Numerical recipes in C: the art of scientific computing
Numerical recipes in C: the art of scientific computing
Design and Analysis of Experiments
Design and Analysis of Experiments
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Particle Image Velocimetry can provide detailed velocity field information that has unparalleled value to both experimentalists and computational fluid dynamicists. As with any measurement technique, it is important to assess the error associated with the measurements. The PIV measurement chain contains several stages where error is introduced. The dynamics of the seed particles determine how well they represent the local fluid velocity. Acquiring the image, whether photographically or electronically, will introduce aberrations, distortion, diffraction, and positioning uncertainties. The image analysis procedure to determine particle displacements is the final step in the measurement chain. This paper considers the error in this step of the measurement chain. Synthetic images were generated with controlled levels of the following quantities: background mean illumination, background illumination standard deviation, mean particle diameter, number of paired particles, the ratio of unpaired particles to paired particles, displacement magnitude, and displacement direction. The analysis method tested is a generic autocorrelation technique using a two-dimensional forward FFT, PSD calculation, inverse FFT, and a peak detection algorithm based on a decreasing threshold search with subsequent sub-pixel interpolation. The error analysis principles demonstrated, however, could easily be applied to other algorithms including those implementing cross-correlation techniques. The error in the analysis technique is characterised by four quantities: the bias in the displacement magnitude, the precision index of the displacement magnitude, the bias in the displacement direction, and the precision index of the displacement direction. Each independent variable was varied over a specified range and the behaviour of the four dependent variables observed. The results showed a clear ability for this error assessment technique to illustrate the reliable operating range for each parameter. The variation in error with parameter level tended to be similar in all cases. There was a significant portion of the range where the error was very low. Then, at some critical value, the analysis technique broke down and the error became quite high.