Integration of non-time-resolved PIV and time-resolved velocity point sensors for dynamic estimation of time-resolved velocity fields

We demonstrate a three-step method for estimating time-resolved velocity fields using time-resolved point measurements and non-time-resolved particle image velocimetry (PIV) data. First, we use linear stochastic estimation to obtain an initial set of time-resolved estimates of the flow field. These initial estimates are then used to identify a linear model of the flow physics. The model is incorporated into a Kalman smoother, which is used to make a second, improved set of estimates. We verify this method with an experimental study of the wake behind a 7.1% thick elliptical-leading-edge flat plate at a chord Reynolds number of 50,000. Time-resolved PIV data are acquired synchronously with a point measurement of velocity. The above method is then applied to a non-time-resolved subset of the PIV data, along with the time-resolved probe signal. This produces a time-resolved, low-dimensional approximation of the velocity field. The original, time-resolved PIV snapshots are then used to compare the accuracy of the initial, stochastic estimates to the latter, dynamic ones, as measured by the kinetic energy contained in the estimation errors. We find that, for this particular flow, the Kalman smoother is able to utilize the dynamic model and the non-time-resolved PIV data to produce estimates that are not only more accurate, but also more robust to noise. Consequently, modal decompositions based on these estimates more accurately identify coherent structures in the flow.