Abstract
Numerical simulations of viscoplastic fluid flows across a circular obstacle are performed using a lattice Boltzmann method. In this study, the Papanastasiou (modified Bingham) model is employed and we focus on physical conditions for the onset of nonlinear flows. It is shown that viscosity profiles are greatly depended on Reynolds (Re) and Bingham (Bi) numbers. For low Re and Bi conditions, low viscosity regions close to the plastic viscosity are widely formed around a circular obstacle. Meanwhile, low viscosity regions are limited to a small area around the obstacle for high Re and Bi conditions. Effective (representative) Reynolds and Bingham numbers defined using effective shear rate and viscosity are proposed in order to organize and understand viscoplastic fluid flows across a circular obstacle. The usefulness of effective dimensionless numbers is demonstrated.
