Receptivity of a supersonic boundary layer over a flat plate. Part 2. Receptivity to free-stream sound
Receptivity of a supersonic boundary layer over a flat plate. Part 2. Receptivity to free-stream sound
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DOI：
10.1017/s0022112003004798
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发表时间：
2003-08-10
影响因子：
3.7
通讯作者：
Zhong, XL
中科院分区：
文献类型：
--
作者：
Ma, YB;Zhong, XL
在本文中，我们继续利用直接数值模拟和线性稳定性理论研究超声速边界层对自由流扰动的接受机制。具体地说，研究了4.5马赫在平板上的流动对自由流快速声波的接受性。对自由流慢声波、熵波和涡度波的接受度将在未来进行研究。由于自由流扰动波在进入边界层之前先经过激波，由边界层位移引起的斜激波在接受度中起着重要的作用。数值模拟中采用了高阶激波拟合格式，以考虑自由流扰动波与斜激波相互作用的影响。结果表明，平板边界层对自由流动的快速声波的接受性导致了Mack模态和一系列稳定模态的激发，即模态I、模态II等。研究发现，强迫快速声波不直接与不稳定的Mack模态相互作用。相反，稳定型I波在接受过程中起重要作用，因为它们与强迫声波和不稳定的Mack-mode波相互作用。通过相互作用，稳定I型波将强迫快速声波的波能量传递给第二马克型波。研究了入射波角度、强迫波频率和壁温扰动条件对接收度的影响。结果表明，第二模态与第一模态和第十一模态的接收机理有很大的不同，这导致了这些离散波模态对不同入射角、频率和不同壁面边界条件下的自由流快速声波的接收特性有很大的不同。当入射波角分别约为26°、45°和18°时，第二模态、ⅰ模态和ⅱ模态对平面自由流快速声波的接受度最大。对一束自由流快速声波的接受度结果表明，前缘是最有效的接受区之一。
In this paper, we continue to study the mechanisms of the receptivity of the supersonic boundary layer to free-stream disturbances by using both direct numerical simulation and linear stability theory. Specifically, the receptivity of a Mach 4.5 flow over a flat plate to free-stream fast acoustic waves is studied. The receptivity to free-stream slow acoustic waves, entropy waves and vorticity waves will be studied in the future. The oblique shock wave induced by the boundary-layer displacement plays an important role in the receptivity because the free-stream disturbance waves first pass through the shock before entering the boundary layer. A high-order shock-fitting scheme is used in the numerical simulations in order to account for the effects of interactions between free-stream disturbance waves and the oblique shock wave. The results show that the receptivity of the flat-plate boundary layer to free-stream fast acoustic waves leads to the excitation of both Mack modes and a family of stable modes, i.e. mode I, mode II, etc. It is found that the forcing fast acoustic waves do not interact directly with the unstable Mack modes. Instead, the stable mode I waves play an important role in the receptivity process because they interact with both the forcing acoustic waves and the unstable Mack-mode waves. Through the interactions, the stable mode I waves transfer wave energy from the forcing fast acoustic waves to the second Mack-mode waves. The effects of incident wave angles, forcing wave frequencies, and wall temperature perturbation conditions on the receptivity are studied. The results show that the receptivity mechanisms of the second mode are very different from those of modes I and 11, which leads to very different receptivity properties of these discrete wave modes to free-stream fast acoustic waves with different incident wave angles, frequencies, and different wall boundary conditions. The maximum receptivities of the second mode, mode I and mode II to planar free-stream fast acoustic waves are obtained when incident wave angles approximately equal 26degrees, 45degrees, and 18degrees, respectively. The results of receptivity to a beam of free-stream fast acoustic waves show that the leading edge is one of the most efficient regions for receptivity.