Dynamics of an unsteady stagnation vortical flow via dynamic mode decomposition analysis

Dynamics of an unsteady stagnation vortical flow via dynamic mode decomposition analysis The dynamics of a large-scale stagnation vortex pair in an axisymmetric stagnation flow subject to a laminar wake disturbance is measured by time-resolved two-dimensional particle image velocimetry, and then quantitatively characterized by both the Eulerian velocity/vorticity fields and the Lagrangian finite-time Lyapunov exponents fields. This vortex pair is found to be the result of the forced response of the stagnation flow to the upstream shearing disturbances, and presents a dynamical evolution of quasi-periodic shedding due to short-wave elliptical instability. Dynamic mode decomposition analysis of both the Eulerian measure and the Lagrangian measure is taken for a quantitative description of this process. The sparsity-promoting scheme (Jovanović et al. Phys Fluids 26(2):024,103, 2014), which integrates the mode identification and truncation as a whole, is used to distinguish those modes with dynamical significance from irrelevant ones with transient behavior. The superiority of this scheme is evidenced by the facts that it avoids the eigenvalue contamination problem, and credits higher priority to the sub-dominant modes directly associated with the system dynamics. It is found that the energetic mode with a frequency of 0.177 Hz, or about 10% of the maximum shear rate of the upstream wake, determines the quasi-periodical vortex formation process. Its half-order harmonic represents the vortex shedding event along one fixed direction. High-order even-quarter harmonics jointly contribute to the circular pattern of the vortex tube. In addition, a set of low-frequency odd-quarter harmonics are highlighted as the elliptical instability and the following vortex deformation process. Based on this finding, a reduce-order representation with 8 Eulerian modes or 56 Lagrangian modes is proposed to characterize the dominant dynamics of this unsteady vortical stagnation flow. In addition, the Eulerian measure seems to be more efficient than the Lagrangian measure in terms of reduced-order representation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Experiments in Fluids Springer Journals

Dynamics of an unsteady stagnation vortical flow via dynamic mode decomposition analysis

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Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag Berlin Heidelberg
Subject
Engineering; Engineering Fluid Dynamics; Fluid- and Aerodynamics; Engineering Thermodynamics, Heat and Mass Transfer
ISSN
0723-4864
eISSN
1432-1114
D.O.I.
10.1007/s00348-017-2306-1
Publisher site
See Article on Publisher Site

Abstract

The dynamics of a large-scale stagnation vortex pair in an axisymmetric stagnation flow subject to a laminar wake disturbance is measured by time-resolved two-dimensional particle image velocimetry, and then quantitatively characterized by both the Eulerian velocity/vorticity fields and the Lagrangian finite-time Lyapunov exponents fields. This vortex pair is found to be the result of the forced response of the stagnation flow to the upstream shearing disturbances, and presents a dynamical evolution of quasi-periodic shedding due to short-wave elliptical instability. Dynamic mode decomposition analysis of both the Eulerian measure and the Lagrangian measure is taken for a quantitative description of this process. The sparsity-promoting scheme (Jovanović et al. Phys Fluids 26(2):024,103, 2014), which integrates the mode identification and truncation as a whole, is used to distinguish those modes with dynamical significance from irrelevant ones with transient behavior. The superiority of this scheme is evidenced by the facts that it avoids the eigenvalue contamination problem, and credits higher priority to the sub-dominant modes directly associated with the system dynamics. It is found that the energetic mode with a frequency of 0.177 Hz, or about 10% of the maximum shear rate of the upstream wake, determines the quasi-periodical vortex formation process. Its half-order harmonic represents the vortex shedding event along one fixed direction. High-order even-quarter harmonics jointly contribute to the circular pattern of the vortex tube. In addition, a set of low-frequency odd-quarter harmonics are highlighted as the elliptical instability and the following vortex deformation process. Based on this finding, a reduce-order representation with 8 Eulerian modes or 56 Lagrangian modes is proposed to characterize the dominant dynamics of this unsteady vortical stagnation flow. In addition, the Eulerian measure seems to be more efficient than the Lagrangian measure in terms of reduced-order representation.

Journal

Experiments in FluidsSpringer Journals

Published: Feb 27, 2017

References

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