Linear optimal control applied to instabilities in spatially developing boundary layers
Linear optimal control applied to instabilities in spatially developing boundary layers
复制标题
线性最优控制应用于空间发展边界层的不稳定性
DOI：
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发表时间：
2002
影响因子：
3.7
通讯作者：
D. Henningson
中科院分区：
文献类型：
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作者：
M. Högberg;D. Henningson
提出的工作扩展了以前的研究线性控制器在时间通道流空间演变的边界层流动。研究的流动是由Falkner-Skan-Cooke（FSC）速度剖面描述的无限后掠楔形体上的流动，包括平板上流动的特殊情况。利用线性最优控制理论，将这些速度分布作为Orr-Sommerfeld-Squire方程的基流，通过壁面吹吸计算最优反馈控制。控制应用于一个不稳定扰动的并行FSC流。通过特征值分析和直接数值模拟（DNS），它表明，不稳定性稳定的控制器在并行的情况下。用于控制的卷积核的局部化也被示出用于FSC轮廓。假设非平行的影响是小的技术开发应用相同的控制器的DNS的空间演变流。这些控制器的性能进行了测试，在Blasius流与Tollmien-Schlichting（TS）波和最佳的空间瞬态增长扰动。结果表明，TS波稳定，瞬态增长降低了控制器。然后，控制也适用于空间FSC流与不稳定的扰动，导致饱和的横流涡在未控制的情况下。结果表明，线性控制器成功地抑制了横流涡的增长到饱和水平，从而延迟了通过二次不稳定性过渡的可能性。它还表明，该控制器的工作相对较高的非线性，以及固定以及随时间变化的扰动。
The work presented extends previous research on linear controllers in temporal channel flow to spatially evolving boundary layer flow. The flows studied are those on an infinite swept wedge described by the Falkner–Skan–Cooke (FSC) velocity profiles, including the special case of the flow over a flat plate. These velocity profiles are used as the base flow in the Orr–Sommerfeld–Squire equations to compute the optimal feedback control through blowing and suction at the wall utilizing linear optimal control theory. The control is applied to a parallel FSC flow with unstable perturbations. Through an eigenvalue analysis and direct numerical simulations (DNS), it is shown that instabilities are stabilized by the controller in the parallel case. The localization of the convolution kernels for control is also shown for the FSC profiles. Assuming that non-parallel effects are small a technique is developed to apply the same controllers to a DNS of a spatially evolving flow. The performance of these controllers is tested in a Blasius flow with both a Tollmien–Schlichting (TS) wave and an optimal spatial transiently growing perturbation. It is demonstrated that TS waves are stabilized and that transient growth is lowered by the controller. Then the control is also applied to a spatial FSC flow with unstable perturbations leading to saturated cross-flow vortices in the uncontrolled case. It is demonstrated that the linear controller successfully inhibits the growth of the cross-flow vortices to a saturated level and thereby delays the possibility of transition through secondary instabilities. It is also demonstrated that the controller works for relatively high levels of nonlinearity, and for stationary as well as time-varying perturbations.