A new viscoelastic benchmark flow: Stationary bifurcation in a cross-slot

Abstract

In this work we propose the cross-slot geometry as a candidate for a numerical benchmark flow problem for viscoelastic fluids. Extensive data of quantified accuracy is provided, obtained via Richardson extrapolation to the limit of infinite refinement using results for three different mesh resolutions, for the upper-convected Maxwell, Oldroyd-B and the linear form of the simplified Phan-Thien–Tanner constitutive models. Furthermore, we consider two types of flow geometry having either sharp or rounded corners, the latter with a radius of curvature equal to 5% of the channel’s width. We show that for all models the inertialess steady symmetric flow may undergo a bifurcation to a steady asymmetric configuration, followed by a second transition to time-dependent flow, which is in qualitative agreement with previous experimental observations for low Reynolds number flows. The critical Deborah number for both transitions is quantified and a set of standard parameters is proposed for benchmarking purposes.