Finite element investigation of inertia and viscous effects on regularized Herschel–Bulkley flows

Finite element simulations of regularized viscoplastic flows through a planar expansion is performed. The mechanical model is made up of the conservation equations of mass and momentum, coupled with a regularized form of the Herschel–Bulkley viscosity function, based on the Papanastasiou equation. This model is approximated by a three-field Galerkin least-squares method, in terms of the extra-stress tensor, the velocity vector and the pressure field. A sensitivity analysis is performed, aiming at an investigation of the influence of yield stress, shear-thinning and inertia effects on the flow pattern and pressure drop. The results show a strong dependence of the position and shape of the yielded and unyielded regions on Herschel–Bulkley and Reynolds numbers.