(372f) Simulation of a Sedimenting Sphere in a Viscoelasticfluid with Openfoam

The simulation of viscoelastic flow past a sphere, or a sedimenting sphere, has attracted considerable
interest since being established as a benchmark problem in computational flow dynamics. As a geometry
exhibiting both shearing and extensional flows, the sedimenting sphere design has the potential to probe
properties of viscoelastic fluids under various conditions. In particular, we explore the low Reynolds, high
Weissenberg number flow regime, in which elastic forces dominate. Using OpenFOAM, an open-source
computational fluid dynamics software, we are able to implement immersed boundary conditions so that we
can demonstrate unsteady startup in addition to steady-state dynamics. We find that these conditions as
specified are currently unstable for reasonable sphere densities under typical gravitational acceleration, and
therefore opt for high densities and reduced accelerations. Nonetheless, we are
able to capture realistic steady-state conditions, which we compare to the Faxen wall correction. We find
that our boundary conditions perform better than the Faxen correction for certain
geometries. In future research, we hope to stabilize our startup dynamics for reasonable sphere densities and
gravitational acceleration.