In a recent article published in the journal Nature Communications, researchers introduced a novel approach to studying the dynamics of wall-bounded turbulent flows using eXplainable artificial intelligence (XAI). They highlighted the significance of various types of coherent structures in the flow and their role in predicting future flow states.
We show a representative horizontal slice, being the streamwise and spanwise directions represented by x+ and z+, at a wall-normal distance y+ = 12 for a single instantaneous field, where left and right columns represent the lower and upper channel walls. (Top) simulated u velocity field, (middle) predicted velocity field, and (bottom) relative error between the two previous fields. The subscripts s and p correspond to the fields in the reference simulation and the prediction, respectively. Image Credit: https://www.nature.com/articles/s41467-024-47954-6
Additionally, they demonstrated the applicability of this new technique to experimental data at higher Reynolds numbers, where the hierarchy of energy-containing scales is broader and more complex.
Background
Wall-bounded turbulence is a complex phenomenon that occurs in many natural and engineering applications, such as aerodynamics, combustion, energy generation, and transportation. It involves a wide range of spatial and temporal scales, which makes it challenging to model and control. This complexity poses challenges in modeling and controlling it effectively.
A fundamental approach to comprehending wall-bounded turbulence involves investigating interactions among energy-containing coherent structures within the flow. These structures, characterized by high Reynolds stress, facilitate momentum and energy transfer across scales. However, identifying and assessing the significance of these structures requires novel perspectives and methodologies.
About the Research
In this paper, the authors employed a combination of direct numerical simulation (DNS), deep convolutional neural networks (CNNs), and Shapley additive explanations (SHAP) to examine the significance of coherent structures in turbulent channel flow which is a fundamental canonical geometry of wall-bounded flows. DNS is a numerical technique that resolves all the scales of the flow by solving the Navier-Stokes equations without any additional assumptions.
CNNs are a type of deep learning model that can extract spatial information from the data and learn to predict complex patterns. SHAP is a game-theoretic method that evaluates the significance of each input feature on the CNN prediction by analyzing the discrepancy between the predicted and simulated flow fields.
The researchers utilized a U-shaped encoder-decoder network (U-net) architecture, which is a type of CNN specially designed for image segmentation and reconstruction, to forecast the velocity field in channel flow at subsequent time steps based on the current velocity field.
Subsequently, they segmented the domain into four coherent structure types via quadrant analysis of Reynolds stress: ejections, sweeps, outward interactions, and inward interactions, categorized by the sign of velocity fluctuations. Each structure served as an input feature for the SHAP algorithm, determining the importance ranking for predicting the next flow field and assessing the relative significance of each structure type.
Research Findings
The outcomes showed that ejections and sweeps were the most important structures for the prediction of the flow, collectively representing 97% of the total SHAP score. These structures were also found to be the primary contributors to Reynolds shear stress, indicative of momentum transfer within the flow. However, the authors also found that the most important structures per unit volume were not necessarily the ones with the highest Reynolds shear stress.
They identified certain small wall-detached ejections and inward interactions that possessed high importance per volume, eluding detection by traditional methods relying solely on Reynolds shear stress. Furthermore, it was observed that the most significant structures exhibited a larger aspect ratio in the streamwise direction than in the spanwise direction, with their wall-normal length being 3-6 times smaller than their streamwise length.
The method was further applied to an experimental database of turbulent boundary layers obtained from a flat plate, measured using particle-image velocimetry (PIV), featuring higher Reynolds numbers and limited data. The experimental Reynolds number exceeded that of the simulation, suggesting a broader range of scales and structures within the flow.
The method successfully identified the most important structures in the experimental data and exhibited a similar distribution of SHAP values as observed in the simulation. Notably, there was a greater significance of sweeps compared to ejections in the experimental data, consistent with previous experimental findings.
Applications
The developed methodologies provide a data-driven approach for analyzing the dynamics of wall-bounded turbulent flows, without relying on any physical assumptions or hypotheses. This methodology holds significant potential and can be extended to various other types of turbulent flows, encompassing homogeneous isotropic turbulence, boundary layers over rough surfaces, and flows with separation and reattachment.
Moreover, the versatility of this novel method extends beyond fluid dynamics and can be applied to other fields where XAI is essential. Furthermore, the method's adaptability makes it suitable for addressing XAI needs in diverse domains such as medicine, biology, and social sciences.
Conclusion
In summary, the novel framework proved effective for studying wall-bounded turbulence using XAI. It efficiently revealed the importance of various coherent structures within the flow and their contributions to predicting future flow states. Moving forward, the researchers suggested applying their method to more complex flow configurations and comparing results with alternative methodologies based on information theory or perturbation analysis.
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