Broadband flow instability attenuation via coiled locally resonant phononic subsurfaces

Phononic materials such as locally resonant elastic metamaterials have become increasingly relevant over the past few decades for their applications in a wide range of disciplines in applied physics. One application that emerged in recent years is the use of phononic materials for passive flow control through the notion of a phononic subsurface (PSub). A PSub is an elastic structure designed to intervene with flow instabilities in a desired manner, enabling favorable effects such as delay of flow transition and reduction of skin-friction drag. Practical applicability requires PSubs to exhibit these effects over a broad range of flow instability frequencies. Here, broadband flow instability attenuation is proposed through the design of a “coiled” metamaterial-based PSub which enables flow stabilization effects over a range of a few thousand hertz. To test our design, we construct a coupled fluid-structure and implement direct numerical simulations. In the simulation, a Tollmien–Schlichting (TS) instability wave is introduced in the inflow conditions, and its kinetic energy is tracked throughout the simulation. We consider several cases involving multiple TS modes spanning a relatively wide frequency range and demonstrate simultaneous passive stabilization of all the modes in the region in the flow neighboring the application of the PSub.