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  • 1.
    Chevalier, Mattias
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Hoepffner, Jérôme
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Åkervik, Espen
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Henningson, Dan S.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Linear feedback control and estimation applied to instabilities in spatially developing boundary layers2007Ingår i: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 588, s. 163-187Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper presents the application of feedback control to spatially developing boundary layers. It is the natural follow-up of Hogberg & Henningson (J. Fluid Mech. vol. 470, 2002, p. 151), where exact knowledge of the entire flow state was assumed for the control. We apply recent developments in stochastic models for the external sources of disturbances that allow the efficient use of several wall measurements for estimation of the flow evolution: the two components of the skin friction and the pressure fluctuation at the wall. Perturbations to base flow profiles of the family of Falkner-Skan-Cooke boundary layers are estimated by use of wall measurements. The estimated state is in turn fed back for control in order to reduce the kinetic energy of the perturbations. The control actuation is achieved by means of unsteady blowing and suction at the wall. Flow perturbations are generated in the upstream region in the computational box and propagate in the boundary layer. Measurements are extracted downstream over a thin strip, followed by a second thin strip where the actuation is performed. It is shown that flow disturbances can be efficiently estimated and controlled in spatially evolving boundary layers for a wide range of base flows and disturbances.

  • 2.
    Hoepffner, Jerome
    KTH, Tidigare Institutioner, Mekanik.
    Control and estimation of wall bounded flow systems2004Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis focuses on the application of linear feedback control and estimation to channel flow. Both the initial stage of the transition and the low Reynolds number turbulent cases are studied. From sensors at the wall, the state of the flow is estimated, using a stochastic description of the flow disturbances. The estimated state is in turn fed back to the flow system in order to achieve a control objective. This model based scheme uses the linearised Navier-Stokes equations as a dynamic model for the flow evolution. The emphasis is here put on the estimation procedure, that was so far the limiting factor for the overall control performance. We show that the estimation performance rely on a correct description of the flow disturbances. We apply model reduction on the controller, and show that we can maintain the control performance even with a highly truncated system. We then introduce a representation of the feedback by means of transfer functions, and discuss the implication of the transfer function for the interpretation of the feedback, and for possible implementation of the control loop.

  • 3.
    Hoepffner, Jeróme
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Control of cavity-driven separated boundary layer2006Ingår i: Proceedings of the Conference on active flow control, Berlin, September 2006, 2006Konferensbidrag (Refereegranskat)
  • 4.
    Hoepffner, Jeróme
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Modeling flow statistics using convex optimization2005Ingår i: 2005 44TH IEEE CONFERENCE ON DECISION AND CONTROL & EUROPEAN CONTROL CONFERENCE, VOLS 1-8, 2005, Vol. 1-8, s. 4287-4292Konferensbidrag (Refereegranskat)
    Abstract [en]

    A method is proposed to estimate the covariance of disturbances to a stable linear system when its state covariance is known and a dynamic model is available. This is an issue of fundamental interest for estimation and control of fluid mechanical systems whose dynamics is described by the linearized Navier-Stokes equations. The problem is formulated in terms of a matrix norm minimisation with linear matrix inequality constraint, and solved numerically by means of alternating convex projection. The method is tested on covariance estimation in a low Reynolds number channel flow.

  • 5.
    Hoepffner, Jeróme
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Chevalier, Mattias
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Bewley, T. R.
    Henningson, Dan S.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    State estimation in wall-bounded flow systems: P. I Laminar flows2005Ingår i: Journal of fluid mechanics, ISSN 0022-1120, Vol. 534, s. 263-394Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In applications involving the model-based control of transitional wall-bounded flow systems, it is often desired to estimate the interior flow state based on a history of noisy measurements from an array of flush-mounted skin-friction and pressure sensors on the wall. This paper considers this estimation problem, using a Kalman filter based on the linearized Navier-Stokes equations and appropriate stochastic models for the relevant statistics of the initial conditions, sensor noise and external disturbances acting on the system. We show that a physically relevant parameterization of these statistics is key to obtaining well-resolved feedback kernels with appropriate spatial extent for all three types of flow measurement available on the wall. The effectiveness of the resulting Kalman and extended Kalman filters that implement this feedback is verified for both infinitesimal and finite-amplitude disturbances in direct numerical simulations of a perturbed laminar channel flow. The consideration of time-varying feedback kernels is shown to be particularly advantageous in accelerating the convergencc of the estimator from unknown initial conditions. A companion paper (Part 2) considers the extension of such estimators to the case of fully developed turbulence.

  • 6.
    Hoepffner, Jerôme
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Chevalier, M.
    Henningson, Dan
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Bewley, T. R.
    State estimation in wall-bounded flow systems: P. II Turbulent flows2006Ingår i: Journal of fluid mechanics, ISSN 0022-1120, Vol. 552, s. 167-187Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This work extends the estimator developed in Part I of this study to the problem of estimating a turbulent channel flow at Re-tau=100 based on a history of noisy measurements on the wall. The key advancement enabling this work is the development and implementation of an efficient technique to extract, from direct numerical simulations, the relevant statistics of an appropriately defined 'external forcing' term on the Navier-Stokes equation linearized about the mean turbulent flow profile. This forcing term is designed to account for the unmodelled (nonlinear) terms during the computation of the (linear) Kalman filter feedback gains in Fourier space. Upon inverse transform of the resulting feedback gains computed on an array of wavenumber pairs to physical space, we obtain, as in Part 1, effective and well-resolved feedback convolution kernels for the estimation problem. It is demonstrated that, by applying the feedback so determined, satisfactory correlation between the actual and estimated flow is obtained in the near-wall region. As anticipated, extended Kalman filters (with the nonlinearity of the actual system reintroduced into the estimator model after the feedback gains are determined) outperform standard (linear) Kalman filters on the full system.

