microactuators for boundary-layer flow have been developed using MEMS technology [Ho and Tai, 1998]. Spatial distribution of the skin friction has been measured using microsensors, and changes in boundary- layer flow due to microactuators have been thoroughly investigated. Researchers are now implementing the reactive control algorithms in laboratory experiments using MEMS technology and are expecting a significant amount of skin-friction reduction comparable to that obtained from numerical studies. In most numerical studies, sensors and actuators are collocated and distributed all over the computa- tional domain. In reality, sensors and actuators cannot be collocated, and actuators should be located downstream of the sensors. Therefore, how to efficiently distribute the sensors and actuators is an impor- tant issue. A second issue is how to develop a new control method that is well suited for experimental approach (note that most control methods investigated so far started from numerical studies). The third issue is the Reynolds number effect. Relaminarization of turbulent flow due to control, as has been observed in numerical studies, might happen because of low Reynolds numbers. At low Reynolds number, the dynamics of boundary-layer flow is mostly governed by near-wall phenomena, whereas it is affected not only by the near-wall behavior but also by the fluid motion in the buffer or outer layer. Therefore, various control algorithms may have to be developed depending on the Reynolds number. Acknowledgments This work has been supported by the Creative Research Initiatives of the Korean Ministry of Science and Technology. References Abergel, F., and Temam, R. (1990) “On Some Control Problems in Fluid Mechanics,” Theor. Comp. Fluid Dyn., 1, pp. 303–325. Bewley, T.R. (2001) “Flow Control: New Challenges for a New Renaissance,” Prog. Aerosp. Sci., 37, pp. 21–58. Bewley, T.R., Moin, P., and Temam, R. (2001) “DNS-based Predictive Control of Turbulence: An Optimal Benchmark for Feedback Algorithms,” J. Fluid Mech., 447, pp. 179–226. Bushnell, D.M., and McGinley, C.B. (1989) “Turbulence Control in Wall Flows,” Annu. Rev. Fluid Mech., 21, pp. 1–20. Cantwell, B.J. (1981) “Organized Motion in Turbulent Flow,” Annu. Rev. Fluid Mech., 13, pp. 457–515. Carlson, A., and Lumley, J.L. (1996) “Active Control in the Turbulent Wall Layer of a Minimal Flow Unit,” J. Fluid Mech., 329, pp. 341–371. Choi, H., Moin, P., and Kim, J. (1993a) “Direct Numerical Simulation of Turbulent Flow Over Riblets,” J. Fluid Mech., 255, pp. 503–539. Choi, H., Temam, R., Moin, P., and Kim, J. (1993b) “Feedback Control for Unsteady Flow and Its Application to the Stochastic Burgers Equation,” J. Fluid Mech., 245, pp. 509–543. Choi, H., Moin, P., and Kim, J. (1994) “Active Turbulence Control for Drag Reduction in Wall-Bounded Flows,” J. Fluid Mech., 262, pp. 75–110. Corino, E.R., and Brodkey, R.S. (1969) “A Visual Investigation of the Wall Region in Turbulent Flow,” J. Fluid Mech., 37, pp. 1–30. Endo, T., Kasagi, N., and Suzuki, Y. (2000) “Feedback Control of Wall Turbulence with Wall Deformation,” Int. J. Heat Fluid Flow, 21, pp. 568–575. Gad-el-Hak, M. (1994) “Interactive Control of Turbulent Boundary Layers: A Futuristic Overview,”AIAA J., 32, pp. 1753–1765. Gad-el-Hak, M. (1996) “Modern Developments in Flow Control,” Appl. Mech. Rev., 49, pp. 365–380. Gad-el-Hak, M., and Blackwelder, R.F. (1989) “Selective Suction for Controlling Bursting Events in a Boundary Layer,” AIAA J., 27, pp. 308–314. Hamilton, J.M., Kim, J., and Waleffe, F. (1995) “Regeneration Mechanisms of Near-Wall Turbulence Structures,” J. Fluid Mech., 287, pp. 317–348. 14-14 MEMS: Applications © 2006 by Taylor & Francis Group, LLC Ho, C H., and Tai, Y C. (1996) “Review: MEMS and Its Applications for Flow Control,” J. Fluids Eng., 118, pp. 437–446. Ho, C M., and Tai, Y C. (1998) “Micro-Electro-Mechanical Systems (MEMS) and Fluid Flows,” Annu. Rev. Fluid Mech., 30, pp. 579–612. Jacobson, S.A., and Reynolds, W.C. (1998) “Active Control of Streamwise Vortices and Streaks in Boundary Layers,” J. Fluid Mech., 360, pp. 179–212. Kang, S., and Choi, H. (2000) “Active Wall Motions for Skin-Friction Drag Reduction,” Phys. Fluids, 12, pp. 3301–3304. Kim, H.T., Kline, S.T., and Reynolds, W.C. (1971) “The Production of Turbulence Near a Smooth Wall in a Turbulent Boundary Layer,” J. Fluid Mech., 50, pp. 133–160. Kim, J., Moin, P., and Moser, R. (1987) “Turbulence Statistics in Fully Developed Channel Flow at Low Reynolds Number,” J. Fluid Mech., 177, pp. 133–166. Kline, S.J., Reynolds, W.C., Schraub, F.A., and Runstadler, P.W. (1967) “The Structure of Turbulent Boundary Layers,” J. Fluid Mech., 30, pp. 741–774. Koumoutsakos,P. (1999) “Vorticity Flux Control for a Turbulent Channel Flow,”Phys. Fluids,11,pp. 248–250. Kravchenko, A.G., Choi, H., and Moin, P. (1993) “On the Relation of Near-Wall Streamwise