Asymptotic transition from Cosserat rod to string models for curved viscous inertial jets

  • This work deals with the modeling and simulation of slender viscous jets exposed to gravity and rotation, as they occur in rotational spinning processes. In terms of slender-body theory we show the asymptotic reduction of a viscous Cosserat rod to a string system for vanishing slenderness parameter. We propose two string models, i.e. inertial and viscous-inertial string models, that differ in the closure conditions and hence yield a boundary value problem and an interface problem, respectively. We investigate the existence regimes of the string models in the four-parametric space of Froude, Rossby, Reynolds numbers and jet length. The convergence regimes where the respective string solution is the asymptotic limit to the rod turn out to be disjoint and to cover nearly the whole parameter space. We explore the transition hyperplane and derive analytically low and high Reynolds number limits. Numerical studies of the stationary jet behavior for different parameter ranges complete the work.

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Metadaten
Author:W. Arne, N. Marheineke, R. Wegener
URN (permanent link):urn:nbn:de:hbz:386-kluedo-16607
Serie (Series number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (192)
Document Type:Report
Language of publication:English
Year of Completion:2010
Year of Publication:2010
Publishing Institute:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Tag:asymptotic limits ; boundary value problems; inertial and viscous-inertial fiber regimes ; rotational spinning processes ; slenderbody theory
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:510 Mathematik

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