The axisymmetric sudden expansion flow of a non-Newtonian viscoplastic fluid

The flow of a non-Newtonian viscoplastic Bingham fluid over an axisymmetric sudden expansion is studied by numerically solving the governing fully-elliptic continuity and momentum equations. Solutions are obtained for a wide range of Reynolds and yield numbers in the laminar flow regime with constant fluid properties. The present work demonstrates that the finite-difference technique can successfully be employed to obtain solutions to separating/reattaching internal flows of Bingham plastics. The results demonstrate the strong effects of the yield and Reynolds numbers on both the integral and the local structure of the separating and reattaching flow. Higher yield numbers result in larger overall effective viscosities and thus faster flow recovery downstream of the sudden expansion. The reattachment length decreases with increasing yield numbers, eventually reaching an asymptotic nonzero value which, in turn, is dependent on the Reynolds number. The strength of the recirculating flow also decreases with increasing yield numbers.