RESUMO
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 ß = 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.
RESUMO
The present work is on laminar recirculating flow-induced deformation as well as motion of a neutrally buoyant flexible elliptical solid, resulting in Lagrangian chaos in a two-dimensional lid-driven cavity flow. Using a fully Eulerian and monolithic approach-based single-solver for the fluid flow and flexible-solid deformation, a chaotic advection study is presented for various aspect ratios ß ( =0.5-1.0) and a constant volume fraction Φ=10% of an elliptical solid at a constant Ericksen number Er=0.05 and Reynolds number Re=100. Our initial analysis reveals maximum chaotic advection at ß=0.5 for which a comprehensive nonlinear dynamical analysis is presented. The Poincaré map revealed elliptic islands and chaotic sea in the fluid flow. Three large elliptic islands, apart from certain smaller islands, were identified near the solid. Periodic point analysis revealed the lowest order hyperbolic/elliptic periodic points to be three. Adaptive material tracking gave a physical picture of a deforming material blob revealing its exponential stretch along with steep folds and demonstrated unstable/stable manifolds corresponding to lowest order hyperbolic points. Furthermore, adaptive material tracking demonstrates heteroclinic connections and tangles in the system that confirm the existence of chaos. For the transient as compared to the periodic flow, adaptive material tracking demonstrates a larger exponential increase of the blob's interfacial area. The finite-time Lyapunov exponent field revealed attracting/repelling Lagrangian coherent structures and entrapped fluid zones. Our work demonstrates an immersed deformable solid-based onset of chaotic advection, for the first time in the literature, which is relevant to a wide range of applications.