In order to understand the effects of inertia and gravity on draw resonance and on the physical mechanism of draw resonance in three-dimensional Newtonian film casting, a linear stability analysis has been conducted. An eigenvalue problem resulting from the linear stability analysis is formulated and solved as a nonlinear two-point boundary value problem to determine the critical draw ratios. Neutral stability curves are plotted to separate the stable/unstable domain in different appropriate parameter spaces. Both inertia and gravity stabilize the process and the process is more unstable to two- than to three-dimensional disturbances. The effects of inertia and gravity on the physical mechanism of draw resonance have been investigated using the eigenfunctions from the eigenvalue problem. A new approach is introduced in order to evaluate the traveling times of kinematic waves from the perturbed thickness at the take-up, which satisfies the same stability criterion illustrating the general stability of the system.
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October 2012
Multiphase Flows
Three Dimensional Film Stability and Draw Resonance
Zahir U. Ahmed,
Zahir U. Ahmed
Department of Mechanical Engineering, Khulna University of Engineering and Technology
, Khulna, 9203, Bangladesh
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Roger E. Khayat
e-mail: rkhayat@eng.uwo.ca
Roger E. Khayat
Department of Mechanical and Materials Engineering, University of Western Ontario
, London, ON, N6A 5B9, Canada
Search for other works by this author on:
Zahir U. Ahmed
Department of Mechanical Engineering, Khulna University of Engineering and Technology
, Khulna, 9203, Bangladesh
Roger E. Khayat
Department of Mechanical and Materials Engineering, University of Western Ontario
, London, ON, N6A 5B9, Canada
e-mail: rkhayat@eng.uwo.ca
J. Fluids Eng. Oct 2012, 134(10): 101302 (11 pages)
Published Online: September 28, 2012
Article history
Received:
November 20, 2011
Revised:
June 5, 2012
Published:
September 24, 2012
Online:
September 28, 2012
Citation
Ahmed, Z. U., and Khayat, R. E. (September 28, 2012). "Three Dimensional Film Stability and Draw Resonance." ASME. J. Fluids Eng. October 2012; 134(10): 101302. https://doi.org/10.1115/1.4007384
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