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中文核心期刊

各向异性柔性壁上二维T-S波演化的数值研究

NUMERICAL INVESTIGATION OF THE EVOLUTION OF TWO-DIMENSIONAL T-S WAVES ON AN ANISOTROPIC COMPLIANT WALL

  • 摘要: 受自然界鸟类羽毛的柔性特征启发, 利用数值模拟的手段进行了各向异性柔性壁面对亚音速边界层中T-S(Tollmien-Schlichting)波空间演化的影响研究. 首先, 刚性壁面上的数值结果与线性理论预测的结果吻合得很好, 验证了所采用的高阶精度格心型有限差分方法的可靠性. 在此基础上, 将部分刚性壁面替换为柔性壁面, 结果表明柔性壁面能够减小甚至消除T-S波的不稳定增长区间, 即抑制T-S波的发展, 因而具有推迟边界层转捩的潜力. 柔性壁面的变形不仅有对应T-S波波形的成分, 还会因柔性段前缘引起波长更长, 与T-S波频率相同的壁面波动. 随后开展的参数研究表明, 增大壁面阻尼削弱了前缘引起的壁面波动; 增大壁面的刚度、张力以及弹性系数都会使得壁面的刚性增强, 整体变形幅度下降; 柔性壁面的支撑杠杆臂倾角越大, 壁面刚性越强. 以上参数的增大均会使得柔性壁面抑制T-S波的效果降低. 此外, 当流动反方向流过时, 抑制T-S波的效果也会明显下降. 这些研究结果旨在揭示鸟类高效飞行的部分奥秘, 为被动减阻提供新的思路.

     

    Abstract: As inspired by the flexible characteristics of the feathers of birds, the influence of an anisotropic compliant wall on the spatial evolution of the T-S wave in the subsonic boundary layer flow is studied numerically in this article. First of all, the numerical results are in good agreement with that predicted by the linear stability theory and also the numerical results obtained by others. This demonstrates the reliability of the cell-centered finite difference method with high-order accuracy, which is adopted in this article. After that, a part of the rigid wall is replaced with an anisotropic compliant wall. The obtained results show that the compliant wall is able to reduce or even remove the unstable growth region of the T-S wave, i.e., suppress the amplitude growth of the T-S wave. Thus, the compliant wall has the potential to delay laminar-turbulent transition. The deformation of the compliant wall not only has components corresponding to the T-S wave waveform, but also the wall vibration with longer wavelength and same frequency compared to the T-S wave, which is caused by the leading edge of the compliant wall. The parameter study shows that with increased damping, the wall vibration by the leading edge is weakened. An increase in the rigidity, tension or elastic coefficient of the compliant wall will result in the wall stiffer and thus lead to smaller deformation. The greater the incline angle of the supporting lever arm, the stiffer the compliant wall. The increase of any of the above parameters will lead to a reduction in the suppression effect of the compliant wall on the T-S wave. When the flow direction is reversed, the suppression effect is also weakened. This research is aimed to reveal some of the mysteries of bird's efficient flying, and provides new ideas for passive flow control to reduce drag.

     

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