FLOW OF OLDROYD-B FLUIDS IN CURVED PIPES OF CIRCULAR AND ANNULAR CROSS-SECTION

Perturbation methods are used to study steady, fully developed flow of Oldroyd-B fluids through curved pipes for both pipes of circular and annular cross-section. The perturbation parameter is the curvature rat io, given: by the cross-sectional radius of the pipe divided by the co nstant radius of the pipe centerline. We compare results for creeping and non-creeping flows for both viscoelastic and Newtonian fluids. In pipes of circular cross-section, the velocity field for creeping flows of Oldroyd-B fluids is qualitatively similar to that found for non-cr eeping flows of Newtonian fluids. Namely, in addition to the primary f low, there is a secondary motion consisting of counter-rotating vortic es. In curved annular pipes, two pairs of counter-rotating vortices ar e generated by either inertial or elastic effects. In this geometry, t he differences between creeping how of viscoelastic fluids and non-cre eping flow of Newtonian fluids are dramatically accentuated at small v alues of inner to outer pipe radius, r(i)/r(o). For Newtonian fluids, as r(i)/r(o) approaches zero, the magnitude and size of the vortices a djacent to the inner cylinder shrink to zero. However, for creeping fl ow of Oldroyd-B fluids, the inner vortex pair is comparable to the out er vortex pair in both size and strength, even for values of r(i)/r(o) as small as 0.01. For pipes of circular cross-section, the effect of elasticity on the drag is considered and earlier predictions by Bowen er al. for the upper convected Maxwell fluid are extended to the Oldro yd-B fluid for non-zero Reynolds number.