Application of the log-conformation technique to 3D free surface flows

Abstract

The numerical simulation of flows of very elastic fluids has been a subject of intense research for the past decades with important industrial applications. Therefore, it comes as no surprise that many efforts have been made to improve the convergence capabilities of the numerical methods used. Recently, an important contribution to the High Weissenberg Number Problem has been presented by Fattal and Kupferman [6], who developed the matrix-logarithm of the conformation tensor technique, henceforth called log-conformation tensor. This methodology guarantees that solutions of viscoelastic flow problems are physically admissible and can deal with sharp elastic stress layers. Several investigators have been using the log-conformation tensor and results for high Weissenberg number flows have been reported. However, this technique has only been applied to simulate confined flows of viscoelastic fluids. In this work we investigate the application of the log-conformation tensor technique to three-dimensional unsteady free surface flows. We applied the log-conformation tensor formulation to solve the Oldroyd-B constitutive equation and solved the momentum equation using a finite difference Marker-and-Cell type method. Results for the simulation of the extrudate swell of Oldroyd-B fluids at high Weissenberg numbers are presented.