Numerical simulation of the Weissenberg effect

Abstract

Weissenberg effect, or Rob-Climbing experiment, is encountered in many important industrial applications involving mixing process. In this experiment we insert a rotating rod into a container with viscoelastic fluid. The behavior of the viscoelastic fluid is striking, the fluid moves in the opposite direction of the centrifugal force and climbs up the rod. This effect has been experimentally reproduced by many researchers. However, in the context of numerical results, there are few works dealing with a rigorous study about this effect. One of the main challenges imposed in this simulation is to provide numerical methods which achieve high elasticity rate and that represent the correct shape of the free surface. In this work is presented a finite difference scheme to simulate the Weissenberg effect. The numerical technique is based on the projection method to simulate viscoelastic two-phase flows. The conformation tensor is employed to solve the viscoelastic fluid model. The interface between the fluids is represented with the efficient least squares volume-of-fluid interface reconstruction algorithm (ELVIRA). A second-order operatorsplit method is used to solve the advection equation and obtain the volume fraction in the next step.In this work, we have performed simulations of the Weissenberg effect for the linear Phan-Thien-Tanner (LPTT) model.