Modal decomposition of fluid-structure interaction with application to flag flapping

TL;DR

This paper introduces a combined fluid-structure modal decomposition framework using POD and DMD, revealing correlated flow and structural modes in flag flapping and the transition to chaos, with implications for understanding FSI phenomena.

Contribution

It presents a novel combined fluid-structure modal analysis approach with a meaningful norm, uncovering coupled modes and transition mechanisms in FSI systems.

Findings

Identified correlated flow and structural modes in flag flapping.

Revealed the transition from limit-cycle to chaotic flapping involves bluff-body wake instability.

Discovered triadic interactions producing non-integer harmonic flapping frequencies.

Abstract

Modal decompositions such as proper orthogonal decomposition (POD), dynamic mode decomposition (DMD) and their variants are regularly used to educe physical mechanisms of nonlinear flow phenomena that cannot be easily understood through direct inspection. In fluid-structure interaction (FSI) systems, fluid motion is coupled to vibration and/or deformation of an immersed structure. Despite this coupling, data analysis is often performed using only fluid or structure variables, rather than incorporating both. This approach does not provide information about the manner in which fluid and structure modes are correlated. We present a framework for performing POD and DMD where the fluid and structure are treated together. As part of this framework, we introduce a physically meaningful norm for FSI systems. We first use this combined fluid-structure formulation to identify correlated flow features and structural motions in limit-cycle flag flapping. We then investigate the transition from limit-cycle flapping to chaotic flapping, which can be initiated by increasing the flag mass. Our modal decomposition reveals that at the onset of chaos, the dominant flapping motion increases in amplitude and leads to a bluff-body wake instability. This new bluff-body mode interacts triadically with the dominant flapping motion to produce flapping at the non-integer harmonic frequencies previously reported by Connell & Yue (2007). While our formulation is presented for POD and DMD, there are natural extensions to other data-analysis techniques.