arXiv subjects

Manuel Wieland

Publications and source records attributed to Manuel Wieland.

5 recordsLinked to original sources

arXiv2019

Modeling and Simulation of Curved Fibers in Dry Spinning Scenarios

Dry spinning is characterized by the simultaneous production of multiple thin polymeric fibers in airflows and the evaporation of the solvent contained in these fibers. This involves fiber-air interactions as well as radial diffusion effects over the fiber cross-sections. Recent models for fibers in such production processes assume the fiber curves to be strictly uni-axial. But there are industrial setups showing airflow induced lateral movements of the fibers which creates the need for curved fiber models. In this paper we present a special Cosserat rod model that describes curved fibers in such dry spinning processes. Adapting the efficient simulation framework from the uni-axial fiber setting makes the simulation of industrial setups for multiple curved fibers with two-way coupled airflows possible, for which we present results for the first time in literature.

physics.app-ph↗

arXiv2019

Melt-Blowing of Viscoelastic Jets in Turbulent Airflows: Stochastic Modeling and Simulation

In melt-blowing processes mico- and nanofibers are produced by the extrusion of polymeric jets into a directed, turbulent high-speed airflow. Up to now the physical mechanism for the drastic jet thinning is not fully understood, since in the existing literature the numerically computed/predicted fiber thickness differs several orders of magnitude from those experimentally measured. Recent works suggest that this discrepancy might arise from the neglect of the turbulent aerodynamic fluctuations in the simulations. In this paper we confirm this suggestion numerically. Due to the complexity of the process direct numerical simulations of the multiscale-multiphase problem are not possible. Hence, we develop a numerical framework for a growing fiber in turbulent air that makes the simulation of industrial setups feasible. For this purpose we employ an asymptotic viscoelastic model for the fiber. The turbulent effects are taken into account by a stochastic aerodynamic force model where the underlying velocity fluctuations are reconstructed from a $k$-$ε$ turbulence description of the airflow. Our numerical results show the significance of the turbulence on the jet thinning and give fiber diameters of realistic order of magnitude.

physics.flu-dyn↗

arXiv2018

An Efficient Numerical Framework for Fiber Spinning Scenarios with Evaporation Effects in Airflows

In many spinning processes, as for example in dry spinning, solvent evaporates out of the spun jets and leads to thinning and solidification of the produced fibers. Such production processes are significantly driven by the interaction of the fibers with the surrounding airflow. Faced with industrial applications producing up to several hundred fibers simultaneously, the direct numerical simulation of the three-dimensional multiphase, multiscale problem is computationally extremely demanding and thus in general not possible. In this paper, we hence propose a dimensionally reduced, efficiently evaluable fiber model that enables the realization of fiber-air interactions in a two-way coupling with airflow computations. For viscous dry spinning of an uni-axial two-phase flow, we deduce one-dimensional equations for fiber velocity and stress from cross-sectional averaging and combine them with two-dimensional advection-diffusion equations for polymer mass fraction and temperature revealing the radial effects that are observably present in experiments. For the numerical treatment of the resulting parametric boundary value problem composed of one-dimensional ordinary differential equations and two-dimensional partial differential equations we develop an iterative coupling algorithm. Thereby, the solution of the advection-diffusion equations is implicitly given in terms of Green's functions and leads for the surface values to Volterra integral equations of second kind with singular kernel, which we can solve very efficiently by the product integration method. For the ordinary differential equations a suitable collocation-continuation procedure is presented. Compared with the referential solution of a three-dimensional setting, the numerical results are very convincing. They provide a good approximation while drastically reducing the computational time.

physics.flu-dyn↗

arXiv2018

FESTUNG: A MATLAB / GNU Octave toolbox for the discontinuous Galerkin method. Part II: Advection operator and slope limiting

This is the second in a series of papers on implementing a discontinuous Galerkin (DG) method as an open source Matlab / GNU Octave toolbox. The intention of this ongoing project is to offer a rapid prototyping package for application development using DG methods. The implementation relies on fully vectorized matrix / vector operations and is comprehensively documented. Particular attention was paid to maintaining a direct mapping between discretization terms and code routines as well as to supporting the full code functionality in GNU Octave. The present work focuses on a two-dimensional time-dependent linear advection equation with space / time-varying coefficients, and provides a general order implementation of several slope limiting schemes for the DG method.

math.NA↗

arXiv2017

Whipping of electrified visco-capillary jets in airflows

An electrified visco-capillary jet shows different dynamic behavior, such as cone forming, breakage into droplets, whipping and coiling, depending on the considered parameter regime. The whipping instability that is of fundamental importance for electrospinning has been approached by means of stability analysis in previous papers. In this work we alternatively propose a model framework in which the instability can be computed straightforwardly as the stable stationary solution of an asymptotic Cosserat rod description. For this purpose, we adopt a procedure by Ribe (Proc. Roy. Soc. Lond. A, 2004) describing the jet dynamics with respect to a frame rotating with the a priori unknown whipping frequency that itself becomes part of the solution. The rod model allows for stretching, bending and torsion, taking into account inertia, viscosity, surface tension, electric field and air drag. For the resulting parametric boundary value problem of ordinary differential equations we present a continuation-collocation method. On top of an implicit Runge-Kutta scheme of fifth order, our developed continuation procedure makes the efficient and robust simulation and navigation through a high-dimensional parameter space possible. Despite the simplicity of the employed electric force model the numerical results are convincing, the whipping effect is qualitatively well characterized.

physics.flu-dyn↗