Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session EJ: Minisymposium: Reduced-Order Modeling for Feedback Flow Control |
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Chair: Dietmar Rempfer, Illinois Institute of Technology Room: Hilton Chicago Williford C |
Sunday, November 20, 2005 4:10PM - 4:36PM |
EJ.00001: Control of the cylinder wake in the laminar regime by Trust-Region methods and POD Reduced Order Models Cordier Laurent, Michel Bergmann, Jean-Pierre Brancher The optimal control approach for the active control of the circular cylinder wake flow considered in the laminar regime ($Re=200$) is investigated. The objective is the mean drag minimization of the wake where the control function is the time harmonic angular velocity of the rotating cylinder. In order to reduce the computational costs, the optimization process is not based on the Navier-Stokes equations as state equations but rather on low-fidelity models derived with the Proper Orthogonal Decomposition (POD). Since the range of validity of this POD Reduced Order Model (ROM) is generally restricted to the vicinity of the design parameters in the control parameter space, the Trust-Region Proper Orthogonal Decomposition (TRPOD) approach, originally introduced by Fahl (2000), is used to update the ROMs during the optimization process. Benefiting from the trust- region philosophy, rigorous convergence results guarantee that the iterates produced by the TRPOD algorithm will converge to the solution of the original optimization problem defined with a high fidelity model. When the TRPOD is applied to the wake flow configuration, this approach leads to a relative mean drag reduction of 30\% for reduced numerical costs. [Preview Abstract] |
Sunday, November 20, 2005 4:36PM - 5:02PM |
EJ.00002: Experiment based Reduced-Order Modeling for Feedback Flow Control: Application to Flow Separation and Jet Aeroacoustics Mark Glauser Under AFOSR support we have been developing closed loop flow control methods for flow separation control over a NACA 4412 airfoil and for jet noise reduction. The methods employ the Proper Orthogonal Decomposition along with Stochastic Measurement to extract the low-dimensional flow characteristics. We have made substantial progress on the NACA 4412 problem wherein we have closed the loop using estimates (obtained form wall pressure via the Stochastic Measurement) of the first time dependent POD coefficient as our feedback signal in a simple proportional controller. Our results to date show that with the feedback we can delay separation from 15 degrees AoA (without any control) to greater than 18 degrees AoA with the feedback control. These initial exciting results will be presented along with our experimental based dynamical models that are being developed so we can incorporate some flow dynamics into the feedback as well as design controllers offline. For the jet aeroacoustics problem we are not yet at the stage were we are closing the loop. However, we will present results that show that substantial progress has been made in our understanding of the relationship between the low-dimensional velocity fields and the far field noise. This is providing us a starting point for eventual implementation of feedback flow control (of the near field jet plume) for far field noise reduction. [Preview Abstract] |
Sunday, November 20, 2005 5:02PM - 5:28PM |
EJ.00003: Nonlinear flow control based on a low dimensional approximation of the Navier-Stokes equation Rudibert King, Bernd R. Noack, Oliver Lehmann, Marek Morzyski, Gilead Tadmor Nonlinear control design is shown to be a critical enabler for robust model-based supression of a flow instability. The onset of oscillatory vortex shedding is chosen as a well investigated benchmark problem of flow control. A low-dimensional POD Galerkin model is adopted from earlier studies of the authors as a control-oriented fluid flow representation. Several strategies of nonlinear controller design are employed, both, to the Galerkin model and to the flow via a direct numerical simulation of the Navier-Stokes equations (NSE). Examples are input-output linearization, Lyapunov-based, backstepping, LPV-type controlles, etc., and physically motivated controllers. Whereas the first test-bed is easily mastered by the formal methods, the application to the NSE is more critical, due to robustness issues. [Preview Abstract] |
Sunday, November 20, 2005 5:28PM - 5:54PM |
EJ.00004: Control-oriented models of channel flow Clarence Rowley This talk addresses low-dimensional models of the transitional flow through a plane channel. Recent improvements to the technique of proper orthogonal decomposition (POD) and Galerkin projection are reviewed, including the use of carefully-chosen inner products, and the relation of POD/Galerkin to balanced truncation, a method commonly used for linear systems. The method naturally incorporates control inputs, and when applied to a linearized plane channel flow with streamwise-constant perturbations, reduced-order models obtained from balanced truncation produce an order of magnitude smaller error in the $H_\infty$ norm, compared to the standard POD procedure using the same number of modes. [Preview Abstract] |
Sunday, November 20, 2005 5:54PM - 6:20PM |
EJ.00005: Snapshot Selection for State Estimation of Wake Flows using Proper Orthogonal Decomposition Stefan Siegel, Kelly Cohen, Juergen Seidel, Thomas McLaughlin Proper Orthogonal Decomposition (POD) has been used extensively in the past for estimation and low dimensional modeling of both steady and time periodic flow fields. If the intended use of the low dimensional POD model is in the area of feedback flow control, the low dimensional state of a flow field needs to be accurately estimated as input for a controller. We investigate POD bases derived from steady state, transient startup and open loop forced data sets for the two dimensional wake of a D-shaped cylinder at Re = 300. We find that only a POD basis derived from a composite snapshot set consisting of both transient startup as well as open loop forced data accurately models the features of the feedback controlled flow. For similar numbers of modes, this POD basis, which can be derived a priori, represents the feedback controlled flow as well as a POD model developed from the feedback controlled data a posteriori. Conclusions: Firstly, an accurate POD basis can be developed without iteration from unforced and open loop data. Secondly, it appears that the feedback controlled flow does not leave the subspace spanned by open loop and unforced startup data, which may have important implications for the performance limits of feedback flow control. [Preview Abstract] |
Sunday, November 20, 2005 6:20PM - 6:46PM |
EJ.00006: Low Order Empirical Galerkin Models for Feedback Flow Control Gilead Tadmor, Bernd Noack Model-based feedback control restrictions on model order and complexity stem from several generic considerations: real time computation, the ability to either measure or reliably estimate the state in real time and avoiding sensitivity to noise, uncertainty and numerical ill-conditioning are high on that list. Empirical POD Galerkin models are attractive in the sense that they are simple and (optimally) efficient, but are notoriously fragile, and commonly fail to capture transients and control effects. In this talk we review recent efforts to enhance empirical Galerkin models and make them suitable for feedback design. Enablers include `subgrid' estimation of turbulence and pressure representations, tunable models using modes from multiple operating points, and actuation models. An invariant manifold defines the model's dynamic envelope. It must be respected and can be exploited in observer and control design. These ideas are benchmarked in the cylinder wake system and validated by a systematic DNS investigation of a 3-dimensional Galerkin model of the controlled wake. [Preview Abstract] |
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