Characteristics of Three-dimensional Vortex Formation and Propulsive Performance in Flapping Locomotion

Citation

Kim, Daegyoum (2010) Characteristics of Three-dimensional Vortex Formation and Propulsive Performance in Flapping Locomotion. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8VZJ-7Z78. https://resolver.caltech.edu/CaltechTHESIS:06072010-114858790

Abstract

Three-dimensional vortex formation and propulsive performance were studied experimentally to identify some of the main characteristic mechanisms of flapping locomotion. Mechanical models with thin plates were used to simulate flapping and translating motions of animal propulsors. Three-dimensional flow fields were mapped quantitatively using defocusing digital particle image velocimetry.

First, vortex structures made by impulsively translating low aspect-ratio plates were studied. The investigation of translating plates with a 90 degree angle of attack is important since it is a fundamental model for a better understanding of drag-based propulsion systems. Rectangular flat-rigid, flexible, and curved-rigid thin plastic plates with the same aspect ratio were used to compare their vortex structures and hydrodynamic forces. The interaction of the tip flow and the nearby vortex is a critical flow phenomenon to distinguish vortex patterns among these three cases. In the flexible plate case, slow development of the vortex structure causes a small initial peak in hydrodynamic force during the acceleration phase. However, after the initial peak, the flexible plate generates large force magnitude comparable to that of the flat-rigid plate case.

Drag-based paddling propulsion was also studied to explain some of the fundamental differences in vortex formation of lift-based and drag-based propulsions. While the temporal change of the inner area enclosed by the vortex loop is an important factor in thrust generation of lift-based propulsion, the temporal change of the vortex strength becomes more important in drag-based propulsion. Spanwise flow behind the paddling plate plays an important role in tip vortex motion and thrust generation. The distribution of spanwise flow depends on the propulsor shape and the Reynolds number. A delta-shaped propulsor generates strong spanwise flow compared to a rectangular propulsor. For the low Reynolds number case, the spanwise flow is not as strong as that of the high Reynolds number case. The flexible propulsor can smooth out force peaks during impulsive motions without sacrificing total impulse, which is advantageous in avoiding structural failures and stabilizing body motion. The role of the stopping vortex was addressed in optimizing a stroke angle of paddling animals.

In addition, vortex formation of clapping propulsion was investigated by varying aspect ratio and stroke angle. A low aspect-ratio propulsor produces larger total impulse than a high aspect-ratio propulsor. As the aspect ratio increases, circulation of the vortex is strengthened, and the inner area enclosed by the vortex structure tends to enlarge. Moreover, in terms of thrust, the advantage of a single plate over double clapping plates is larger for the lower aspect-ratio case. These results offer information to better understand the benefit of low aspect-ratio wings in force generation under specific locomotion modes. When a pair of plates claps, a vortex loop forms from two counter-rotating tip vortices by a reconnection process. The dynamics of wake structures are dependent on the aspect ratio and the stroke angle.

Vortex formation and vorticity transport processes of translating and rotating plates with a 45 degree angle of attack were investigated as well. In both translating and rotating cases, the spanwise flow over the plate and the vorticity tilting process inside the leading-edge vortex were observed. The distribution of spanwise flow is a prominent distinction between the vortex structures of these two cases. While spanwise flow is confined inside the leading-edge vortex for the translating case, it is widely present over the plate and the wake region of the rotating case. As the Reynolds number decreases, due to the increase in viscosity, leading-edge and tip vortices tend to spread inside the area swept by the rotating plate, which results in lower lift force generation.

Lastly, for translating motion, the dynamics of the vortex in corner regions was compared among three different corner shapes. For a large corner angle, the forward movement of the vortex tends to be uniform along the plate edges. However, for a small corner angle, the vortex close to the corner moves forward following the plate while the vortex away from the corner retards its forward movement.

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