Subcritical insability of viscoelastic flow over a circular cylinder: A numerical study

TL;DR

This study uses numerical simulations to investigate the nature of viscoelastic flow instability over a circular cylinder, revealing subcritical behavior through path-dependent transition observations.

Contribution

It demonstrates the subcritical nature of flow instability in viscoelastic flow around a cylinder using the Oldroyd-B model and path-dependent simulation analysis.

Findings

Flow transition is path-dependent, indicating subcritical instability.

Numerical stabilization achieved with Log-conformation reformulation.

Flow becomes unsteady at certain Re and Wi, with hysteresis observed.

Abstract

In this paper, we discuss whether the instability of viscoelastic flow around a circular cylinder is subcritical or supercritical by numerical simulation. The Oldroyd-B model is selected to describe the viscoelastic constitutive relationship. The Log-conformation reformulation is employed to stabilize numerical simulation. The parameter ranges investigated are the Reynolds numbers ($Re$) spanning from 5 to 100 and the Weissenberg number ($Wi$) spanning from 0 to 10, with a fixed viscosity ratio of $\beta = 0.9$. Simulations are performed under two paths, i.e., 1) increasing $Re$ (or $Wi$) and 2) decreasing $Re$ (or $Wi$) slowly and gradually from one state to the next. The results show that the statistical solutions such as the time-averaged velocity obtained along the two paths are not identical over certain parameter range, which is around the transition point from the steady to unsteady flow. This loading path dependence behaviour indicates that the flow instability is subcritical.