Elasto-inertial transitions in viscoelastic flows through cylinder arrays

TL;DR

This study investigates the transition to elasto-inertial turbulence in cylinder arrays using numerical simulations, revealing a bifurcation route to chaos driven by vortex interactions and flow dynamics.

Contribution

It provides new insights into the bifurcation sequence and flow interactions leading to elasto-inertial turbulence in porous media-like cylinder arrays.

Findings

EIT occurs via saddle-node and supercritical bifurcations.

Interaction between vortex shedding and bulk flow drives the transition.

Distinct energy spectrum slopes indicate different flow regimes.

Abstract

For dilute solutions of polymers, chaotic flow states can occur at lower Reynolds numbers than required for inertial turbulence in Newtonian fluids, offering the potential for increased mixing efficiency. These states may be promoted by the flow geometry, and in recent years, porous media have gained attention as a promising setting in which viscoelastic instabilities may be exploited, although studies have primarily been in the creeping flow regime. Cylinder arrays serve as a prototypical porous media, giving a controlled setting in which to investigate flow dynamics. Here we explore the transition to elasto-inertial turbulence (EIT) in cylinder arrays via detailed numerical simulations. With increasing elasticity, EIT is reached via an initial sub-critical saddle-node bifurcation from the Newtonian state and then follows a series of supercritical bifurcations, in a Ruelle-Takens-Newhouse route to chaos. This transition is driven by the interaction between vortex shedding in cylinder wakes, and the bulk flow between cylinders. Within the EIT regime, we observe an interaction between slow dynamics in cylinder wakes, and fast dynamics in channels between cylinders, leading to two distinct slopes in the energy spectra. At low Reynolds numbers arrowhead structures are present, but these are suppressed at higher inertia. In the present configuration, we find no direct connection between EIT and purely elastic instabilities.