Peak-locking full characterization: PIV error assessment and velocity ensemble measurement correction

Abstract

Concluding a few previous approaches, the last work by the authors presented a complete analytic model for peak-locking error. That work was devoted to the mathematical foundation of the model. This paper separately focuses on the procedure for calibrating a given particle-image velocimetry measurement setup using the model. In addition to error assessment, it allows for the measurement correction of statistical ensembles such as: (a) the local velocity average and (b) the local velocity root mean square (RMS). This calibration is done by means of an inexpensive multiple Δt strategy, consisting of measuring the same flow field with different Δt subsets. This paper offers a comparison with previous empirical models produced by the authors, showing the advantages of the robust theoretical foundation established for this model. A real case corresponding to a hot high-speed coaxial jet, representative of the turbofan engine propulsion systems used for civil transport aircraft, is used for this comparison. The discrepancy plots between the different Δt subsets indicate that the peak-locking error description and correction are improved by 30% for the local velocity average. For the local velocity RMS, the results are even more striking, as the peak locking error can be almost completely corrected in situations where previous models only provided the order of magnitude of the error. Together with a detailed explanation of the calibration procedure, the paper offers guidelines to avoid getting into an ill-conditioned mathematical problem.