Numerical Study of Viscoelastic Upstream Instability

TL;DR

This study uses numerical simulations to analyze flow instability and bifurcation in viscoelastic fluids around a cylinder, revealing how various parameters influence upstream recirculation and contributing to understanding this new instability mechanism.

Contribution

It provides the first detailed numerical analysis of viscoelastic upstream instability using the FENE-P model, highlighting parameter effects on flow bifurcation and recirculation.

Findings

Viscoelastic constitutive relation captures upstream instability.

Recirculation length depends on $BR$, $Wi$, $eta$, and $L$.

Bifurcation type varies with $L$ and $eta$.

Abstract

In this work, we report numerical results on the flow instability and bifurcation of a viscoelastic fluid in the upstream region of a confined cylinder in a narrow channel. Two-dimensional direct numerical simulations based on the FENE-P model (the finite-extensible nonlinear elastic model with the Peterlin closure) are conducted with numerical stabilization techniques. Our results show that the macroscopic viscoelastic constitutive relation can capture the viscoelastic upstream instability reported in previous experiments for low-Reynolds-number flows. The numerical simulations reveal that the non-dimensional recirculation length ($L_D$) is affected by the cylinder blocking rate ($BR$), the Weissenberg number ($Wi$), the viscosity ratio ($\beta$), and the maximum polymer extension ($L$). Close to the onset of upstream recirculation, depending on the values of $L$ and $\beta$, the bifurcation can be supercritical or subcritical. $\beta$ has a nonlinear influence on the upstream recirculation length. This work contributes to our theoretical understanding of this new instability mechanism in viscoelastic wake flows.