# Aerodynamic Effects of Ceiling and Ground Vicinity on Flapping Wings
###### Abstract
In more recent research, the ground effect on a three-dimensional (3D) flapping insect wing model was studied at \(Re=100\) and \(5000\). Both numerical and experimental studies were carried out in this work, and they concluded that the effect on a 3D wing is similar, but less noteworthy, compared to a 2D wing. It was reasoned that the \"three force regimes\" effect could be attributed to the positional shift in the vortex wake, causing a non-monotonic trend in the downwash [23]. The work of a recent numerical 3D study extends the \(Re\) to as low as 10 and compares the ground effect at low and high \(Re\)[24]. Unlike the above-mentioned \"three force regimes\" at \(Re=100\) or higher, it revealed that reducing the \(Re\) to a very low level causes a monotonic \"single force regime\". The force increases monotonically with reducing ground clearance. The different force trend behaviors stem from different evolution processes of the vortex wake. Additionally, the \"cramming effect\" also contributes to the force enhancement by increasing the positive pressure on the wing surface. Studies also show the aerodynamic ground effect on the wing in an insect's take-off [25; 26; 27; 28]. The experimental study on the takeoff of a 3D beetle model wing at \(Re=10,\!000\) showed that the overall vertical force for the initial two strokes was increased by the LEV enhancement of the downstroke [25]. However, other works argue that the ground effect on the oscillating wings of a drone fly and a fruit fly was insignificant during takeoff [26; 27; 28]. It is believed that the rapid dynamic process of takeoff is responsible for the negligible effect. This is because the insect wings rapidly move off the ground to above a wing-chord-length distance of 3 within one or two strokes [24]. The ceiling effect, when the wall is above the flapping wing, was not investigated until recently, and was inspired by the observed landing flight of a bee on a ceiling (inverted surface) and a flapping-wing MAV that could take off and perch on the overhangs of materials such as a natural leaf, wood, glass, etc. [29; 30]. Studies claim that the aerodynamic forceson a hovering insect wing increase monotonically as the wing approaches the ceiling [31]. They state that the ceiling's presence acts like a mirror, as if a mirroring LEV exists there, thus increasing the relative oncoming flow velocity to the wing, and also producing an upwash to be experienced by the wing. Another work further studied the ceiling effect in forward flight, and comprehended that the aerodynamic forces monotonically increase with reducing ceiling clearance at a lower advance ratio (_J_), but that the ceiling effect reduces with increasing _J_[32]. As an initial stage, the aforementioned works [20; 21; 32; 31] studied the ground effect and the ceiling effect on flapping wings separately. However, an actual flapping insect often flies in confined areas where the ceiling and the ground co-exist in the flapping wing's vicinity. This situation leads to two problems that need to be clarified. The first answer to obtain is the combined ceiling and ground effect on the aerodynamics of the flapping wing. Second, it is necessary to determine whether there exists aerodynamic coupling between the ceiling effect and the ground effect. If no coupling exists, then the combined ceiling and ground effect on a flapping wing is merely a superposition of the separate ceiling and ground effect. However, if some coupling exists, then the aerodynamic effect will differ from the superposition of the separate ceiling and ground effects. In this study, we will try to answer the above two queries. This paper is organized as follows: First, the wing motion and numerical method are introduced. Second, the combined effect of the ceiling and ground on the aerodynamic forces at _Re_ = 10 is investigated. Then, the reasons for the combined effect as well as the coupling effect at _Re_ = 10 are answered. Following this, the same situations at _Re_ = 100 are investigated.