Fluid trajectory evaluation based on an ensemble-averaged cross-correlation in time-resolved PIV

Abstract

A novel multi-frame particle image velocimetry (PIV) method, able to evaluate a fluid trajectory by means of an ensemble-averaged cross-correlation, is introduced. The method integrates the advantages of the state-of-art time-resolved PIV (TR-PIV) methods to further enhance both robustness and dynamic range. The fluid trajectory follows a polynomial model with a prescribed order. A set of polynomial coefficients, which maximizes the ensemble-averaged cross-correlation value across the frames, is regarded as the most appropriate solution. To achieve a convergence of the trajectory in terms of polynomial coefficients, an ensemble-averaged cross-correlation map is constructed by sampling cross-correlation values near the predictor trajectory with respect to an imposed change of each polynomial coefficient. A relation between the given change and corresponding cross-correlation maps, which could be calculated from the ordinary cross-correlation, is derived. A disagreement between computational domain and corresponding physical domain is compensated by introducing the Jacobian matrix based on the image deformation scheme in accordance with the trajectory. An increased cost of the convergence calculation, associated with the nonlinearity of the fluid trajectory, is moderated by means of a V-cycle iteration. To validate enhancements of the present method, quantitative comparisons with the state-of-arts TR-PIV methods, e.g., the adaptive temporal interval, the multi-frame pyramid correlation and the fluid trajectory correlation, were carried out by using synthetically generated particle image sequences. The performances of the tested methods are discussed in algorithmic terms. A high-rate TR-PIV experiment of a flow over an airfoil demonstrates the effectiveness of the present method. It is shown that the present method is capable of reducing random errors in both velocity and material acceleration while suppressing spurious temporal fluctuations due to measurement noise.