Effects of the regularization parameter on the flow characteristics of a viscoplastic fluid

Viscoplastic fluid of Herschel–Bulkley type is a non-Newtonian fluid in which the strain experienced by the fluid is related to the stress in a non-linear way. It flows like a viscous liquid when the applied stress is greater than a critical value, i.e. the so-called yield stress, otherwise it behaves like a solid. To smooth out the liquid–solid transition and for the sake of easy computational implementation, Papanastasiou's regularization approach can be utilized, in which the regularization parameter, m, controlling the exponential growth of the stress can play an important role. This work aims to examine the influence of m on the flow characteristics of a Herschel–Bulkley fluid past a circular cylinder near a moving wall. The flow is at a very low Reynolds number, i.e. Re = 10−3, and the Oldroyd number, Od, is in the range of 1-50. Simulation results show that the regularization parameter greatly affects the yield surface; the effect is more pronounced at greater Oldroyd numbers. In addition, its effect on the drag force becomes significant at great Od; and in general, the viscous drag force coefficient increases with m.