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Nonlinear stability of Newtonian fibres

Published online by Cambridge University Press:  20 April 2006

William W. Schultz ,
Abdelfattah Zebib ,
Stephen H. Davis  and
Yee Lee
William W. Schultz
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University
Abdelfattah Zebib
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University
Stephen H. Davis
Affiliation:
Department of Applied Mathematics and Engineering Sciences, Northwestern University
Yee Lee
Affiliation:
Owens-Corning Fiberglas Corporation, Granville, Ohio
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Abstract

The stability of steady isothermal flow of one-dimensional Newtonian fibres is considered. Bifurcation theory yields a stable supercritical Hopf bifurcation, with frequency decreasing for increasing winder speeds near the critical winder speed. A new Chebyshev expansion procedure is used with time-marching to obtain accurate numerical solutions valid far from the critical point. Our numerical solution agrees well with our analytical solution near the critical winder speed, but differs significantly from those of previous numerical models. There is qualitative agreement with a previous isothermal experiment for oscillation amplitude but not for oscillation frequency. These comparisons are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 149 , December 1984 , pp. 455 - 475
Copyright
© 1984 Cambridge University Press

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