Numerical evidance for the non-existing of solutions of the equations desribing rotational fiber spinning
- Abstract. The stationary, isothermal rotational spinning process of fibers is considered. The investigations are concerned with the case of large Reynolds (± = 3/Re ¿ 1) and small Rossby numbers (\\\" ¿ 1). Modelling the fibers as a Newtonian fluid and applying slender body approximations, the process is described by a two–point boundary value problem of ODEs. The involved quantities are the coordinates of the fiber’s centerline, the fluid velocity and viscous stress. The inviscid case ± = 0 is discussed as a reference case. For the viscous case ± > 0 numerical simulations are carried out. Transfering some properties of the inviscid limit to the viscous case, analytical bounds for the initial viscous stress of the fiber are obtained. A good agreement with the numerical results is found. These bounds give strong evidence, that for ± > 3\\\"2 no physical relevant solution can exist. A possible interpretation of the above coupling of ± and \\\" related to the die–swell phenomenon is given.
Author: | Th. Götz, A. Klar, A. Unterreiter, R. Wegener |
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URN: | urn:nbn:de:hbz:386-kluedo-15291 |
Series (Serial Number): | Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (108) |
Document Type: | Report |
Language of publication: | English |
Year of Completion: | 2007 |
Year of first Publication: | 2007 |
Publishing Institution: | Fraunhofer-Institut für Techno- und Wirtschaftsmathematik |
Creating Corporation: | Fraunhofer ITWM |
Date of the Publication (Server): | 2008/05/28 |
Tag: | Boundary Value Problem; Existence of Solutions; Rotational Fiber Spinning; Viscous Fibers |
Faculties / Organisational entities: | Fraunhofer (ITWM) |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |