Adaptive separation control of a laminar boundary layer using online dynamic mode decomposition

Deem, Eric A.; Cattafesta, Louis N.; Hemati, Maziar S.; Zhang, Hao; Rowley, Clarence W.; Mittal, Rajat

doi:10.1017/jfm.2020.546

Cited by 36 publications

(9 citation statements)

References 75 publications

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“…The basic mechanism of control is the formation of a synthetic jet that injects momentum into the shear layer; this enhances mixing and allows the flow to overcome a greater adverse pressure gradient. Research into SJAs is now being pursued towards the development of flow control schemes suitable for real applications (e.g., [3,4]). Despite the progress in this field, effective flow control has not been characterized for the entire parameter space spanned by excitation frequency, blowing ratio, Reynolds number, orifice geometry and angle of attack.…”

Section: Nomenclaturementioning

confidence: 99%

PIV Visualization of Flow Around Airfoil Controlled by Synthetic Jet Actuators at Shear-Layer and Wake Instability Frequencies

Yang

Sullivan

2021

Volume 3: Fluid Mechanics; Micro and Nano Fluid Dynamics; Multiphase Flow

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The response of a separated boundary layer to synthetic jet flow control at the global wake instability (F+ ≈ 𝒪(1)) and the shear-layer instability (F+ ≈ 𝒪(10)) measured by particle image velocimetry are presented. The visualization shows that in each of the control cases, coherent vorticity develops and breaks down into a turbulent wake. When the jets are actuated by burst-modulation at the wake instability frequency, they induce regular formation and detachment of large-scale vorticity to form a wide turbulent wake. Excitation at the shear-layer instability frequency, on the other hand, produces a train of alternating velocity fluctuations in the boundary layer which dissipate to a narrower wake. Proper orthogonal decomposition of the velocity fields show that the physical extent of the jet-induced coherent structures is decreased with increasing addition of momentum for both excitation frequencies.

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Section: Nomenclaturementioning

confidence: 99%

PIV Visualization of Flow Around Airfoil Controlled by Synthetic Jet Actuators at Shear-Layer and Wake Instability Frequencies

Yang

Sullivan

2021

Volume 3: Fluid Mechanics; Micro and Nano Fluid Dynamics; Multiphase Flow

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“…2016; Proctor, Brunton & Kutz 2016; Korda & Mezić 2018; Loiseau & Brunton 2018; Deem et al. 2020; Klus et al. 2020; Baddoo et al.…”

Section: Introductionmentioning

confidence: 99%

Residual dynamic mode decomposition: robust and verified Koopmanism

2023

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Dynamic mode decomposition (DMD) describes complex dynamic processes through a hierarchy of simpler coherent features. DMD is regularly used to understand the fundamental characteristics of turbulence and is closely related to Koopman operators. However, verifying the decomposition, equivalently the computed spectral features of Koopman operators, remains a significant challenge due to the infinite-dimensional nature of Koopman operators. Challenges include spurious (unphysical) modes and dealing with continuous spectra, which both occur regularly in turbulent flows. Residual dynamic mode decomposition (ResDMD), introduced by Colbrook & Townsend (Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems. 2021. arXiv:2111.14889), overcomes such challenges through the data-driven computation of residuals associated with the full infinite-dimensional Koopman operator. ResDMD computes spectra and pseudospectra of general Koopman operators with error control and computes smoothed approximations of spectral measures (including continuous spectra) with explicit high-order convergence theorems. ResDMD thus provides robust and verified Koopmanism. We implement ResDMD and demonstrate its application in various fluid dynamic situations at varying Reynolds numbers from both numerical and experimental data. Examples include vortex shedding behind a cylinder, hot-wire data acquired in a turbulent boundary layer, particle image velocimetry data focusing on a wall-jet flow and laser-induced plasma acoustic pressure signals. We present some advantages of ResDMD: the ability to resolve nonlinear and transient modes verifiably; the verification of learnt dictionaries; the verification of Koopman mode decompositions; and spectral calculations with reduced broadening effects. We also discuss how a new ordering of modes via residuals enables greater accuracy than the traditional modulus ordering (e.g. when forecasting) with a smaller dictionary. This result paves the way for more significant dynamic compression of large datasets without sacrificing accuracy.

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“…DMD may be thought of as a combination of SVD/POD in space with the Fourier transform in time, combining the strengths of each approach [1,9]. DMD is modular owing to its simple formulation in terms of linear algebra, resulting in innovations related to control [10,11], compression [12,13], reduced-order modelling [14] and multi-resolution analysis [15,16], among others. In a related line of work, the spectral POD (SPOD) method and its modes are optimally averaged DMD modes obtained from an ensemble DMD problem for stationary flows [17].…”

Section: Introductionmentioning

confidence: 99%

Bagging, optimized dynamic mode decomposition for robust, stable forecasting with spatial and temporal uncertainty quantification

Sashidhar

Kutz

2022

Phil. Trans. R. Soc. A.

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Dynamic mode decomposition (DMD) provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of temporal, or spatio-temporal, data. A variety of regression techniques have been developed for producing the linear model approximation whose solutions are exponentials in time. For spatio-temporal data, DMD provides low-rank and interpretable models in the form of dominant modal structures along with their exponential/oscillatory behaviour in time. The majority of DMD algorithms, however, are prone to bias errors from noisy measurements of the dynamics, leading to poor model fits and unstable forecasting capabilities. The optimized DMD algorithm minimizes the model bias with a variable projection optimization, thus leading to stabilized forecasting capabilities. Here, the optimized DMD algorithm is improved by using statistical bagging methods whereby a single set of snapshots is used to produce an ensemble of optimized DMD models. The outputs of these models are averaged to produce a bagging, optimized dynamic mode decomposition (BOP-DMD). BOP-DMD improves performance by stabilizing and cross-validating the DMD model by ensembling; it also robustifies the model and provides both spatial and temporal uncertainty quantification (UQ). Thus, unlike currently available DMD algorithms, BOP-DMD provides a stable and robust model for probabilistic , or Bayesian, forecasting with comprehensive UQ metrics. This article is part of the theme issue ‘Data-driven prediction in dynamical systems’.

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Adaptive separation control of a laminar boundary layer using online dynamic mode decomposition

Abstract: Abstract

Cited by 36 publications

References 75 publications

PIV Visualization of Flow Around Airfoil Controlled by Synthetic Jet Actuators at Shear-Layer and Wake Instability Frequencies

PIV Visualization of Flow Around Airfoil Controlled by Synthetic Jet Actuators at Shear-Layer and Wake Instability Frequencies

Residual dynamic mode decomposition: robust and verified Koopmanism

Bagging, optimized dynamic mode decomposition for robust, stable forecasting with spatial and temporal uncertainty quantification

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