Chaotic advection in a recirculating flow: Effect of a fluid multiple-flexible-solid interaction

Abstract

This paper deals with chaotic advection due to a two-way interaction between flexible elliptical-solids and a laminar lid-driven cavity flow in two dimensions. The present Fluid multiple-flexible-Solid Interaction study involves various number N(= 1–120) of equal-sized neutrally buoyant elliptical-solids (aspect ratio β = 0.5) such that they result in the total volume fraction Φ = 10 % as in our recent study on single solid, done for non-dimensional shear modulus G ∗ = 0.2 and Reynolds number R e = 100. Results are presented first for flow-induced motion and deformation of the solids and later for chaotic advection of the fluid. After the initial transients, the fluid as well as solid motion (and deformation) attain periodicity for smaller N ≤ 10 while they attain aperiodic states for larger N > 10. Adaptive material tracking (AMT) and Finite-Time Lyapunov Exponent (FTLE)-based Lagrangian dynamical analysis revealed that the chaotic advection increases up to N = 6 and decreases at larger N(= 6–10) for the periodic state. Similar analysis for the transient state revealed an asymptotic increase in the chaotic advection with increasing N ≤ 120. These findings are demonstrated with the help of two types of chaos signatures: exponential growth of material blob’s interface and Lagrangian coherent structures, revealed by the AMT and FTLE, respectively. Our work, which is relevant to several applications, presents a novel technique based on the motion of multiple deformable-solids for enhancement of chaotic advection.