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. Additionally, the selection of the probe time-span to perform the POD analysis on the probe signal is discussed. The method is validated with a synthetic test case and an experimental one. A Direct Numerical Simulation database of a channel flow is selected since its spectral richness is expected to represent a significant challenge for this method. This dataset allows isolating the effects of correlation between field measurements and point measurements, removing issues connected to noise contamination or to the finite spatial resolution which would inevitably affect experimental data. The experimental test case is the wake-flow behind a high-angle-of-attack airfoil with a relatively small number of samples, affected by significant noise. The quality of the dynamic estimation is found to be affected by the noise contamination of the data and by the poor convergence of the POD modes, which add on the effect of the probe location, i.e. on the correlation between probe events and flow features. The squared correlation coefficient between reconstructed data and in-sample data is proposed as an assessment of the flow fields estimation quality. The use of the squared correlation coefficient directly on in-sample data is allowed by the truncation itself.