Near-Critical Swirling Flow of Viscoelastic Fluids in a Pipe

Abstract

The interaction between flow inertia and elasticity in high Reynolds number, axisymmetric, and near-critical swirling flows of an incompressible and viscoelastic fluid in a straight circular pipe is studied. The stresses of the viscoelastic fluid are described by the Oldroyd-B constitutive model (representing the low constant-viscosity Boger fluids). A nonlinear small-disturbance analysis is developed from the governing equations of motion in order to understand the complicated interactions between flow inertia and fluid viscosity and elasticity. The effects of the fluid viscosity, relaxation time, and retardation time on the flow development in the pipe and on the critical swirl for vortex breakdown are explored. It is found that increasing the relaxation time with other parameters being fixed increases the critical swirl for vortex breakdown whereas increasing the retardation time with other parameters being fixed decreases the critical swirl for breakdown. Also, when the relaxation and retardation times are the same the critical swirl is the same as that of a Newtonian fluid. The viscoelastic characteristic times also effect the size of the flow perturbation. These results may explain the changes in the appearance of breakdown zones as function of Reynolds numbers (swirl level) that have been recently observed in the experiments by Stokes et al. (2001) where Boger fluids were used. This work extends for the first time the theory of vortex stability and breakdown to include effects of non-Newtonian fluids.