Uncertainty of PIV/PTV based Eulerian pressure estimation using velocity uncertainty
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Uncertainty of PIV/PTV based Eulerian pressure estimation using velocity uncertainty

This work introduces a method to estimate the uncertainty of the pressure fields reconstructed from particle image velocimetry / particle tracking velocimetry (PIV/PTV) measurements by propagating the instantaneous velocity vector uncertainty through the pressure reconstruction. The uncertainty propagations through the calculation and integration of pressure gradients are modelled as linear transformations. The autocorrelation coefficient was modelled and incorporated in the uncertainty estimation to reproduce the effect of the autocorrelation of velocity errors on the reconstructed pressure’s accuracy. The method was first tested on synthetic velocity fields contaminated with varying levels of artificial noise correlated in space, time, or between components. The error analysis shows that the proposed method could predict the spatiotemporal variations of the pressure errors. The estimated pressure uncertainty also captures the effects of the velocity noise level, the autocorrelation, and the different pressure-gradient integration methods, with more than 80% accuracy in most test cases. The method was applied to an experimental vortex ring flow with planar PIV and a laminar pipe flow with volumetric PTV. The error analysis shows that the obtained pressure uncertainty possessed similar spatial and statistical distributions as the pressure errors. The results also indicate that the performance of the proposed uncertainty estimation method depends on the accuracy of the velocity uncertainty. The proposed uncertainty estimation method exhibits reliability in obtaining the local and instantaneous pressure uncertainty from the PIV/PTV measurements.

The schematic demonstrates the procedure of PIV/PTV based pressure reconstruction (a, blue arrows) and the estimation of pressure uncertainty (b, red arrows).
The uncertainty coverage for the velocity and pressure reconstructed with PPE, OLS, WLS, and GLS methods for the laminar pipe flow measured using PTV with triangulation and IPR reconstructions.

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