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A REVIEW ON THE CROSS-CORRELATION METHODS FOR PIV

机译：PIV的互相关方法综述

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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.
机译：在用于粒子成像测速的图像互相关方法（PIV的缩写）中，使用互相关系数，基于两次连续图片之间的粒子云或粒子图像的分布模式来计算流体流速矢量。互相关方法分为两种：一种称为亮度分布方法，它使用原始统计领域中定义的互相关方程；另一种称为二进制图像方法，它使用互相关方程。无需严格的数学推导就可以为高速计算的便利设计相关性。本文表明，可以通过使用集合论和阶跃函数，以积分形式定义的一般方程，通过数学方法得出亮度分布方法的互相关的精确形式和二进制图像方法的常规互相关方程。基于互相关方程，讨论了两种互相关方法的特点。此外，作者提出了时间间隔，识别域大小，虚粒子大小和速度梯度张量的相关参数之间的新关系，以提高互相关方法对任何流场（例如湍流）的适用性，包括膨胀和压缩，剪切和旋转的速度梯度张量。

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    Fujio Yamamoto; Ari-isa Wada; Manabu Iguchi; Masa-aki Ishikawa;

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    Department of Mechanical Engineering, Fukui University, 3-9-1 Bunkyo, Fukni-shi, 910, Japan;

    Div. of Eng., Aisin AW-Industry Co., Ltd., 38 Ikenokami-cho, Takefu-shi, 915, Japan;

    Faculty of Engineering, Osaka University, 2-1 Yamada-oka, Suita-shi, Osaka, 565, Japan;

    Graduate Student, Fukui University, 3-9-1 Bunkyo, Fukui-shi, 910, Japan;

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