Numerical prediction of extensional flows in contraction geometries: hybrid finite volume/element method

We examine the flow of viscoelastic fluids with various shear and elongational properties in axisymmetric and planar 4:1 contractions, under creeping flow conditions. Particular attention is paid to the influence of elongational viscosity upon vortex enhancement/inhibition. Simulations are performed with a novel hybrid finite volume/element algorithm. The momentum and continuity equations are solved by a Taylor–Galerkin/pressure-correction finite element method, whilst the constitutive equation is dealt with by a cell-vertex finite volume algorithm. Both abrupt and rounded-corner configurations are considered. The Oldroyd-B fluid exhibits vortex enhancement in axisymmetric flows, and vortex reduction in planar flows, qualitatively reproducing experimental observation for some Boger fluids. For shear-thinning fluids (Phan-Thien/Tanner models, PTT), both vortex enhancement and inhibition is observed. This follows trends in extensional viscosity. Lip-vortex activity has been observed in planar and sharp-corner instances, but not in axisymmetric or rounded-corner flows. Finally, cross-flow extensional-stress contours in the salient-corner neighbourhood reflect the size and curvature of the associated vortex structure.