Estimation of time-resolved turbulent fields through correlation of non-time-resolved field measurements and time-resolved point measurements

Abstract

A method for the estimation of time-resolved turbulent fields from the combination of non-time-resolved field measurements and time-resolved point measurements is proposed. The approach poses its fundaments on a stochastic estimation based on the Proper Orthogonal Decomposition (POD) of the field measurements and of the time-resolved point measurements. The correlation between the temporal modes of the field measurements and the temporal modes of the point measurements at synchronized instants is evaluated; this correlation is extended to the "out-of-sample" time instants for the field measurements, i.e. those in which field data are not available. In the "out-of-sample" instants, POD modes time coefficients are estimated and the flow fields are reconstructed. The proposed method extends the work by Hosseini et al. (Experiments in fluids, 56, 2015) by proposing a truncation criterion which allows removing the uncorrelated part of the signal from the reconstruction of the flow fields. The truncation is fundamental in case of turbulent flow fields, in which a great wealth of scales is involved, thus reducing the correlation between the probe signal and the field measurements. The threshold selection is based on the random distribution of the uncorrelated signal.