The Background Oriented Schlieren (BOS) imaging technique, often used for visualizing and quantifying fluid flow, has been advanced by researchers from Brown University, LaVision GmbH in Germany, and LaVision Inc. in USA. They’ve developed a method using Physics-Informed Neural Networks (PINNs) to deduce complete 3D velocity and pressure fields from 3D temperature snapshots obtained via Tomographic BOS (Tomo-BOS) imaging. Despite the challenges of quantifying complete fluid velocity and pressure fields from BOS images, the method is effective and cost-efficient compared to Particle Image Velocimetry (PIV) and Laser-Induced Fluorescence (LIF) technologies.
The researchers conducted a Tomo-BOSPINN experiment using downsampling data. They applied a time interval of 0.1 s to the training data and calculated the relative L2-norm temperature error for unseen data using trained parameters. The results showed that the inferred velocity field was consistent with the displacement generated from Schlieren-tracking, demonstrating that the Tomo-BOSPINN method can accurately estimate full temperature and velocity fields.
Unlike traditional data assimilation methods that heavily lean on accurately choosing initial guesses for velocity and pressure conditions, the researchers’s PINN algorithm functions as a data assimilation technique, making predictions by analyzing visualization data across a spatio-temporal domain without needing initial and boundary conditions for velocity or pressure.
One of the studies documented the results of the Tomo-BOSPINN experiment, which included using Schlieren characteristics in sequential images to estimate 2-D pressure fields. The study showed that the average residual of the momentum equations along the x, y, and z axes was in the order of 10^-4 m s^-2. Researchers presented a comparison of velocity profiles at various time instances between Tomo-BOSPINN and planar PIV results, supporting the viability of their method.
In summary, the researchers have successfully developed a machine-learning algorithm based on PINNs that can estimate velocity and pressure fields from temperature data in Tomo-BOS experiments. This method is evaluated through a 2D buoyancy-driven flow simulation and has shown accurate performance with sparse and noisy data, even when tested on flow over an espresso cup. The flexibility of this proposed method suggests its potential to solve varied fluid mechanics problems.
