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

• Published in: Journal of non-Newtonian fluid mechanics Vol. 58; no. 2-3; pp. 279 - 313
• Main Authors: SINGH, P, LEAL, L. G
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier 1995
• Subjects: Approximation theory; Computational methods in fluid dynamics; Convergence of numerical methods; Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; Finite element method; Flow computation (e.g. Finite element); Fluid dynamics; Fundamental areas of phenomenology (including applications); Kinematics of deformation and flow; Mathematical models; Non-newtonian fluid flows; Physics; Polymers; Rheology; Stress analysis; Techniques and apparatus; Viscoelasticity; Wall flow; Finite element method; Rheology; Numerical simulation; Non-Newtonian fluids; Wedge; Modeling; Stokes flow
• ISSN: 0377-0257; 1873-2631
• DOI: 10.1016/0377-0257(95)01346-W

In this paper we numerically simulate flow of the FENE dumbbell model around a 3 pi /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 not equal to 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 theta . 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.