空间相干性递推本征正交分解方法及流场分析中的应用

Spatial coherence-based recurrence proper orthogonal decomposition method and its application in flow field analysis

  • 摘要: 数据驱动模态分解方法是复杂涡流场中多尺度相干结构识别与提取的核心手段,针对经典本征正交分解(proper orthogonal decomposition, POD)在多尺度涡流结构模态提取中存在频谱混杂、物理可解释性差等问题,提出基于空间相干性分析的递推本征正交分解方法(coherence-recurrence POD, CR-POD)。该方法从多尺度流动结构的相干性密度分布特性出发,基于嵌入DBSCAN密度聚类算法的空间相干性分析,构建逐层对流场快照残差矩阵进行奇异值分解的分析框架,将全局低秩近似转化为逐层局部最优近似,实现了流场结构从主导向次要再到精细尺度的自然剥离。将CR-POD应用于65°后掠三角翼大振幅俯仰运动非定常流场演化过程分析,结果表明:仅用5层模态即可捕捉超90%的流动,分析结果与大尺度主涡经过涡破裂逐步发展为湍流耗散的物理演化规律高度吻合,模态正交且无频谱混叠,各层模态对应明确的物理结构具有较好的物理可解释性。与标准POD相比,CR-POD在保持正交性和最优收敛性的同时,能有效解决复杂涡流场中多尺度相干结构难以自适应层次化分离的问题。

     

    Abstract: Data-driven modal decomposition is a fundamental approach for identifying and extracting multiscale coherent structures in complex vortical flow fields. To address the limitations of classical proper orthogonal decomposition, including spectral mixing among multiscale vortical structures and limited physical interpretability, this study proposes a Coherence-Recurrence Proper Orthogonal Decomposition method, abbreviated as CR-POD, based on spatial coherence analysis. Starting from the coherence-density distribution characteristics of multiscale flow structures, the proposed method integrates coherence analysis with the DBSCAN density-based clustering algorithm and establishes a hierarchical framework in which singular value decomposition is recursively applied to residual fields. In this way, the conventional global low-rank approximation is transformed into a sequence of layer-wise local optimal approximations, enabling the natural separation of flow-field structures from dominant, secondary, to fine-scale components. CR-POD is applied to the analysis of unsteady pressure-field evolution over a 65° swept delta wing undergoing large-amplitude pitching motion. The results show that more than 90% of the total energy can be captured using only five modal layers. The decomposed modes are highly consistent with the physical evolution from large-scale primary vortices to fine-scale turbulent structures. Moreover, the obtained modes remain orthogonal, exhibit no evident spectral aliasing, and each modal layer corresponds to physically meaningful flow structures with clear interpretability. Compared with standard POD, CR-POD preserves modal orthogonality and optimal convergence while effectively overcoming the difficulty of adaptive hierarchical separation of multiscale coherent structures in complex vortical flows.

     

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