Control of a canonical separated flow

Griffin, John; Oyarzun, Matias; Cattafesta, Louis N.; Tu, Jonathan H.; Rowley, Clarence W.

doi:10.2514/6.2013-2968

Cited by 16 publications

(15 citation statements)

References 23 publications

(15 reference statements)

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“…We note that TDMD identifies a mode at 49Hz, while standard DMD identifies a similarly shaped mode at 58Hz. Local hot-wire measurements on the same flow configuration, previously reported in [40,39], corroborate the presence of a frequency peak in the range 45Hz-50Hz, as identified by TDMD. In Figure 4, the real components of the dominant oscillatory vorticity modes-computed as the curl of DMD/TDMD velocity modes-are plotted.…”

Section: Dmd On Flow Separation Experimentssupporting

confidence: 81%

“…As such, we now consider an experiment of separated flow over a flat plate (Re=10 5 with respect to chord length), with snapshots of the velocity field (n = 42 976, m = 3 000) measured using timeresolved particle image velocimetry (TR-PIV) in a wind tunnel sampled at a rate of f s = 1600Hz (δt = 0.625ms). Further details of the experimental setup can be found in [39]. DMD and TDMD are performed using a rankreduction level r = 25, which corresponds to retaining over 99% of energy content based on an SVD of X.…”

Section: Dmd On Flow Separation Experimentsmentioning

confidence: 99%

See 1 more Smart Citation

De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets

Hemati

Rowley

Deem³

et al. 2017

Theor. Comput. Fluid Dyn.

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292

209

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The Dynamic Mode Decomposition (DMD)-a popular method for performing data-driven Koopman spectral analysis-has gained increased adoption as a technique for extracting dynamically meaningful spatiotemporal descriptions of fluid flows from snapshot measurements. Often times, DMD descriptions can be used for predictive purposes as well, which enables informed decision-making based on DMD modelforecasts. Despite its widespread use and utility, DMD regularly fails to yield accurate dynamical descriptions when the measured snapshot data are imprecise due to, e.g., sensor noise. Here, we express DMD as a two-stage algorithm in order to isolate a source of systematic error. We show that DMD's first stage, a subspace projection step, systematically introduces bias errors by processing snapshots asymmetrically. To remove this systematic error, we propose utilizing an augmented snapshot matrix in a subspace projection step, as in problems of total least-squares, in order to account for the error present in all snapshots. The resulting unbiased and noise-aware total DMD (TDMD) formulation reduces to standard DMD in the absence of snapshot errors, while the two-stage perspective generalizes the de-biasing framework to other related methods as well. TDMD's performance is demonstrated in numerical and experimental fluids examples.

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Section: Dmd On Flow Separation Experimentssupporting

confidence: 81%

Section: Dmd On Flow Separation Experimentsmentioning

confidence: 99%

De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets

Hemati

Rowley

Deem³

et al. 2017

Theor. Comput. Fluid Dyn.

Self Cite

292

209

View full text Add to dashboard Cite

show abstract

“…Several studies have shown that effective separation control strategies exploit the most amplified frequency of the shear-layer instability. [9][10][11][12][13]22 Since the dynamical characteristics of the separated flow (including the modality of the vortex generation due to the Kelvin-Helmholtz instability) are identified by the surface pressure measurements, the pressure array DMD results may be viable for state estimation in closed loop control of the separated flow. To illustrate how this can be implemented to provide dynamical characteristics on the fly, online DMD is performed for the surface microphone measurements of the baseline separated flow with the weighting factor λ set to 0.996.…”

Section: Unsteady Surface Pressure Dmdmentioning

confidence: 99%

“…Irrespective of the form of actuation, several studies have shown that efficient control is achieved for forcing frequencies near the frequency of the shear layer instability. [9][10][11][12] Recently, Griffin et al 13 provide results of varying the actuation frequency of a ZNMF jet in the vicinity of the characteristic frequencies of a canonical separated flow. The authors find that forcing near the shear layer frequency has the most dramatic impact on reducing separation.…”

Section: Introductionmentioning

confidence: 99%

Identifying Dynamic Modes of Separated Flow Subject to ZNMF-Based Control from Surface Pressure Measurements

Deem

Cattafesta

Zhang

et al. 2017

47th AIAA Fluid Dynamics Conference

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Fluid systems are most efficient for fully attached flows, and designers therefore seek to avoid flow separation. Active flow control can help achieve this goal, and closed-loop control offers improved performance at off-design conditions. However, this requires feedback of accurate state estimates to the controller in real time. This motivates a physics-based, state-estimation technique that economically extracts key dynamical features of the flow. This work aims to extract dynamical characteristics of a laminar separation bubble on a flat plate at a chord Reynolds number of 10 5 using a linear array of unsteady surface pressure measurements. First, Dynamic Mode Decomposition (DMD) is employed on high-dimensional time-resolved PIV velocity and corresponding estimated pressure fields to identify the dynamically relevant spatial structure and temporal characteristics of the separated flow. Then, results are presented of various open-loop control cases using pulse-modulation of a zero-net mass-flux actuator slot located just upstream of separation. Real-time estimates of the dynamical characteristics are provided by performing online DMD on measurements from a linear array of 13 unsteady surface pressure transducers. The results show that this method provides reliable estimates of the modal characteristics of the separated flow subject to forcing at a rate much faster than the characteristic time scales of the flow. Therefore, online DMD applied to the surface pressure measurements provides a time-varying linear estimate of the evolution of the controlled flow, thereby enabling closed-loop control.

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“…Sketch of the canonical separated flow experiment setup (adapted from[10]) and the PIV measurement region.…”

mentioning

confidence: 99%

Evaluating the accuracy of the dynamic mode decomposition

Zhang

Dawson

Rowley

et al. 2020

Journal of Computational Dynamics

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Dynamic mode decomposition (DMD) gives a practical means of extracting dynamic information from data, in the form of spatial modes and their associated frequencies and growth/decay rates. DMD can be considered as a numerical approximation to the Koopman operator, an infinite-dimensional linear operator defined for (nonlinear) dynamical systems. This work proposes a new criterion to estimate the accuracy of DMD on a mode-by-mode basis, by estimating how closely each individual DMD eigenfunction approximates the corresponding Koopman eigenfunction. This approach does not require any prior knowledge of the system dynamics or the true Koopman spectral decomposition. The method may be applied to extensions of DMD (i.e., extended/kernel DMD), which are applicable to a wider range of problems. The accuracy criterion is first validated against the true error with a synthetic system for which the true Koopman spectral decomposition is known. We next demonstrate how this proposed accuracy criterion can be used to assess the performance of various choices of kernel when using the kernel method for extended DMD. Finally, we show that our proposed method successfully identifies modes of high accuracy when applying DMD to data from experiments in fluids, in particular particle image velocimetry of a cylinder wake and a canonical separated boundary layer. *

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Control of a canonical separated flow

Cited by 16 publications

References 23 publications

De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets

De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets

Identifying Dynamic Modes of Separated Flow Subject to ZNMF-Based Control from Surface Pressure Measurements

Evaluating the accuracy of the dynamic mode decomposition

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