# Bio-Inspired Aerodynamic Noise Control: A Bibliographic Review
## 3 Leading Edge Serrations
### Aerodynamic Properties of Leading Edge Serrations
#### 3.2.2 Sinusoidal Serrations  
Several experimental and numerical studies have shown that all of the modified airfoils with leading edge sinusoidal serrations had lower lift coefficient slopes, stall angle and maximum lift coefficients \(C_{Lmax}\), while mildly higher drag coefficient \(C_{D}\) in the pre-stall region of the unmodified airfoils (Saderman, 2019; Saderman, 2019; Saderman, 2019; Saderman, 2019; Saderman, 2019). However, in the post-stall regime, airfoils with leading edge serrations produced higher lift coefficient (by as much as 25% at \(Re_{c}=0.5\times 10^{5}\)(Saderman, 2019) or 50% at \(Re_{c}=1.83\times 10^{5}\)(Saderman, 2019; Saderman, 2019) for the NACA 634-021 airfoil, 48% for the NACA 0020 airfoil at approximately \(Re_{c}=2.75\times 10^{5}\)(Saderman, 2019), or 48% for the NACA 2412 airfoil at approximately \(Re_{c}=5.7\times 10^{5}\)(Saderman, 2019)), little or no drag penalty(Saderman, 2019; Saderman, 2019; Saderman, 2019) and larger lift-to-drag ratios. Similar to the observations on sawtooth serrations, sinusoidal serrations also reduced the fluctuating lift and drag ([PERSON], 2019). Previous studies [47; 68; 69; 75; 80; 89; 90; 91] showed that the amplitude of the serrations had a distinct effect on the resulting aerodynamic performance, whereas the wavelength played a minor role. Lift coefficient decreased with larger amplitude at low and medium angles of attack, while it increased with larger amplitude and wavelength in the post-stall region. Over the majority of angles of attack examined, \(C_{D}\) values increased with larger amplitude and wavelength. [PERSON] et al. [80] attributed these observations to the fact that the serrations with higher amplitude had less pressure at the roots and more pressure variations on the surface, which in turn significantly delayed separation and stall. [PERSON] et al. [79] found different effect of the serration amplitude for the small aspect ratio flat plates at \(Re_{c}=1.9\times 10^{5}\). The small serrated plate showed some increase in \(C_{L}\) at almost all angles, the medium serrations demonstrated similar increases in \(C_{L}\) at low angles of attack but no improvements at higher angles, while the large serrations showed an overall decrease in \(C_{L}\) at almost every angle of attack. However, these observations might be affected by the fact that the mean chord or the aerodynamic area was decreased with the increasing of the amplitude of the serrations. At a low Reynolds number of \(Re_{c}=1.2\times 10^{4}\), an efficient numerical 3D panel method conducted by [PERSON] and [PERSON] [92] showed that sinusoidal leading edge serrations offered no detrimental effects at zero angle of attack, while enhanced aerodynamic performance at modest angles of attack. [PERSON] et al. [78] numerically studied the effect of serration ratio (the spanwise length covered by the serrations to the entire span length of the NACA 0020 airfoil) on the aerodynamic characteristics at a fixed wavelength of \(0.2c_{0}\) and amplitude of \(0.025c_{0}\). The numerical results show that the stall occurred earlier and the lift coefficient became larger in the post-stall region as the serration ratio increased. [PERSON] [93] noticed that the aerodynamic benefits of the sinusoidal leading edge serrations were highly sensitive to the aspect ratio of the airfoils. Different from all the above studies, which focused on nominally 2D models, [PERSON] et al. [60; 76] experimentally investigated the effect of the sinusoidal leading edges on the performance of a 3D scale model of an idealized humpback whale flipper in a wind tunnel (see Figure 7). The results [60] show vastly different results from 2D configurations: the presence of sinusoidal leading edges increased the stall angle of attack by nearly 40% (from \(\alpha=12^{\circ}\) to \(\alpha=16.3^{\circ}\)) and the value of maximum lift coefficient \(C_{Lmax}\) by approximately 6% (from 0.88 to 0.93) (see Figure 8a).