Fluid–metamaterial interaction: Coupling phononic materials with unsteady aerodynamic flows

Phononic materials (PM) are periodic media that enable an engineered elastodynamic response, supporting behaviors such as band gaps and localized modes. An opportunity exists to couple phononic materials with wall-bounded fluid flows, toward the aim of passive, adaptive flow control. Here, we explore this domain and compute the fluid–structure interaction (FSI) that arises when a PM is coupled with an unsteady aerodynamic flow using a high-fidelity, strongly coupled immersed boundary simulation framework. We simulate a flat plate at an angle just before the onset of vortex shedding, and embed a 1-D PM in a compliant section of the plate, oriented normal to the flow direction. The PM is engineered with a truncation resonance eigenmode in the phononic bandgap, that localizes energy at the fluid–PM interface. The characteristics of this truncation resonance are tuned with respect to the vortex shedding frequency, to modify the coupled flow–PM dynamics. We introduce a framework to recast the PM parameters into “behavioral” parameters directly connected to the coupled FSI. The utility of these parameters in governing the FSI dynamics is demonstrated through an analysis of the PM deformation and coefficient of lift.