Pressure from data-driven estimation of velocity fields using snapshot PIV and fast probes

Abstract

The most explored path to obtain pressure fields from Particle Image Velocimetry (PIV) data roots its basis on accurate measurement of instantaneous velocity fields and their corresponding time derivatives. This requires time-resolved measurements, which are often difficult to achieve due to hardware limitations and expensive to implement. In alternative, snapshot PIV experiments are more affordable but require enforcing physical constraints (e.g. Taylor’s hypothesis) to extract the time derivative of the velocity field. In this work, we propose the use of data-driven techniques to retrieve time resolution from the combination of snapshot PIV and high-repetition-rate sensors measuring flow quantities in a limited set of spatial points. The instantaneous pressure fields can thus be computed by leveraging the Navier–Stokes equations as if the measurement were time-resolved. Extended Proper Orthogonal Decomposition, which can be regarded as one of the simplest algorithm for estimating velocity fields from a finite number of sensors, is used in this paper to prove the feasibility of this concept. The method is fully data-driven and, after training, it requires only probe data to obtain field information of velocity and pressure in the entire flow domain. This is certainly an advantage since model-based methods can retrieve pressure in an observed snapshot, but show increasing error as the field information is propagated over time. The performances of the proposed method are tested on datasets of increasing complexity, including synthetic test cases of the wake of a fluidic pinball and a channel flow, and experimental measurements in the wake of a wing. The results show that the data-driven pressure estimation is effective in flows with compact POD spectrum. In the cases where Taylor’s hypothesis holds well, the in-sample pressure field estimation can be more accurate for model-based methods; nonetheless, the proposed data-driven approach reaches a better accuracy for out-of-sample estimation after less than 0.20 convective times in all tested cases.