control of rotor trailing edge noise using porous additively manufactured blades. In Proceedings of the 25th AIAA/CEAS Aeroacoustics Conference, Vancouver, BC, Canada, 5–7 May 2018. [Google Scholar]
- Vathylakis, A.; Chong, T.P.; Joseph, P.F. Poro-serrated trailing-edge devices for airfoil self-noise reduction. AIAA J.
**2015**, 53, 3379–3394. [Google Scholar] [CrossRef] - Kisil, A.; Ayton, L.J. Aerodynamic noise from rigid trailing edges with finite porous extentions. J. Fluid Mech.
**2018**, 836, 117–144. [Google Scholar] [CrossRef] - Bae, Y.; Moon, Y.J. Effect of passive porous surface on the trailing-edge noise. Phys. Fluids
**2011**, 23, 126101. [Google Scholar] [CrossRef] - Faßmann, B.W.; Rautmann, C.; Ewert, R.; Delfs, J.W. Prediction of porous trailing edge noise reduction via acoustic perturbation equations and volume averaging. In Proceedings of the 21st AIAA/CEAS Aeroacoustics Conference, Atlanta, GA, USA, 16–20 June 2015. [Google Scholar]
- Zhou, B.Y.; Gauger, N.R.; Koh, S.R.; Meinke, M.; Schröder, W. On the adjoint-based control of trailing-edge turbulence and noise minimization via porous material. In Proceedings of the 21st AIAA/CEAS Aeroacoustics Conference, Dallas, TX, USA, 22–26 June 2018. [Google Scholar]
- Koh, S.R.; Meinke, M.; Schröder, W. Numerical analysis of the impact of permeability on trailing-edge noise. J. Sound Vib.
**2018**, 421, 348–376. [Google Scholar] [CrossRef] - Geyer, T.F.; Sarradj, E. Trailing edge noise of partially porous airfoils. In Proceedings of the 20th AIAA/CEAS Aeroacoustics Conference, Atlanta, GA, USA, 16–20 June 2014. [Google Scholar]
- Selig, M.S.; Donovan, J.F.; Fraser, D.B. Airfoils at Low Speeds; Stokely, H.A., Ed.; SoarTech Publications: Virginia Beach, VA, USA, 1989; Volume 121. [Google Scholar]
- ISO 9053. Acoustics—Materials for Acoustical Applications—Determination of Airflow Resistance; International Organization for Standardization: Geneva, Switzerland, 1993. [Google Scholar]
- Jaouen, L.; Chevillotte, F. The acoustic characterization of porous media and its standards. In Proceedings of the INTER-NOISE and NOISE-CON Congress and Conference Proceedings, Hamburg, Germany, 21–24 August 2016; Volume 253, pp. 725–730. [Google Scholar]
- Sarradj, E.; Fritzsche, C.; Geyer, T.F.; Giesler, J. Acoustic and aerodynamic design and characterization of a small-scale aeroacoustic wind tunnel. Appl. Acoust.
**2009**, 70, 1073–1080. [Google Scholar] [CrossRef] - Geyer, T.F. Trailing edge noise generation of porous airfoils. Ph.D. Thesis, Brandenburg University of Technology, Cottbus, Germany, 2011. [Google Scholar]
- Merino-Martinez, R.; et al. A review of acoustic imaging methods using phased microphone arrays. CEAS Aeronautical J.
**2019**. [Google Scholar] [CrossRef] - Sijtsma, P. CLEAN based on spatial source coherence. Int.J. Aeroacoust.
**2007**, 6, 357–374. [Google Scholar] [CrossRef] - Sarradj, E. Three-dimensional acoustic source mapping with different beamforming steering vector formulations. Adv. Acoust. Vib.
**2012**. [Google Scholar] [CrossRef] - Sarradj, E. A fast ray casting method for sound refraction at shear layers. Int. J. Aeroacoust.
**2016**, 16, 65–77. [Google Scholar] [CrossRef] - Von Schulz-Hausmann, F.K. Wechselwirkung ebener Freistrahlen mit der Umgebung. VDI Fortschr. Strömungstech.
**1985**, 52, 56. [Google Scholar] [CrossRef] - Brooks, T.F.; Pope, D.S.; Marcolini, M.A. Airfoil Self-Noise and Prediction; National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division: Washington, DC, USA, 1989. [Google Scholar]
- Gruber, M.; Joseph, P.; Chong, T.P. Experimental investigation of airfoil self noise and turbulent wake reduction by the use of trailing edge serrations. In Proceedings of the 16th AIAA/CEAS Aeroacoustics Conference, Stockholm, Sweden, 7–9 June 2010. [Google Scholar]
- Moreau, D.J.; Doolan, C.J. Noise-reduction mechanism of a flat-plate serrated trailing edge. AIAA J.
**2013**, 51, 2513–2522. [Google Scholar] [CrossRef] - Blake, W. Noncavitating lifting sections. In Mechanics of Flow-Induced Sound and Vibration, Volume II: Complex Flow-Structure Interactions; Academic Press, Inc.: Cambridge, MA, USA, 1986; pp. 718–836. [Google Scholar]
- Cleveland, W.S. Robust locally weighted regression and smoothing scatterplots. J. Am. Stat. Assoc.
**1979**, 74, 829–836. [Google Scholar] [CrossRef] - Cleveland, W.S.; Devlin, S.J. Locally weighted regression: An approach to regression analysis by local fitting. J. Am. Stat. Assoc.
**1988**, 83, 596–610. [Google Scholar] [CrossRef]

