The log-conformation formulation for single- and multi-phase axisymmetric viscoelastic flows

Abstract

A computational model for predicting axisymmetric single- and multi-phase viscoelastic flows based on the log-conformation formulation of the constitutive equation is presented. The governing equations are discretised using the finite element method and advanced in time using a projection scheme. The single-phase benchmark problem of viscoelastic flow past a sphere in a cylinder is considered and excellent agreement is found with the literature for the drag coefficient for an extensive range of Weissenberg numbers. The cause of the breakdown in stability due to a velocity inflection near the sphere is investigated. For multi-phase flows, enhanced stability of the conservative level-set method is obtained by introducing a diffused interface approach for normal calculations. This novel method is used to investigate the jump discontinuity phenomenon exhibited for a bubble rising in a viscoelastic fluid. Qualitative and quantitative agreement is found with contemporary literature in terms of the critical bubble volume as well as other phenomena such as the negative wake and trailing cusp.