Acoustic metasurfaces for stabilization of broadband unstable modes in high speed boundary layer
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摘要:
以声学超表面为研究对象，使用线性稳定性理论（LST），研究了声学超表面导纳相位与幅值对超声速平板边界层内宽频不稳定模态的影响规律。结果表明：当导纳相位
$ \theta $ 接近0.5$ \text{π}$ 时，第1模态被抑制的同时第2模态会被激发，且在较低频率范围内导纳幅值的增大能够使第1模态更加稳定；当导纳相位$ \theta $ 接近$ \text{π} $ 时，可抑制第2模态但同时激发第1模态；整体上，导纳幅值越大，对不稳定模态的抑制或激发效果越明显。在此基础上，结合缝隙几何参数对导纳的影响，提出一种可实现性宽频抑制方案，通过分段设计声学超表面微结构的几何尺寸，实现了同时抑制第1模态和高频第2模态的目标,并使用$ {\mathrm{e}}^{N} $ 方法验证了转捩抑制效果。Abstract:The influences of the admittance phase and amplitude of acoustic metasurfaces on the broadband unstable modes in a high-speed flat plate boundary layer are analyzed using linear stability theory (LST). It is demonstrated that when the admittance phase goes to 0.5 π, the first mode is suppressed while the second mode is simultaneously motivated. Moreover, the increase of amplitude within the lower frequency range can enhance the stability of the first mode. The Mack second mode is suppressed when the admittance phase tends to π, while the first mode is motivated. Generally, the larger the admittance amplitude is, the more obvious the suppression or excitation effect of unstable modes becomes. Besides, combined with the effect of aperture geometry parameters on the admittance, an engineering realizable broadband acoustic metasurface is proposed to suppress both the first and Mack second modes in Mach 4 boundary layer flow. It elaborately designs the piecewise microstructures to achieve the local favorite admittance phase and amplitude, and its performance is verified by the
$ {\mathrm{e}}^{N} $ method. -
图 1 缝隙型声学超表面的示意图
Figure 1. Schematic diagram of the aperture type acoustic metasurface
图 3 声学超表面导纳相位与幅值对不稳定模态增长率的影响
Figure 3. Effects of admittance phase and amplitude of acoustic metasurface on the growth rates of unstable modes
图 4 不同导纳相位对第1模态增长率的影响
Figure 4. Effects of admittance phase on the growth rates of the first mode
图 9 不同频率下扰动模态在声学超表面与光滑表面的增长率对比
Figure 9. Growth rates of unstable modes at different frequencies on acoustic metasurface and smooth surface
图 10 声学超表面与光滑表面的N值曲线对比
Figure 10. Comparisons of N-value curves of acoustic metasurface and smooth surface
图 11 声学超表面与光滑表面N值包络线对比
Figure 11. Comparisons of N-value envelopments of acoustic metasurface and smooth surface
表 1 不同
${\boldsymbol{x}} $ 位置处的最优缝隙参数Table 1. Optimal gap parameters at different
${\boldsymbol{x}} $ positions流向位置x/m H/mm n Ar 0.10 0.28 0.12 0.7 0.15 0.37 0.12 0.7 0.20 0.44 0.13 0.7 0.25 0.51 0.13 0.7 0.30 0.57 0.14 0.7 0.35 0.63 0.14 0.7 0.40 0.68 0.14 0.7 
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