F2DPR: a fast and robust cross-correlation technique for volumetric PIV

The current state-of-the-art in cross-correlation based time-resolved particle image velocimetry (PIV) techniques are the fluid trajectory correlation, FTC (Lynch and Scarano 2013) and the fluid trajectory evaluation based on an ensemble-averaged cross-correlation, FTEE (Jeon et al 2014a). These techniques compute the velocity vector as a polynomial trajectory Gamma in space and time, enabling the extraction of beneficial quantities such as material acceleration whilst significantly increasing the accuracy of the particle displacement prediction achieved by standard two-frame PIV. In the context of time-resolved volumetric PIV, the drawback of trajectory computation is the computational expense of the three-dimensional (3D) cross-correlation, exacerbated by the requirement to perform N - 1 cross-correlations, where N (for typically 5 <= N <= 9) is the number of sequential particle volumes, for each velocity field. Therefore, the acceleration of this calculation is highly desirable. This paper re-examines the application of two-dimensional (2D) cross-correlation methods to three-dimensional (3D) datasets by Bilsky et al (2011) and the binning techniques of Discetti and Astarita (2012). A new and robust version of the 2D methods is proposed and described, called fast 2D projection-re-projection (f2dpr). Performance tests based on computational time and accuracy for both two-frame and multi-frame PIV are carried out on synthetically generated data. The cases presented herein include uniaxial uniform linear displacements and shear, and simulated turbulence data. The proposed algorithm is shown to be in the order of 10 times faster than a standard 3D FFT without loss of precision for a wide range of synthetic test cases, while combining with the binning technique can yield 50 times faster computation. The algorithm is also applied to reconstructed synthetic turbulent particle fields to investigate reconstruction noise on its performance and no significant loss of precision is observed.