Abstract
In this chapter, a simplified mathematical model of the recording and subsequent statistical evaluation of PIV images will be presented. For this purpose the mathematical representation of the particle image locations, the image intensity field and the mean value, the auto-correlation, and the variance of a single exposure recording are described. Then, we analyze the cross-correlation of two frames of singly exposed recordings and expand the theory for the evaluation of doubly exposed recordings.
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Notes
- 1.
The local sample of a PIV image from which a velocity vector is determined is referred to as the interrogation window. Its size determines to what degree the recovered velocity field is spatially smoothed.
- 2.
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Raffel, M., Willert, C.E., Scarano, F., Kähler, C.J., Wereley, S.T., Kompenhans, J. (2018). Mathematical Background of Statistical PIV Evaluation. In: Particle Image Velocimetry. Springer, Cham. https://doi.org/10.1007/978-3-319-68852-7_4
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DOI: https://doi.org/10.1007/978-3-319-68852-7_4
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