Non-Newtonian flow characteristics in a steady two-dimensional flow

Abstract

The two-dimensional steady flow of a non-Newtonian fluid (a dilute polymer solution) is examined. The flow domain is composed of a parallel-walled inflow region, a contraction region in which the walls are rectangular hyperbolae, and a parallel-walled outflow region. The problem is formulated in terms of the vorticity, stream function and appropriate rheological equation of state, i.e. an Oldroyd-type constitutive equation (with no shear-thinning) for the total shear and normal-stress components. Computational results from the numerical solution of the equations are presented. In particular, the molecular extension and pressure distribution along the centre-line are presented as well as contour plots of the different flow variables. The alignment of the molecules with the principal axes of strain rate is shown by a qualitative comparison of the streamwise normal-stress contours with contours of the eigenvalues of the strain-rate matrix.