Fluid-Structure Interaction Between an Unsteady Vortex-Driven Aerodynamic Flow and a Diatomic Phononic Subsurface

We use fully coupled high-fidelity simulations to probe the flow past an airfoil equipped with a compliant section on the suction surface, whose dynamics we model via a diatomic-chain phononic material in the subsurface of the compliant section creating the potential for passive and adaptive alteration of the surrounding aerodynamic flow. We consider a flow at a Reynolds number of Re=400 past an airfoil at angles of attack of α1=12◦ and α2=15◦. These parameters are chosen because for the baseline (rigid) case, the lower angle of attack does not exhibit vortex shedding but the higher angle of attack does. These give one natural scenarios to explore with a phononic material: for what material parameters does the material (i) trigger a steady aerodynamic flow into unsteadiness versus (ii) modulate vortex shedding in the nominally unsteady case. We focus in this manuscript in aligning the frequency of the phononic material’s truncation resonance, with the underlying vortex shedding frequency inherent in the 15◦ case and latent in the 12◦ case. The truncation resonance is a natural (resonant) frequency of the diatomic chain that lies within its band gap—a behavioral regime where stimuli applied to one end of the structure do not spatially propagate along the material. Aligning temporal frequencies of key flow behavior near the truncation resonance frequency has been argued to be beneficial for passive, adaptive attenuation of instabilities in wall-bounded transitional flows [1]. It is natural to ask, therefore, whether truncation resonance behavior can interact with aerodynamic flows, and if so what fluid-structure interplay arises. To address this question, we design the phononic material parameters such that the truncation resonance frequency matches that of the underlying vortex shedding behavior, and demonstrate that the triggered structural response is of the first structural mode, not the truncation resonance. We explain this outcome as a result of the near-constant mean lift imposed on the aerodynamic body—the vortex shedding yields an oscillatory lift component that is of small amplitude relative to the near-constant mean lift. This outcome implies that, in these aerodynamic settings with a lifting body, fluid-structure interaction must be tailored to either leverage a different phononic material behavior (e.g., pass band dynamics) or alternate architectures.