Experiments in Vortex Formation of Flapping Flat Plates

The concept of formation parameter has been applied to flat plates with a constant plunge velocity profile and with a constantly accelerating plunge profile at several fixed pitch angles in an effort to apply the formation parameter more broadly. The inspiration for this work arose from the application of the formation parameter concept to 21 species of insect. The formation number for these insects was found to fall between 0.47 and 4.35, with the majority of insects falling in the range of 0.47 to 1.45. The two exceptions falling outside of this range, were the only insects with an aspect ratio larger than 10. To better understand this result, an investigation was subsequently conducted on thin flat plates with square edges. Three different aspect ratios were used; an infinite aspect ratio model was tested in pure plunge, while the aspect ratio 3 and 6 models were tested by flapping in a two-dimensional arc about the root of the semi-span. In all cases, both a constant velocity profile and quarter-sine velocity profile with average Reynolds number (Re) of 3,000 were used. Hinged flapping, as well as flapping a finite aspect ratio wing, greatly hinder the production of 2-d circulation, but does not reduce the physical size (area) of the vortices generated. Hinged flapping tests were also conducted on an aspect ratio 6 plate at Re 12,000. Flapping at this Reynolds number produced a similar amount of normalized circulation as well as physical size (area), as a function of formation time, compared to the Reynolds number 3000 data. Different results were obtained with different velocity profiles and aspect ratios, despite being at the same average Reynolds number and formation number. Nomenclature AR = Aspect ratio