TY - RPRT
A1 - Götz, Th.
A1 - Klar, A.
A1 - Unterreiter, A.
A1 - Wegener, R.
T1 - Numerical evidance for the non-existing of solutions of the equations desribing rotational fiber spinning
N2 - 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.
T3 - Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) - 108
KW - Rotational Fiber Spinning
KW - Viscous Fibers
KW - Boundary Value Problem
KW - Existence of Solutions
Y1 - 2007
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1961
UR - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hbz:386-kluedo-15291
ER -