TY - JOUR
T1 - A posteriori uncertainty quantification of PIV-based pressure data
AU - Azijli, Iliass
AU - Sciacchitano, Andrea
AU - Ragni, Daniele
AU - Palha Da Silva Clérigo, Artur
AU - Dwight, Richard
PY - 2016/4/28
Y1 - 2016/4/28
N2 - A methodology for a posteriori uncertainty quantification of pressure data retrieved from particle image velocimetry (PIV) is proposed. 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 properties of the velocity field, e.g., divergence-free) and the statistical model of 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 in 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. Simultaneously with the PIV measurements, microphone measurements were carried out at the wall. The pressure reconstructed from the tomographic PIV data is compared to the microphone measurements. Realizing that the uncertainty of the latter is significantly smaller than the PIV-based pressure, this allows us to obtain an estimate for the true error of the former. The comparison between true error and estimated uncertainty demonstrates the accuracy of the uncertainty estimates on the pressure. In addition, enforcing the divergence-free constraint is found to result in a significantly more accurate reconstructed pressure field. The estimated uncertainty confirms this result.
AB - A methodology for a posteriori uncertainty quantification of pressure data retrieved from particle image velocimetry (PIV) is proposed. 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 properties of the velocity field, e.g., divergence-free) and the statistical model of 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 in 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. Simultaneously with the PIV measurements, microphone measurements were carried out at the wall. The pressure reconstructed from the tomographic PIV data is compared to the microphone measurements. Realizing that the uncertainty of the latter is significantly smaller than the PIV-based pressure, this allows us to obtain an estimate for the true error of the former. The comparison between true error and estimated uncertainty demonstrates the accuracy of the uncertainty estimates on the pressure. In addition, enforcing the divergence-free constraint is found to result in a significantly more accurate reconstructed pressure field. The estimated uncertainty confirms this result.
UR - http://resolver.tudelft.nl/uuid:a85bf6df-fcce-42f4-9e44-c457acf12dab
U2 - 10.1007/s00348-016-2159-z
DO - 10.1007/s00348-016-2159-z
M3 - Article
SN - 0723-4864
VL - 57
SP - 57
EP - 72
JO - Experiments in Fluids: experimental methods and their applications to fluid flow
JF - Experiments in Fluids: experimental methods and their applications to fluid flow
IS - 5
ER -