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.
In this paper, we discuss a novel approach to the description of atmospheric flows in urban geometries. Our technique is based on the method of proper orthogonal decomposition ͑POD͒. We devise a method that enables us to compute the time-varying coefficients of a Karhunen-Loève expansion of the urban flow field using knowledge of instantaneous velocity data taken at a minimum number of locations simultaneously. Using the POD basis functions and these velocity data, we solve a set of linear equations which gives us an estimate of the exact expansion coefficients. This method allows us to compute estimates for all coefficients thereby enabling us to reconstruct a close approximation to the flow field which is optimal in a certain sense. A quantitative comparison of the approximate coefficients with the coefficients of an exact Karhunen-Loève expansion shows that the method works very well. Our method provides a practical approach to reconstructing the flow field using a minimum amount of information.
SUMMARYThe Lattice Boltzmann method (LBM) is used to simulate turbulent channel flow. Two simulations are performed. One uses high enough grid resolution in order for it to be considered a direct numerical simulation (DNS). LBM in its traditional form is adopted for this simulation. The other simulation uses lower resolution for which the original method becomes unstable. An entropy condition is used to render this simulation stable. Results from these two numerical experiments are compared with the results from a DNS performed with traditional numerical techniques. It is concluded that LBM can be used as tool to simulate turbulent flows and entropy stabilized LBM schemes can be used to achieve accurate results with reasonably low grid resolution.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.