The application of optimal control theory to complex problems in fluid mechanics has proven to be quite effective when complete state information from high-resolution numerical simulations is available [P. Moin, T.R. Bewley, Appl. Mech. Rev., Part 2 47 (6) (1994) S3--S13; T.R. Bewley, P. Moin, R. Temam, J. Fluid Mech. (1999), submitted for publication]. In this approach, an iterative optimization algorithm based on the repeated computation of an adjoint field is used to optimize the controls for finite-horizon nonlinear flow problems [F. Abergel, R. Temam, Theoret. Comput. Fluid Dyn. 1 (1990) 303--325]. In order to extend this infinite-dimensional optimization approach to control externally disturbed flows in which the controls must be determined based on limited noisy flow measurements alone, it is necessary that the controls computed be insensitive to both state disturbances and measurement noise. For this reason, robust control theory, a generalization of optimal control theory, has been examined as a technique by which effective control algorithms which are insensitive to a broad class of external disturbances may be developed for a wide variety of infinite-dimensional linear and nonlinear problems in fluid mechanics. An aim of the present paper is to put such algorithms into a rigorous mathematical framework, for it cannot be assumed at the outset that a solution to the infinite-dimensional robust control problem even exists. In this paper, conditions on the initial data, the parameters in the cost functional, and the regularity of the problem are established such that existence and uniqueness of the solution to the robust control problem can be proven. Both linear and nonlinear problems are treated, and the 2D and 3D nonlinear cases are treated separately in order...

The goal of this paper is to provide a perspective on the current status and future directions for active flow-control technology with particular emphasis on oscillatory control. This is not a comprehensive review of the literature; rather, certain issues that are often neglected in studies are highlighted showing their importance or impact on the reported observations and targeted outcomes. Feasible routes using flow instability as an efficiency enhancement tool are discussed as an emerging means to explain the physical phenomena of active flow-control and as a tool for control law design and development. Traditional and more recent theoretical approaches to control design are discussed and recommendations are made relevant to numerical complications on the route to design oscillatory flow-control systems. A generic flow control process is put forward and illustrated using experimental examples.

this paper, these two approaches produce the same control input #. 5. Results As was mentioned in 4, the pressures on the cylinder surface are measured at # 6 # 6 # and the blowing and suction are applied at # 6 # 6 #.In 5.1, sensings and actuations are carried out all over the cylinder surface, i.e. (#, #)=(#,#)=(0, 2#). Local sensings and actuations are performed in 5.2. Finally, open-loop controls are investigated in 5.3. For all cases investigated in this study, we have used the computational time step #t = 0.015, and the control time interval #t c = 0.06. That is, the sensing and actuation are updated at every four computational time steps. We have also 136 C. Min and H. Choi 1.5 1.4 1.3 1.2 1.1 1.0 0 30 60 90 120 t J 3 (c) 1.4 0.8 1.2 1.0 0.4 0 30 60 90 120 J 2 (b) 1.1 1.0 0.9 0.8 0.7 0 30 60 90 120 J 1 (a) 0.6 Figure 4. Time histories of the cost functional with (#, #)=(#,#)=(0, 2#): , # max =0.1; --------, 0.2; ---, 0.3; --------, 0.4. (a) J 1 ;(b) J 2 ;(c) J 3 . investigated a few di#erent combinations of #t and #t c , but the results showed only a slight change compared to those obtained from #t = 0.015 and #t c = 0.06. The Reynolds numbers investigated in this study (two-dimensional computations) are 100 and 160; according to the recent result by Henderson (1997), the two-dimensional wake becomes absolutely unstable to long-wavelength spanwise perturbations and bifurcates to a three-dimensional flow at Re # 190 (mode A; see also Williamson 1988). All controls begin at t = 30 and the maximum blowing/suction value relative to the free-stream velocity, # max = max 06#<2# |#(#)|, is kept constant during the control. 5.1. Sensing and actuation all over the cylinder surface We have applied the actuation values of decreasing J 1 and J 2...

