Numerical simulation of Weissenberg phenomena – the rod-climbing of viscoelastic fluids Original Research Article

A finite element simulation of the Weissenberg effect, i.e., the rod-climbing of viscoelastic fluids, is presented. The flow features axisymmetric swirling, free surface, gravity, surface tension, centrifugal force and all six viscoelastic stresses. An operator splitting algorithm is employed to solve the highly non-linear system of equations governing the upper-convected Maxwell (UCM) or the Phan-Thien–Tanner (PTT) fluid. Normal displacement of free surface is tracked explicitly in time and an elaborate orthogonal trajectory scheme applicable to unstructured as well as structured grids is developed to update the mesh. Comparison of numerical and experimental results shows good agreement.