A posteriori uncertainty quantification of PIV-derived pressure fields

The present work proposes a methodology for the a posteriori quantification of the uncertainty of pressure data retrieved from PIV measurements. It relies upon the Bayesian framework, where the posterior distribution (probability distribution of the true velocity, given the PIV measurements) is obtained from the prior distribution (prior knowledge of the velocity, e.g., within a certain bound or divergence-free) and the distribution representing the PIV measurement uncertainty. Once the posterior covariance matrix of the velocity is known, it is propagated through the discretized Poisson equation for pressure. Numerical assessment of the proposed method on a steady Lamb Oseen vortex shows excellent agreement with Monte Carlo simulations, while linear uncertainty propagation underestimates the uncertainty of the pressure by up to 30%. The method is finally applied to an experimental test case of a turbulent boundary layer in air, obtained using time-resolved tomographic PIV. The pressure reconstructed from tomographic PIV data is compared to a microphone measurement conducted simultaneously at the wall to determine the actual error of the former. The comparison between actual error and estimated uncertainty shows the accuracy of the proposed method for uncertainty quantification of pressure data from tomographic PIV experiments: for a 95% confidence level, 93% of the data points fall within the estimated uncertainty bound with the Eulerian approach, and 90% with the Lagrangian approach. When using the prior knowledge that the velocity field should be divergence-free, these values are 98% with the Eulerian approach and 94% with the Lagrangian approach. The Lagrangian approach results in more accurate reconstructed pressure fields than the Eulerian approach. Also, enforcing the divergence-free constraint is found to result in a more accurate reconstructed pressure field. Both observations also follow from the uncertainty quantification, through a decrease in the estimated uncertainty.Aerodynamics, Wind Energy & PropulsionAerospace Engineerin