Generalized displacement estimation for averages of non-stationary flows

When dealing with particle image velocimetry data sets with a relatively poor signal-to-noise ratio, averaged velocity fields are often the only achievable result. These average fields can be determined in a number of ways, of which correlation averaging has become the most prominent. We show that for instationary flows, the use of correlation averaging can lead to unreliable results: summation of individual correlation peaks from a transient flow creates a broadened peak. The location of the maximum of this peak generally does not coincide with the true temporal mean displacement. We propose to use the centroid of the correlation result as a better estimator. This method is demonstrated with simulated and experimental data, showing that it gives more reliable results, at the price of a small increase in noise level. For relatively small displacements, where the conventional method is not biased, the method is less suitable due to this increase in noise. Therefore, a straightforward hybrid method optimizes the displacement estimation for optimal results.