Nicole Marheineke

Fiber Dynamics in Turbulent Flows: General Modeling Framework

The paper at hand deals with the modeling of turbulence effects on the dynamics of a long slender elastic fiber. Independent of the choice of the drag model, a general aerodynamic force concept is derived on the basis of the velocity field for the randomly fluctuating component of the flow. Its construction as a centered differentiable Gaussian field complies thereby with the requirements of the stochastic k-epsilon turbulence model and Kolmogorovs universal equilibrium theory on local isotropy.

Asymptotic model for the dynamics of curved viscous fibres with surface tension

In this paper, we derive and investigate an asymptotic model for the dynamics of curved viscous inertial Newtonian fibres subjected to surface tension, as they occur in rotational spinning processes. Accordingly, we extend the slender body theory of Panda, Marheineke & Wegener ( Math. Meth. Appl. Sci ., vol. 31, 2008, p. 1153) by including surface tension and deducing boundary conditions for the free end of the fibre. The asymptotic model accounts for the inner viscous transport and places no restrictions on either the motion or the shape of the fibre centreline. Depending on the capillary number, the boundary conditions yield an explicit description for the temporal evolution of the fibre end. We study numerically the behaviour of the fibre as a function of the effects of viscosity, gravity, rotation and surface tension.

A Stochastic Model and Associated Fokker–Planck Equation for the Fiber Lay-Down Process in Nonwoven Production Processes

In this paper we present and investigate a stochastic model and its associated Fokker–Planck equation for the lay-down of fibers on a conveyor belt in the production process of nonwoven materials. The model is based on a stochastic differential equation taking into account the motion of the fiber under the influence of turbulence. A reformulation as a stochastic Hamiltonian system and an application of the stochastic averaging theorem lead to further simplifications of the model. Finally, the model is used to compute the distribution of functionals of the process that are important for the quality assessment of industrial fabrics.

NUMERICAL ANALYSIS OF COSSERAT ROD AND STRING MODELS FOR VISCOUS JETS IN ROTATIONAL SPINNING PROCESSES

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.,18 in the incompressibility approximation and reduces to the string model of Marheineke and Wegener13 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 jets 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 Gotz et al.10 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.

Hydrodynamic Limit of a Fokker–Planck Equation Describing Fiber Lay-Down Processes

In this paper, a stochastic model for the turbulent fiber lay-down in the industrial production of nonwoven materials is extended by including a moving conveyor belt. In the hydrodynamic limit corr...

Fiber Dynamics in Turbulent Flows: Specific Taylor Drag

In [N. Marheineke and R. Wegener, SIAM J. Appl. Math., 66 (2006), pp. 1703–1726], an aerodynamic force concept for a general air drag model based on a stochastic k-

Asymptotic transition from Cosserat rod to string models for curved viscous inertial jets

\epsilon

Finite volume approach for the instationary Cosserat rod model describing the spinning of viscous jets

description for a turbulent flow field is derived. The turbulence effects on the dynamics of a long, slender, elastic fiber are specifically modeled by a correlated random Gaussian force and in its asymptotic limit on a macroscopic fiber scale by Gaussian white noise with flow-dependent amplitude. The present paper states quantitative similarity estimates and numerical comparisons for the choice of a Taylor drag model in a given application.

Random Field Sampling for a Simplified Model of Melt-Blowing Considering Turbulent Velocity Fluctuations

This work deals with the modeling and simulation of slender viscous jets exposed to gravity and rotation, as they occur in rotational spinning processes. In terms of slender-body theory, we show the asymptotic reduction of a viscous Cosserat rod to a string system for vanishing slenderness parameter. We propose two string models, i.e. inertial and viscous-inertial string models, that differ in the closure conditions and hence yield a boundary value problem and an interface problem, respectively. We investigate the existence regimes of the string models in the four-parametric space of Froude, Rossby, Reynolds numbers and jet length. The convergence regimes where the respective string solution is the asymptotic limit to the rod turn out to be disjoint and to cover nearly the whole parameter space. We explore the transition hyperplane and derive analytically low and high Reynolds number limits. Numerical studies of the stationary jet behavior for different parameter ranges complete the work.

On a nonlinear partial differential algebraic system arising in the technical textile industry: analysis and numerics

The spinning of slender viscous jets can be asymptotically described by one-dimensional models that consist of systems of partial and ordinary differential equations. Whereas well-established string models only possess solutions for certain choices of parameters and configurations, the more sophisticated rod model is not limited by restrictions. It can be considered as an ?-regularized string model, but containing the slenderness ratio ? in the equations complicates its numerical treatment. We develop numerical schemes for fixed or enlarging (time-dependent) domains, using a finite volume approach in space with mixed central, up- and down-winded differences and stiffly accurate Radau methods for the time integration. For the first time, results of instationary simulations for a fixed or growing jet in a rotational spinning process are presented for arbitrary parameter ranges.