Finite element simulation of flow around a 3π 2 corner using the FENE dumbbell model

In this paper we numerically simulate flow of the FENE dumbbell model around a 3π 2 corner. By refining the radial mesh at the corner in both the radial and tangential directions, we show that a bounded converged solution can be obtained for large values of the Deborah number, and for arbitrarily large values of the finite-extensibility parameter. For non-zero polymer concentrations, our numerical results show that for r ≠ 0 in the vicinity of the corner both velocity and configuration fields can be approximated by generalized power laws with exponents depending on the angular position θ. Away from the two walls there is an angular region within which the exponents of the governing power laws are approximately constant. We also find that the polymeric stress singularity is stronger than the Newtonian stress singularity. These results are in agreement with the analytical results obtained by Hinch (J. Non-Newtonian Fluid Mech., 34 (1993) 319-349).