Vortices to Wall Skin Friction in Turbulent Boundary Layer,” Phys. Fluids A, 5, pp. 3307–3309. Lee, C., Kim, J., Babcock, D., and Goodman, R. (1997) “Application of Neural Networks to Turbulence Control for Drag Reduction,” Phys. Fluids, 9, pp. 1740–1747. Lee, C., Kim, J., and Choi, H. (1998) “Suboptimal Control of Turbulent Channel Flow for Drag Reduction,” J. Fluid Mech., 358, pp. 245–258. Moin, P., and Bewley, T.R. (1994) “Feedback Control of Turbulence,” Appl. Mech. Rev., 47, pp. S3–S13. Rathnasingham, R., and Breuer, K.S. (1997) “System Identification and Control of a Turbulent Boundary Layer,” Phys. Fluids, 9, pp. 1867–1869. Robinson, S.K. (1991) “Coherent Motions in the Turbulent Boundary Layer,” Annu. Rev. Fluid Mech., 23, pp. 601–639. Walsh, M.J. (1982) “Turbulent Boundary Layer Drag Reduction Using Riblets,” AIAA Paper No. 82-0169, AIAA, Washington, DC. Reactive Control for Skin-Friction Reduction 14-15 © 2006 by Taylor & Francis Group, LLC 15 Toward MEMS Autonomous Control of Free-Shear Flows 15.1 Introduction 15-1 15.2 Free-Shear Flows: A MEMS Control Perspective 15-2 15.3 Shear-Layer MEMS Control System Components and Issues 15-3 Sensors • Actuators • Closing the Loop: The Control Law 15.4 Control of the Roll Moment on a Delta Wing 15-9 Sensing • Actuation • Flow Control • System Integration 15.5 Control of Supersonic Jet Screech 15-17 Sensing • Actuation • Flow Control • System Integration 15.6 Control of Separation over Low-Reynolds-Number Wings 15-29 Sensing • Flow Control 15.7 Reflections on the Future 15-32 15.1 Introduction Interest in the application of microelectromechanicalsystems (MEMS) technology to flow control and diag- nostics started around the early 1990s. During this relatively short time, there have been a handful attempts aimed at using the new technology to develop and implement reactive control of various flow phenom- ena. The ultimate goal of these attempts has been to capitalize on the unique ability of MEMS to inte- grate sensors, actuators, driving circuitry, and control hardware in order to attain autonomous active flow management. To date, however, there remains to be a demonstration of a fully functioning MEMS flow control system whereby the multitude of information gathered from a distributed MEMS sensor array is suc- cessfully processed in real time using on-chip electronics to produce an effective response by a distributed MEMS actuator array. Notwithstanding the inability of the research efforts in the 1990s to realize autonomous MEMS control systems, the lessons learned so far are valuable in understanding the strengths and limitations of MEMS in flow applications. In this chapter, the research work aimed at MEMS-based autonomous control of free-shear flows over the past decade is reviewed. The main intent is to use the outcome of these efforts as a telescope to peek through and project a vision of future MEMS systems for free-shear flow control. 15-1 Ahmed Naguib Michigan State University © 2006 by Taylor & Francis Group, LLC The presentation of the material is organized as follows: first, important classifications of free-shear flows are introduced in order to facilitate subsequent discussions; second, a fundamental analysis concerning the usability of MEMS in different categories of free-shear flows is provided. This is followed by an out- line of autonomous flow control system components, with a focus on MEMS in free-shear flow applica- tions and related issues. Finally, the bulk of the chapter reviews prominent research efforts in the 1990s, leading to a vision of future systems. 15.2 Free-Shear Flows: A MEMS Control Perspective Free-shear flows refer to the class of flows that develop without the influence imposed by direct contact with solid boundaries. However, in the absence of thermal gradients, nonuniform body-force fields, or similar effects, the vorticity in free-shear flows is actually acquired through contact with a solid boundary at one point in the history of development of the flow. The “free-shear state” of the flow is attained when it separates from the solid wall, carrying with it whatever vorticity was contained in the boundary layer at the point of separation. The mean velocity profile of the shear layer at the point of separation is inflectional, and hence is inviscidly unstable; that is, extremely sensitive to small perturbations if excited at the appropri- ate frequencies. This point is of fundamental importance to MEMS-based control. Since MEMS devices are micron in scale they are only capable of delivering proportionally small energies when used as actuators. Therefore, if it were not for the high sensitivity of free-shear flows to disturbances at the point of separation, there would be no point in attempting to use MEMS actuators for shear-layer control. Moreover, active control of free-shear flows using MEMS as a disturbance source must be applied