Convergence enhancement of single-pixel PIV with symmetric double correlation

Abstract

A symmetric correlation approach is proposed to improve the convergence of the single-pixel technique for particle image velocimetry (PIV). Nogueira et al. (Exp Fluids 30:309–316, 2001) introduced this method to remove a source of random errors in PIV when small interrogation windows are used; it consists in applying the cross-correlation operator by considering fixed the first exposure and moving the second one, and vice versa, and then calculating the cross-correlation map as the average of the two maps. The symmetric correlation suppresses the effects of truncation of the particles lying on the border of the interrogation windows. In this paper, the application of symmetric correlation to single-pixel PIV algorithms is reported. Since symmetric direct correlation provides a significant improvement in the cross-correlation peak shape with respect to the standard asymmetric single-pixel implementation, a faster convergence in estimating the average velocity components and turbulence statistics is achieved. An additional improvement is due to the possibly limited correlation between the background noise for the two exposures. The algorithm is tested via synthetic images with imposed constant and sinusoidal displacement and then tested with real data of a jet flow. The technique has shown that the same accuracy of the standard asymmetric approach can be achieved with 50 % of the samples and that a reduction in the measurement error by 30 % is obtained when using the same number of samples.