Creeping flow around a finite row of slender bodies in close proximity

Abstract

The flow through and around a finite row of parallel slender bodies in close proximity moving in a viscous incompressible fluid is studied. The motion occurs under creeping flow ($\hbox{\it Re}\,{\ll}\,1$) conditions. This row is a model of a comb-wing configuration found in insects of the Thrips family and being developed for use for flying vehicles of mm size, operating in the creeping flow regime. We show here that such wings utilize viscous effects to carry along enough fluid to approximate continuous surfaces. The comb is described as a row of rod-like ellipsoids of slenderness ratio smaller than 0.01 at distances apart of order 10 times the minor axis and the flow field is computed by distributing singularities along the major axes of the ellipsoids. Results for the drag on the individual rods, as well as for the full row are presented. It is shown that above a certain number of rods, dependent on the geometric parameters of the comb, the row acts very much like a continuous surface, with over 95% of the flow moving around, and not through the comb. This allows a potential saving of tens of percents in wing weight. Parametric results for number of rods, rod density (ratio of inter-rod distance to rod length) and slenderness ratio are presented demonstrating the dependence of the flow field on the configuration. It is found that 50–80 rods are required to approach the asymptotic limit of large number of rods, for various combinations of rod parameters with inter-rod distances of order of the cross-section diameter.

The effect of permeability on the flow past permeable disks at low Reynolds numbers

“…25 In some organisms, for example, the function of the recirculating wake may be for food capture; 26 other organisms, such as small flying insects, have evolved highly porous wings, which weigh much less than an impervious wing but with little loss in aerodynamic function. 10,27 The objective of the present study is to characterize the steady flow past a permeable circular disk. We will examine the low-Re flow past a permeable disk for a range of permeabilities (characterized by the disk's Darcy number).…”

“…These wings supply 90% of the force produced by an impervious wing but weigh about 10% of such a wing. 10 The drag force experienced by permeable bodies such as permeable spheres 3 and permeable cylinders 4,11 can also exceed that of an equivalent impervious body.…”

Bristles reduce the force required to ‘fling’ wings apart in the smallest insects

“…The fluid dynamics of flow through bristled appendages similar to those on the wings of small insects has been explored with physical (Loudon et al, 1994;Sunada et al, 2002), analytical (Cheer and Koehl, 1987;Koehl,1993) and numerical models (Barta and Weihs, 2006;Weihs and Barta, 2008;Barta, 2011;Davidi and Weihs, 2012). Previous analytical studies, however, have only considered cases with 2-4 bristles, and most numerical studies have assumed Stokes flow and did not consider wing-wing interactions.…”

Characteristic evaluation of a bristled wing using mechanical models of a thrips wings with MEMS piezoresistive cantilevers

“…A number of studies have been performed to estimate the aerodynamic forces acting on bristled wings of a thrips to understand the aerodynamic mechanism behind a thrips' flight. These studies have mainly been performed using theoretical analyses (Weihs and Barta, 2008, Davidi and Weihs, 2012, Shawn et al, 2013, Barta and Weihs, 2006 and large-scale robotic wings (Sunada et al, 2002, Sunada et al, 2003. In computational studies, the aerodynamic forces were calculated by theoretical models based on simple arrayed rods.…”