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

Abstract

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 β ( =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 β=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.