Theoretical Modeling and Optimization of Porous Coating for Hypersonic Laminar Flow Control

Impedance-Near-Zero Acoustic Metasurface for Hypersonic Boundary-Layer Flow Stabilization

“…This is not in line with our conventional physics understanding of hypersonic boundary-layer stabilization. Actually, our findings can be evidently explained by examining the pressure distributions of the Mack second mode using a high-order accurate direct numerical simulation (DNS) [8,12]. As shown in the upper subplot of Fig.…”

“…For hypersonic boundary-layer flow problems [9][10][11][12]31], the boundary condition at the wall surface is generally modeled as v w = p w /Z, where v w and p w are the vertical flow velocity and acoustic pressure at the wall, respectively. Z is the surface acoustic impedance, which depends on the properties of the wall material, mean flow characteristics at the wall surface, and flow-perturbation parameters such as wave frequency [31].…”

“…Z is the surface acoustic impedance, which depends on the properties of the wall material, mean flow characteristics at the wall surface, and flow-perturbation parameters such as wave frequency [31]. Z becomes infinite for a rigid wall and is often designed to match the specific acoustic impedance of the background medium to maximize the absorption effect [11,12]. Note that, as a trapped mode within a waveguide, the sound ray of the Mack second mode is almost normal to the wall surface [32], which means the absorption reaches a maximum for the matched impedance.…”

“…The half-width and depth of the cavities are b and H, respectively, with the unit-cell period being s. The porosity and aspect ratio are φ = 2b/s and A r = 2b/H, respectively. Assuming that the periodicity s is much smaller than the acoustic wavelength λ acs , the plane wave expansion method [12,29,30] can be used to derive the normalized effective surface acoustic impedance of the proposed metasurface as…”

“…As the Mack second mode exhibits acoustic-wavelike behavior, one straightforward way to suppress its development while minimally disturbing the mean flow is to dissipate the acoustic wave energy by implementing an absorptive boundary [5,6]. Following this idea, a so-called ultrasonic absorptive coating (UAC) was proposed and optimized to obtain the required dissipation effect through the thermal and viscous boundary layers inside the narrow cavities [9][10][11][12]. Contrary to this intuitive thinking, here we show that an effective boundary with hardly any absorptive capability can still suppress the Mack second mode provided that its surface acoustic impedance approaches zero.…”