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The Flow of A Falling Ellipse: Numerical Method and Classification

Published online by Cambridge University Press:  20 August 2015

R.-J. Wu  and
S.-Y. Lin
R.-J. Wu
Affiliation:
Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan
S.-Y. Lin*
Affiliation:
Department of Aeronautics and Astronautics, National Cheng Kung University, Tainan, Taiwan
*
* Corresponding author ([email protected])
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Abstract

A modified direct-forcing immersed-boundary (IB) pressure correction method is developed to simulate the flows of a falling ellipse. The pressure correct method is used to solve the solutions of the two dimensional Navier-Stokes equations and a direct-forcing IB method is used to handle the interaction between the flow and falling ellipse. For a fixed aspect ratio of an ellipse, the types of the behavior of the falling ellipse can be classified as three pure motions: Steady falling, fluttering, tumbling, and two transition motions: Chaos, transition between steady falling and fluttering. Based on two dimensionless parameters, Reynolds number and the dimensionless moment of inertia, a Reynolds number-inertia moment phase diagram is established. The behaviors and characters of five falling regimes are described in detailed.

Keywords

Falling ellipsePressure correction methodFlutteringTumbling
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 6 , December 2015 , pp. 771 - 782
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

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