at or extremely close to the point of separation. The same statement can be extended to the more powerful conventional actuators, such as glow-discharge, large-scale piezoelectric devices, large-scale flaps, etc., if high- gain or efficient control is desired. From a control point of view, it is useful to classify free-shear flows according to whether the separation line is stationary or moving. Stationary separation line (SSL) flows include jets, single- or two-stream shear layers, and backward facing step flows. In these flows, separation takes place at the sharply defined trailing edge of a solid boundary at the origin of the free-shear flow. On the other hand, moving separation line (MSL) flows include dynamic separation over pitching airfoils and wings, periodic flows through compres- sors, and forward facing step flows. The separation point in the latter,although steady on average, jitters due to the lack of a sharp definition of the geometry at separation (such as the nozzle lip for the shear layer sur- rounding a jet). Whether the free-shear flow to be controlled is of the SSL or MSL type is extremely important, not only from the point of view of control feasibility and ease but also in terms of the need for MEMS versus conven- tional technology.In particular, in SSL flows, actuators — whether MEMS or conventional — can be located directly at the known point of separation where they would be effective. As the operating conditions change (for example, through a change in the speed of a jet) the same set of actuators can be used to affect the desired control. In contrast, in an MSL flow, the instantaneous location of the separation line has to be known and only actuators located along this line should be used for control. To explain further, consider controlling dynamic separation over a pitching two-dimensional airfoil. As the airfoil is pitched from, say, zero to a sufficiently large angle of attack, a separated shear layer is formed. The separation line of this shear layer moves with the increasing angle of attack. To control this separat- ing flow using MEMS or other conventional actuators, it is necessary to track the location of the sepa- ration point in real time in order to activate only those actuators that are located along the separation line. This would require distributed, or array, measurements on the surface of the airfoil. Furthermore, since the separation-line-locating algorithm is likely to employ spatial derivatives of the surface measurements, the surface sensors must have high spatial resolution and be packed densely. Therefore, in MSL problems, it seems inevitable to use MEMS sensor arrays if autonomous control is to be successful. This is believed to be true regardless of whether MEMS or conventional technology is used for actuation. When considering MEMS control systems, another useful classification is that associated with the characteristic size of the flow. With the advent of MEMS, it is now common to observe flows confined to 15-2 MEMS: Applications © 2006 by Taylor & Francis Group, LLC domains that are no larger than a few hundred microns in characteristic size. Such flows may be found in different microdevices including pumps, channels, nozzles, turbines, and others. Therefore, it is impor- tant to distinguish between microscale (MIS) flows and their macro counterparts (MAS). In particular, there should be no ambiguity that within a microdevice, only MEMS, or perhaps even NEMS (nano electro mechanical systems) are the only feasible method of control. A good example of microdevices where free-shear flows may be encountered is the MIT microengine project [Epstein et al., 1997]. In the intricate,yet complex devices engineered in this project, shear layers exist in the microflows over the stator and rotor of the compressor and turbine and in the sudden expansion leading to the combustion chamber. Whether those shear layers and their susceptibility to excitation within the confines of the microdevice mimic that of macroscale shear layers is yet to be established. However, as indicated above, if control is to be exercised, the limitation imposed by the scale of the device dictates that any actuators and or sensors have to be as small as, if not smaller than, the device itself. Active control of MIS flows is an area that is yet to be explored. This is in part because of the fairly short time since the interest in such flows started. Therefore, further discussion of the subject would be appro- priately left until sufficient literature is available. 