Finite obstacle effect on the aerodynamic performance of a hovering wing

The finite obstacle effect on the aerodynamic performance of a normal hovering wing is studied using the immersed boundary method. Phenomena of a two-dimensional wing hovering above, under, or on the side of a circular obstacle are presented. Parameters including obstacle size, distance, location, and flapping angle are investigated to study how the aerodynamic force and flow field are affected. The diameter of the obstacle ranges from 0.5c to 12c and the distance between the centroid of the wing and obstacle surface from 0.5c to 6c (c is the wing chord length). Previous observations of ground effects including force enhancement, reduction, and recovery occur similarly when the wing hovers above the obstacle of diameter greater than 2c. However, finite obstacles affect the aerodynamic performance differently when the size shrinks to a critical value. Force drops when the wing moves close and rises when moving away, opposite to the ground effect. As flapping angle amplitude increases, the force change tends to be consistent for different-sized obstacles. The top or side effect shows a different influence on the force change. Force monotonically increases as the distance decreases when the wing hovers under the obstacle. The side effect places a less important factor on the aerodynamic performance. All force changes under such circumstance are less than 13% referring to nonobstacle result. The gap between the leading or trailing edge of the wing and obstacle surface plays a significant role in the leading and trailing edge vortices generating, shedding, and pairing, which greatly affects the force change.