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Uncertainty quantification for particle image velocimetry (PIV) is critical for comparing experimentally measured flow fields with computational fluid dynamics results, and model design and validation. However, PIV features a complex measurement chain with coupled, non-linear error sources, and quantifying the uncertainty is challenging. Multiple assessments show that none of the current methods can reliably measure the actual uncertainty across a wide range of experiments, and estimates can vary. Because the current methods differ in assumptions regarding the measurement process and calculation procedures, it is not clear which method is best to use for an experiment where the error distribution is unknown. To address this issue, we propose a method to estimate an uncertainty method's sensitivity and reliability, termed the Meta-Uncertainty. The novel approach is automated, local, and instantaneous, and based on perturbation of the recorded particle images. We developed an image perturbation scheme based on adding random unmatched particles to the interrogation window pair considering the signal-to-noise of the correlation plane. Each uncertainty scheme's response to several trials of random particle addition is used to estimate a reliability metric, defined as the rate of change of the inter-quartile range of the uncertainties with increasing levels of particle addition. We also propose applying the meta-uncertainty as a weighting metric to combine uncertainty estimates from individual schemes, based on ideas from the consensus forecasting literature. We use planar and stereo PIV measurements across a range of canonical flows to assess the performance of the uncertainty schemes. Further, a novel method is introduced to assess an uncertainty scheme's performance based on a quantile comparison of the error and uncertainty distributions, generalizing the current method of comparing the RMS of the two distributions. The results show that the combined uncertainty method outperforms the individual methods, and this work establishes the meta-uncertainty as a useful reliability assessment tool for PIV uncertainty quantification. [ABSTRACT FROM AUTHOR]

A novel pressure reconstruction method is proposed to use the uncertainty information to improve the instantaneous pressure fields from velocity fields measured using particle image velocimetry (PIV) or particle tracking velocimetry (PTV). First, the pressure gradient fields are calculated from velocity fields, while the local and instantaneous pressure gradient uncertainty is estimated from the velocity uncertainty using a linear-transformation-based algorithm. The pressure field is then reconstructed by solving an overdetermined linear system which involves the pressure gradients and boundary conditions. This linear system is solved with generalized least squares (GLS) which incorporates the previously estimated variances and covariances of the pressure gradient errors as inverse weights to optimize the reconstructed pressure field. The method was validated with synthetic velocity fields of a 2D pulsatile flow, and the results show significantly improved pressure accuracy. The pressure error reduction by GLS was 50% with 9.6% velocity errors and 250% with 32.1% velocity errors compared to the existing baseline method of solving the pressure Poisson equation (PPE). The GLS was more robust to the velocity errors and provides greater improvement with spatially correlated velocity errors. For experimental validation, the volumetric pressure fields were evaluated from the velocity fields measured using 3D PTV of a laminar pipe flow with a Reynolds number of 630 and a transitional pipe flow with a Reynolds number of 3447. The GLS reduced the median absolute pressure errors by as much as 96% for the laminar pipe flow compared to PPE. The mean pressure drop along the pipe predicted by GLS was in good agreement with the empirical estimation using Darcy–Weisbach equation for the transitional pipe flow. [ABSTRACT FROM AUTHOR]

Nonintrusive measurement techniques such as particle image velocimetry (PIV) are growing in both capability and utility for turbomachinery applications. However, the restrictive optical access afforded by multistage research compressors typically requires the use of a periscope probe to introduce the laser sheet for measurements in a rotor passage. This paper demonstrates the capability to perform three-dimensional PIV in a multistage compressor without the need for intrusive optical probes and requiring only line-of-sight optical access. The results collected from the embedded second stage of a three-stage axial compressor highlight the rotor tip leakage flow, and PIV measurements are qualitatively compared with high-frequency response piezoresistive pressure measurements to assess the tip leakage flow identification. [ABSTRACT FROM AUTHOR]

We introduce the first comprehensive approach to determine the uncertainty in volumetric Particle Tracking Velocimetry (PTV) measurements. Volumetric PTV is a state-of-the-art non-invasive flow measurement technique, which measures the velocity field by recording successive snapshots of the tracer particle motion using a multi-camera set-up. The measurement chain involves reconstructing the three-dimensional particle positions by a triangulation process using the calibrated camera mapping functions. The non-linear combination of the elemental error sources during the iterative self-calibration correction and particle reconstruction steps increases the complexity of the task. Here, we first estimate the uncertainty in the particle image location, which we model as a combination of the particle position estimation uncertainty and the reprojection error uncertainty. The latter is obtained by a gaussian fit to the histogram of disparity estimates within a sub-volume. Next, we determine the uncertainty in the camera calibration coefficients. As a final step, the previous two uncertainties are combined using an uncertainty propagation through the volumetric reconstruction process. The uncertainty in the velocity vector is directly obtained as a function of the reconstructed particle position uncertainty. The framework is tested with synthetic vortex ring images. The results show good agreement between the predicted and the expected RMS uncertainty values. The prediction is consistent for seeding densities tested in the range of 0.01–0.1 particles per pixel. Finally, the methodology is also successfully validated for an experimental test case of laminar pipe flow velocity profile measurement where the predicted uncertainty in the streamwise component is within 9% of the RMS error value. [ABSTRACT FROM AUTHOR]