Pressure From Data-Driven-Estimated Velocity Fields Using Snapshot PIV And Fast Probes

Abstract

The pressure field estimation can be performed from Particle Image Velocimetry (PIV) data on the basis of the Navier-Stokes equation. This requires time-resolved velocity fields to directly compute time derivatives, which are often difficult to achieve due to hardware limitations or cost. Alternatively, snapshot PIV experiments are more affordable but require additional assumptions to model the time derivatives. In this work, we propose the use of data-driven techniques to combine snapshot PIV and high-repetition-rate sensors measurement, and obtain time-resolved estimated velocity fields. The instantaneous pressure fields can thus be computed.We explore building the relation between temporal modes of the flow field and the probe data is built using either linear and non-linear estimators, i.e. Extended Proper Orthogonal Decomposition (Extended POD) and a Multilayer Perceptron (MLP), respectively. The performances of both data-driven methods, as well as Taylor’s hypothesis model for the time derivatives, are tested on the synthetic dataset of a fluidic pinball and on experimental measurements in the wake of a wing. The results show that the data-driven pressure estimations have sufficient accuracy and are not affected by time propagation of the error. Both data-driven methods outperform the model-based method rooted on the Taylor’s hypothesis for the tested cases having compact POD spectra.