Volumetric correlation PIV: a new technique for 3D velocity vector field measurement

A method is proposed that allows threedimensional (3D) two-component measurements to be made by means of particle image velocimetry (PIV) in any volume illuminated over a finite thickness. The method is based on decomposing the cross-correlation function into various contributions at different depths. Because the technique is based on 3D decomposition of the correlation function and not reconstruction of particle images, there is no limit to particle seeding density as experienced by 3D particle tracking algorithms such as defocusing PIV and tomographic PIV. Correlations from different depths are differentiated by the variation in point spread function of the lens used to image the measurement volume over that range of depths. A number of examples are demonstrated by use of synthetic images which simulate micro-PIV (lPIV) experiments. These examples vary from the trivial case of Couette flow (linear variation of one velocity component over depth) to a general case where both velocity components vary by different complex functions over the depth. A final validation—the measurement of a parabolic velocity profile over the depth of a microchannel flow—is presented. The same method could also be applied using a thick light sheet in macro-scale PIV and in a stereo configuration for 3D three-component PIV. 1 Background Since its general acceptance as a powerful measurement tool for fluid mechanics, researchers have been searching for means of increasing the dimensionality of PIV above the standard two component velocity measurement over a plane. Throughout the paper the mDnC notation will be used, where m represents the dimension of the measurement volume and n represents the dimension of the resolved displacements. As an example, two component velocity measurements over a plane are expressed as 2D2C measurements in this notation. For three components of velocity vectors over a measurement plane, stereo PIV (SPIV) was one of the first variations in PIV methodology to be introduced. Since its first development (Arroyo and Greated 1991) through to more recent advances (Fouras et al. 2007a, 2008), SPIV has been becoming better understood, more accurate and simpler to implement. With 2D3C systems, six of the nine terms of the velocity gradient tensor are available. In order to obtain all nine terms of the velocity gradient tensor, a pseudo 3D3C system is available by conducting SPIV on two adjacent planes. Multi-plane SPIV (Schroder and Kompenhans 2004; Kahler 2004) allows for differentiation across planes to obtain those additional three spatial velocity gradients. Holographic PIV (HPIV) (Barnhart et al. 1994; Zhang et al. 1997) allows for truly 3D3C velocity measurements. This broad range of techniques has, in its various forms, advantages and disadvantages. In-line HPIV, and more recently available Digital In-line HPIV, is perhaps the simplest and easiest to implement, but is limited by signal to noise ratio (SNR). Furthermore, there is a limit to the total number of particles that can be resolved and therefore a limited number of vectors is achievable. Off-axis HPIV, A. Fouras K. Hourigan Division of Biological Engineering, Monash University, Melbourne, Australia A. Fouras (&) D. Lo Jacono C. V. Nguyen K. Hourigan Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Monash University, Melbourne, Australia e-mail: [email protected] 123 Exp Fluids (2009) 47:569–577 DOI 10.1007/s00348-009-0616-7