Flow interactions of two- and three-dimensional networked bio-inspired control elements in an in-line arrangement

Abstract

We present experiments that examine the modes of interaction, the collective performance and the role of three-dimensionality in two pitching propulsors in an in-line arrangement. Both two-dimensional foils and three-dimensional rectangular wings of AR = 2 are examined. In contrast to previous work, two interaction modes distinguished as the coherent and branched wake modes are not observed to be directly linked to the propulsive efficiency, although they are linked to peak thrust performance and minimum power consumption as previously described (Boschitsch et al 2014 Phys. Fluids 26 051901). In fact, in closely-spaced propulsors peak propulsive efficiency of the follower occurs near its minimum power and this condition reveals a branched wake mode. Alternatively, for propulsors spaced far apart peak propulsive efficiency of the follower occurs near its peak thrust and this condition reveals a coherent wake mode. By examining the collective performance, it is discovered that there is an optimal spacing between the propulsors to maximize the collective efficiency. For two-dimensional foils the optimal spacing of X = 0.75 and the synchrony of ϕ = 2π / 3 leads to a collective efficiency and thrust enhancement of 42% and 38%, respectively, as compared to two isolated foils. In comparison, for AR = 2 wings the optimal spacing of X = 0.25 and the synchrony of ϕ = 7 π / 6 leads to a collective efficiency and thrust enhancement of 25% and 15%, respectively. In addition, at the optimal conditions the collective lateral force coefficients in both the two- and three-dimensional cases are negligible, while operating off these conditions can lead to non-negligible lateral forces. Finally, the peak efficiency of the collective and the follower are shown to have opposite trends with increasing spacing in two- and three-dimensional flows. This is correlated to the breakdown of the impinging vortex on the follower wing in three-dimensions. These results can aid in the design of networked bio-inspired control elements that through integrated sensing can synchronize to three-dimensional flow interactions.

Flow-mediated organization of two freely flapping swimmers

“…In order to simplify the problem and consider the fact that most fish and birds are using flapping fins/wings to generate propulsive forces, fish schools and bird flocks are often simplified as two flapping foils in regular arrangements (Dewey et al 2014). It has been indicated that the hydrodynamic benefit can be achieved by flapping foils in a variety of regular arrangements, including the tandem arrangement (Kurt & Moored 2018), the side-by-side arrangement (Dewey et al 2014) and the staggered arrangement (Huera-Huarte 2018). In the tandem formation, the performance augmentation can be achieved by the upstream body when the separation distance is small .…”

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

“…Garrick's solution assumes potential flow over: (a) a two-dimensional, (b) infinitesimally-thin hydrofoil, (c) undergoing small amplitude, (d) harmonic motions with (e) a non-deforming, planar wake behind the hydrofoil. Moreover, since this is an inviscid flow solution, induced shedding of vorticity at the leading edge from interaction with the gust field is not accounted for, even though it is known to exist in schooling interactions [12,19]. In the present study, we will compare direct force measurements of the follower hydrofoil to the quasi-steady Garrick solution with three-dimensional corrections.…”

“…These highly three-dimensional spatial configurations found within collectives can be decomposed into canonical in-line, side-by-side, or tip-to-tip arrangements as presented in Figure 1 . To date, these interactions have mostly been studied for propulsors in in-line arrangements [ 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ], although a few efforts have been made to understand interactions in side-by-side arrangements [ 20 , 21 , 22 , 23 ], as well as staggered arrangements [ 24 , 25 , 26 , 27 ]. Here, our focus is on the propulsive performance and flow interactions in in-line , and staggered arrangements.…”

“…Including hydrodynamic interactions in a model of a fish school is a challenging task without simplifications made with theoretical approximations [ 28 ]. Our current understanding of flow interactions and energetics within fish schools is mostly based on two-dimensional flow analyses [ 10 , 11 , 12 , 13 , 14 , 20 , 21 , 24 , 25 , 29 , 30 ], but there are far fewer three-dimensional studies focusing on these interactions that employ finite-span wings or hydrofoils, or fish-like bodies [ 15 , 19 , 22 , 25 , 31 , 32 ]. Amongst these studies, some consider the interaction of an oscillatory body with a classic drag-producing von Kármán street [ 30 , 33 ], and the others consider an interaction with a thrust-producing reverse von Kármán street [ 12 , 19 , 20 ].…”

Collective locomotion of two-dimensional lattices of flapping plates. Part 1. Numerical method, single-plate case and lattice input power

“…A number of works have investigated multiple flapping foils interacting in a fluid (Sparenberg & Wiersma 1975; Akhtar et al. 2007; Wang & Russell 2007; Boschitsch, Dewey & Smits 2014; Kurt & Moored 2018; Lin et al. 2019).…”