**Figure 1.**Photograph of the porous materials used for the present study (from left to right: Porex, Siperm R200, Damtec estra, Damtec SBM K 20, Recemat Ni-4753, M-Pore Al 45 ppi).

**Figure 2.**Modification of the surface of the airfoil made of Siperm R200 due to the water jet cutting.

**Figure 3.**Airflow resistance R of the porous airfoils. (

**a**) Schematic of the setup used for the airflow resistance measurements (not to scale); (

**b**) Relation between airflow resistance R at different chordwise positions and airflow resistivity r.

**Figure 4.**Schematic of a partially porous airfoil (gray: porous airfoil, red: flexible, impermeable foil used to cover the pores at the front part of the airfoil, s: chordwise extent of the porous material).

**Figure 6.**Schematic of the measurement setup (top view), the hatched area symbolizes the part of the airfoil covered by the thin, impermeable foil.

**Figure 7.**Sample sound map obtained for the non-porous reference airfoil for a third octave band with a center frequency of 5 kHz (U = 81.5 m/s, M = 0.238, $Re$ = 1,266,000), including the chosen prismatic integration volume (blue) used to derive spectra of the noise contributions generated by the noise source of interest (shown are translucently rendered iso surfaces colored according to the measured sound pressure level ${L}_{p}$).

**Figure 8.**Overview of the aerodynamic performance of the partially porous airfoils as a function of angle of attack for a constant flow speed of 57.6 m/s (M = 0.168, $Re$ = 901,000, cyan: Recemat, r = 8200 Pa·s/m

^{2}, brown: Porex, r = 316,500 Pa·s/m

^{2}, blue: M-Pore Al, r = 1000 Pa·s/m

^{2}, black: non-porous reference airfoil, r = ∞).

**Figure 9.**Influence of the material of the fully porous airfoils on the aerodynamic performance at 4${}^{\xb0}$ angle of attack ( non-porous reference airfoil, r = ∞, Porex, r = 316,500 Pa·s/m

^{2}, Siperm, r = 150,000 Pa·s/m

^{2}, Damtec estra, r = 86,100 Pa·s/m

^{2}, Damtec SMB K 20, r = 12,900 Pa·s/m

^{2}, Recemat, r = 8200 Pa·s/m

^{2}, M-Pore Al 45, r = 1000 Pa·s/m

^{2}). (

**a**) Lift coefficient as a function of chord based Reynolds number; (

**b**) Drag coefficient as a function of chord based Reynolds number.

**Figure 10.**Influence of the streamwise extent s of the porous trailing edge on the aerodynamic performance at 4${}^{\xb0}$ angle of attack (black: non-porous reference airfoil, r = ∞, cyan: Recemat, r = 8200 Pa·s/m

^{2}, porous extent: ◼ $s/b$ = 0.05, ⬟ $s/b$ = 0.1, ▶ $s/b$ = 0.2, 🞣 $s/b$ = 0.3, 🞪 $s/b$ = 0.5, ● $s/b$ = 1). (

**a**) Lift coefficient as a function of chord based Reynolds number; (

**b**) Drag coefficient as a function of chord based Reynolds number.

**Figure 11.**Sound maps obtained for a set of airfoils at a flow speed of 57.6 m/s (M = 0.168, $Re$ = 901,000) and a geometrical angle of attack of 4${}^{\xb0}$, 4 kHz octave band, CLEAN-SC beamforming (gray line indicates location of tripping, light blue line indicates boundary between non-porous front part and porous trailing edge).

