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# Bridging Experimental shadowgraphs and DNS in Turbulent Convection Using physically-informed U-Net

Jai Kumar, Anne Sergent, Francesca Chillà, Julien Salort, Didier Lucor

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Jai Kumar, Anne Sergent, Francesca Chillà, Julien Salort, Didier Lucor. Bridging Experimental shadowgraphs and DNS in Turbulent Convection Using physically-informed U-Net. Joint event Euromech Colloquium on Data-Driven Fluid Dynamics/2nd ERCOFTAC Workshop on Machine Learning for Fluid Dynamics, Apr 2025, London, United Kingdom. hal-04924440

HAL Id: hal-04924440

https://hal.science/hal-04924440v1

Submitted on 31 Jan 2025

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# Bridging Experimental shadowgraphs and DNS in Turbulent Convection Using physically-informed U-Net

Jai Kumar¹, Anne Sergent¹,², Francesca Chillà³, Julien Salort³, Didier Lucor¹

¹ LISN-CNRS, Université Paris-Saclay, Orsay, France, ² Sorbonne Université, Paris, France, ³ Lab. Phys. ENS Lyon, France

Corresponding author: Jai Kumar (jai.kumar@lisn.fr)

Shadowgraph data holds significant potential, as it incorporates depth-of-field effects, enabling the extraction of richer physical information [1, 2]. The integration of physical information into it using Physics-Informed Neural Networks (PINNs) has been shown to successfully reconstruct flow fields in compressible, inviscid flows [3]. In this study, we aim to extract 3D field information from experimental shadowgraph data of turbulent convection using a trained deep learning model. Specifically, we employ a U-Net architecture to predict the temperature field over a 2D slice from shadowgraph. However, ground-truth field data is often unavailable or incomplete from experiments. Therefore, as first step, we use numerical shadowgraphs (simply modeled as Laplacian of temperature field) as input and temperature field as output from direct numerical simulation (DNS). Preliminary results, presented in Figure 1, highlight the potential of this approach. Furthermore, we investigate the feasibility of simultaneously extracting velocity fields alongside temperature fields. Finally, we apply the trained model to experimental shadowgraph images as DNS complements the experimental conditions.

This work benefits from the French National Research Agency funding (ANR-22-CE30-0018-02). Calculations were performed using HPC resources from GENCI-IDRIS (Grant 2a0326).

<figure><img src="image_4.png" /><figcaption>Figure 1: Results for predicting temperature field for a slice at a particular timestep in test-data from DNS simulation at Rayleigh number of $5 \times 10^9$ for the given shadowgraph image to U-Net, predicting highly accurate temperature field as output.</figcaption></figure>

## References

[1] J. P. Molnar, E. J. LaLonde, C. S. Combs, O. Léon, D. Donjat, and S. J. Grauer. Forward and inverse modeling of depth-of-field effects in background-oriented schlieren, February 2024. arXiv:2402.15954 [physics].

[2] M. Belkadi, L. Guislain, A. Sergent, B. Podvin, F. Chillà, and J. Salort. Experimental and numerical shadowgraph in turbulent Rayleigh-Bénard convection with a rough boundary: investigation of plumes. *Journal of Fluid Mechanics*, 895:A7, July 2020.

[3] J. P. Molnar, S. J. Grauer, O. Léon, D. Donjat, and F. Nicolas. Physics-Informed Background-Oriented Schlieren of Turbulent Underexpanded Jets. In *AIAA SCITECH 2023 Forum*, National Harbor, MD & Online, January 2023. American Institute of Aeronautics and Astronautics.