Application of the log-conformation tensor to three-dimensional time-dependent free surface flows

Abstract

A finite-volume method is applied to the numerical simulation of creeping flows of viscoelastic fluids through a 4:1 square-square three dimensional abrupt contraction. The calculation of the polymer stress contribution is carried out with the log-conformation methodology [1]. The log-conformation scheme allowed converged solutions at higher Deborah numbers for the Oldroyd-B fluid than the standard method when imposing steady flow conditions, but not for the UCM model. This does not mean that the log-conformation technique is less effective for the UCM fluid, but suggests that this flow is most probably time-dependent above a critical Deborah number. In any case, this work confirms the advantages of the log-conformation approach vis-a-vis the standard procedure.