Flow of a quasi-Newtonian fluid through a planar contraction

• Published in: Journal of non-Newtonian fluid mechanics 1999-08, Vol.85 (1), p.11-27
• Main Authors: Ryssel, E., Brunn, P.O.
• Format: Article
• Language: English
• Subjects: Dilute polymer solution; Exact sciences and technology; Finite volume method; Flow type sensitivity; Flows in ducts, channels, nozzles, and conduits; Fluid dynamics; Fundamental areas of phenomenology (including applications); Inelastic fluid; Non-newtonian fluid flows; Physics; Planar contraction
• ISSN: 0377-0257; 1873-2631
• DOI: 10.1016/S0377-0257(98)00180-3

Flows through abrupt contractions are dominated by the rapid extension experienced in passing through the contraction. Thus, it is useful to employ a fluid model which considers the extensional viscosity explicitly in its constitutive equation. In this paper, the quasi-Newtonian fluid model, which admits shear thinning and extension thickening of the viscosity depending on the local type of flow as proposed by Schunk and Scriven [P. Schunk, L. Scriven, J, Rheol 34 (1990) 1085], is applied to the numerical simulation of the flow of a dilute polyacrylamide solution through a planar 4 : 1 contraction. In this theory the extra stress tensor does not only depend on the rate of strain tensor but also on the relative rate of rotation of the fluid. The material function – the viscosity function – is allowed to depend on the invariants of these two kinematic tensors yielding a local distinction between extensional, shear or rotation dominated flow. The governing equations are discretized using a finite volume method. Different model parameters are varied and the simulation results are compared with the generalized Newtonian fluid and experimental data.