part of "Mechanics USA 1994" edited by AS Kobayashi ASME Reprint No AMR146 Appl Mech Rev vol 47, no 6, part 2, June 1994 S3  Copyright 1994 American Society of Mechanical Engineers Feedback control of turbulence Parviz Moin and Thomas Bewley Department of Mechanical Engineering, Stanford University, Stanford CA 94305-3030 A brief review of current approaches to active feedback control of the fluctuations arising in turbulent flows is presented, emphasizing the mathematical techniques involved. Active feedback control schemes are categorized and compared by examining the extent to which they are based on the governing flow equations. These schemes are broken down into the following categories: adaptive schemes, schemes based on heuristic physical arguments, schemes based on a dynamical systems approach, and schemes based on optimal control theory applied directly to the Navier- Stokes equations. Recent advances in methods of implementing small scale flow control ideas are also reviewed. CONTENTS INTRODUCTION...............................................................................S3 FEEDBACK CONTROL SCHEMES..................................................S4 Adaptive schemes..........................................................................S4 Schemes based on physical arguments .........................................S5 Schemes based on dynamical systems ..........................................S5 Optimal control schemes ...............................................................S6 Discussion ......................................................................................S8 IMPLEMENTATION ISSUES ...........................................................S9 Methods of sensing ........................................................................S9 Methods of actuation ...................................................................S10 Other considerations....................................................................S11 CONCLUDING REMARKS.............................................................S11 REFERENCES ...................................................................................S12 INTRODUCTION Many important advances have been made in the past decade in the field of turbulence control; recent reviews include: Bandyopadhyay (1986), Bushnell and McGinley (1989), Blackwelder (1989), Fiedler and Fernholz (1990), and Gad-el- Hak (1989, 1993). This paper will concentrate on one aspect of this subject: active feedback control of turbulence. Active control schemes refer to methods which add energy to a flow, such as unsteady wall transpiration or the prescribed motion of an actuator. These are in contrast to passive techniques, which modify a flow without unsteady external input. Passive techniques include the placement of longitudinal grooves (riblets) on a surface to reduce the drag caused by turbulence (Choi et al. 1993b, Walsh 1990) and the use of compliant walls which deform in response to the overlying flow to stabilize a laminar boundary layer (Riley et al. 1988). The external energy added in an active control scheme may be determined in advance (in which case the control scheme is termed open-loop or feedforward) or coordinated with real- time measurements of the flow itself (termed closed-loop or feedback control). The periodic forcing of a round jet (Lee and Reynolds 1985) to produce bifurcation (splitting into two jets) or blooming (expansion to a wide spray of vortex rings) and the hydrodynamic Lorenz forcing of an electrolytic fluid (Nosenchuck and Brown 1993) to restructure flow perturbations in the near wall region are excellent examples of effective open-loop control configurations in turbulent flows. However, in cases in which the control must interact with a specific set of turbulent fluctuations already present in the flow, such as the coherent structures, the random aspect of these structures reduces the effectiveness of an open-loop configuration. In these cases, we seek a feedback control law to relate measurements of the state of the turbulence in the flow to the resulting distribution in space and time of the control energy. It is this mathematical relation between what is sensed and what control is applied which will be systematically discussed in this paper. The feedback referred to in this context should not be confused with the feedback of information caused by the upstream influence of events which take place downstream through the flow itself, as discussed by Ho and Huerre (1984). Adam Smith in The Division of Labour (1776) recalls: In the first fire-engines, a boy was constantly employed to open and shut alternately the communication between the boiler and the cylinder, according as the piston either ascended or descended. One of those boys, who loved to play with his companions, observed that, by tying a string from the handle of the valve which opened this communication to another part of the machine, the valve would open and shut without his assistance, and leave him at liberty to divert himself with his play fellows. In the present study, our valves are the actuators, the points on the machine that we have access to tie to are the sensors, and our string is the feedback control law. As the resourceful boy, we seek the best arrangement of this string.