Numerical simulation of the cast film process

Abstract

The cast film process is studied and a numerical simulation is performed using a finite element method. Two dimensional equations involving the thickness and a mean velocity are used by considering the film as a thin layer. The process is assumed to be isothermal between the die exit and the quick cooling on the chill roll. The width of the film is computed iteratively as a free surface problem by means of a finite element method. The thickness distribution of the film is obtained by a finite volume method. This approach allows modeling of the well known “dog‐bone” or “edge bead” defect with a reasonable computation time.

Optimal control of film casting processes

“…In this paper we consider the stationary three-dimensional Newtonian, isothermal model for the film casting process, derived earlier by Demay and co-workers [1,2,4] or in [3]. The geometry of the film casting process is shown in Figure 1.…”

“…In this thin film limit, we average the mass and momentum equations describing the polymer flow over the z-direction. This leads to the following reduced equations, see [1,2] ∇ · (eU ) = 0 (1a)…”

“…The question of minimizing our cost functional J(z, ϕ) belongs to the class of constrained optimization problem, where the cost functional (3) is minimized with respect to the constraint given by the state system (1), minimize J(z, ϕ) with respect to ϕ subject to (1). (4) Optimization problems with differential equations constraints have gained a huge interest in the recent years, see [5,6].…”

On Optimal Control of a Free Surface Flow

“…We split off the kinematic boundary condition, see [1,5]. Then we iterate between solving the remaining system of equations for a given domain and computing a new domain using the kinematic boundary condition.…”

“…Motivated by the industrial process of film manufacturing [1,5], this work is concerned with shape design of polymer films. They are produced in a casting process where liquid polymer is pressed through a nozzle forming a thin film that is finally winded up by a spindle.…”