Time-resolved reconstruction of turbulent flows using linear stochastic estimation and sequential data assimilation

The present work concentrates on the reconstruction of the time-resolved turbulent flows from probe signals and low sampling rate flow fields using linear stochastic estimation (LSE) and sequential data assimilation (DA). The separated and reattached flow over a blunt plate is used as the benchmark configuration. Experimental data are acquired with a microphone array (34 probes) installed on the plate surface to capture the pressure fluctuation at a sampling rate 1000 Hz, and with planar particle image velocimetry (PIV) measuring the two-dimensional two-component (2D2C) velocity fields synchronized with the microphones at 1 Hz. LSE is conducted first to estimate the raw temporal sequence of the flow field from PIV and microphone data. This temporal sequence then serves as the observations for the DA process based on continuous adjoint formulation for the flow field correction and pressure determination. The LSE results show that an appropriate size of proper orthogonal decomposition (POD) database should be evaluated considering the combined error induced by the truncation of the mapping function M, the size of the POD database, and the scaling of the model coefficient for the compensation of M truncation. Subsequently, the LSE reconstructions using the POD database of size N-t = 100 are employed as the observations in the DA process. The mean flow field is recovered quite well, while the normal Reynolds stress also has a significant improvement compared to large-eddy simulation. The temporal variation of the LSE reconstruction is significantly improved, and the resultant fluctuating pressure coefficient distribution agrees reasonably well with the microphone measurement.