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Journal of Mathematics in Industry (2011) 1:2 DOI 10.1186/2190-5983-1-2 R E S E R AC H Open

Journal of Mathematics in Industry (2011) 1:2 DOI 10.1186/2190-5983-1-2 R E S E R AC H Open Access Fluid-fiber-interactions in rotational spinning process of glass wool production Walter Arne · Nicole Marheineke · Johannes Schnebele · Raimund Wegener Received: 9 December 2010 / Accepted: 3 June 2011 / Published online: 3 June 2011 © 2011 Arne et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License Abstract The optimal design of rotational production processes for glass wool manufacturing poses severe computational challenges to mathematicians, natural scientists and engineers. In this paper we focus exclusively. | Journal of Mathematics in Industry 2011 1 2 DOI 10.1186 2190-5983-1-2 Journal of Mathematics in Industry a SpringerOpen Journal RESERACH Open Access Fluid-fiber-interactions in rotational spinning process of glass wool production Walter Arne Nicole Marheineke Johannes Schnebele Raimund Wegener Received 9 December 2010 Accepted 3 June 2011 Published online 3 June 2011 2011 Arne et al. licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License Abstract The optimal design of rotational production processes for glass wool manufacturing poses severe computational challenges to mathematicians natural scientists and engineers. In this paper we focus exclusively on the spinning regime where thousands of viscous thermal glass jets are formed by fast air streams. Homogeneity and slenderness of the spun fibers are the quality features of the final fabric. Their prediction requires the computation of the fluid-fiber-interactions which involves the solving of a complex three-dimensional multiphase problem with appropriate interface conditions. But this is practically impossible due to the needed high resolution and adaptive grid refinement. Therefore we propose an asymptotic coupling concept. Treating the glass jets as viscous thermal Cosserat rods we tackle the multiscale problem by help of momentum drag and heat exchange models that are derived on basis of slender-body theory and homogenization. A weak iterative coupling algorithm that is based on the combination of commercial software and self-implemented code for W Arne J Schnebele R Wegener Fraunhofer Institut fur Techno- und Wirtschaftsmathematik Fraunhofer Platz 1 D-67663 Kaiserslautern Germany J Schnebele e-mail johannes.schnebele@itwm.fraunhofer.de R Wegener e-mail raimund.wegener@itwm.fraunhofer.de W Arne Fachbereich Mathematik und Naturwissenschaften Universitat Kassel Heinrich Plett Str. 40 D-34132 Kassel Germany e-mail arne@mathematik.uni-kassel.de N .