Nonlinear frequency-domain reduced-order modelling of turbulent flows

Li, Xiaodong and Lasagna, Davide (2024) Nonlinear frequency-domain reduced-order modelling of turbulent flows. 13th International Symposium on Turbulence and Shear Flow Phenomena (TSFP13), , Montreal, Canada. 25 - 28 Jun 2024. 6 pp .

Abstract

We present a frequency-domain nonlinear reducedorder modelling technique to find pproximate periodic orbits (APOs) in turbulent flow problems and predict physical quantities and dynamical features. Although finding Unstable Periodic Orbits (UPOs) is feasible in low-dimensional dynamic systems or low-Re turbulent flows, computing costs become expensive for high-Re turbulent flows. Rather than finding UPOs in full-state space, we propose to build a ReducedOrder Model (ROM) to circumvent such impediment while the benefit of periodicity is maintained by considering the ROM in the frequency domain, which naturally accommodates time-periodic velocity fields. To this end, the space-time basis functions of the low-order space are extracted using Spectral Proper Orthogonal Decomposition (SPOD). The NavierStokes equations are converted into a low-order algebraic system via Galerkin projection onto selected SPOD modes. Numerical solutions of the ROM are achieved using gradientbased optimization of the amplitude coefficients, letting the solutions in the ROM satisfy conservation laws. The proposed approach is demonstrated in chaotic flows in a 2D liddriven cavity at Re=20,000. Numerical results show that the frequency-domain ROM admits multiple solutions that capture dominant dynamical flow features, such as vorticity structures, and predicts well statistical quantities, such as mean turbulent kinetic energy.

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Contributors

Author: Xiaodong Li

Author: Davide Lasagna

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