Numerical analysis of Cosserat rod and string models for viscous jets in rotational spinning processes

Arne W, Marheineke N, Meister A, Wegener R (2010)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2010

Journal

Mathematical Models & Methods in Applied Sciences World Scientific Publishing

Publisher: World Scientific Publishing

Book Volume: 20

Pages Range: 1941-1965

Journal Issue: 10

DOI: 10.1142/S0218202510004738

Abstract

This work deals with the curling behavior of slender viscous jets in rotational spinning processes. In terms of slender-body theory, an instationary incompressible viscous Cosserat rod model is formulated which differs from the approach of Ribe et al., in the incompressibility approximation and reduces to the string model of Marheineke and Wegener for a vanishing slenderness parameter. Focusing exclusively on viscous and rotational effects on the jet in the exit plane near the spinning nozzle, the stationary two-dimensional scenario is described by a two-point boundary value problem of a system of first-order ordinary differential equations for jet's center-line, tangent, curvature, velocity, inner shear and traction force and couple. The numerical analysis shows that the rod model covers the string model in an inertia-dominated jet regime. Beyond that it overcomes the limitations of the string model studied by Götz et al. and enables even the handling of the viscous-inertial jet regime. Thus, the rod model shows its applicability for the simulation of industrially relevant parameter ranges and enlarges the domain of validity with respect to the string approach. © 2010 World Scientific Publishing Company.

Authors with CRIS profile

Nicole Marheineke Professur für Wissenschaftliches Rechnen

Involved external institutions

Fraunhofer-Institut für Techno- und Wirtschaftsmathematik (ITWM) / Fraunhofer Institute for Industrial Mathematics DE Germany (DE) Universität Kassel DE Germany (DE)

How to cite

APA:

Arne, W., Marheineke, N., Meister, A., & Wegener, R. (2010). Numerical analysis of Cosserat rod and string models for viscous jets in rotational spinning processes. Mathematical Models & Methods in Applied Sciences, 20(10), 1941-1965. https://doi.org/10.1142/S0218202510004738

MLA:

Arne, Walter, et al. "Numerical analysis of Cosserat rod and string models for viscous jets in rotational spinning processes." Mathematical Models & Methods in Applied Sciences 20.10 (2010): 1941-1965.

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