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Experimental investigation of freely falling thin disks. Part 2. Transition of three-dimensional motion from zigzag to spiral

Published online by Cambridge University Press:  30 August 2013

Cunbiao Lee*
Affiliation:
State Key Laboratory for Turbulence and Complex System, College of Engineering, Peking University, Beijing, 100871, China
Zhuang Su
Affiliation:
State Key Laboratory for Turbulence and Complex System, College of Engineering, Peking University, Beijing, 100871, China
Hongjie Zhong
Affiliation:
State Key Laboratory for Turbulence and Complex System, College of Engineering, Peking University, Beijing, 100871, China
Shiyi Chen
Affiliation:
State Key Laboratory for Turbulence and Complex System, College of Engineering, Peking University, Beijing, 100871, China
Mingde Zhou
Affiliation:
State Key Laboratory for Turbulence and Complex System, College of Engineering, Peking University, Beijing, 100871, China
Jiezhi Wu
Affiliation:
State Key Laboratory for Turbulence and Complex System, College of Engineering, Peking University, Beijing, 100871, China
*
Email address for correspondence: cblee@mech.pku.edu.cn

Abstract

The free-fall motion of a thin disk with small dimensionless moments of inertia (${I}^{\ast } \lt 1{0}^{- 3} $) was investigated experimentally. The transition from two-dimensional zigzag motion to three-dimensional spiral motion occurs due to the growth of three-dimensional disturbances. Oscillations in the direction normal to the zigzag plane increase with the development of this instability. At the same time, the oscillation of the nutation angle decreases to zero and the angle remains constant. The effects of initial conditions (release angle) were investigated. Two kinds of transition modes, zigzag–spiral transition and zigzag–spiral–zigzag intermittence transition, were observed to be separated by a critical Reynolds number. In addition, the solution of the generalized Kirchhoff equations shows that the small ${I}^{\ast } $ is responsible for the growth of disturbances in the third dimension (perpendicular to the planar motion).

Type
Papers
Copyright
©2013 Cambridge University Press 

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