15.3 Shear-Layer MEMS Control System Components and Issues To facilitate subsequent discussion of the research pertaining to MEMS-based control of free-shear flows, the different components of the control system will be discussed and analyzed here. Of particular importance are the issues specific to utilization of MEMS technology to realize the control system components. Figure 15.1 displays a general functional block diagram for feedback control systems in SSL and MSL flows. As seen from Figure 15.1, for both types of flows the information obtained from surface-mounted sensor arrays is fed to a flow-field estimator in order to predict the state of the flow field being controlled. If the desired flow field and deviations from it can be defined in terms of a signature measurable at the surface, the flow estimator may be bypassed altogether. Any difference between the measured and desired flow states is used to drive surface mounted actuators in a manner that would force the flow toward the desired state. In the case of the MSL flow, the current location of the separation line must also be identified and fed to the controller in order to operate the actuator set nearest to or at the position of separation (see Figure 15.1, bottom). 15.3.1 Sensors When attempting to use MEMS sensors for implementing autonomous control of free-shear flows, several issues should be considered. 15.3.1.1 Sensor Types From a practical point of view,it is very difficult if not impossible to use sensors that are embedded inside the flow to achieve the information feedback necessary for implementing closed-loop control. This is due pri- marily to the inability to use a sufficiently large number of sensors to provide the needed information with- out blocking and/or significantly altering the flow. Therefore, the deployment of the MEMS sensor arrays should be restricted to the surface. For flows where no heat transfer occurs, this limits the measurements primarily to the surface stresses: wall shear ( τ w ), or tangential component; and wall pressure (p w ), or nor- mal component. The former has one component in the streamwise (x) direction and the other in the spanwise (z) direction. In addition to surface stresses, near-wall measurements of flow velocity may be achieved nonintrusively via optical means. An example of such system is currently being developed by Gharib et al. (1999), who are utilizing miniature diode lasers integrated with optics in a small package to develop mini-LDAs (laser doppler anemometers) for measurements of the wall shear and near-wall velocity. With the continued Towards MEMS Autonomous Control of Free-shear Flows 15-3 © 2006 by Taylor & Francis Group, LLC miniaturization of components, it is not difficult to envision an array of MEMS-based LDA sensors deployed over surfaces of aero- and hydro-dynamic devices. Of course, with LDA sensors flow seeding is necessary. Hence, such optical techniques may be practical only for flows where natural contamination is present or when practical means for seeding the flow locally in the vicinity of the measurement volume can be devised. Whereas surface sensors for MSL flows should cover the surface surrounding the flow to be controlled, those for SSL flows typically would be placed at the trailing edge. However, in certain instances, placement of the sensors downstream of the trailing edge may be feasible. Examples include sudden expansion and backward facing step flows (Figure 15.1, top) and jet flows, where a sting may be extended at the center of the jet for sensor mounting. 15.3.1.2 Sensor Characteristics Properly designed and fabricated MEMS sensors should possess very high spatial and temporal resolu- tion because of their extremely small size. Therefore, when considering the response of MEMS sensors for surface measurements, only the sensitivity and signal-to-noise ratio (SNR) are of concern. The need for high sensitivity and SNR is particularly important in detecting separation because the wall shear values are near zero in the vicinity of the separation line ( τ w ϭ 0 at separation for steady flows). Also, hydrodynamic surface pressure fluctuations are typically small for low-speed flows and require microphone-like sensitivities for measurements. 15-4 MEMS: Applications Flow field estimator – Desired flow field Controller Error Flow Separation line locator Flow field estimator – Desired flow field Controller Error Flow Actuators Sensors Sensors and actuators FIGURE 15.1 Conceptual block diagram of autonomous control systems for SSL (top) and MSL (bottom) flows. © 2006 by Taylor & Francis Group, LLC The concern regarding MEMS sensor sensitivity does not include indirect measurements of surface shear, such as that conducted using thermal anemometry, which can be achieved with higher sensitivity using MEMS sensors than using conventional sensors (e.g., [Liu et al., 1994; and Cain et al., 2000]). On the other hand, both direct measurements of the surface shear (using a floating element) and pressure measurements (through a deflecting diaphragm) rely on the force produced by those stresses acting on the area of the sen- sor. Since typical MEMS sensor dimensions are less than 500µm on the side, the resulting force is extremely small. Because of this, no MEMS pressure sensor currently is known to have a sensitivity comparable to that of 1/8Љ capacitive microphones [Naguib et al., 1999a]. Also, notwithstanding the creativity involved in devel- oping a number of floating element designs and detection schemes [Padmanabhan et al., 1996; and Reshotko et al., 1996], the signal-to-noise ratio of such sensors remains significantly below that achievable with ther- mal sensors. Because of the direction reversing nature of separated flows, however, thermal shear sensors gen- erally are not too useful in MSL flows. Direct or other-direction-sensitive sensors are required for conducting appropriate measurements in such flows. 