Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session H19: Flow Control III 
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Chair: Qiqi Wang, Massachusetts Institute of Technology Room: 322 
Monday, November 21, 2011 10:30AM  10:43AM 
H19.00001: Adjoint sensitivity analysis of time averaged quantities for unsteady flows Qiqi Wang Sensitivity analysis is an essential gradient for data assimilation, aerodynamic design, uncertainty quantification and optimal flow control. In particular. the adjoint sensitivity analysis method has been shown to solve very high dimensional optimization problems typically found these applications. This talk focuses on recent developments in extending adjoint sensitivity analysis to unsteady flows. The adjoint equation of unsteady flows must be integrated backwards in time. Each backward time step must use the flow solution at the corresponding time. As a result, the entire time history of the flow solution must be either stored or recalculated. The invention of checkpointing schemes provides an economic solution to this challenge. In particular, the dynamic checkpointing scheme makes this solution more practical for computational fluid dynamics problems. In unsteady flows, the quantities of interest are often long time averages. We demonstrate that sensitivity analysis of these long time averaged quantities poses significant new challenge. A novel windowing scheme is developed to compute correct sensitivity for periodic unsteady flows, such as in laminar vortex shedding. Initial investigation of sensitivity analysis of chaotic unsteady flows, i.e., transitional and turbulent flows, is also discussed. [Preview Abstract] 
Monday, November 21, 2011 10:43AM  10:56AM 
H19.00002: Optimal perturbations in plane Poiseuille flow based on the optimization of the pnorm of the energy density D.P.G. Foures, C.P. Caulfield, P.J. Schmid Over the last twenty years, much attention has been given to the consideration of transient nonmodal growth of infinitesimal perturbations in shear flows. Indeed, it is now wellaccepted that marked transient growth of the energy is possible for intermediate times even though all normal modes are linearly stable. It is often postulated that such amplification of an initial perturbation could trigger nonlinear behaviour within the flow and hence be responsible for the transition toward a turbulent state. Most of these studies have been based on the optimization of an initial perturbation in order to maximize the ``gain,'' i.e. the amplification of the integrated kinetic energy over the flow domain. In many realistic circumstances, it is of more interest to identify initial perturbations which maximize flow quantities locally. Therefore, we investigate the implications of switching from the 1norm of the energy density to a general pnorm which will approximate the infinity norm for large values of p. By considering a simple model problem of twodimensional plane Poiseuille flow, we show that identifying ``optimal'' perturbations which maximize the pnorm of the energy density at some finite time horizon typically leads to enhanced localization, at the cost of reduction in the gain in the energy of the perturbation. [Preview Abstract] 

H19.00003: ABSTRACT WITHDRAWN 
Monday, November 21, 2011 11:09AM  11:22AM 
H19.00004: Model reduction using snapshotbased realizations Dirk M. Luchtenburg, Clarence W. Rowley A number of methods can be used to develop reducedorder models (ROM) for flow control, including proper orthogonal decomposition (POD), approximate snapshotbased balanced truncation (balanced POD), and the eigenvalue realization algorithm (ERA). We present a new method for obtaining a ROM from snapshots of the impulse response of a linear system. The idea is to use snapshots to identify a dynamical system that exactly reconstructs the impulse response. The dimension of this dynamical system is given by the rank of the controllable subspace (the number of states that respond to inputs). This system can be reduced even further by projecting out the unobservable subspace (the subspace that cannot be inferred from the output history), leading to a minimal realization. If the dimension of this realization is sufficiently small, balanced truncation can be readily performed. This is usually the case for active flow control applications, where the dimension of the flow field is large compared to the number of controllable / observable states. One advantage of the proposed method is that it avoids the construction of (large) Hankel matrices, as is necessary for methods like ERA or BPOD. Moreover, in general fewer snapshots are required for a more accurate balanced model. The findings are illustrated using several numerical examples. [Preview Abstract] 
Monday, November 21, 2011 11:22AM  11:35AM 
H19.00005: Performance and robustness comparison between reducedplantbased and directlyreduced optimal control Kevin Chen, Clarence Rowley A common objective in flow control is the construction of a lowdimensional controller from a highdimensional plant modeling the fluid dynamics. Traditionally, the controller is constructed from a reducedorder model of the original plant. Recent advances, however, have allowed the construction of the $H_2$ optimal controller directly from the fulldimensional plant; this controller could then be reduced to a lower dimension. This study explores these two methods of arriving at a lowdimensional optimal controller, using the GinzburgLandau equation as a testbed. The controller's performance is evaluated by the $H_2$ norm of the transfer function from state disturbances and sensor noise to costs on the state and input magnitude. The robustness is measured primarily by the coprime stability margin, for which analytic bounds are available via the $\nu$gap metric. The directlyreduced controller generally achieves greater performance and robustness than the reducedplantbased controller, but takes longer to compute for largedimensional plants. A decrease in performance and robustness is attributed to faster growth rates of an instability, greater nonnormality or time lag, and lower model reduction order. [Preview Abstract] 

