Transition delay using control theory

Bagheri, Shervin; Henningson, Dan S.

doi:10.1098/rsta.2010.0358

Cited by 42 publications

(44 citation statements)

References 36 publications

(57 reference statements)

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“…For thev equation, the magnitude e −(κ 2 +κ 2 2 )x peaks at the leading edge of the plate and decays exponentially; increasing κ 2 results in a faster viscous decay. For thew equation, the magnitude κ 2 (2x) 1/2 e −(κ 2 +κ 2 2 )x is 0 at the leading edge and peaks at locationx min = 0.5(κ 2 + κ 2 2 ) −1 (see Fig. 2) before decaying.…”

Section: Mathematical Formulation Of the Physical Problemmentioning

confidence: 99%

“…This leads to a smooth variation of the control signal. It is possible to add extra penalty onv 2 w by multiplying q p Q a i q p by a positive constant greater than 1, but this was found to be unnecessary.…”

Section: Definition Of the Cost Function And Formulation Of The Omentioning

confidence: 99%

“…where k (1) 1 and k (2) 1 are the two streamwise wave numbers computed using Taylor's hypothesis from the frequencies f 1 and f 2 that define the frequency band.…”

Section: B Control Of the Full Spectrummentioning

confidence: 99%

“…research in fluid mechanics in the past 15 years or so, and thorough reviews have already appeared in the literature [1][2][3][4][5]. To set the context of the present contribution, we first briefly review work on control of disturbances in boundary layers.…”

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confidence: 99%

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Closed-loop control of boundary layer streaks induced by free-stream turbulence

Papadakis

Riccó

2016

Phys. Rev. Fluids

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The central aim of the paper is to carry out a theoretical and numerical study of active wall transpiration control of streaks generated within an incompressible boundary layer by free-stream turbulence. The disturbance flow model is based on the linearized unsteady boundary-region (LUBR) equations, studied by Leib, Wundrow, and Goldstein [J. Fluid Mech. 380, 169 (1999)], which are the rigorous asymptotic limit of the NavierStokes equations for low-frequency and long-streamwise wavelength. The mathematical formulation of the problem directly incorporates the random forcing into the equations in a consistent way. Due to linearity, this forcing is factored out and appears as a multiplicative factor. It is shown that the cost function (integral of kinetic energy in the domain) is properly defined as the expectation of a random quadratic function only after integration in wave number space. This operation naturally introduces the free-stream turbulence spectral tensor into the cost function. The controller gains for each wave number are independent of the spectral tensor and, in that sense, universal. Asymptotic matching of the LUBR equations with the free-stream conditions results in an additional forcing term in the state-space system whose presence necessitates the reformulation of the control problem and the rederivation of its solution. It is proved that the solution can be obtained analytically using an extension of the sweep method used in control theory to obtain the standard Riccati equation. The control signal consists of two components, a feedback part and a feed-forward part (that depends explicitly on the forcing term). Explicit recursive equations that provide these two components are derived. It is shown that the feed-forward part makes a negligible contribution to the control signal. We also derive an explicit expression that a priori (i.e., before solving the control problem) leads to the minimum of the objective cost function (i.e., the fundamental performance limit), based only on the system matrices and the initial and free-stream boundary conditions. The adjoint equations admit a self-similar solution for large spanwise wave numbers with a scaling which is different from that of the LUBR equations. The controlled flow field also has a self-similar solution if the weighting matrices of the objective function are chosen appropriately. The code developed to implement this algorithm is efficient and has modest memory requirements. Computations show the significant reduction of energy for each wave number. The control of the full spectrum streaks, for conditions corresponding to a realistic experimental case, shows that the root-mean-square of the streamwise velocity is strongly suppressed in the whole domain and for all the frequency ranges examined.

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Section: Mathematical Formulation Of the Physical Problemmentioning

confidence: 99%

Section: Definition Of the Cost Function And Formulation Of The Omentioning

confidence: 99%

“…where k (1) 1 and k (2) 1 are the two streamwise wave numbers computed using Taylor's hypothesis from the frequencies f 1 and f 2 that define the frequency band.…”

Section: B Control Of the Full Spectrummentioning

confidence: 99%

mentioning

confidence: 99%

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Closed-loop control of boundary layer streaks induced by free-stream turbulence

Papadakis

Riccó

2016

Phys. Rev. Fluids

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“…In a low-turbulence environment the initial phase of the transition process is an exponential growth of Tollmien-Schlichting (TS) waves (Saric, Reed & Kerschen 2002). Both numerical and laboratory experiments have shown that it is possible to use linear control techniques to damp the amplitude of the instabilities by several orders of magnitude, with the consequences that the transition is delayed and the skin-friction drag is reduced (Lundell 2007;Bagheri & Henningson 2011;Goldin et al 2013;Semeraro et al 2013a). However, the linear control approach has not yet been established as a competitive technique in applied settings, and essentially all work is at a proof-of-concept level.…”

Section: Introductionmentioning

confidence: 99%

On the role of adaptivity for robust laminar flow control

et al. 2015

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In boundary-layer flows, one may reduce skin-friction drag by delaying the onset of laminar-to-turbulent transition via the attenuation of small-amplitude Tollmien-Schlichting (TS) waves. In this work, we use numerical simulations and experiments to compare the robustness of adaptive and model-based techniques for reducing the growth of two-dimensional TS disturbances. In numerical simulations, the optimal linear quadratic Gaussian (LQG) regulator shows the best performance under the conditions it was designed for. However, it is found that the performance deteriorates linearly with the drift of the Reynolds number from its nominal value. As a result, an order-of-magnitude loss of performance is observed when applying the computation-based LQG controller in wind-tunnel experiments. In contrast, it is shown that the adaptive filtered-X least-mean-squares (FXLMS) algorithm is able to maintain an essentially constant performance for significant deviations of the nominal values of the disturbance amplitude and Reynolds number.

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An Interconnected Systems Approach to Flow Transition Control

Chughtai

Werner

2015

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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Transition delay using control theory

Cited by 42 publications

References 36 publications

Closed-loop control of boundary layer streaks induced by free-stream turbulence

Closed-loop control of boundary layer streaks induced by free-stream turbulence

On the role of adaptivity for robust laminar flow control

An Interconnected Systems Approach to Flow Transition Control

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