15.3.1.3 Nature of the Measurements Fundamentally, the information inferred from measurements of the wall-shear stress and near-wall velocity differs from that obtained from the surface pressure. The latter is known to be a global quantity that is influ- enced by both near-surface as well as remote flow structures. On the other hand, measurements of the shear stress and flow velocity provide information concerning flow structures that are in direct contact with the sensors. Because of the global nature of pressure measurements, pressure sensors are probably the most suitable type of sensors for conducting measurements at the trailing edge in SSL flows. More specifically, in most if not all instances involving SSL flows, the control objective is aimed at controlling the flow downstream of the trailing edge. Therefore, local measurements of the wall shear and velocity would not be of great use in predicting the flow structure downstream of the trailing edge. A possible exception is when hydrodynamic feedback mechanisms are present, as is the case in a backward facing step where some structural influences downstream are naturally fed back to the trailing edge. In such flows, however, the instability of the shear layer may be absolute rather than convective [Huerre and Monkewitz, 1990]. Fiedler and Fernholz (1990) suggested that absolutely unstable flows are less susceptible to local periodic excitation such as that dis- cussed here. Control provisions aimed at blocking the hydrodynamic feedback loop seem to be more effective in such cases. Another important issue concerning the nature of surface pressure measurements is that they inevitably contain contributions from hydrodynamic as well as acoustic sources. The latter could be either a conse- quence of the flow itself (such as jet noise) or of the environment, emanating from other surrounding sources that are not related to the flow field. Typically, when the sound is produced by the flow, knowledge of the general characteristics of the acoustic field (direction of propagation, special symmetries, etc.) enables separation of the hydrodynamic and acoustic contributions to pressure measurements. In general, attention must be paid to ensure that the appropriate component of the pressure measurements is extracted. 15.3.1.4 Robustness and Packaging Perhaps the primary concern for the use of MEMS in practical systems is whether the minute, fairly fragile devices can withstand the operating environment. One solution is to package the devices in isolation from their environment. This solution has been adopted, for example, in the commercially available MEMS accelerometers from Analog Devices, Inc. Such a solution, although possibly feasible for the mini-LDA systems discussed above, in general is not useful for flow applications. Most wall-shear and wall-pressure sensors and all actuators must interact directly with the flow. Therefore, the ability of the minute devices to withstand harsh, high-temperature, chemically reacting environments is of concern. Also, the possibility for mechanical failure during routine operation and maintenance must be accounted for. 15.3.1.5 Ability to Integrate with Actuators and Electronics Although many types of MEMS sensors have been fabricated and characterized for use in flow applica- tions, most of these sensors have been designed for isolated operation individually or in arrays.If autonomous Towards MEMS Autonomous Control of Free-shear Flows 15-5 © 2006 by Taylor & Francis Group, LLC control is to be achieved using the unique capability of MEMS for integration of components, the sensor fab- rication technology must be compatible with that of the actuators and the circuitry. More specifically, if a particular fabrication sequence is successful in constructing a pressure sensor with certain desired charac- teristics, the same sequence may be unusable when the sensors are to be integrated with actuators on the same chip.Examples of the few integrated MEMS systems that were developed for autonomous control include the fully integrated system used by Tsao et al. (1997) for controlling the drag force in turbulent boundary layers and the actuator-sensor systems from Huang et al. (1996) aimed at controlling supersonic jet screech (dis- cussed in detail later in this chapter). Tsao et al. (1997) utilized a CMOS compatible technology to fabricate three magnetic flap-type actuators integrated with 18 wall-shear stress sensors and control electronics. In contrast, Huang et al. (1996 and 1998) developed hot-wire and pressure sensor arrays integrated with resonant electrostatic actuators. Typi- cally two actuators were integrated with three to four sensors in the immediate vicinity of the actuators. 