Dynamic mode decomposition and Koopman spectral analysis of boundary layer separation-induced transition

We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an infinite-dimensional linear operator associated with the full nonlinear system. These modes, referred to as Koopman modes, are associated with a particular observable, and may be determined directly from data (either numerical or experimental) using a variant of a standard Arnoldi method. They have an associated temporal frequency and growth rate and may be viewed as a nonlinear generalization of global eigenmodes of a linearized system. They provide an alternative to proper orthogonal decomposition, and in the case of periodic data the Koopman modes reduce to a discrete temporal Fourier transform. The Arnoldi method used for computations is identical to the dynamic mode decomposition recently proposed by Schmid & Sesterhenn (Sixty-First Annual Meeting of the APS Division of Fluid Dynamics, 2008), so dynamic mode decomposition can be thought of as an algorithm for finding Koopman modes. We illustrate the method on an example of a jet in crossflow, and show that the method captures the dominant frequencies and elucidates the associated spatial structures.

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Analysis of unsteady behaviour in shockwave turbulent boundary layer interaction

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.37 ◽

2012 ◽

Vol 700 ◽

pp. 16-28 ◽

Cited By ~ 104

Author(s):

Muzio Grilli ◽

Peter J. Schmid ◽

Stefan Hickel ◽

Nikolaus A. Adams

Keyword(s):

Boundary Layer ◽

Turbulent Boundary Layer ◽

Separation Bubble ◽

Low Frequency ◽

Dynamic Mode Decomposition ◽

Dynamic Mode ◽

Layer Interaction ◽

Mode Decomposition ◽

Boundary Layer Interaction ◽

Low Frequency Motion

AbstractThe unsteady behaviour in shockwave turbulent boundary layer interaction is investigated by analysing results from a large eddy simulation of a supersonic turbulent boundary layer over a compression–expansion ramp. The interaction leads to a very-low-frequency motion near the foot of the shock, with a characteristic frequency that is three orders of magnitude lower than the typical frequency of the incoming boundary layer. Wall pressure data are first analysed by means of Fourier analysis, highlighting the low-frequency phenomenon in the interaction region. Furthermore, the flow dynamics are analysed by a dynamic mode decomposition which shows the presence of a low-frequency mode associated with the pulsation of the separation bubble and accompanied by a forward–backward motion of the shock.

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Dynamic Mode Decomposition Analysis of Separated Boundary Layers Under Variable Reynolds Number and Free-Stream Turbulence

Volume 2E: Turbomachinery ◽

10.1115/gt2020-16322 ◽

2020 ◽

Author(s):

M. Dellacasagrande ◽

J. Verdoya ◽

D. Barsi ◽

D. Lengani ◽

D. Simoni

Keyword(s):

Boundary Layer ◽

Growth Rate ◽

Reynolds Number ◽

Shear Layer ◽

Large Scale ◽

Dynamic Mode Decomposition ◽

Dynamic Mode ◽

Data Set ◽

Separated Shear Layer ◽

Mode Decomposition

Abstract A flat plate boundary layer has been surveyed by means of time-resolved particle image velocimetry (PIV) under variable Reynolds number (70000 < Re < 150000) and turbulence intensity level (1.5% < Tu < 2.5%). The PIV visualizations were completed in two measuring planes, that are oriented both normal and parallel to the wall. For the wall-parallel configuration, the measuring plane is located inside the boundary layer. The PIV data were post-processed by applying Dynamic Mode Decomposition (DMD), which provides frequency based modes and their corresponding growth rate. The effects of Re and Tu variation on the amplification of the dominant wavelength within the separated shear layer, which is responsible for transition, is the main subject of the present work. The DMD modes and related eigenvalues were computed with reference to the main streamwise coordinate. This allowed discussing the effects due to the main flow parameters on the amplification of the dominant streamwise wavelengths within the separated shear layer (Kelvin-Helmholtz modes). The growth of such streamwise modes ends with the formation of large scale vortices, whose breakup forces transition. In order to obtain the effective distribution of the maximum growth rate of fluctuations at different locations and times, the DMD domain was continuously extended in the streamwise direction, accounting for a specified number of periods characterizing the large scale K-H vortices. In order to reduce the time-space dependent results obtained by the DMD procedure, a probability density function of the most unstable wavelength and the corresponding growth rate has been computed. For the present data set, the spatial growth rate of fluctuations is found to increase at the higher Reynolds number, while it slightly reduces with increasing the Tu level. The procedure and findings discussed in this work shall be suitable for designing active control systems, such as harmonic blowing for separation control.

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Experimental Measurement of In-Plane Rolling Nonpneumatic Tire Vibrations Using High-Speed Imaging

Tire Science and Technology ◽

10.2346/tire.18.470101 ◽

2019 ◽

Vol 47 (3) ◽

pp. 196-210

Author(s):

Meghashyam Panyam ◽

Beshah Ayalew ◽

Timothy Rhyne ◽

Steve Cron ◽

John Adcox

Keyword(s):

High Speed ◽

Image Correlation ◽

Dynamic Mode Decomposition ◽

Dynamic Mode ◽

High Speed Imaging ◽

Correlation Algorithm ◽

Mode Decomposition ◽

Series Of Experiments ◽

Plane Deformations ◽

Dominant Frequencies

ABSTRACT This article presents a novel experimental technique for measuring in-plane deformations and vibration modes of a rotating nonpneumatic tire subjected to obstacle impacts. The tire was mounted on a modified quarter-car test rig, which was built around one of the drums of a 500-horse power chassis dynamometer at Clemson University's International Center for Automotive Research. A series of experiments were conducted using a high-speed camera to capture the event of the rotating tire coming into contact with a cleat attached to the surface of the drum. The resulting video was processed using a two-dimensional digital image correlation algorithm to obtain in-plane radial and tangential deformation fields of the tire. The dynamic mode decomposition algorithm was implemented on the deformation fields to extract the dominant frequencies that were excited in the tire upon contact with the cleat. It was observed that the deformations and the modal frequencies estimated using this method were within a reasonable range of expected values. In general, the results indicate that the method used in this study can be a useful tool in measuring in-plane deformations of rolling tires without the need for additional sensors and wiring.

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