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

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.