15.3.2 Actuators 15.3.2.1 Actuator Types and Receptivity There seems to be a multitude of possible of ways to excite a shear layer that differ in their nature of excita- tion (mechanical, fluidic, acoustic, thermal, etc.), relative orientation to the flow (e.g., tangential versus lateral actuation), domain of influence (local versus global), and specific positioning with respect to the shear layer. Given the wide range of actuator types, it is confusing to choose the most appropriate type of actua- tion for a particular flow control application. Because of the micron-level disturbances introduced by MEMS actuators, however, it is not ambiguous that the actuation scheme providing “the most bang for the money” should be utilized; that is, the type of actuation that is most efficient or to which the flow has the largest receptivity. The ambiguity in picking and choosing from the list of actuators is for the most part due to our lack of understanding of the receptivity of flows to the different types of actuation. When selecting a MEMS actuator, or a conventional actuator for that matter,for flow control, one is faced with a few fundamental questions. What type of actuator will achieve the control objective with minimum input energy? That is, what type of actuator produces the largest receptivity? Is it a mechanical, fluidic, acoustic, or other type of actuator? If mechanical, should it oscillate in the normal, streamwise, or spanwise direction? What actuator amplitude is needed to generate a certain flow-velocity disturbance magnitude? In the vicinity of the point of separation, is there an optimal location for the chosen type of actuator? All of these questions are fundamental not only to the design of the actuation system but also to the assessment of the feasibility of using MEMS actuators to accomplish the control goal. 15.3.2.2 Forcing Parameters Perhaps one of the most limiting factors in the applicability of MEMS actuators in flow control is their micron-size forcing amplitude. Typical mechanical MEMS actuators are capable of delivering oscillation amplitudes ranging from a few microns to tens of microns. In shear flows evolving from the separation of a thin laminar boundary layer, such small amplitudes can be comparable to the momentum thickness of the separating boundary layer, resulting in significant flow disturbance. This is particularly true in SSL flows, where the actuator location can be maintained in the immediate vicinity of the separation point. To appreciate the susceptibility of shear-layers to very low-level actuation, it is instructive to consider an order of magnitude analysis. For example, consider a situation where it is desired to attenuate or eliminate naturally existing two-dimensional disturbances in a laminar incompressible single-stream shear layer. One approach to attain this goal is through “cancellation”of the disturbance during its initial linear growth phase, where the streamwise development of the instability velocity amplitude, or rms, is given by: uЈ(x) ϭ uЈ o e Ϫ α i (xϪx o ) (15.1) where, uЈ is an integral measure of the instability amplitude at streamwise location x from the point of separation of the shear layer (trailing edge in this example), uЈ o is the initial instability amplitude, x o is the 15-6 MEMS: Applications © 2006 by Taylor & Francis Group, LLC virtual origin of the shear layer, and α i is the imaginary wavenumber component, or spatial growth rate, of the instability wave. To cancel the flow instability, a periodic disturbance at the same frequency but 180° out of phase may be introduced at some location x ϭ x* near the point of separation of the shear layer. The amplitude of the disturbance introduced by the control should be of the same order of magnitude as that of the natu- ral flow instability at the location of the actuator. This may be estimated from Equation (15.1) as follows: uЈ(x*) ϭ uЈ o e Ϫ α i (x*Ϫx o ) (15.2) The location of the actuator should be less than one to two wavelengths ( λ ) of the flow instability down- stream of the trailing edge to be within the linear region. This allows superposition of the control and natural instabilities, leading to cancellation of the latter. At the end of the linear range (approximately 2 λ ), the natural instability amplitude may be calculated from Equation (15.1) as: uЈ(2 λ ) ϭ uЈ o e