## The Dynamics of Viscous Fibers

• This work deals with the mathematical modeling and numerical simulation of the dynamics of a curved inertial viscous Newtonian fiber, which is practically applicable to the description of centrifugal spinning processes of glass wool. Neglecting surface tension and temperature dependence, the fiber flow is modeled as a three-dimensional free boundary value problem via instationary incompressible Navier-Stokes equations. From regular asymptotic expansions in powers of the slenderness parameter leading-order balance laws for mass (cross-section) and momentum are derived that combine the unrestricted motion of the fiber center-line with the inner viscous transport. The physically reasonable form of the one-dimensional fiber model results thereby from the introduction of the intrinsic velocity that characterizes the convective terms. For the numerical simulation of the derived model a finite volume code is developed. The results of the numerical scheme for high Reynolds numbers are validated by comparing them with the analytical solution of the inviscid problem. Moreover, the influence of parameters, like viscosity and rotation on the fiber dynamics are investigated. Finally, an application based on industrial data is performed.
• Dynamik viskoser Fäden

Author: Satyananda Panda urn:nbn:de:hbz:386-kluedo-19408 Axel Klar Doctoral Thesis English 2006 2006 Technische Universität Kaiserslautern Technische Universität Kaiserslautern 2006/03/21 2006/03/27 "Slender-Body"-Theorie; Gebogener viskoser Faden; StrömungsdynamikCurved viscous fibers; Fluid dynamics; Slender body theory Asymptotik ; Faden; Mathematisches Modell Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 30-XX FUNCTIONS OF A COMPLEX VARIABLE (For analysis on manifolds, see 58-XX) / 30Exx Miscellaneous topics of analysis in the complex domain / 30E25 Boundary value problems [See also 45Exx] 41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15] 76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX) / 76Dxx Incompressible viscous fluids / 76D05 Navier-Stokes equations [See also 35Q30] Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

$Rev: 13581$