Abstract
A new correlation method for particle image velocimetry (PIV) is proposed that yields velocity data at single-pixel spatial resolution. This method is an extension of the ensemble correlation method for PIV. This ‘single-pixel ensemble correlation’ method is particularly suited for (quasi-) stationary and periodic flows, which are typically encountered in many micro-PIV applications, such as microfluidics and micro-scale biological flows. The method can yield data at the same level of precision and reliability as conventional PIV data. The main advantage of the new method is that it can resolve steep velocity gradients and obtain unbiased measurements of the velocity in the vicinity of flow boundaries (viz. walls). The performance as a function of the ensemble size is investigated by means of synthetic PIV images. Both ensemble correlation and single-pixel correlation are applied to micro-channel flow. With single-pixel ensemble correlation we obtained a spatial resolution of 300 nm. The results demonstrate that ensemble correlation over-estimates the measured channel width, whereas single-pixel correlation yields a result that is in agreement with the actual channel dimensions.
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Notes
This scaling also applies to differently sized interrogation windows, in which the smaller window is zero-padded to match the size of the larger window.
However, the practical implementation differs from conventional ensemble-correlation PIV, as it does not rely on the FFT algorithm for the computation of the correlation.
These ripples did not occur in our microchannel measurements; we think that the effect is augmented for the case of our idealized synthetic images.
For a shear layer with a finite width the velocity bias can be avoided by means of window shifting; in this particular case a window shift would not avoid the velocity bias, as a shift of either 2 or 4 pixels would be applied.
The correlation results for data points that lie in the wall have been retained in this graph. In this region no particles are present, so that the fluctuations in the result are due to the sensor noise. In view of the estimated error, these fluctuations are not significant. The apparent oscillations in these data point are possibly due to the median filtering of the image data.
References
Delnoij E, Westerweel J, Deen NG, Kuipers JAM, Van Swaaij WPM (1999) Ensemble correlation PIV applied to bubble plumes rising in a bubble column. Chem Eng Sci 54:5159–5171
Meinhart CD, Werely ST, Santiago JG (2000) A PIV algorithm for estimating time-averaged velocity fields. J Fluids Eng 122:285–289
Wereley ST, Gui L, Meinhart CD (2002) Advanced algorithms for microscale particle image velocimetry. AIAA J 40:1047–1055
Adrian RJ (1988) Statistical properties of particle image velocimetry measurements in turbulent flow. In: RJ Adrian et al (eds) Laser anemometry in fluid mechanics—Part III. LADOAN Instituto Superior Tecnico, Lisbon, pp 115–129
Westerweel J (1993) Particle image velocimetry—Theory and application. Delft University Press
Westerweel J (1997) Fundamentals of digital particle image velocimetry. Meas Sci Technol 8:1379–1392
Rosenfeld A, Kak AC (1982) Digital picture processing, 2nd ed. Academic Press, Orlando
Keane RD, Adrian RJ (1993) Theory of cross-correlation analysis of PIV images. Appl Sci Res 49:191–215
Willert CE (1996) The fully digital evaluation of photographic PIV recordings. Appl Sci Res 56:79
Westerweel J (2000a) Theoretical analysis of the measurement precision in particle image velocimetry. Exp Fluids 29(Suppl):3–12
Westerweel J (2000b) Effect of sensor geometry on the performance of PIV interrogation. In: Adrian RJ et al (eds) Laser techniques applied to fluid mechanics. Springer, Berlin Heidelberg New York, pp 37–55
Hart DP (1997) Sparse array correlation. In: Adrian RJ et al (eds) Developments in laser techniques and fluid mechanics. Springer, Berlin Heidelberg New York, pp 53–74
Stone SW, Meinhart CD, Wereley ST (2002) A microfluidic-based nanoscope. Exp Fluids 33:613–619
Westerweel J, Dabiri D, Gharib M (1997) The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings. Exp Fluids 23:20–28
Rohály J, Frigerio F, Hart DP (2002) Reverse hierarchical PIV processing. Meas Sci Technol 13:984–996
Hohreiter V, Wereley ST, Olsen MG, Chung JN (2002) Cross-correlation analysis for temperature measurement. Meas Sci Technol 13:1072–1078
Acknowledgement
The authors would like to thank Dr. Christian Poelma for his assistance in programming the single-pixel ensemble correlation method and Dr. Steve Wereley of Purdue University for comments and suggestions with respect to certain parts of the manuscript. This research has been sponsored by the Technology Foundation STW grant DSF.5695 (http://www.stw.nl), and the Foundation for Fundamental Research on Matter (FOM) grant 01ILP011 (http://www.fom.nl).
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Parts of this paper were previously presented at the 11th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisbon, 8–11 July 2002, and the 5th International Symposium on Particle Image Velocimetry, Busan, 22–24 September 2003.
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Westerweel, J., Geelhoed, P.F. & Lindken, R. Single-pixel resolution ensemble correlation for micro-PIV applications. Exp Fluids 37, 375–384 (2004). https://doi.org/10.1007/s00348-004-0826-y
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DOI: https://doi.org/10.1007/s00348-004-0826-y