Ϫ α i (2 λ Ϫx o ) (15.3) Dividing Equation (15.2) by Equation (15.3), one may obtain an estimate for the required actuator-induced disturbance amplitude in terms of the flow instability amplitude at the end of the linear growth zone: uЈ(x*) ϭ uЈ(2 λ )e Ϫ α i (x*Ϫ2 λ ) (15.4) The instability amplitude at the end of the linear region may be estimated from typical amplitude satu- ration levels (about 10% of the freestream velocity, U). Also, if the natural instability corresponds to the most unstable mode, its frequency would be given by (e.g., [Ho and Huerre, 1984]): St ϭ f θ /U ϭ 0.016 (15.5) where St is the Strouhal number and θ is the local shear layer thickness. For the most unstable mode, the instability convection speed is equal to U/2 and Ϫ α i θ ϭ 0.1 (see [Ho and Huerre, 1984], for instance). Using this information and writing the frequency in terms of the wavelength and convection velocity, Equation (15.5) reduces to: Ϫ α i λ Ϸ (2 ϫ 0.16) Ϫ1 (15.6) for the most unstable mode. Now, for the sake of the argument, assuming the actuator to be located at the shear layer separation point (x* ϭ 0), estimating uЈ(2 λ ) as 0.1U, and substituting from Equation (15.6) in Equation (15.4), one obtains: uЈ(x*) ϭ 0.1Ue Ϫ ᎏ 2ϫ 2 0.16 ᎏ Ϸ 10 Ϫ4 U (15.7) That is, the required actuator–generated disturbance velocity amplitude should be about 0.01% of the free stream velocity. Also, the actual forcing amplitude is not that given by Equation (15.7) but rather one that is related to it through an amplitude receptivity coefficient. That is: uЈ act. ϭ uЈ(x*) ϫ R (15.8) where R is the receptivity coefficient and uЈ act. is the actuation amplitude. Thus, if R is a number of order one, the required actuator velocity amplitude for exciting flow structures of comparable strength to the natural coherent structures in a high-speed shear layer (say, U ϭ 100 m/s) is equal to 1 cm/s (i.e., of the order of a few cm/s). If the actuator can oscillate at a frequency of 10 kHz (easily achievable with MEMS), the corresponding actuation amplitude is only about a few microns! In MSL flows, the ability of the sensor array and associated search algorithm to locate the instantaneous separation location of the shear layer and the actuator-to-actuator spacing may not permit flow excitation Towards MEMS Autonomous Control of Free-shear Flows 15-7 © 2006 by Taylor & Francis Group, LLC as close to the separation point as desired. In this case, even for extremely thin laminar shear layers, stronger actuators may be needed to compensate for the possible suboptimal actuation location. MEMS actuators that are capable of delivering hundreds of microns up to order of 1 mm excitation amplitude have been devised. These include the work of Miller et al. (1996) and Yang et al. (1997). Although the more powerful, large-amplitude actuators provide much needed “muscle” to the miniature devices, they nullify one of the main advantages of MEMS technology: the ability to fabricate actuators that can oscillate mechanically at frequencies of hundreds of kHz. Traditionally, high-frequency (few to tens of kHz) excitation of flows was possible only via acoustic means. With the ability of MEMS to fabricate devices with “microinertia,”it is now possible to excite high-speed flows using mechanical devices (e.g., see [Naguib et al., 1997]). To estimate the order of magnitude of the required excitation frequency, the frequency of the linearly most unstable mode in two-dimensional shear layers may be used. This frequency may be estimated from Equation (15.5). Using such an estimate, it is straightforward to show that the most unstable mode fre- quency for typical high-speed MAS shear layers, such as that in transonic and supersonic jets, is of the order of tens to hundreds of kHz. On the other hand, if one considers a microscale (MIS) shear layer with a momentum thickness in the range of one to 10 microns and a modest speed of 1m/s, the correspon- ding most unstable frequency is in the range of 1.6–16 kHz. Of course, this estimate assumes the MIS shear layer instability characteristics are similar to those of the MAS shear layer, an assumption that awaits verification. An inherent characteristic of high-frequency MEMS actuators with tens of microns oscillation amplitudes is that they tend to be of the resonant type. Moreover, the Q factor of such large-amplitude microres- onators tends to be large. Therefore, these high-frequency actuators are typically useful only at or very close to the resonant frequency of the actuator. This is a limiting factor not only from the perspective of shear layer control under different flow conditions, but also when multimode forcing is desired. For instance, Corke and Kusek (1993) have shown that resonant subharmonic forcing of the shear layer surrounding an axi-symmetric jet leads to a substantial enhancement in the growth of the shear layer. To implement this forcing technique it was necessary to force the flow at two different frequencies simultaneously using an array of miniature speakers.Although the modal shapes of the forcing employed by Corke and Kusek (1993) can be implemented easily using a MEMS actuator array distributed around the jet exit, only one frequency of forcing can be targeted with a single actuator design as discussed above. A possible remedy would use the MEMS capability of fabricating densely packed structures to develop an interleaved array of two different actuators with two different resonant frequencies. 