The influence of surface-embedded phononic crystals on the amplification of Tollmien-Schlichting waves

This study explores a novel approach to control convective boundary layer instabilities (TS-waves) by leveraging metamaterial concepts, specifically using one-dimensional phononic crystals (PCs) embedded in the surface, leveraging on the inherent frequency band stop characteristic of PCs. By employing analytical models derived from transfer matrix and interface response theories, the PC is fine-tuned to match the desired TS wave properties. The accuracy of the models is verified through finite elements analysis. To investigate the interaction between TS waves and a single PC, coupled two-dimensional fluid structure interaction simulations are conducted in the frequency domain. The study demonstrates that the behavior of TS-waves is determined by the phase relationship between the displacement of the PC's free-face surface and the unsteady perturbation pressure at the wall. When these two factors are in-phase, TS waves are amplified, while they are attenuated when out-of-phase. The mechanical oscillation of the PC is solely driven by the perturbation pressure. The hydrodynamic coupling between TS waves and the PC is governed by a combination of the Orr mechanism and wall-normal velocity linear superposition near the wall. Furthermore, the effectiveness of a metasurface composed of a streamwise-distributed array of PCs is evaluated. The metasurface results in a delay in the amplitude growth of the TS wavelength along its extent, achieving an 11.3% increase in wavelength delay.