Resonant growth of three-dimensional modes in Falkner–Skan boundary layers with adverse pressure gradients
Resonant growth of three-dimensional modes in Falkner–Skan boundary layers with adverse pressure gradients
复制标题
具有逆压力梯度的 Falkner-Skan 边界层三维模式的共振增长
DOI：
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发表时间：
1996
影响因子：
3.7
通讯作者：
S. Gruber
中科院分区：
文献类型：
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作者：
T. Corke;S. Gruber
这项工作的文件的空间发展的三重不稳定波组成的平面TS模式和一对斜波的角度相等，相反的模式正在经历亚谐过渡的Falkner-Skan边界层与不利的压力梯度。本研究的动机是，对于零后掠角或中等后掠角的机翼，过渡最有可能发生在最大厚度点之后的逆压梯度区域，从低初始振幅开始，预计次谐波模态过渡是三维模态第一次增长的主要机制。这个实验遵循Corke & Mangano（1989）的实验，在该实验中，通过位于分支I附近的沿展向排列的加热丝引入扰动，以产生波的三波。初始条件受到严格控制。这些包括初始振幅、频率、相对相位和斜波角。基本流动由Falkner-Skan（Hartree）边界层组成，无量纲压力梯度参数在-0.06 [les ] βH [les ]-0.09范围内。基于线性理论，选择TS波的频率接近最大放大。斜波的频率是TS频率的次谐波。倾斜波角被设置为产生最大的二次生长（± 60°）。与Blasius边界层中的类似条件相比，观察到逆压梯度导致二维和三维模式的额外快速增长。在这种情况下，与零压力梯度情况相比，基本模式的最大振幅相对较大，并且振幅饱和区域显著缩短。这些结果的分析包括频谱，每个模式的振幅的壁正态分布，和平均速度剖面。最后，将流向振幅发展与Goldstein & Lee（1992）非线性临界层分析的振幅模型进行了比较。
This work documents the spatial development of a triad of instability waves consisting of a plane TS mode and a pair of oblique modes with equal-opposite wave angles which are undergoing subharmonic transition in Falkner–Skan boundary layers with adverse pressure gradients. The motivation for this study is that for wings with zero or moderate sweep angles, transition is most likely to occur in the adverse pressure gradient region past the maximum thickness point and, starting with low initial amplitudes, subharmonic mode transition is expected to be the predominant mechanism for the first growth of of three-dimensional modes. The experiment follows that of Corke & Mangano (1989) in which the disturbances to produce the triad of waves are introduced by a spanwise array of heating wires located near Branch I. The initial conditions are carefully controlled. These include the initial amplitudes, frequencies, relative phase and oblique wave angles. The basic flow consisted of a Falkner–Skan (Hartree) boundary layer with a dimensionless pressure gradient parameter in the range -0.06 [les ] βH [les ] -0.09. The frequency of the TS wave was selected to be near the most amplified based on linear theory. The frequency of the oblique waves was the subharmonic of the TS frequency. The oblique wave angles were set to give the largest secondary growth (≈ 60°). Compared to similar conditions in a Blasius boundary layer, the adverse pressure gradient was observed to lead to an extra rapid growth of the two- and three-dimensional modes. In this there was a relatively larger maximum amplitude of the fundamental mode and considerably shortened amplitude saturation region compared to zero pressure gradient cases. Analysis of these results includes frequency spectra, the wall-normal distributions of each mode amplitude, and mean velocity profiles. Finally, the streamwise amplitude development is compared with the amplitude model from the nonlinear critical layer analysis of Goldstein & Lee (1992).