POD-Based Estimations of the Flowfield From PIV Wall Gradient Measurements in the Backward-Facing Step Flow Available to Purchase

In this paper, particle image velocimetry (PIV) results from a backward-facing step flow, of which Reynolds number is 2800 based on free stream velocity and step height (h = 16.5 mm), are used to demonstrate the capability of proper orthogonal decomposition (POD)-based estimation models. Three-component PIV velocity fields are decomposed into a set of spatial basis functions and a set of temporal coefficients. The estimation models are built to relate the low-order POD coefficients, determined from an ensemble of 1050 PIV fields by the “snapshot” method, and the time-resolved wall gradients, measured by a near-wall measurement technique called stereo interfacial PIV. These models are evaluated in terms of reconstruction and prediction of the low-order temporal POD coefficients of the velocity fields. In order to determine the coefficients of the estimation models, linear stochastic estimation (LSE), quadratic stochastic estimation (QSE), principal component regression (PCR) and kernel ridge regression (KRR) are applied. In addition, we introduce a possibility of multi-time POD-based estimations in which past and future information of the wall gradient events is used separately or combined. The results show that the multi-time estimation approaches can improve the prediction process. Among these approaches, the proposed multi-time KRR-POD estimation with optimized time duration of wall gradient information in the past yields the best prediction.