Fluid-fiber-interactions in rotational spinning process of glass wool production

Abstract

The optimal design of rotational production processes for glass wool manufacturing poses severe computational challenges to mathematicians, natural scientists and engineers. In this paper we focus exclusively on the spinning regime where thousands of viscous thermal glass jets are formed by fast air streams. Homogeneity and slenderness of the spun fibers are the quality features of the final fabric. Their prediction requires the computation of the fluid-fiber-interactions which involves the solving of a complex three-dimensional multiphase problem with appropriate interface conditions. But this is practically impossible due to the needed high resolution and adaptive grid refinement. Therefore, we propose an asymptotic coupling concept. Treating the glass jets as viscous thermal Cosserat rods, we tackle the multiscale problem by help of momentum (drag) and heat exchange models that are derived on basis of slender-body theory and homogenization. A weak iterative coupling algorithm that is based on the combination of commercial software and self-implemented code for flow and rod solvers, respectively, makes then the simulation of the industrial process possible. For the boundary value problem of the rod we particularly suggest an adapted collocation-continuation method. Consequently, this work establishes a promising basis for future optimization strategies.

Geometrically exact Cosserat rods with Kelvin–Voigt type viscous damping

“…Klar et al (2009) and Arne et al (2011) likewise use Ribe's Maxwell type constitutive law in their related work on the simulation of viscous fibers aiming at applications in the area of textile and nonwoven production. Lorenz et al (2012) extend constitutive modelling for viscous strings by deriving an upper convected Maxwell model using mathematical methods of asymptotic analysis.…”

Melt-blowing of viscoelastic jets in turbulent airflows: Stochastic modeling and simulation

“…System 8 is a boundary value problem of ordinary differential equations of first order on a fixed domain. For its numerical solution we employ the continuation-collocation method, which has been used successfully in [2,3,31]. The collocation method is a three-stage Lobatto IIIa formula, see, e.g., [15].…”

“…3 shows the results for scalar speed u, stress σ, pressure p and temperature T as well as the induced elongation e of the steady viscous uni-axial fiber model in an Eulerian parameterization…”

Fiber spinnability of glass melts

“…However, the required high temperature makes the fiberizing devices suffer from intensive corrosion, which shortens their operational lifetime. Cascade process has been modelled by using the finite element simulation, providing valuable information on the optimum conditions of the cascade process of stone wool fiber spinning …”

“…Cascade process has been modelled by using the finite element simulation, providing valuable information on the optimum conditions of the cascade process of stone wool fiber spinning. [5][6][7][8][9] This work also contributes to stabilization of fiber spinning process by properly modifying processing parameters in response to the variation of fiber spinnability of melts as a result of compositional variation. The mechanical, thermal and optical properties of glass fibers can dramatically be changed by variation in the process parameters such as fiber stretching force, melt flow, cooling rate, viscosity, and heat-treatment.…”