Numerical simulation and modeling of the die swell for fiber suspension flows

Abstract

A numerical model is developed to examine the die swell for fiber suspensions, which occurs in 3D printing extrusion processes. More specifically, it focuses on the fiber orientation distribution in a Newtonian suspending fluid and its effects on the shape of the free surface. In a first step, the flow in a 2D axisymmetric capillary die is explored in order to validate the numerical implementation for the fiber orientation model. It is found that the coupling effect flattens the velocity profile but has a small impact on the fiber orientation distribution in the suspension flow. In a second step, the modeling of die swell is considered and result from the literature for the final swelling height is obtained for an uncoupled flow. For fully coupled flows, different values for the coupling parameter and the fiber-fiber interaction coefficient have been tested in order to observe their effects on the free surface shape and on the final fiber orientation distribution. The increase of the fiber coupling parameter increases the die swell ratio when fibers are randomly distributed at the flow inlet, but the opposite behavior, i.e., a decrease of the swelling ratio, is noticed when a perfect fiber alignment condition is imposed at the entrance for low fiber interaction coefficients. The Tanner model, initially developed for viscoelastic fluids, is updated to estimate extrudate swell for fibers suspended in a Newtonian fluid in terms of the coupling parameter and the interaction coefficient. Although this analytical approach used a quadratic closure approximation, it gives qualitative results when compared with the numerical simulations.