A Numerical method for the Viscoelastic Melt Spinning Model with Radial resolutions of Temperature and Stress Fields

Abstract

A numerical method to compute the viscoelastic melt-spinning model with radial resolutions of temperature and stress fields is formulated and applied to the low speed range. The starting framework is the reduction of the complete continuous model into both the perturbed two-dimensional model and the perturbed average model obtained from a first-order regular perturbation analysis available in the literature. The polymer rheology is described with the nonisothermal Phan-Thien and Tanner and Giesekus constitutive equations. By using the implicit tridiagonal scheme of finite differences coupled to the fourth-order Runge−Kutta method, an iterative numerical algorithm is proposed for the computation of the coupled balance equations. The temperature and stress fields in the filament as functions of axial and radial positions are obtained for a well-refined mesh and with high numerical precision. The numerical algorithm considers the appropriate interplay between axial and radial varying temperature and stress fields and the rigorous averaged balances of momentum and energy and averaged constitutive equation. The development of a skin-core structure is predicted with the two rheological models.