Multiscale Proper Orthogonal Decomposition (mPOD) of TR-PIV data-- a Case Study on Stationary and Transient Cylinder Wake Flows (2001.01971v2)

Abstract: Data-driven decompositions of Particle Image Velocimetry (PIV) measurements are widely used for a variety of purposes, including the detection of coherent features (e.g., vortical structures), filtering operations (e.g., outlier removal or random noise mitigation), data reduction and compression. This work presents the application of a novel decomposition method, referred to as Multiscale Proper Orthogonal Decomposition ( Mendez J Fluid Mech 870:988-1036, 2019) to Time-Resolved PIV (TR-PIV) measurement. This method combines Multiresolution Analysis (MRA) and standard Proper Orthogonal Decomposition (POD) to achieve a compromise between decomposition convergence and spectral purity of the resulting modes. The selected test case is the flow past a cylinder in both stationary and transient conditions, producing a frequency-varying Karman vortex street. The results of the mPOD are compared to the standard POD, the Discrete Fourier Transform (DFT) and the Dynamic Mode Decomposition (DMD). The mPOD is evaluated in terms of decomposition convergence and time-frequency localization of its modes. The multiscale modal analysis allows for revealing beat phenomena in the stationary cylinder wake, due to the three-dimensional nature of the flow, and to correctly identify the transition from various stationary regimes in the transient test case.

• The paper presents mPOD as a novel hybrid method combining MRA and POD to achieve superior mode separation and spectral purity in fluid dynamics analysis.
• The paper demonstrates that mPOD effectively distinguishes vortex shedding behaviors in both stationary and transient flows, overcoming limitations of traditional POD and DMD.
• The paper highlights mPOD’s near-optimal convergence and improved interpretability of complex flow dynamics, indicating promising applications for reduced-order modeling.

Analysis of Multiscale Proper Orthogonal Decomposition (mPOD) Applied to TR-PIV Data for Cylinder Wake Flows

The paper presents an investigation into the efficacy of a novel data decomposition technique termed Multiscale Proper Orthogonal Decomposition (mPOD). This technique is applied to time-resolved particle image velocimetry (TR-PIV) data in the context of cylinder wake flows under stationary and transient conditions. The paper is particularly relevant for researchers interested in fluid dynamics and data-driven methods for analyzing complex flow phenomena, as it offers both a methodological advancement and a case paper showcasing the potential applications and limitations of existing decompositions.

Framework and Methodology

The authors introduce mPOD as a hybrid decomposition method combining the strengths of Multiresolution Analysis (MRA) and Proper Orthogonal Decomposition (POD). By doing so, mPOD strives to achieve both decomposition convergence and spectral purity in the resulting modes, addressing the shortcomings of existing approaches such as POD, DMD, and DFT. The core idea is to partition data into frequency-based scales, allowing each decomposition scale to capture the relevant dynamics optimally in both energy and frequency domains.

The paper's experimental setup leverages TR-PIV to observe the flow past a cylinder both in steady and transient regimes, offering a comprehensive dataset to test the mPOD. The analysis involves decomposing this dataset using various methods to illustrate the strengths of mPOD compared to classical techniques.

Key Findings

1. Stationary Wake Flow: The application of mPOD on stationary cylinder wake flow identified beat phenomena directly linked to vortex shedding, due to the flow's three-dimensional nature. The standard DMD did capture the dominant modes but exhibited convergence issues, whereas the mPOD achieved better mode separation and detail retention in both spatial and temporal domains.
2. Transient Flow Analysis: In the transient case, mPOD successfully differentiated between the vortex shedding during the different steady states and the transition phase, a task that proved challenging for both POD and DMD. The spectral partitioning in mPOD facilitated this differentiation, allowing for a clearer temporal localization.
3. Convergence and Accuracy: Notably, mPOD maintained a near-optimal convergence similar to POD while significantly enhancing the clarity and interpretability of the modes concerning their physical relevance and spectral characteristics.

Implications and Future Directions

The findings suggest that mPOD holds considerable promise for fluid dynamics applications, particularly in contexts where traditional POD or DMD might fall short in resolving complex, multiscale datasets. While the paper primarily focuses on cylinder wake flows, the adaptability of mPOD to other turbulent flow scenarios is evident.

The ability of mPOD to achieve spectral purity without sacrificing energy capture is significant for developing reduced-order models, which could potentially lead to more efficient computations in control systems and simulations. Furthermore, the insights into three-dimensional flow structures and transient dynamics underscore the potential for broader applicability in fluid mechanics and beyond.

Future work should explore the objective determination of MRA scales and aim to refine computational efficiency, possibly by exploiting the sparsity of correlation matrices. Additionally, an extensible paper is warranted to assess the mPOD's generality across different flow regimes and its integration with machine learning tools for automated feature extraction and analysis.

The paper provides a comprehensive case paper demonstrating both theoretical and practical advancements in the decomposition of complex flow data. The mPOD technique emerges as a robust tool, promising to aid researchers in unveiling deeper insights from intricate data structures present in fluid dynamics phenomena.