Multiple Δtstrategy for particle image velocimetry (PIV) error correction, applied to a hot propulsive jet

Abstract

PIV (particle image velocimetry) is a measurement technique with growing application to the study of complex flows with relevance to industry. This work is focused on the assessment of some significant PIV measurement errors. In particular, procedures are proposed for estimating, and sometimes correcting, errors coming from the sensor geometry and performance, namely peak-locking and contemporary CCD camera read-out errors. Although the procedures are of general application to PIV, they are applied to a particular real case, giving an example of the methodology steps and the improvement in results that can be obtained. This real case corresponds to an ensemble of hot high-speed coaxial jets, representative of the civil transport aircraft propulsion system using turbofan engines. Errors of ∼0.1 pixels displacements have been assessed. This means 10% of the measured magnitude at many points. These results allow the uncertainty interval associated with the measurement to be provided and, under some circumstances, the correction of some of the bias components of the errors. The detection of conditions where the peak-locking error has a period of 2 pixels instead of the classical 1 pixel has been made possible using these procedures. In addition to the increased worth of the measurement, the uncertainty assessment is of interest for the validation of CFD codes.

Multi-frame pyramid correlation for time-resolved PIV

“…The technique assumes a second-order polynomial displacement in time, whose coefficients are calculated by maximizing the matching of correlation functions computed at different time. Nogueira et al (2009Nogueira et al ( , 2010) introduced a multiple Dt strategy for the quantitative estimate of the magnitude of peak-locking and CCD read-out bias errors. However, because no correction can be obtained for the instantaneous velocity measurement, the method can only be applied to lower the error of the time-averaged velocity field.…”

Simultaneous assessment of peak-locking and CCD readout errors through a multiple Δt strategy

“…But the random part of peak-locking error is much less documented, although Willert et al (1998) and Raffel et al (1997) already mentioned it; later Nogueira et al (2011) showed that peak locking do not only bias the measurement ensemble average, but also originate a strong rms component that affects the measurement of velocity fluctuations. In addition, Nogueira et al (2009) reveal another error type, identifying the existence of significant readout errors from contemporary 12-bit CCD cameras, and quantifying it for some PIV applications.…”

“…In the previous works (Nogueira et al 2009(Nogueira et al , 2011, the authors took advantage of this property in order to assess these errors separately using a multiple Dt strategy. Instead of the classical procedure involving a constant Dt for a measurement series, the only difference when this technique is applied consists on acquiring two or more subseries, each with a specific Dt.…”

“…A major limitation in Nogueira et al (2009) and (2011) is that they treat the errors separately. The procedures proposed in those works fail when dealing with the combination of both errors if they are of similar magnitude, which is not uncommon.…”

“…The results indicate that the flow variability is relevant for the peak-locking error assessment. Nogueira et al (2009) reviewed different sources of peak locking: subpixel peak-fitting algorithms (Lourenco and Krothapalli 1995), insufficient resolution to describe the particle images (Westerweel 1998), truncation of the particles at the window border (Nogueira et al 2001), and image interpolation algorithms (Astarita and Cardone 2005). A later work, Nogueira et al (2011), showed that peak locking may correspond only to bias error, only to rms error, or that both may be present.…”