Impact of the formation angle on the drag of bio-inspired $\pmb \vee$-formations

Abstract

Bio-inspired $\pmb \vee$ flight formation is a well known technique for energy saving among groups of fixed-wing aircraft, and as of recently, for groups of quad-rotors. Here, we study the effect of the formation angle on the performance of each of the members of a 5-member $\pmb \vee$-formation in terms of the flow field, and drag force. We employ axisymmetric cylinders, which are non-lifting in solo condition to reduce/eliminate the effect of the lift (lateral force) on the group performance, and use time-resolved, multi-illumination, consecutive-overlapping particle image velocimetry (PIV) to capture the velocity field around and in-between the members. Over a range of $\pmb \vee$-formation angles, we see various degree of drag reduction, with the highest drag reduction ($\sim 80\%$) for the interior members of the tightest formation (formation with the smallest $\pmb \vee$-angle and the most overlap in frontal views). All formation members experience some levels of drag reduction up for $\pmb \vee$-angle of around $50^{\circ}$ and in formation with $\pmb \vee$-angle greater than $50^{\circ}$, only the leading member experiences observable drag reduction. We explore the complex flow dynamics between the formation members in terms of wake-body and wake-wake interactions, and the bleeding (gap) flow. We present the mean and fluctuating quantities, as well as the dynamics of the vortex shedding and circulation in the wakes of the members, and discuss how these flow characteristics relate to the drag of each member, both as a function of their position within the $\pmb \vee$ and the angle of the formation. This current study serves as a baseline for further explorations of wake-body and wake-wake interactions of flow past groups of bodies, and demonstrates how changing formation angle can help achieve a desired group performance (like minimum drag).