Reduced-order models for closed-loop wake control
Reduced-order models for closed-loop wake control
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DOI：
10.1098/rsta.2010.0367
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发表时间：
2011-04
期刊：
影响因子：
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通讯作者：
G. Tadmor;O. Lehmann;B. R. Noack;L. Cordier;J. Delville;J. Bonnet;M. Morzynski
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文献类型：
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作者：
G. Tadmor;O. Lehmann;B. R. Noack;L. Cordier;J. Delville;J. Bonnet;M. Morzynski
我们回顾了一种适用于尾迹闭环稳定化设计的低阶和最低阶Galerkin模型的策略。这些低阶模型基于一套固定的主导相干结构，由于两个挑战，往往脆弱得无可救药。首先，它们忽略了与基流和随机波动相互作用的重要稳定作用。其次，它们的有效范围受到忽略自然和激励瞬变过程中的模式变形的限制。我们通过包括移位模式(S)和非线性湍流模型来解决第一个挑战。由此产生的稳健的最低阶模型建立在惯性流形上，该流形将基流的缓慢变化与相干和随机波动幅度联系起来。第二个挑战，相干结构的变形，通过参数相关模式来解决，允许在操作条件之间平滑过渡。现在，Galerkin模型生活在包含模式变形的精致流形上。控制设计是模型结构提炼的一个简单推论。我们举例说明了驱动尾迹流的建模路径。
We review a strategy for low- and least-order Galerkin models suitable for the design of closed-loop stabilization of wakes. These low-order models are based on a fixed set of dominant coherent structures and tend to be incurably fragile owing to two challenges. Firstly, they miss the important stabilizing effects of interactions with the base flow and stochastic fluctuations. Secondly, their range of validity is restricted by ignoring mode deformations during natural and actuated transients. We address the first challenge by including shift mode(s) and nonlinear turbulence models. The resulting robust least-order model lives on an inertial manifold, which links slow variations in the base flow and coherent and stochastic fluctuation amplitudes. The second challenge, the deformation of coherent structures, is addressed by parameter-dependent modes, allowing smooth transitions between operating conditions. Now, the Galerkin model lives on a refined manifold incorporating mode deformations. Control design is a simple corollary of the distilled model structure. We illustrate the modelling path for actuated wake flows.