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.

Graphic abstract

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.

中文翻译：

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通过正交函数全面表征峰锁定误差，并将其应用于直升机机身模型背后的流动

这项工作为峰值锁定误差提供了一维完全解析的完整模型。除了误差评估之外，该模型还可以进行测量校正。再次讨论了峰值锁定的范例。对于测量统计的两个最相关的组件，获得了误差的函数相关性表达式：（1）局部速度平均值，和（2）局部速度rms。峰锁定误差的预测与粒子图像大小和形状与测量算法（峰拟合，图像插值等）之间的复杂相互作用有关。所提出的模型通过使用仅需要校准几个系数的通用方法，就包含了不同的相互作用。通过便宜的倍数Δt进行校准策略，包括测量具有不同Δt的相同流场子集。与作者先前的经验模型不同，已经建立了可靠的理论基础。除了提供该程序的原理外，结果还更加准确。仅使用三个系数的校准最多可以校正90％的峰锁定误差，而以前的经验模型只能进行50％左右的校正。这样就留下了10％的残余峰值锁定误差而不是50％的残余峰值锁定误差，从而将最终入射降低了5倍。在湍流的背景下，在与实测图像相对应的情况下对方法进行了测试。直升机模型的机身。测试活动是在意大利航空航天研究中心（CIRA）的CT-1低速风洞中进行的。所提出的方法，结合多个Δt如果采用这种策略，则误差预测精度足以校正测量结果。平均流量的校正量约为0.1个像素（对流速度的〜3％，但局部流量变化量约为100％）。rms的校正顺序相同。由于湍流较小，它们消除了非常大的相对均方根误差（〜100％）。在实际情况下，预测误差与实际误差之间的一致性还可以通过与流场统计信息相关联的，在其空间模式上可以观察到的一致匹配来进一步支持。

图形摘要

正交展开可全面评估PIV峰锁定偏差误差。直升机机身模型后面的湍流用作测试案例。使用多重Δt策略对扩展进行校准和验证。最终的评估结果足够好，可以校正测量平均值和均方根值中约0.1个像素的误差。