Predicting numerically the large increases in extra pressure drop when boger fluids flow through

Recent numerical studies on pressure-drops in contraction flows have introduced a variety of constitutive models to compare and contrast the competing influences of extensional viscosity, normal stress and shear-thinning. Early work on pressure-drops employed the constant viscosity Oldroyd-B and Upper Convected Maxwell (UCM) models to represent the behavior of so-called Boger fluids in axisymmetric contraction flows, in (unsuccessful) attempts to predict the very large enhancements that were observed experimentally. In more recent studies, other constitutive models have been employed to interpret observed behavior and some progress has been made, although finding a (respectable) model to describe observed contraction-flow behavior, even qualitatively, has been frustratingly difficult. With this in mind, the present study discusses the ability of a wellknown FENE type model (the so-called FENECR model) to describe observed behavior. For various reasons, an axisymmetric (4:1:4) contraction/expansion geometry, with rounded corners, is singled out for special attention, and a new hybrid finite element/volume algorithm is utilized to conduct the modeling, which reflects an incremental pressure-correction time-stepping structure. New to this algorithmic formulation are techniques in time discretization, discrete treatment of pressure terms, and compatible stress/velocity-gradient representation. We shall argue that the current simulations for the FENE-CR model have resulted in a major improvement in the sort-for agreement between theory and experiment in this important bench-mark problem.