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ISSN 印刷: 1065-3090
ISSN オンライン: 1940-4336

# Journal of Flow Visualization and Image Processing

DOI: 10.1615/JFlowVisImageProc.v3.i1.50
pages 65-78

## DISCUSSION OF THE CROSS-CORRELATION METHODS FOR PIV

Fujio Yamamoto
Faculty of Engineering, University of Fukui, Fukui 910-8507, Japan
Div. of Eng., Aisin AW-Industry Co., Ltd., 38 Ikenokami-cho, Takefu-shi, 915, Japan
Manabu Iguchi
Faculty of Engineering, Osaka University, 2-1 Yamada-oka, Suita-shi, Osaka, 565, Japan
Masa-aki Ishikawa
Fukui University, 3-9-1 Bunkyo, Fukui-shi, 910, Japan

### 要約

In the image cross-correlation method for the particle imaging velocimetry (PIV acronym), fluid flow velocity vectors are calculated on the grounds of distribution pattern of particle clouds or particle images between two-consecutive pictures using the cross-correlation coefficient. Cross-correlation methods are classified into two types: one is called the brightness distribution method, which uses the equation of cross-correlation defined in the field of primary statistics, and the other is called the binary image method, which uses the equation of cross-correlation devised for the convenience of high-speed calculation without strict mathematical derivation.
This article shows that an exact form of cross-correlation for the brightness distribution method and the conventional equation of cross-correlation for the binary image method can be derived mathematically by using set theory and step function from a general equation defined in an integral form. The characteristics of the two types of cross-correlation methods are discussed based on the derived equations of cross-correlation.
Furthermore, the authors propose a new relation among the correlation parameters of time interval, identification domain size, imaginary particle size, and the velocity gradient tensors in order to raise applicability of the cross-correlation method to any flow fields such as turbulent flows, which include velocity gradient tensors of expansion and compression, shearing, and rotation.

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