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

Cohen, Kelly; Seidel, Jurgen; Siegel, Stefan; McLaughlin, Thomas; Aradag, Selin

Low-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=20000 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.

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