Unsteady aerodynamics of a model bristled wing in rapid acceleration motion

Abstract

Tiny insects with bristled wings perform the “rowing” motion: the wings accelerate rapidly from zero-velocity to certain reference velocity at 90° angle-of-attack, and the drag produced in this motion provides the weight-supporting force. A flat-plate wing will produce a large drag in such a motion, but it is unknown whether a bristled wing could do so. Here, we study this problem using numerical simulation and simple model wings. The acceleration is large: the wing translates only about half the wing chord length to reach the reference velocity. The following is shown. The bristled wing can produce a very large unsteady drag peak and large time-averaged drag as a flat-plate wing does; the time-averaged drag is about 2.5 times as large as the quasi-steady value. The force production mechanisms are different between the two wings: for the flat-plate wing, because of the large acceleration, the added-mass and the strong free vorticity in the flow produce a large pressure difference between the windward and leeward surfaces of the plate, resulting in large drag (surface frictional force has negligible contribution). Yet for the bristled wing, although the acceleration of the wing is large, a bristle needs to translate about 80 diameters to reach the reference velocity; thus, the effect of acceleration is very weak. Each bristle operates in a quasi-steady Stokes flow and the large drag of the bristled wing is due to the very large surface pressure and frictional forces on each bristle, generated by the strong viscous effect of the Stokes flow (the drag is equally contributed by the surface pressure and frictional forces).

Aerodynamics of two parallel bristled wings in low Reynolds number flow

“…SimpleFoam uses the classic SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm to calculate the coupling of pressure and velocity. Detailed description of the simpleFoam solver can be found in our previous studies 12 , 13 .…”

“…2 ). Similar to the grid of the single bristled wing 12 , 13 , each cylinder has a body-fitted, O-type sub-grid on the wall. The layer number of the sub-grid is 31, and the thickness of the innermost layer of it is 0.0001 c .…”

“…For the grid of two flat-plate wings, there is a body-fitted H-type grid between two flat-plate wings, and an O-type grid with a radius of 60c is constructed for the rest of the fluid domain. For comparison, the cases of a single bristled wing and a single flat-plate wing are also calculated, and their grids are the same as those of the previous www.nature.com/scientificreports/ studies 12,13 . In order to verify the grid-independence of the calculation results, we conducted a grid density test and finally determined the grid cell number of two bristled wings to be about 1 × 10 6 and the grid cell number of two flat-plate wings to be 6 × 10 5 .…”

“…Recently, Wu et al . 13 showed that when conducting fast acceleration motion, the bristled wing could produce a large aerodynamic force similar to that of a membrane wing; however, unlike the membrane wing that rely on unsteady effect to generate aerodynamic forces, the aerodynamic forces generated by the bristled wing are formed by the superposition of large drag forces produced by each bristle on the quasi-steady Stokes flow.…”

“…By carefully analyzing the flow structure of each bristle on the bristled wings, Wu et al 12 showed that the aerodynamic force production mechanisms of the bristled wings and the membrane wings are different; the aerodynamic force generation of the bristled wings is due to the large surface friction and surface pressure on each bristle in Stokes flow. Recently, Wu et al 13 showed that when conducting fast acceleration motion, the bristled wing could produce a large aerodynamic force similar to that of a membrane wing; however, unlike the membrane wing that rely on unsteady effect to generate aerodynamic forces, the aerodynamic forces generated by the bristled wing are formed by the superposition of large drag forces produced by each bristle on the quasi-steady Stokes flow.…”