# Aerodynamic Effects of Ceiling and Ground Vicinity on Flapping Wings
###### Abstract  
The combined ceiling and ground effect on the aerodynamics of a hovering flapping wing is investigated using numerical simulations. In the simulations, the wing was located between the ceiling and the ground. Simulations were carried out for different wall clearances at two Reynolds numbers (\(Re=10\) and \(100\)). Special efforts were paid to whether there exists aerodynamic coupling between the ceiling effect and the ground effect. At \(Re=10\), the combined ceiling and ground effect increases the aerodynamic forces monotonically through two effects, namely the narrow-channel effect and the downwash-reducing effect. Additionally, there exists a coupling effect of the ceiling and the ground for the combined case at \(Re=10\), where the force enhancement of the combined effect is much more significant than the sum of the ceiling-only effect and the ground-only effect. At \(Re=100\), the combined effect of ceiling and ground causes three non-monotonic force regimes (force enhancement, reduction and recovery) with increasing wall clearance. The narrow-channel effect at \(Re=100\) leads to a monotonic force trend, while the downwash-reducing effect results in a non-monotonic force trend. The two effects eventually lead to the three force regimes at \(Re=100\). Unlike the \(Re=10\) case, the coupling effect at \(Re=100\) is small. c 2022 2022 2022 20222 20222 2022 20222 2022 2022  
mechanism is used by most insects. It is related to the continued attachment of the leading-edge vortex (LEV) to the wing in individual strokes, and is the leading cause of the high lift coefficient of the insect's flapping wing. In addition to the attached LEV, the tip vortex (TV), trailing-edge vortex (TEV) and root vortex (RV) continuously detach from the wing, forming a vortex wake. The attached LEV, together with the detached vortices forms a doughnut-shaped vortex ring that also produces a downwash [14]. Since there is significant fluid separation above the wing and a complex vortex wake under the wing, it is easy to predict that a surface above or below the wing will affect the vortex structures around the wing and the induced downwash of the vortex ring, thus leading to changes in the aerodynamics of the flapping wing. The ground effect, when the wall is below the flapping wing, has already been investigated. It is inspired by the long-existing study of the ground effect on a fixed aircraft wing. For a fixed-symmetry airfoil at a positive angle of attack, the ground effect generally causes increase in lift and a larger lift-to-drag ratio by increasing the pressure on the lower surface [15; 16]. However, for different airfoil configurations, the aerodynamic effects caused by the ground are different. For an asymmetric airfoil in Ref. [17], the ground decreased the lift at a negative angle of attack and caused a non-monotonic lift trend at a low-to-moderate angle of attack. By installing a front wing, a racing car can also take advantage of the ground effect to increase the downward force, and this ground effect can be further enhanced by adding a gurney flap on the fixed wing [18; 19]. It is interesting to know whether the ground effect for a flapping wing is the same as that for a fixed wing. The pioneering work of [PERSON] et al. numerically studied the ground effect on a two-dimensional (2D) flapping foil at a Reynolds number of 100. Unlike those for the fixed wing, the aerodynamics of the flapping wing were found to experience three non-monotonic force regimes as the wall clearance increased [20]. This non-monotonic force trend is further confirmed by later studies, including a particle image velocimetry (PIV) work [21] on a 2-D hovering airfoil at \(Re=1000\), and a numerical simulation [22] using a NACA-0015 airfoil at \(Re=100\). In the PIV study, the force increment was mainly due to a stronger wake capture, the force decrease was due to a weak LEV and the negative effect of the wake, and the recovery was because of the LEV's attachment to the airfoil during mid-stroke.