Dynamics of a flexible beam in the wake of a cylinder in shear-thinning flow*

Fluid-Structure Interaction (FSI) between shear-thinning flow and a flexible structure is studied numerically. The simulation is conducted by coupling the fluid solver, OpenFOAM, and the solid solver, deal.II, through an open-source library preCICE. We model a two-dimensional fluid domain with an incompressible, shear-thinning fluid that resembles the rheological properties of human blood with uniform and steady inlet flow. The shear-dependent viscosity is described using the Carreau model. The solid structure is an elastic beam modeled as incompressible, uniaxial neo-Hookean material, placed in the wake of a fixed, rigid, non-slip cylinder. We study the response of the beam for a range of zero-shear Reynolds numbers and with beams of different lengths. The degree of shear-thinning is varied by changing the Carreau number while keeping the Reynolds number constant. We study the changes in the  frequency and amplitude of the beam’s oscillations with the Rynolds number and the Carreau umber. We show that the shear-thinning effects cause flow instability at subcritical Reynolds numbers, and cause oscillations of the flexible beam in the wake of the cylinder.