Flow Interactions Between Low Aspect Ratio Hydrofoils in In-line and Staggered Arrangements

Abstract

Many species of fish gather in dense collectives or schools where there are significant flow interactions from their shed wakes. Commonly, these swimmers shed a classic reverse von Kármán wake, however, schooling eels produce a bifurcated wake topology with two vortex rings shed per oscillation cycle. To examine the schooling interactions of a hydrofoil with a bifurcated wake topology, we present tomographic particle image velocimetry (tomo PIV) measurements of the flow interactions and direct force measurements of the performance of two low-aspect-ratio hydrofoils ( A R = 0.5 ) in an in-line and a staggered arrangement. Surprisingly, when the leader and follower are interacting in either arrangement there are only minor alterations to the flowfields beyond the superposition of the flowfields produced by the isolated leader and follower. Motivated by this finding, Garrick’s linear theory, a linear unsteady hydrofoil theory based on a potential flow assumption, was adapted to predict the lift and thrust performance of the follower. Here, the follower hydrofoil interacting with the leader’s wake is considered as the superposition of an isolated pitching foil with a time-varying cross-stream velocity derived from the wake flow measurements of the isolated leader. Linear theory predictions accurately capture the time-averaged lift force and some of the major peaks in thrust derived from the follower interacting with the leader’s wake in a staggered arrangement. The thrust peaks that are not predicted by linear theory are likely driven by spatial variations in the flowfield acting on the follower or nonlinear flow interactions; neither of which are accounted for in the simple theory. This suggests that unsteady potential flow theory that does account for spatial variations in the flowfield acting on a hydrofoil can provide a relatively simple framework to understand and model the flow interactions that occur in schooling fish. Additionally, schooling eels can derive thrust and efficiency increases of 63-80% in either a in-line or a staggered arrangement where the follower is between two branched momentum jets or with one momentum jet branch directly impinging on it, respectively.

Three-dimensional effects on the aerodynamic performance of flapping wings in tandem configuration

“…The flapper self-propels at a mean speed, U p,s = 0.88V , shedding a vortex ring during each stroke. The vortex rings move away from the flapper with an oblique trajectory due to their own induced velocity, leading to a bifurcating wake (Kurt et al 2020). These vortices are visible in figure 3a, which shows a visualization of the flow around the isolated flapper at mid-downstroke.…”

Flow interaction of three-dimensional self-propelled flexible plates in tandem

“…The flapper self-propels at a mean speed, Ūp,s = 0.88V, shedding a VR during each stroke. The VRs move away from the flapper with an oblique trajectory due to their own induced velocity, leading to a bifurcating wake (Kurt, Eslam & Moored 2020). These vortices are visible in figure 3(a), which shows a visualization of the flow around the isolated flapper at mid-downstroke.…”

Two-dimensionally stable self-organization arises in simple schooling swimmers through hydrodynamic interactions

“…Yet, both the spatial organization (3,8) and temporal synchronization (9)(10)(11) have emerged as major drivers of the hydrodynamic interactions, and, consequently, the energetic cost of locomotion and traveling speed of individuals in a collective. Still, our understanding of the force production and energetics of schooling swimmers is mostly limited to canonical spatial arrangements such as a leader-follower in-line arrangement (12)(13)(14)(15) and a side-by-side arrangement (11,(16)(17)(18), while there are fewer studies of staggered arrangements (19)(20)(21)(22).…”