  We present a new uncertainty estimation method for Particle Image Velocimetry
(PIV), that uses the correlation plane as a model for the probability density
function (PDF) of displacements and calculates the second order moment of the
correlation (MC). The cross-correlation between particle image patterns is the
summation of all particle matches convolved with the apparent particle image
diameter. MC uses this property to estimate the PIV uncertainty from the shape
of the cross-correlation plane. In this new approach, the Generalized
Cross-Correlation (GCC) plane corresponding to a PIV measurement is obtained by
removing the particle diameter contribution. The GCC primary peak represents a
discretization of the displacement PDF, from which the standard uncertainty is
obtained by convolving the GCC plane with a Gaussian function. Then a Gaussian
least-squares-fit is applied to the peak region, accounting for the stretching
and rotation of the peak, due to the local velocity gradients and the effect of
the convolved Gaussian. The MC method was tested with simulated image sets and
the predicted uncertainties show good sensitivity to the error sources and
agreement with the expected RMS error. Subsequently, the method was
demonstrated in three PIV challenge cases and two experimental datasets and was
compared with the published image matching (IM) and correlation statistics (CS)
techniques. Results show that the MC method has a better response to spatial
variation in RMS error and the predicted uncertainty is in good agreement with
the expected standard uncertainty. The uncertainty prediction was also explored
as a function PIV interrogation window size, and the MC method outperforms the
other uncertainty methods.

Fluid Dynamics;Data Analysis, Statistics and Probability