An assessment of the PTT model on the impacting drop problem

Abstract

This work presents a numerical method and simulations of axisymmetric free-surface flows of a polymeric fluid using the Phan-Thien-Tanner (PTT) constitutive relationship. The governing equations are solved by finite differences on a staggered grid that employs accurate boundary conditions on the free surface together with bounded, monotone, high-order upwinding approximation of the convection terms. The numerical method is partially verified by solving fully developed flow in a tube and comparing it to a known analytic solution. The problem of a drop impacting on a rigid plate is considered. The effect of varying the five parameters, characterizing the PTT model, is studied extensively, and the results are interpreted physically. The expansion-contraction phenomenon of the viscoelastic drop that occurs when it hits a flat surface is tracked, and the time evolution of the normal and shear components of the extra-stress tensor is analyzed. To further verify the code, the impacting drop of an Oldroyd-B fluid is simulated and the time evolution of the drop width is compared to that of other authors.

Numerical simulation of complex fluid flows with moving interfaces

“…The recent works developed in the Applied Mathematics and Scientific Computing LAB (LMACC) group still do not cover surface tension effects very extensively in viscoelastic simulations. This can be observed in the papers: (JUNIOR et al, 2016;TOMÉ et al, 2016;TOMÉ et al, 2018). In order to bridge this gap, we have tried to give special attention to studying problems in which the surface tension has an important role.…”