On least-order flow representations for aerodynamics and aeroacoustics
On least-order flow representations for aerodynamics and aeroacoustics
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空气动力学和气动声学的最小阶流表示
DOI：
10.1017/jfm.2012.70
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发表时间：
2012
影响因子：
3.7
通讯作者：
Tadmor
中科院分区：
文献类型：
--
作者：
Schlegel;Jordan;Dillmann;Gröschel;Schröder;Freund;Lehmann;Tadmor
我们提出了适当正交分解（POD）的推广，以实现线性相关可观测量的最佳流分辨率。这种伽辽金展开式被称为“可观测推断分解”（OID），通过识别对这些可观测值贡献最大的模式来满足空气动力学和气动声学应用的需求。因此，OID 构成了物理理解、最小偏差条件采样、状态估计和控制设计的构建块。从 OID 版本的连续体中，两个变体分别针对观察者和控制设计的目的而定制。首先，与可观察到的最可能的流动状态是由“最小残差”变体构造的。该版本构成了对最可能的流体动力学状态的简单且易于推广的重建，以预处理有效的观测器设计。其次，“能量最小”变体识别可观察到的增益最大的模式。该版本是李亚普诺夫控制设计的构建块。与 POD 相比，OID 可以在多种剪切流中有效降维。特别是，研究了三个空气动力学和气动声学目标泛函：（i）二维圆柱尾流的升力和阻力波动； (ii) 由传感器阵列测量并从二维可压缩混合层发射的气动声学密度波动； (iii) 由传感器阵列监测并从三维可压缩射流发射的气动声压。最“与阻力相关”、“与升力相关”和“响亮”的结构是根据已知的物理过程进行提炼和解释的。
We propose a generalization of proper orthogonal decomposition (POD) for optimal flow resolution of linearly related observables. This Galerkin expansion, termed ‘observable inferred decomposition’ (OID), addresses a need in aerodynamic and aeroacoustic applications by identifying the modes contributing most to these observables. Thus, OID constitutes a building block for physical understanding, least-biased conditional sampling, state estimation and control design. From a continuum of OID versions, two variants are tailored for purposes of observer and control design, respectively. Firstly, the most probable flow state consistent with the observable is constructed by a ‘least-residual’ variant. This version constitutes a simple, easily generalizable reconstruction of the most probable hydrodynamic state to preprocess efficient observer design. Secondly, the ‘least-energetic’ variant identifies modes with the largest gain for the observable. This version is a building block for Lyapunov control design. The efficient dimension reduction of OID as compared to POD is demonstrated for several shear flows. In particular, three aerodynamic and aeroacoustic goal functionals are studied: (i) lift and drag fluctuation of a two-dimensional cylinder wake flow; (ii) aeroacoustic density fluctuations measured by a sensor array and emitted from a two-dimensional compressible mixing layer; and (iii) aeroacoustic pressure monitored by a sensor array and emitted from a three-dimensional compressible jet. The most ‘drag-related’, ‘lift-related’ and ‘loud’ structures are distilled and interpreted in terms of known physical processes.
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