On PIV random error minimization with optimal POD-based low-order reconstruction

Random noise removal from particle image velocimetry (PIV) data and spectra is of paramount importance, especially for the computation of derivative quantities and spectra. Data filtering is critical, as a trade-off between filter effectiveness and spatial resolution penalty should be found. In this paper, a filtering method based on proper orthogonal decomposition and low-order reconstruction (LOR) is proposed. The existence of an optimal number of modes based on the minimization of both reconstruction error and signal withdrawal is demonstrated. A criterion to perform the choice of the optimal number of modes is proposed. The method is validated via synthetic and real experiments. As prototype problems, we consider PIV vector fields obtained from channel flow DNS data and from PIV measurement in the wake of a circular cylinder. We determine the optimal number of modes to be used for the LOR in order to minimize the statistical random error. The results highlight a significant reduction in the measurement error. Dynamic velocity range is enhanced, enabling to correctly capture spectral information of small turbulent scales down to the half of the cutoff wavelength of original data. In addition to this, the capability of detecting coherent structures is improved. The robustness of the method is proved, both for low signal-to-noise ratios and for small-sized ensembles. The proposed method can significantly improve the physical insight into the investigation of turbulent flows.