Prior studies of wall bounded turbulence control have utilized Direct Numerical Simulation (DNS) which has limited investigations to low Reynolds numbers where viscous effects may play an important role. The current paper utilizes Large Eddy Simulation (LES) with the dynamic subgrid-scale model to explore the influence of viscosity on one popular turbulence control strategy, opposition control, that has been extensively studied using low Reynolds number DNS. Exploiting the efficiency of LES, opposition control is applied to fully developed turbulent flow in a planar channel for turbulent Reynolds numbers in the range Re # = 100 to 720. As Reynolds number increases, the predicted drag reduction drops from 30% at Re # = 100 to 19% at Re # = 720. Furthermore, the ratio of power saved to power input drops by more than a factor of four when Reynolds number increases over this range, indicating that the drag reduction mechanism in opposition control is indeed less effective at higher Reynolds numbers. However, for sufficiently high Reynolds numbers, Re # > 400, the ratio of power saved to power input becomes constant at a value near 40 indicating that opposition control is a viable turbulence control strategy at high Reynolds numbers.

About fourty years ago Rechenberg and Schwefel (Reehenberg, 1994) came up with the idea of evolution strategies for flow optimization. Since then advances in computer architectures and numerical algorithms have greatly deercard computational costs of reafistic flow simulations, and today Computational Fluid Dynamics (CFD) is complementiug flow experiments as a key guiding tool for aerodynamic design. Of particular interest are designs wSth active devices controlling the inherently unsteady flow fields, promising potentially drastic performance leaps. Here we demonstrate that CFD-based design of active control strategies can benefit from evolutionary computation. We optimize the flow past an actively controlled circular cylinder, a fundamen- tal prototypical configuration. The flow is controlled us- ing surface-mounted vortex generators; evolutionary algorithms are used to optimize actuator placement and operating parameters. We achieve drag reduction of up to 60 percent, outperforming the best methods previously reported in the fluid dynamics literature on this benchmark problem.

iTo my parents, my brother, and my best friend who contributed to this work in ways they did not realize ii Nonlinear traveling waves that are precursors to laminar-turbulent transition and cap-ture the main structures of the turbulent buffer layer have recently been found to exist in all the canonical parallel flow geometries. The present work examines the effect of poly-mer additives on these “exact coherent states ” (ECS) in the plane Poiseuille geometry, using the FENE-P constitutive model for polymer solutions. In experiments with a given fluid, Reynolds and Weissenberg numbers are linearly related (i.e. Wi/Re = const). In this situation, we study the effects of viscoelasticity on velocity field and polymer stress field along some experimental paths, which represent different flow behaviors as Re (and Wi) increases. The changes to the velocity field for the viscoelastic nonlinear traveling waves qualitatively capture many of those experimentally observed in fully tur-bulent flows of polymer solutions at low to moderate levels of drag reduction: drag is

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This paper reviews LES methods, based on the dynamic subgrid-scale model, that greatly improve the e#ciency of turbulence control simulations in the context of drag reduction for plane turbulent channel flow. We begin by performing simulations of opposition control at Reynolds numbers in the range Re # = 100 to 590 which demonstrate a decrease in e#ectiveness of this control strategy with increased Reynolds number. We then review techniques for optimal control of turbulent flows and discuss our implementation using an instantaneous control framework where the flow sensitivity is computed from the adjoint LES equations. Detailed optimal control results are presented that demonstrate excellent agreement with available DNS at a fraction of the computational expense. Given the added e#ciency of LES, a receding horizon control framework is also explored that results in increased drag reduction along with improved control distributions. Results are also presented for a hybrid LES/DNS method where optimization is performed using LES but the flow is advanced using DNS. This approach demonstrates that even coarse grid LES can serve as a viable reduced order model for DNS. In our ongoing e#orts to seek greater model reductions for predictive control, we also explore the influence of control on the basis functions obtained from proper orthogonal decomposition. 1

The snapshot form of the proper orthogonal decomposition is used to compute approximate solutions and to develop suboptimal openand closed-loop control strategies for the perturbed Gelfand equation. The behaviour of the reduced system is investigated numerically wrt perturbations of the external heating and the initial values. In the control part of this note several suboptimal control approaches using the reduced dynamics are discussed. In particular the performance of a simple feedback control law is numerically validated against the solution of the full optimal control problem. Contents 1 Introduction 4 2 The instationary perturbed Gelfand equation 5 3 Proper orthogonal decomposition with snapshots 6 4 Proper orthogonal decomposition applied to the perturbed Gelfand equation 7 4.1 Mode generation for the perturbed Gelfand equation . . . . . 7 4.2 Numerical solution of the perturbed Gelfand equation using proper orthogonal decomposition . . . . . . . . . . . . . . . . 9 4.2.1 Hom...

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