Flow-induced flapping of an inverted flag with non-uniform stiffness distribution

TL;DR

This study uses high-fidelity simulations to show that nonuniform stiffness in an inverted flag system can be effectively characterized by an equivalent uniform stiffness, influencing its flapping dynamics and potential energy harvesting applications.

Contribution

It demonstrates that nonuniform stiffness distributions can be modeled by an effective uniform stiffness, simplifying analysis of complex FSI dynamics in inverted flags.

Findings

Nonuniform stiffness can be represented by an effective uniform stiffness.

FSI dynamics of nonuniform flags mirror those of uniform ones when scaled properly.

Effective stiffness can be computed via in-vacuo Euler-Bernoulli beam analysis.

Abstract

We perform high-fidelity, two-dimensional (2D), fluid-structure interaction (FSI) simulations at a Reynolds number of $Re=200$ of uniform flow past an inverted flag (i.e., clamped at its trailing edge). The inverted flag system can exhibit large-amplitude flapping motions (on the order of the flag length) that can be converted to electricity via, e.g., piezoelectric materials. We investigate the effect of structural nonuniformity in altering the FSI dynamics compared with the uniform-stiffness scenario that has been thoroughly characterized. We consider linear, quadratic, and cubic stiffness distributions, and demonstrate that the FSI dynamics mirror those of a uniform-stiffness flag with an appropriately defined effective stiffness. We show that this effective stiffness can be computed simply via analysis of an \emph{in-vacuo} Euler-Bernoulli beam. When expressed in terms of the effective stiffness, the FSI dynamics of the nonuniform-stiffness flag exhibit the same regimes -- with many similarities in the detailed dynamics -- as a uniform-stiffness flag. This study opens questions about (i) what the optimal stiffness distribution is for, e.g., energy harvesting capacity, and (ii) how to use nonuniform (and possibly time-varying) stiffness distributions to control the flag dynamics towards a desired state.