**Figure 12.**Third octave band sound pressure level spectra of a subset of the airfoils at different geometric angles of attack $\alpha $, U = 57.6 m/s (M = 0.168, $Re$ = 901,000); colors and symbols match those from Figure 8. (

**a**) $\alpha $ = −20${}^{\xb0}$; (

**b**) $\alpha $ = −16${}^{\xb0}$; (

**c**) $\alpha $ = −12${}^{\xb0}$; (

**d**) $\alpha $ = −8${}^{\xb0}$; (

**e**) $\alpha $ = −4${}^{\xb0}$; (

**f**) $\alpha $ = 0${}^{\xb0}$; (

**g**) $\alpha $ = 4${}^{\xb0}$; (

**h**) $\alpha $ = 8${}^{\xb0}$; (

**i**) $\alpha $ = 12${}^{\xb0}$; (

**j**) $\alpha $ = 16${}^{\xb0}$; (

**k**) $\alpha $ = 20${}^{\xb0}$; (

**l**) $\alpha $ = −24${}^{\xb0}$.

**Figure 13.**Scaled sound pressure level of the reference airfoil (black) and the partially porous airfoils with varying porous extent at 4${}^{\xb0}$ angle of attack (markers for the different porous extents as in Figure 8).

**Figure 14.**Scaled sound pressure levels of the reference airfoil (black) and the partially porous airfoils with varying porous extent (porous materials color-coded as in Figure 9), filtered using a LOWESS algorithm [32,33]. (

**a**) $s/b$ = 0.05; (

**b**) $s/b$ = 0.1; (

**c**) $s/b$ = 0.2; (

**d**) $s/b$ = 0.3; (

**e**) $s/b$ = 0.5; (

**f**) $s/b$ = 1.

**Figure 15.**Sound pressure level difference of the partially porous airfoils with varying porous extent compared to the reference airfoil at 4${}^{\xb0}$ angle of attack (porous materials color-coded as in Figure 9, positive value denotes noise reduction, negative noise increase), filtered using a LOWESS algorithm [32,33]. (

**a**) $s/b$ = 0.05; (

**b**) $s/b$ = 0.1; (

**c**) $s/b$ = 0.2; (

**d**) $s/b$ = 0.3; (

**e**) $s/b$ = 0.5; (

**f**) $s/b$ = 1.

**Figure 16.**Overall sound pressure level of the partially porous airfoils with varying porous extent compared to the reference airfoil at 4${}^{\xb0}$ angle of attack, calculated according to Equation (6) (black: non-porous reference airfoil, porous materials color-coded as in Figure 9) (

**a**) $s/b$ = 0.05; (

**b**) $s/b$ = 0.1; (

**c**) $s/b$ = 0.2; (

**d**) $s/b$ = 0.3; (

**e**) $s/b$ = 0.5; (

**f**) $s/b$ = 1.

Name | Material | Airflow Resistivity r (Pa·s/m^{2}) | Porosity $\mathit{\sigma}$ |
---|---|---|---|

Reference | non-porous | ∞ | 0 |

Porex | polyethylene granulate | 316,500 | 0.40–0.46 |

Siperm R200 | metal foam | 150,000 | 0.49–0.54 |

Damtec estra | rubber granulate | 86,100 | 0.18–0.29 |

Damtec SBM K 20 | rubber granulate | 12,900 | 0.29–0.32 |

Recemat Ni-4753 | metal foam | 8200 | 0.95 |

M-Pore Al 45 ppi | metal foam | 1000 | 0.90 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Geyer, T.F.; Sarradj, E.
Self Noise Reduction and Aerodynamics of Airfoils with Porous Trailing Edges. *Acoustics* **2019**, *1*, 393-409.
https://doi.org/10.3390/acoustics1020022

**AMA Style**

Geyer TF, Sarradj E.
Self Noise Reduction and Aerodynamics of Airfoils with Porous Trailing Edges. *Acoustics*. 2019; 1(2):393-409.
https://doi.org/10.3390/acoustics1020022

**Chicago/Turabian Style**

Geyer, Thomas Fritz, and Ennes Sarradj.
2019. "Self Noise Reduction and Aerodynamics of Airfoils with Porous Trailing Edges" *Acoustics* 1, no. 2: 393-409.
https://doi.org/10.3390/acoustics1020022