Impact of compliant coating on Mack-mode evolution in hypersonic boundary layers
Impact of compliant coating on Mack-mode evolution in hypersonic boundary layers
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DOI：
10.1017/jfm.2023.731
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发表时间：
2023-10
影响因子：
3.7
通讯作者：
Xiaoyang Ji;Ming Dong;Lei Zhao
中科院分区：
文献类型：
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作者：
Xiaoyang Ji;Ming Dong;Lei Zhao
摘要本文研究了高超声速平板边界层中Mack不稳定模态的线性演化。顺应性部分是覆盖在由微孔组成的多孔壁上的薄的柔性膜。不稳定压力会引起膜的振动，从而通过横向速度波动反馈到边界层流体。这样一个过程是制定由导纳边界条件的边界层扰动，这是依赖于膜的厚度和张力，多孔壁的属性，和Mack模式扰动的频率。利用此导纳条件，通过求解可压缩Orr-Sommerfeld方程，系统地研究了柔顺涂层对Mack生长速率的影响。结果发现，顺应性涂层可以抑制Mack不稳定性与附近的最不稳定的频率的频带，和稳定的频带加宽的膜厚度和张力的减少，表明一个更有利的效果较软的膜。对于具有特定维度频率的Mack模式-由于其无量纲频率（由局部边界层厚度和迎面而来的速度归一化）随着其向下游传播而增加-第二模式频带通常出现在下游位置，膜的稳定效应也是如此。因此，有利的是在下游区域处应用顺应性面板。在这种情况下，固体柔顺结可能会产生额外的散射效应的Mack模式的演变，由于其边界条件的突变。散射效应由透射系数来量化，透射系数由柔性壁扰动到固体壁扰动的等效振幅来定义，其可以通过谐波线性化Navier-Stokes（HLNS）方法来获得。如果导纳很弱，那么传输系数也可以通过基于留数定理的解析解来预测。研究发现，只要导纳幅角在[150 ^\circ，210 ^\circ]$范围内，散射效应对大部分二阶模都有抑制作用，这与大多数物理情况相符.当导纳模小于O（0.1）时，解析预测与HLNS计算吻合得很好。
Abstract This paper focuses on the linear evolution of Mack instability modes in a hypersonic boundary layer over a flat plate that is partially coated by a compliant section. The compliant section is a thin, flexible membrane covering on a porous wall consisting of micro holes. The instability pressure could induce a vibration of the membrane, leading to a feedback to the boundary-layer fluids through the transverse velocity fluctuation. Such a process is formulated by an admittance boundary condition for the boundary-layer perturbation, which is dependent on the thickness and tension of the membrane, the properties of the porous wall, and the frequency of the Mack-mode perturbation. Using this admittance condition, the impact of the compliant coating on the Mack growth rate is studied systematically by solving the compressible Orr–Sommerfeld equations. It is found that the compliant coating could suppress the Mack instability with a frequency band in the neighbourhood of the most unstable frequency, and the stabilising frequency band widens as the membrane thickness and tension decrease, indicating a more favourable effect of a softer membrane. For a Mack mode with a specified dimensional frequency – since its dimensionless frequency, normalised by the local boundary-layer thickness and oncoming velocity, increases as it propagates downstream – the second-mode frequency band usually appears in downstream locations, and so does the stabilising effect of the membrane. Thus it is favourable to apply a compliant panel at a downstream region. In this situation, the solid–compliant junction could produce an additional scattering effect on the evolution of the Mack mode due to the sudden change of its boundary condition. The scattering effect is quantified by a transmission coefficient defined by the equivalent amplitude of the compliant-wall perturbation to the solid-wall perturbation, which can be obtained by the harmonic linearised Navier–Stokes (HLNS) approach. If the admittance is weak, then the transmission coefficient can also be predicted by an analytical solution based on the residue theorem. It is found that most of the second modes are suppressed by the scattering effect as long as the argument of the admittance is in the interval $[150^\circ, 210^\circ ]$, agreeing with most of the physical situation. The analytical predictions agree well with the HLNS calculations when the modulus of the admittance is less than $O(0.1)$.