  • 7.
    Hoepffner, Jérôme
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Stability and control of shear flows subject to stochastic excitations2006Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    In this thesis, we adapt and apply methods from linear control theory to shear flows. The challenge of this task is to build a linear dynamic system that models the evolution of the flow, using the Navier--Stokes equations, then to define sensors and actuators, that can sense the flow state and affect its evolution. We consider flows exposed to stochastic excitations. This framework allows to account for complex sources of excitations, often present in engineering applications. Once the system is built, including dynamic model, sensors, actuators, and sources of excitations, we can use standard optimization techniques to derive a feedback law. We have used feedback control to stabilize unstable flows, and to reduce the energy level of sensitive flows subject to external excitations.

  • 8.
    Hoepffner, Jérôme
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Brandt, L.uca
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Henningson, Dan S.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Transient growth on boundary layer streaks2005Ingår i: Journal of fluid mechanics, ISSN 0022-1120, Vol. 537, s. 91-100Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The linear perturbations evolving on streamwise boundary layer streaks which yield maximum energy growth are computed. The steady and spanwise-periodic streaks arising from the nonlinear saturation of optimally growing streamwise vortices are considered as base flow. It is shown that significant transient growth may occur for both sinuous antisymmetric perturbations and for varicose symmetric modes. The energy growth is observed at amplitudes significantly below the threshold beyond which the streaks become linearly unstable and is largest for sinuous perturbations, to which the base flow considered first become unstable. The optimal initial condition consists of velocity perturbations localized in the regions of highest shear of the streak base flow, tilted upstream from the wall. The optimal response is still localized in the areas of largest shear but it is tilted in the flow direction. The most amplified perturbations closely resemble the unstable eigenfunctions obtained for streaks of higher amplitudes. The results suggest the possibility of a transition scenario characterized by the non-modal growth of primary perturbations, the streaks, followed by the secondary transient growth of higher frequency perturbations. The implication for turbulent flow is also discussed.

  • 9.
    Hoepffner, Jérôme
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW.
    Chevalier, Mattias
    KTH, Skolan för teknikvetenskap (SCI), Mekanik. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW.
    Bewley, T
    Henningson, Dan S
    KTH, Skolan för teknikvetenskap (SCI), Mekanik. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW.
    Linear feedback control of transition in shear flows2006Ingår i: Sixth IUTAM Symposium on Laminar-Turbulent Transition / [ed] Govindarajan, R, DORDRECHT: SPRINGER , 2006, Vol. 78, s. 213-218Konferensbidrag (Refereegranskat)
    Abstract [en]

    This work focuses on the application of linear feedback control to transition to turbulence in shear flows. The controller uses wall-mounted sensor information to estimate the flow disturbances and uses wall actuators to prevent transition to turbulence. The flow disturbances are induced by external sources of perturbations described by means of a stochastic volume forcing. We show that improved performance can be achieved if the proper destabilisation mechanisms are targeted.

  • 10.
    Åkervik, Espen
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Brandt, Luca
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Henningson, Dan S.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Hoepffner, Jérôme
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Marxen, Olaf
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Schlatter, Philipp
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Steady solutions of the Navier-Stokes equations by selective frequency damping2006Ingår i: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 18, nr 6, s. 068102-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A new method, enabling the computation of steady solutions of the Navier-Stokes equations in globally unstable configurations, is presented. We show that it is possible to reach a steady state by damping the unstable (temporal) frequencies. This is achieved by adding a dissipative relaxation term proportional to the high-frequency content of the velocity fluctuations. Results are presented for cavity-driven boundary-layer separation and a separation bubble induced by an external pressure gradient.

  • 11.
    Åkervik, Espen
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW.
    Hoepffner, Jérôme
    KTH, Skolan för teknikvetenskap (SCI), Mekanik. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW.
    Uwe, Eherenstein
    IRPH́E, Université de Provence.
    Henningson, Dan S.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik. KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW.
    Optimal growth, model reduction and control in a separated boundary-layer flow using global eigenmodes2007Ingår i: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 579, s. 305-314Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Two-dimensional global eigenmodes are used as a projection basis both for analysing the dynamics and building a reduced model for control in a prototype separated boundary-layer flow. In the present configuration, a high aspect ratio smooth cavity-like geometry confines the separation bubble. Optimal growth analysis using the reduced basis shows that the sum of the highly non-normal global eigenmodes are able to describe a localized disturbance. Subject to this worst-case initial condition, a large transient growth associated with the development of a wavepacket along the shear layer followed by a global cycle related to the two unstable global eigenmodes is found. The flow simulation procedure is coupled to a measurement feedback controller, which senses the wall shear stress at the downstream lip of the cavity and actuates at the upstream lip. A reduced model for the control optimization is obtained by a projection on the least stable global eigenmodes, and the resulting linear-quadratic-gaussian controller is applied to the Navier--Stokes time integration. It is shown that the controller is able to damp out the global oscillations.

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