Proper orthogonal decomposition-based estimations of the flow field from particle image velocimetry wall-gradient measurements in the backward-facing step flow

Abstract

In this paper, particle image velocimetry (PIV) results from the recirculation zone of a backward-facing step flow, of which the Reynolds number is 2800 based on bulk velocity upstream of the step and step height (h = 16.5 mm), are used to demonstrate the capability of proper orthogonal decomposition (POD)-based measurement models. Three-component PIV velocity fields are decomposed by POD into a set of spatial basis functions and a set of temporal coefficients. The measurement models are built to relate the low-order POD coefficients, determined from an ensemble of 1050 PIV fields by the 'snapshot' method, to 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 estimation coefficients of the measurement models, linear stochastic estimation (LSE), quadratic stochastic estimation (QSE), principal component regression (PCR) and kernel ridge regression (KRR) are applied. We denote such approaches as LSE-POD, QSE-POD, PCR-POD and KRR-POD. In addition to comparing the accuracy of measurement models, we introduce 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 an optimized window of past wall-gradient information yields the best prediction. Such a multi-time KRR-POD approach offers a useful tool for real-time flow estimation of the velocity field based on wall-gradient data.

Effects of wall roughness on turbulent junction flow characteristics

“…On the other hand, POD yields an increased number of modes for highly unsteady and inhomogeneous flows (high dimensionality). Nguyen et al 2010). In our study, it required 10 modes for the SB case and 4 modes for the RB case to capture 50% of the total kinetic energy.…”

Wall pressure and conditional flow structures downstream of a reattaching flow region

“…However, increasing the time window on which the pressure is considered amounts to increase the number of independent variables used as reference. Following Hekmati et al (2011) andNguyen et al (2010), this can lead to an artificially good estimation of the velocity field. The quadratic error between the original and the estimated fields is shown on and for the estimation, the error is decreasing when T increases.…”

Use of proper orthogonal decomposition and linear stochastic estimation technique to investigate real-time detailed airflows for building ventilation

“…There are techniques in related research fields characterizing turbulent behaviour that may provide alternative methods potentially applicable to analysing the dynamics of building ventilation. In particular, POD is a statistical analysis tool that has been used to study many different turbulent flows including shear flows, 26 wake dynamics, 27 boundary layers, 28 flows in an open cavity, 29 flow over a backward facing step, 30 and more. This technique has also been used to reconstruct temperature and velocity fields of indoor building environments through numerical simulation.…”

“…30 More detailed presentations for the POD technique are available in literature. 30,[33][34][35] POD attempts to project the fluctuating velocity field onto a set of linear orthogonal basis functions (x) such that the average variance captured by the projection is greater than any other set of basis functions.…”