The dynamics of fibres dispersed in viscoelastic turbulent flows

Abstract

This study explores the dynamics of finite-size fibres suspended freely in a viscoelastic turbulent flow. For a fibre suspended in Newtonian flows, two different flapping regimes were identified by Rosti et al. (Phys. Rev. Lett., vol. 121, issue 4, 2018, 044501): one dominated by time scales from the flow, and another dominated by time scales associated with its natural frequency. We explore in this work how the fibre dynamics is modified by the elasticity of the carrier fluid. For this, we perform direct numerical simulations of a two-way coupled fibre–fluid system in a parametric space spanning different Deborah numbers, fibre bending stiffness (flexible to rigid) and linear density difference between the fibre and the flow (neutrally buoyant to denser-than-fluid fibres). We examine how these parameters influence various fibre characteristics such as the frequency of flapping, curvature, and alignment with the fluid strain and polymer stretching directions. Results reveal that the neutrally buoyant fibres, depending on their flexibility, oscillate with large and small time scales transpiring from the flow, but the smaller time scales are suppressed as the polymer elasticity increases. Polymer stretching is uncommunicative to denser-than-fluid fibres, which flap with large time scales from the flow when flexible, and with their natural frequency when rigid. Thus the characteristic elastic time scale has a subdominant effect when the fibres are neutrally buoyant, while its effect is absent when the fibres become more inertial. In addition, we also explore the fibre's bending curvature and its preferential alignment with the flow to identify the other roles of viscoelasticity in modifying the coupled fluid–structure dynamics. Inertial fibres have larger curvatures and are less responsive to the polymer presence, whereas the neutrally buoyant fibres show quantitative changes. The perceptible passivity of the denser fibres is again reflected in the way they align preferentially with the polymeric stretching directions: the neutrally buoyant fibres show a higher alignment with the polymer stretching directions compared to the denser ones. In a nutshell, the polymers exert a larger influence on neutrally buoyant fibres, which are more reflective of the polymeric influence in the flow. The study addresses comprehensively the interplay between polymer elasticity and the fibre structural properties in determining its response behaviour in an elasto-inertial turbulent flow.