Abstract
We examine two dimensional properties of vortex shedding past elliptical cylinders through numerical simulations. Specifically, we investigate the vortex formation length in the Reynolds number regime 10 to 100 for elliptical bodies of aspect ratio in the range 0.4 to 1.4. Our computations reveal that in the steady flow regime, the change in the vortex length follows a linear profile with respect to the Reynolds number, while in the unsteady regime, the time averaged vortex length decreases in an exponential manner with increasing Reynolds number. The transition in profile is used to identify the critical Reynolds number which marks the bifurcation of the Karman vortex from steady symmetric to the unsteady, asymmetric configuration. Additionally, relationships between the vortex length and aspect ratio are also explored. The work presented here is an example of a module that can be used in a project based learning course on computational fluid dynamics.
Highlights
Vortex development in a fluid’s flow is a highly nonlinear phenomenon which goes through multiple bifurcations
The rising trend is similar for both criteria employed to measure the vortex length
Our overall computations and qualitative profiles are in agreement with previous experimental results [24], where measurements of variations in vortex length were made through flow visualization and imaging techniques of flow past various cylinders in a flow tank
Summary
Vortex development in a fluid’s flow is a highly nonlinear phenomenon which goes through multiple bifurcations. There are simple ways to talk about vortex development by combining qualitative and quantitative approaches that go beyond examining classical images or the use of sophisticated particle image velocimetry (PIV) techniques. We introduce one such method of talking about the physics of vortex development in this paper, which can be used in the form of a lesson plan for a lecture or to motivate computational projects in more advanced classes in fluids. Instructional methods related to PBL promote a more inductive approach to learning whereby generalizations and abstractions follow from first understanding specific cases [1].
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