Asymmetric flows of viscoelastic fluids in symmetric planar expansion geometries

Abstract

The flow of viscoelastic liquids with constant shear viscosity through symmetric sudden expansions is studied by numerical means. The geometry considered is planar and the constitutive model follows the modified FENE-CR equation, valid for relative dilute solutions of polymeric fluids. For Newtonian liquids in a 1:3 expansion we predict the result that the flow becomes asymmetric for a Reynolds number (based on upstream mean velocity and channel height) of about 54, in agreement with previously published results. For the non-Newtonian case the transition depends on both the concentration and the extensibility parameters of the model, and the trend is for the pitch-fork bifurcation to occur at higher Reynolds numbers. Detailed simulations are carried out for increasing Reynolds number, at fixed concentration and Weissenberg number, and for increasing concentration at a fixed Reynolds number of 60. The results given comprise size and strength of the recirculation zones, bifurcation diagrams, and streamline plots.

On extensibility effects in the cross-slot flow bifurcation

“…Numerically, any of theses two solutions may be obtained, depending on the exact initial conditions, time step employed, or any other "numerical" parameter. The bifurcation is thus very similar to the viscoelastic Coanda effect predicted in two-dimensional planar expansions (Oliveira [19]; Rocha et al [21])-compare Fig. 3 here with Fig.…”

“…For the FENE-CR model, on account of the constant shear viscosity, the fully developed velocity profile is parabolic as in the Newtonian case and it is a relatively straightforward matter (e.g. Oliveira [19]) to derive the shear xy and normal xx stress component profiles to be applied at the two inlet sections. For the FENE-P model, and especially whenˇ/ = 0, the problem of obtaining fully developed velocity and stress profiles is much more involved and the analytical solution obtained by Cruz et al [20] was applied at the inlet sections.…”

“…3 here with Fig. 13 in Oliveira [19] (for a 1:3 expansion) for example. However an important difference should be pointed out: while in the planar expansion the pitchfork bifurcation was essentially an inertial effect (for increasing Re) with elasticity tending to promote stability, here for the cross-slot it is a purely elastic instability (Re = 0) and elasticity through extensional viscosity (Á E increases with L 2 ) having a destabilising effect.…”

Wellbore to fracture proppant-placement-fluid rheology

“…Conversely, shear thickening fluids have an opposite effect by elongating the recirculation zone (Dhinakarana et al, 2013). When the fluid in a sudden expansion has elastic properties however, the recirculation zones are smaller -thus elasticity has a damping effect (Oliviera, 2003).…”

Influence Study of the Viscoelastic Fluids Features in Drag Reduction in Laminar Regime Flow in Pipeline

“…Oliveira [8] had also simulated for the same geometry and conditions of Zheng et al [7], but using DNS (Direct Numerical Simulation) and the FENE-CR viscoelastic model. His results from the point of view of the drag reduction coincide with the Zheng et al [7].…”