On the origin of the inflectional instability of a laminar separation bubble
On the origin of the inflectional instability of a laminar separation bubble
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层流分离气泡弯曲不稳定性的起源
DOI：
10.1017/s002211200900634x
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发表时间：
2009
影响因子：
3.7
通讯作者：
O. N. Ramesh
中科院分区：
文献类型：
--
作者：
Sourabh S. Diwan;O. N. Ramesh
本文对层流分离气泡及其线性稳定机制进行了实验和理论研究。实验是在风洞中的平板上进行的，翼型具有典型的外加压力梯度，包括层流分离气泡。用热线风速仪测量了分离气泡的表面压力分布和流向速度，并对分离气泡进行了表征。用单组分热线风速仪对相变动力学进行了详细的研究。结果发现，气泡前部所谓的死气区对应于扰动幅度较小的区域，其幅度在接近再附着点时达到最大值。在气泡平均最大高度的上游区域，扰动的指数增长速率，这表明线性不稳定机制在起作用。在分离位置上游的边界层中引入了一个无限小的扰动，当波包向下游平流时，波包被跟踪(集合平均意义上)。这次扰动被发现是对流性质的。对平均速度剖面进行了线性稳定性分析(Orr-Sommerfeld和Rayleigh计算)，从附加的逆压梯度边界层一直向上到分离气泡区的前部(即直到死气区的末端，在那里可以预期扰动的线性演变)。本文的结论是，分离气泡的主要不稳定性机制本质上是弯曲的，其起源可以追溯到分离位置的上游。换言之，分离剪切层的无粘性弯曲不稳定性在逻辑上应该被视为上游附加的逆压梯度边界层不稳定性的延伸。这修正了将分离气泡中不稳定的起源与气泡外部分离的剪切层联系在一起的传统观点，以及与之相关的开尔文-亥姆霍兹机制。我们认为，只有当分离的剪切层离开壁面相当远时(这发生在平均气泡的最大高度位置附近)，Kelvin-Helmholtz不稳定性范例及其相关的标度原理的描述才可能变得相关。我们还提出了一个关于壁面剪切层最大放大频率与拐点高度和涡度厚度的新标度，并证明了它的普适性。
This is an experimental and theoretical study of a laminar separation bubble and the associated linear stability mechanisms. Experiments were performed over a flat plate kept in a wind tunnel, with an imposed pressure gradient typical of an aerofoil that would involve a laminar separation bubble. The separation bubble was characterized by measurement of surface-pressure distribution and streamwise velocity using hot-wire anemometry. Single component hot-wire anemometry was also used for a detailed study of the transition dynamics. It was found that the so-called dead-air region in the front portion of the bubble corresponded to a region of small disturbance amplitudes, with the amplitude reaching a maximum value close to the reattachment point. An exponential growth rate of the disturbance was seen in the region upstream of the mean maximum height of the bubble, and this was indicative of a linear instability mechanism at work. An infinitesimal disturbance was impulsively introduced into the boundary layer upstream of separation location, and the wave packet was tracked (in an ensemble-averaged sense) while it was getting advected downstream. The disturbance was found to be convective in nature. Linear stability analyses (both the Orr–Sommerfeld and Rayleigh calculations) were performed for mean velocity profiles, starting from an attached adverse-pressure-gradient boundary layer all the way up to the front portion of the separation-bubble region (i.e. up to the end of the dead-air region in which linear evolution of the disturbance could be expected). The conclusion from the present work is that the primary instability mechanism in a separation bubble is inflectional in nature, and its origin can be traced back to upstream of the separation location. In other words, the inviscid inflectional instability of the separated shear layer should be logically seen as an extension of the instability of the upstream attached adverse-pressure-gradient boundary layer. This modifies the traditional view that pegs the origin of the instability in a separation bubble to the detached shear layer outside the bubble, with its associated Kelvin–Helmholtz mechanism. We contend that only when the separated shear layer has moved considerably away from the wall (and this happens near the maximum-height location of the mean bubble), a description by the Kelvin–Helmholtz instability paradigm, with its associated scaling principles, could become relevant. We also propose a new scaling for the most amplified frequency for a wall-bounded shear layer in terms of the inflection-point height and the vorticity thickness and show it to be universal.