# Bio-Inspired Aerodynamic Noise Control: A Bibliographic Review
## 4 Trailing Edge Serrations
### Aeroacoustic Performance of Trailing Edge Serrations  
#### 4.1.1 Broadband Self-Noise  
The first theoretical model for the noise reducing effect of serrated trailing edges was developed by [PERSON] [113; 114] in 1991. Assuming that trailing edge serrations do not introduce other extraneous noise sources, change the surface pressure frequency spectrum and affect the turbulent eddies close to the trailing edge, [PERSON] derived analytical noise radiation models for a flat plate airfoil with both sinusoidal and sawtooth trailing edge serrations, at zero angle of attack in low Mach number turbulent flow. It was shown that turbulent boundary layer trailing edge noise reductions of order \(10\times log(6h/\lambda)\) dB for the sinusoidal profile [113] and \(10\times log[1+(4h/\lambda)^{2}]\) dB for the sawtooth profile [114] are possible, at acoustic frequencies \(f\) such that \(fh/u_{\infty}\gg 1\), where \(u_{\infty}\) is the main stream velocity, \(\lambda\) and \(h\) are the wavelength and amplitude of the serrations. According to [PERSON]'s theory, the attenuation relative to that produced by the unserrated trailing edge was significant when the edges of the serrations were inclined at an angle of less than about \(45^{\circ}\) (i.e., \(\lambda/h<4\)) to the direction of the mean flow. Moreover, the noise spectrum was shifted to lower frequencies when the amplitude \(h\) increased (see Figure 10). Noise reduction increased with increasing frequency and decreasing values of \(\lambda/h\). In other words, a greater noise reduction can be obtained by narrower, shaper serrations (supported by experimental measurements of [97; 100; 104; 115; 116; 117]). Comparison of the corresponding spectra between sinusoidal type serrations and sawtooth type serrations revealed that the predictions were very similar when \(\lambda/h>1\) while the latter led to greater noise reduction than the former when \(\lambda/h<1\), due to the sharpness of the tooth at the root and peak regions of the serrations. Later, [PERSON] et al. [98] experimentally investigated [PERSON]'s noise reducing potential under more realistic flow conditions and model geometries. Trailing edge serrations with an amplitude of 25 mm and wavelength of 5 mm was attached to six flat plates and eight 2D NACA airfoils of \(c=250\) mm chord length with different geometries at high Reynolds numbers of \(7\times 10^{5}<Re_{c}<1.4\times 10^{6}\). Comparative analysis of the radiated octave band sound pressure levels between the serrated flat plates/airfoils and the reference flat plates/airfoils showed that significant noise reductions (up to 10 dB in the range of 1 kHz to 6 kHz for the serrated flat plates) can be obtained by the serrated trailing  
Figure 10: Normalized acoustic pressure frequency spectrum of noise produced by different trailing edge serrations ( - - for an unserrated edge, reprinted from [114] with permission from AIP Publishing): (**a**) sawtooth serrations; and (**b**) sinusoidal serrations. edges. Moreover, the noise reductions of the serrated flat plates were not affected by the inclination of the trailing edge, the inclination of both the leading edge and trailing edge, or the orientations of the teeth in the chord plane. However, misalignment of the serrations with respect to the flow direction and chord plane by \(15^{\circ}\) gave rise to about 10 dB increase of the radiated noise. On the other hand, the measured noise attenuations were significantly smaller than that predicted by the theoretical model of [PERSON] [114] (also observed in several other experimental studies [102; 118; 119; 120; 121; 122]). Furthermore, the highest noise reduction was achieved at low to middle frequencies and noise increase occurred at high frequencies (see also [100; 101; 102; 103; 104; 107; 120; 121; 122]), contrary to [PERSON]'s model that the theoretical noise reduction predictions occurred only at high frequencies \(fh/u_{\infty}\gg 1\).