Filtered POD‐based low‐dimensional modeling of the 3D turbulent flow behind a circular cylinder

Abstract

SUMMARYLow-dimensional models have proven essential for feedback control and estimation of flow fields. While feedback control based on global flow estimation can be very efficient, it is often difficult to estimate the flow state if structures of very different length scales are present in the flow. The conventional snapshot-based proper orthogonal decomposition (POD), a popular method for low-order modeling, does not separate the structures according to size, since it optimizes modes based on energy. Two methods are developed in this study to separate the structures in the flow based on size. One of them is Hybrid Filtered POD method and the second one is 3D FFT-based Filtered POD approach performed using a fast Fourier transform (FFT)-based spatial filtering. In both the methods, a spatial low-pass filter is employed to precondition snapshot sets before deriving POD modes. Three-dimensional flow data from the simulation of turbulent flow over a circular cylinder wake at Re = 20 000 is used to evaluate the performance of the two methods. Results show that both the FFT-based 3D Filtered POD and Hybrid Filtered POD are able to capture the large-scale features of the flow, such as the von Karman vortex street, while not being contaminated by small-scale turbulent structures present in the flow.

Vortex Shedding of Various Bluff Bodies in Cross Flow

“…al. 12 Even though the method of POD and Reynolds number used by Aradag was different, the results proved to be similar. A side-by-side comparison of the first two modes from this study and the study performed by Aradag et.…”

An evolve‐then‐filter regularized reduced order model for convection‐dominated flows

“…The second goal is to investigate the effect of explicit ROM spatial filtering (the Proj and the DF) on the L-ROM and EF-ROM. x/ D 1 T L y L´X t;y;´q .x; y;´; t/ ; (25) where T is the total time length (i.e., T D 300), L y is the dimension of the computational domain in the y-direction, and L´is the dimension of the computational domain in the´-direction. We also include results for the G-ROM (6).…”

“…We emphasize, however, that the spatial filtering used in Reg-ROMs is fundamentally different. Indeed, in the preprocessing spatial filtering used in [25], the snapshots (i.e., the input data) are spatially filtered, but the ROMs (i.e., the mathematical models) are not. In Reg-ROMs, on the other hand, some of the ROM terms are explicitly filtered, and thus, the mathematical model is modified.…”

Modeling the Wake Behind Bluff Bodies for Flow Control at Laminar and Turbulent Reynolds Numbers Using Artificial Neural Networks

“…Since it is inevitable to use the POD technique to obtain a low-dimensional description of the original data ensembles for further ANN applications, the classical "Snapshot Method" is combined with the Fast Fourier Transform (FFT) filtering procedure for turbulent flow POD analyses as suggested by Aradag et al (2010). The combined FFT-POD technique is performed to the turbulent CFD data ensembles to eliminate the undesired effects of small scale turbulent structures in the wake region, and to observe flow characteristics in more detail by separating spatial (modes) and temporal (mode amplitudes) structures.…”