Finite element analysis of steady viscoelastic flow around a sphere in a tube: calculations with constant viscosity models

Finite element analysis is used to compute the inertialess flow of a viscoelastic fluid around a sphere falling in a cylindrical tube. Calculations are reported for three differential constitutive models with constant viscosities: the Upper-Convected Maxwell model (UCM), the Oldroyd-B model (OLDB) and the dumbbell model of Chilcott and Rallison (CR). Calculations are based on the Explicitly Elliptic Momentum Equation (EEME) and the Elastic Viscous Split Stress (EVSS) methods for calculations with models without and with a Newtonian solvent contribution, respectively. The calculations converged with mesh refinement for all three models for values of De below 1.6. Calculations with the UCM and OLDB models are limited below De = 2 by loss of convergence of the Newton iteration. Mesh refinement does not seem to alleviate these limits. Calculations with the CR model and moderate values of the maximum extensibility of the dumbbell L converge to higher values of De ; however, computations for large values of L require fine meshes in the stagnation region behind the sphere.