Flow dynamics from flow field measurements and a Galerkin Model.*

A novel methodology is proposed to improve the temporal resolution of non-time-resolved PIV measurements, allowing a better understanding of the dynamics of turbulent flows. In most cases, due to technological limitations such as maximum acquisition frequency or limited light source intensity, among others, time-resolved PIV can only be performed for specific cases where the maximum flow velocity is limited to low to moderate Reynolds number.

This work presents a physically informed data-driven model for time supersampling based on an empirical Galerkin projection of the Navier-Stokes equations, where the chosen basis corresponds to the eigenfunctions obtained from the Proper Orthogonal Decomposition (POD) of the NTR velocity fields. The inputs to the model are non-time-resolved measurements obtained with Particle Image Velocimetry, and the outputs correspond to the reconstructed time-resolved snapshots. The results obtained indicate that our methodology is able to reconstruct the main flow dynamics for temporal separations of several flow characteristic times. In addition, it was observed that the reconstruction is highly dependent on the mode order chosen for the reconstruction, which determines the error of the reconstruction.