LOCAL SIMILARITY SOLUTIONS IN THE PRESENCE OF A SLIP BOUNDARY CONDITION

The local solution behavior near corners formed by the intersection of a slip surface with either a no-slip or a shear-free boundary is analyzed by finite element calculations of the two-dimensional flow of an inertialess Newtonian fluid in several model flow geometries; these flows are the flow in a tapered contraction, a sudden expansion and the extrudate swell from a planar die. Local finite element mesh refinement based on irregular, embedded elements is used to obtain extremely fine resolution of the velocity and pressure fields near the region where there is a sudden change in boundary condition. The calculations accurately reproduce the expected asymptotic behavior for a shear-free surface intersecting a no-slip boundary, where the solution is given by a self-similar form for the velocity and pressure fields. Replacing the shear-free condition with a slip condition yields a similar form for the local velocity and pressure fields and indicates that the slip boundary behaves, to leading order, as a s...