Flow over an espresso cup: Inferring 3D velocity and pressure fields from tomographic background oriented schlieren videos via physics-informed neural networks (2103.02807v2)

Abstract: Tomographic background oriented schlieren (Tomo-BOS) imaging measures density or temperature fields in 3D using multiple camera BOS projections, and is particularly useful for instantaneous flow visualizations of complex fluid dynamics problems. We propose a new method based on physics-informed neural networks (PINNs) to infer the full continuous 3D velocity and pressure fields from snapshots of 3D temperature fields obtained by Tomo-BOS imaging. PINNs seamlessly integrate the underlying physics of the observed fluid flow and the visualization data, hence enabling the inference of latent quantities using limited experimental data. In this hidden fluid mechanics paradigm, we train the neural network by minimizing a loss function composed of a data mismatch term and residual terms associated with the coupled Navier-Stokes and heat transfer equations. We first quantify the accuracy of the proposed method based on a 2D synthetic data set for buoyancy-driven flow, and subsequently apply it to the Tomo-BOS data set, where we are able to infer the instantaneous velocity and pressure fields of the flow over an espresso cup based only on the temperature field provided by the Tomo-BOS imaging. Moreover, we conduct an independent PIV experiment to validate the PINN inference for the unsteady velocity field at a center plane. To explain the observed flow physics, we also perform systematic PINN simulations at different Reynolds and Richardson numbers and quantify the variations in velocity and pressure fields. The results in this paper indicate that the proposed deep learning technique can become a promising direction in experimental fluid mechanics.

• The paper proposes a novel method combining Tomo-BOS imaging with PINNs to infer 3D velocity and pressure fields from temperature data.
• The approach integrates experimental tomographic reconstruction with physical laws in the neural network to ensure robust inference even with sparse data.
• Results are validated against PIV experiments, demonstrating accuracy and potential for cost-effective, real-time fluid dynamics analysis.

Analyzing 3D Flow Over an Espresso Cup Using Tomo-BOS and PINNs

The research paper "Flow over an espresso cup: Inferring 3D velocity and pressure fields from tomographic background oriented schlieren videos via physics-informed neural networks" provides an in-depth exploration into a novel methodology for fluid dynamics analysis. The authors propose a synergistic approach combining Tomographic Background Oriented Schlieren (Tomo-BOS) imaging with Physics-Informed Neural Networks (PINNs) to infer 3D velocity and pressure fields from temperature data. This paper elaborates on both experimental and computational fronts, offering a comprehensive workflow from data acquisition to final inference validation.

Overview of Methodology

To address the challenge of inferring comprehensive 3D flow metrics from limited experimental data, the authors leverage PINNs due to their ability to integrate physical laws directly into the learning process. The paper centers on buoyancy-driven flow over an espresso cup, utilizing Tomo-BOS to capture the temperature field. The Tomo-BOS technique, while traditionally restricted to visualizing scalar fields such as temperature, is extended here through PINNs to estimate velocity and pressure fields. The neural network is trained by minimizing a loss function that encompasses data fidelity and compliance with governing Navier-Stokes and heat transfer equations.

Experimental Setup

The experimental setup involves capturing a 3D field around a heated cup using a six-camera system configured for tomographic imaging. Schlieren images acquired reveal the variations in temperature due to the flow, necessitating conversion into refractive index gradients and ultimately temperature fields. The images are then processed using tomographic reconstruction for a 3D estimation of these fields. Essential physical properties, such as thermal diffusivity and expansion coefficients, are identified for use within the neural network model, alongside typical non-dimensional parameters such as Reynolds, Péclet, and Richardson numbers.

Results and Validation

The velocity and pressure inferred via PINNs from the Tomo-BOS temperature field portray sensible and smooth distributions across the spatial domain. These results are compared qualitatively with independent Planar Particle Image Velocimetry (PIV) experiments conducted separately to ensure rigorous validation. Notably, PINNs demonstrate robustness to data sparsity, maintaining accuracy even when the spatiotemporal resolution of the input data is reduced. This effective employment of PINNs showcases their capability in dealing with sparse datasets—a common issue in experimental fluid mechanics.

Theoretical and Practical Implications

This paper has significant implications for both theoretical understanding and practical application in experimental fluid mechanics. Theoretically, it demonstrates how PINNs can act as a robust data assimilation tool, adept at integrating empirical observations with fundamental equations. Practically, the approach simplifies the detailed measurement of velocity and pressure from scalar visualizations, making complex flow analysis more accessible and cost-effective. This paves the way for robust, real-time analysis and control in practical fluid systems, potentially impacting industries reliant on fluid dynamics insights.

Future Prospects and Directions

Future prospects hinge on extending this methodology to various fluid dynamics problems by encoding different governing equations into the PINN framework. The qualitative success of integrating Tomo-BOS and PINNs also prompts considerations for enhancing model accuracy and efficiency, possibly incorporating uncertainty quantification via Bayesian PINNs. Such enhancements would broaden the scope and precision of this technique across broader applications within complex, multi-physical fluid scenarios.

Overall, the paper presents a detailed examination of an innovative approach in fluid dynamics research, providing a valuable template for employing machine learning in tandem with experimental methods to solve complex, multi-dimensional fluid flow problems.