Reconstructing turbulent velocity and pressure fields from under-resolved noisy particle tracks using physics-informed neural networks, Color particle imaging velocimetry and its applications to various 3D flows

Abstract

Volume-resolving imaging techniques are rapidly advancing progress in experimental fluid mechanics. However, reconstructing the full and structured Eulerian velocity and pressure fields from under-resolved and noisy particle tracks obtained experimentally remains a significant challenge. We {adopt and characterize} a method based on Physics-Informed Neural Networks (PINNs). In this approach, the network is regularized by the Navier-Stokes equations to interpolate the velocity data and simultaneously determine the pressure field. We compare this approach to the state-of-the-art Constrained Cost Minimization method. Using data from direct numerical simulations and various types of synthetically generated particle tracks, we show that PINNs are able to accurately reconstruct both velocity and pressure even in regions with low particle density and small accelerations. We analyze both the root mean square error of the reconstructions as well their energy spectra. PINNs are also robust against increasing the distance between particles and the noise in the measurements, when studied under synthetic and experimental conditions. Both the synthetic and experimental datasets used correspond to moderate Reynolds number flows. Three-dimensional three-component (3D-3C) particle imaging velocimetry can be set up even with a single camera when volumetric color-coded illumination is applied to the measurement space. The idea itself was very old as reported a lot in early PIV conferences in 1990s. However, most of PIV developers abandoned to make it feasible in those days due to various limitations struggled for quantitative color extraction required to capture the displacement of color-dependent particle coordinates. Our team spent a long time to overcome such problems to date and reached a certain level of feasibility gradually approaching to tomographic PIV. Our efforts to improve the measurement performance are i) algorithm for easy color calibration, ii) multi-cycle color illumination, iii) intentional particle defocusing, iv) animated color coding, and v) introduction of artificial neural network. In the seminar, I will explain these techniques and their applications including delta-wing wakes, boundary layer on rough surfaces, flows behind wind turbine, wall-impinging vortex rings, and thermal turbulence.