H19.00006: ABSTRACT WITHDRAWN 
Monday, November 21, 2011 11:48AM  12:01PM 
H19.00007: Comparison of two different approaches for the control of convectively unstable flows Fabien Juillet, Peter Schmid, Beverley McKeon, Patrick Huerre The probably most widely used control strategy in the literature is based on the Linear Quadratic Gaussian (LQG) framework. However, this approach seems to be difficult to apply to some fluid systems. In particular, due to their high sensitivity to external noise, amplifier flows are hard to control and the classical LQG compensator may be unable to describe the noise with sufficient accuracy. Another strategy aims at directly measuring these noise sources through a sensor called ``spy.'' The LQG and the spy approaches will be presented and compared using the GinzburgLandau equation as a model. It will be shown that the use of a spy is particularly relevant for convectively unstable systems. In addition, the ability of Subspace Identification Methods to provide satisfactory models is demonstrated. Finally, the findings from the GinzburgLandau investigation are generalized and applied to a more realistic system, namely a backwardfacing step at $Re=350.$ Support from Ecole Polytechnique and the Partner University Fund (PUF) is gratefully acknowledged. [Preview Abstract] 
Monday, November 21, 2011 12:01PM  12:14PM 
H19.00008: Application of systemidentification by ARMarkov and sensitivity analysis to noiseamplifier models Nicolas Dovetta, Peter Schmid, Denis Sipp, Beverley McKeon Separated flow often exhibit amplification of external noise sources via an interaction with shear layer instabilities. In order to manipulate this amplification process we consider a databased control design strategy. The first step is to build a statespace representation of the inputoutput transfer function. An autoregressive representation is used that explicitly includes Markov parameters (ARMarkov). This is then coupled with the eigensystem realization algorithm (ERA) which yields a reducedorder statespace representation of the problem. In real experiments the data is contaminated by measurement noise or by nonlinearities which are not accounted for by the present approach. In order to enforce robustness of the identificationrealization procedure a sensitivity analysis of the algorithm is performed. These sensitivities provide quantitative criteria to find the most robust way of identifying the system using the ARMarkov/ERA algorithm. The systemidentification and sensitivity framework will be demonstrated on the GinzburgLandau equation. Support from the Partner University Fund (PUF) is gratefully acknowledged. [Preview Abstract] 
Monday, November 21, 2011 12:14PM  12:27PM 
H19.00009: Estimation of the Proximity and Density Field of a Moving Gaseous Source Using a Sensing Aerial Vehicle Nikolaos Gatsonis, Jeff Court, Michael Demetriou This work considers the estimation of the density field arising from an unknown moving gaseous source in the troposphere using measurements obtained with a sensor onboard an aerial vehicle. The gas dispersion process is modeled by the advectiondiffusion partial differential equation in 3d with spatially and time varying ambient mean velocity and eddy diffusivities. Our approach strongly couples the adaptive, multigrid numerical solution of the advectiondiffusion PDE with the estimate of the process state (spatiotemporal density) as provided by the maxima of concentration localization estimation scheme. The guidance of the sensing aerial vehicle is dictated by the performance of the estimation scheme. Computational results demonstrate the effectiveness of the approach in estimating the density of the plume and the proximity of the gaseous source under realistic atmospheric conditions. [Preview Abstract] 
Monday, November 21, 2011 12:27PM  12:40PM 
H19.00010: Numerical Modeling and Simulations on ElectoActive Polymer Flow Control Andrew Weddle, Michael Amitay, Lucy Zhang The primary focus of this study is to identify the effects of vibrating ElectroActive Polymer (EAP) flow control on the flow field, specifically within the boundary layer. The EAPs represent a lightweight and adaptable flow control solution for microair vehicles (MAV). In this study, the interaction of the flow field over a flat plate and NACA 0009 airfoil are modeled at a Reynolds number of 20,000 using an Arbitrary Lagrangian Eulerian finite element formulation. In the simulations, the EAP vibration is prescribed based on the measurements from the experiments. The results show the EAPs do alter the boundary layer flow field and the size of the separation bubble. Three different diameter EAPs are examined on the flat plate model: 6mm, 9mm, and 12mm. Each is evaluated at different vibrational frequencies and maximum amplitudes. The performance of the EAPs on the NACA 0009 model are also evaluated while the airfoil is experiencing a pitching motion and gusts. Both instantaneous and time averaged flow fields are analyzed. The results from the numerical simulations are compared to baseline CFD simulations and wind tunnel results. [Preview Abstract] 
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