# Bio-Inspired Aerodynamic Noise Control: A Bibliographic Review
## 3 Leading Edge Serrations
### Aeroacoustic Performance of Leading Edge Serrations
#### 3.1.2 Sinusoidal Serrations  
The application of sinusoidal serrations (also known as tubercles) to the leading edge of the models as a noise attenuator was partly inspired by the flipper of a humpback whale [59; 60], which has enhanced maneuverability during prey capture. [PERSON] et al. [47; 61] found that leading edge sinusoidal serrations significantly reduced the tonal noise (emitted from boundary layer turbulence scattering at the trailing edge) of a NACA 0021 airfoil at a Reynolds number of \(Re_{c}=1.2\times 10^{5}\), as well as the overall broadband noise (generated by the interaction between turbulence and the leading edge of the airfoil) surrounding the peak of the tonal noise. The most effective configurations for tonal noise elimination at \(\alpha=5^{\circ}\) were those serrations with a smaller value of \(\lambda/h\) ratio (smaller wavelength and larger amplitude). Turbulence-airfoil interaction noise generated by the interaction of turbofan turbulent wakes and the outlet guide vanes is known to be the main contribution to the broadband noise emission of aero-engines during landing approach phases [62]. Generally, turbulence-airfoil interaction mechanism (the near-isotropic inflow turbulence) can be obtained by using either a turbulence grid located inside the nozzle near the outlet of wind tunnel [48; 49; 50; 63; 64] or a circular cylinder located in a tandem configuration [49; 53]. Several acoustic measurements conducted in different anechoic open-jet wind tunnels revealed that a significant broadband noise reduction of turbulence-airfoil interaction noise could be obtained by almost all the modified airfoils with leading-edge sinusoidal serrations over a quite wide range of frequencies and Reynolds numbers: sound power level reduction of about 3-4 dB for the non-symmetrical NACA 65-(12)10 lifting airfoil [48; 64], a maximum of about 10 dB (in grid-generated turbulence) or 5-6 dB (in the wake of cylinders) dimensionless reduction for the symmetrical NACA 0012 airfoil [49], and more than 3 dB for a flat plate [50; 63]. Comparison of sound power reduction level (\(\Delta\)PWL) between sinusoidal airfoil and sawtooth airfoil under the same wavelength and amplitude of the serrations by [PERSON] et al. [65] revealed that the latter provided consistently higher noise reductions than the corresponding sinusoidal case above the frequencies of \(f(2h)/u_{\infty}=1\), due to a lower source strength and the singular behavior near the sawtooth root. The effectiveness of the sinusoidal serrations to suppress noise was also sensitive to several factors listed below, especially the first one, which is the focus and the most studied:  
1. **Serration geometry**: [PERSON] et al. [49] suggested that the key parameter for the noise reduction of NACA 0012 airfoil was the serration wavelength, however only one sinusoidal serration configuration (i.e., \(\lambda=0.1c_{0}\), and \(H=0.12c_{0}\), where \(c_{0}\) is the mean chord) was used in their study. [PERSON] et al. [65] found that, when the serration amplitude of two different NACA 0065 airfoil was the same, the one with wider wavelength produced less low-frequency noise but more high-frequency noise (supported by the generalized Amiet model in [66]). Both analytical [66] and experimental [50; 63] studies on flat plate demonstrated that the amplitude of the serrations is a key parameter for reducing broadband noise: the level of sound power reductions generally increases with increasing serration amplitude, and wider and longer serrations obtain higher overall noise reductions [63]. However, the parameter study on a realistic NACA 0065 airfoil with the same serration profile showed that sound power reductions generally increased with increasing inclination angle \(\theta=atan(4h/\lambda)\), which implied that narrower and longer serrations could achieve higher noise reductions [51] (see Figure 5). All these studies showed that noise reductions were less sensitive to the serration wavelength than the serration amplitude.