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Clustering the Flow: A VQPCA-Based Framework for Pattern Discovery in Fluid Dynamics

Juan Angel Martin, Eva Muñoz, Himansu Dave, Alessandro Parente, Soledad Le Clainche

Abstract

Clustering techniques offer a powerful framework for analyzing complex flow dynamics and reducing computational costs in large-scale simulations. In this work, we propose a novel clustering-based approach using Vector Quantization Principal Component Analysis (VQPCA) to identify structural sensitivity zones, namely the regions where the fluid flow is more receptive to changes. To the authors knowledge, this is the first application of VQPCA to a fluid dynamics problem for the identification of flow patterns and dynamically relevant regions. As a fully data-driven technique, it does not rely on adjoint methods; therefore, this approach has the advantage of having low computational cost, since it depends exclusively on data from the direct problem. The VQPCA technique demonstrates its ability to extract dominant flow features by clustering the flow field into regions characterized by their intrinsic dynamics. To assess the validity of this method, it is used to investigate the wake behind a circular cylinder, revealing similarities to previously established structural sensitivity regions. The robustness of the approach is further assessed through validation and calibration in different operating conditions in this flow scenario. As an extension of the analysis, we address the complex dynamics of two planar synthetic jets, where the clustering insights can lead to develop flow control strategies. These results highlight the potential of clustering-based methods as practical and effective tools to analyze and optimize fluid flows.

Clustering the Flow: A VQPCA-Based Framework for Pattern Discovery in Fluid Dynamics

Abstract

Clustering techniques offer a powerful framework for analyzing complex flow dynamics and reducing computational costs in large-scale simulations. In this work, we propose a novel clustering-based approach using Vector Quantization Principal Component Analysis (VQPCA) to identify structural sensitivity zones, namely the regions where the fluid flow is more receptive to changes. To the authors knowledge, this is the first application of VQPCA to a fluid dynamics problem for the identification of flow patterns and dynamically relevant regions. As a fully data-driven technique, it does not rely on adjoint methods; therefore, this approach has the advantage of having low computational cost, since it depends exclusively on data from the direct problem. The VQPCA technique demonstrates its ability to extract dominant flow features by clustering the flow field into regions characterized by their intrinsic dynamics. To assess the validity of this method, it is used to investigate the wake behind a circular cylinder, revealing similarities to previously established structural sensitivity regions. The robustness of the approach is further assessed through validation and calibration in different operating conditions in this flow scenario. As an extension of the analysis, we address the complex dynamics of two planar synthetic jets, where the clustering insights can lead to develop flow control strategies. These results highlight the potential of clustering-based methods as practical and effective tools to analyze and optimize fluid flows.
Paper Structure (22 sections, 3 equations, 21 figures, 6 tables)

This paper contains 22 sections, 3 equations, 21 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Structural sensitivity
  4. Clustering method: Vector Quantization Principal Component Analysis (VQPCA)
  5. Application on the wake of a circular cylinder
  6. Instabilities on the wake of a circular cylinder
  7. Datasets
  8. Data preparation
  9. Clustering results
  10. Hyperparameters calibration
  11. Robustness assessment of the method and its calibration
  12. Application on the flow of two synthetic jets
  13. Flow and instabilities on two synthetic jets
  14. Dataset
  15. Data preparation
  16. ...and 7 more sections

Figures (21)

  • Figure 1: Scheme of VQPCA algorithm, adapted from Ref. DaveSwaminathanParente2022
  • Figure 2: Contour plots of the velocity components of 2D60 and 2D100 in their sampling domain.
  • Figure 3: (a) Streamwise component of the velocity $u_x$ and (b) vorticity $\omega_z$ of 3D280
  • Figure 4: Scheme of the matrix $\boldsymbol X$
  • Figure 5: Clustering contours corresponding to the streamwise velocity component, $u_x$, of the reference case 2D100. Each subfigure corresponds to a number of clusters, $k \in [2,8]$.
  • ...and 16 more figures