## 1 Introduction  
For decades, the quiet flight of owls has drawn interest from researchers in the aerodynamic and aeroacoustics fields. Owl-wing-inspired modifications on either leading-edge or trailing-edge designs have attracted plenty of research interest aiming to improve the aerodynamic performance and/or, in the meanwhile, suppress the aerodynamic noise from airfoils or turbine/fan blades. Multiple bio-inspired airfoil designs have been evaluated, including the trailing-edge or leading-edge serrations, trailing-edge flaplets, flapping wings, the compliant surface, and the flexible trailing-edge fringe, etc. [1, 2, 3, 4, 5, 6, 7, 8, 9]. It has been found that the soft trailing edge fringe can attenuate the primary noise source generated from the trailing edge through the modification of the coherent scattering mechanism. Consequently, aeroacoustic noise above 2 kHz can be effectively attenuated by the compliant surface covered by the down feathers through a bypass dissipation mechanism [10, 11]. In the last decade, the use of an owl-wing-inspired trailing edge design as a passive control approach for an airfoil model to minimize drag and improve lift coefficients has gained attention [12, 13, 14, 15, 16]. The brush-like trailing edge has been utilized as the trailing edge extension to reduce both the narrowband bluntness noise and broadband turbulent boundary-layer trailing-edge noise, as it contains the characteristics of both porosity and flexibility as the natural fringe [17, 18, 19, 20, 21]. A remarkable noise reduction was observed for an airfoil with a flexible trailing edge equipped to the suction side of the airfoil experimentally [21]. The attachment of flaplets on the trailing edge of an airfoil has clearly shown reductions in tonal noise, primarily resulting from the generation of small-scale vortices by the flaplets [22]. Recently, [PERSON] et al. (2021) carried out an experiment to study the effects of flexible flaps with various gaps on the aerodynamic characteristics of a fixed-wing [23]. The results indicated that the adjustable flaps enabled the suppression of the large-scale vortex shedding, and thus, reduced the fluctuation of aerodynamic forces. This finding is consistent with our experimental findings of an airfoil with soft feathers installed on the trailing edge [24]. Our previous experiment demonstrated that the real bird feather enabled the large-scale vortex to break up into small-scale turbulence. It is illustrated that the vibrating porous feather fringe produces a significant vertical velocity in the flow field around the trailing edge. As a result, it suppressed the leading-edge vortices approaching the flexible tail, and accelerated the shedding vortices' dissipation. Additionally, [PERSON] et al. (2020) performed computational fluid dynamics (CFD) simulations on an airfoil with an extended trailing-edge fringe [25]. The effects of the fringe lengths and flapping frequencies on shedding vortices have been investigated. The flapping behavior with a certain length and frequency can attenuate the strength of the vortices, and improve the aerodynamics in terms of reducing the drag coefficients, and increasing the lift coefficients. The abovementioned studies aimed at improving the aerodynamics of an airfoil, and reducing the noise. The flapping trailing edge fringe can be applied to wind turbine blades and airplanes to improve noise reduction from the aerodynamic perspective. In this study, to leverage the influence of the extended flapping trailing edge fringe on the aerodynamic performance of the airfoil, CFD simulations are performed for the S833 airfoil with an extended flapping trailing edge fringe. This numerical simulation model is different from our previous experimental study. First, the experimental model was equipped with real feathers at the trailing edge of the airfoil as a passive flow control without any controlled flapping motion.