Full characterization of the peak-locking error by means of orthogonal functions and application to the flow behind a helicopter fuselage model

Abstract

This work offers a 1D fully analytic complete modeling of the peak-locking error. Besides error assessment, this model allows for measurement correction. The paradigm of peak locking is revisited. The expressions of the functional dependence of the error are obtained for the two most relevant components of the measurement statistics: (1) the local velocity average, and (2) the local velocity rms. The prediction of the peak-locking error is related to complex interactions between the particle images size and shape and the measurement algorithms (peak fitting, image interpolation, etc.). The proposed model incorporates the different interactions by using a generalized approach that only requires the calibration of a few coefficients. This calibration is done by means of an inexpensive multiple Δt strategy, consisting in measuring the same flow field with different Δt subsets. Differently to previous empirical models from the authors, a robust theoretical foundation has been established. Besides providing rationale to the procedure, the results are significantly more accurate. A calibration using only three coefficients may correct up to 90% of the peak-locking error, while the previous empirical models would correct just in the order of 50%. This leaves a 10% of residual peak-locking error instead of 50%, reducing the final incidence by a factor of 5. The methodology is tested, in the context of turbulent flows, on real images corresponding to the measurement of the flow around the fuselage of a helicopter model. The test campaign was performed in the Italian Aerospace Research Centre (CIRA) CT-1 low speed wind tunnel. The proposed method, combined with the multiple Δt strategy, results in an error prediction accuracy that is good enough for correcting the measurements. Corrections to the average flow are in the order of 0.1 pixel (~ 3% of the convective velocity but in the order of 100% of the local flow variations). Corrections to the rms are in the same order; being the turbulence small, they cancel very large relative rms errors (~ 100%). The coherence between predicted error and actual error in real cases is further supported by the consistent matching that can be observed on their spatial patterns, associated with flow field statistics. An orthogonal expansion allows for full assessment of PIV peak-locking bias errors. The turbulent flow behind a helicopter fuselage model is used as test case. The expansion is calibrated and validated using a multiple Δt strategy. The resulting assessment is good enough to allow for correcting errors in the order of 0.1 pixel in the measured average as well as in the rms.