Lid-driven cavity flow-induced dynamics of a neutrally buoyant solid: Effect of Reynolds number, flexibility, and size

Abstract

The present work is on Fluid flexible–Solid Interaction (FfSI), involving a recirculating flow-induced motion of a neutrally buoyant and deformable circular solid. For a Newtonian fluid flow and neo-Hookean flexible-solid deformation, a single FfSI solver—based on fully Eulerian and monolithic approaches—is used. The effect of Reynolds Number Re (20–500), volume fraction Φ (1%–12%) of the solid, and its non-dimensional shear modulus G*(0.02–1) on transient/periodic flow-induced solid-motion and the associated FfSI analysis is presented. The solid undergoes a transient spiraling motion before attaining a periodic orbit-based limit cycle. The flow also attains the periodic state after the initial transients. Time-averaged flow velocity-magnitude ⟨v*⟩ surrounding the limit cycle increases with increasing Re, increasing G*, and decreasing Φ. Equivalent radius req* of the limit cycle and time-averaged velocity-magnitude ⟨vc*⟩ of the centroid of the solid increase with increasing Re and decrease with decreasing G* (or increasing flexibility) and increasing volume fraction Φ (or size) of the solid. Also, frequency f* of the limit cycle decreases with increasing Re and remains almost constant with G* and Φ. With increasing Φ, the limit cycle undergoes a transition from the single loop to double loop beyond a critical volume fraction Φc=2%. A critical Reynolds number Rec, below which the periodic limit cycle collapses to a point, decreases with decreasing Φ. Our findings will help in the prediction and control of the motion of the solid in a bounded fluid flow involving solids of varying flexibility, which is relevant to a wide range of industrial and biological applications.