15.3.2.3 Robustness, Packaging and Ability to Integrate With Sensors and Electronics Similar to sensors, robustness of the MEMS actuators is essential if they are to be useful in practice. In fact, actuators tend to be more vulnerable to adverse effects of the flow environment than sensors are, as they typically protrude farther into the flow, exposing themselves to higher flow velocities, temperatures, forces, etc. Additionally, as discussed earlier, the fabrication processes of the actuators must be compatible with those of the sensors and circuitry if they are to be packaged together into an autonomous control system. 15.3.3 Closing the Loop: The Control Law Perhaps one of the most challenging aspects of realizing MEMS autonomous systems in practice is one that is not related to the microfabrication technology itself. Given an integrated array of MEMS sensors and actuators that meets the characteristics described above, a fundamental question arises. How should the information from the sensors be processed to decide where, when, and how much actuation should be exercised to maintain a desired flow state? That is, what is the appropriate control law? Of course, to arrive at such a control law, one needs to know the response of the flow to the range of pos- sible actuation. This is far from being a straightforward task, however, given the nonlinearity of the system being controlled: the Navier–Stokes Equations. Moin and Bewley (1994) provide a good summary of various approaches that have been attempted to develop control laws for flow applications. Detailed discussion of 15-8 MEMS: Applications © 2006 by Taylor & Francis Group, LLC [...]... than 1/10 of the most unstable frequency) was quite an impressive demonstration of the potential of the technology Helical mode cross-spectrum amplitude 0.5 1 Uj = 70 m/s m 0 0.4 22 .5° 4 |φxy| 5 13 1 0.3 2 Helical (m=1) 8 9 Axisymmetric 0 .2 0.1 0 5 10 15 Device # Helical mode phase 3000 25 00 1 Uj = 70 m/s 2 Slope = 179 .2 22. 5° φ1 (deg.) 20 00 13 m 1500 5 1 9 Slope = 91 .2 4 1000 8 Slope = 22 .2 500 0 5 10... than the natural frequency of the flow is believed to be responsible for the resulting small disturbance level at the Mach number of 0. 42 when forcing with the 5 kHz actuator The ability of the MEMS devices to excite the flow on a par with other macro forcing devices is believed to be due to the ability to position the MEMS extremely close to the point of high-receptivity at the nozzle lip where the. .. Figure 15 .26 , for most cases of MEMS forcing the MEMS- generated disturbance grows to a level that is similar to that produced by glow discharge and acoustic forcing For a Mach number of 0 .2, © 20 06 by Taylor & Francis Group, LLC 1 5 -2 4 MEMS: Applications 100 /Uj Mj 0 .2 0.4 0.6 10–1 10 2 10–3 0.04 0.06 0. 08 0.1 0. 12 0.14 0.16 0. 18 x/D FIGURE 15 .25 Streamwise development of the MEMS- induced... array skin 100 10 m/s 60 20 m/s ° 80 40 30 m/s 20 0 0 5 10 15 20 25 Distance from apex (cm) 30 35 FIGURE 15.6 Separation line along the edge of the delta wing for different flow velocities © 20 06 by Taylor & Francis Group, LLC 1 5-1 2 MEMS: Applications FIGURE 15.7 SEM view of passive-type flap actuators The permalloy layer caused the flap to align itself with the magnetic field lines of a permanent... thick permalloy (80 % Ni and 20 % Fe) was electroplated on the surface of the 1 .8 µm thick flap © 20 06 by Taylor & Francis Group, LLC Towards MEMS Autonomous Control of Free-shear Flows 1 5-1 1 10 rms (mV) 8 Wing edge 6 4 2 0 MEMS shear sensor 0 20 40 60 80 100 ° FIGURE 15.4 Distribution of surface-shear stress rms values around the edge of the delta wing FIGURE 15.5 UCLA/Caltech flexible shear-stress sensor... control of the rolling moment is desired © 20 06 by Taylor & Francis Group, LLC 1 5-1 6 MEMS: Applications FIGURE 15.14 Flow visualization of the vortex structure on the suction side of the delta wing without (top) and with (bottom) actuation Change of normalized roll moment (%) 40 30 20 10 0 –10 20 0 20 40 60 80 100 120 140 80 100 120 140 ° Change of normalized roll moment (%) 40 30 20 10 0 –10 20 0 20 40... Uj = 21 0 m/s [Mj = 0.6] –1 10 fu′u′ (m2/s2 Hz) fu′u′ (m2/s2 Hz) –4 10 –6 100 fu′u′ (m2/s2 Hz) –3 10 10 (a) (c) 10 2 10–5 0 10 Forced Jet: Uj = 70 m/s [Mj = 0 .2] x/D 0.09 0.13 0.17 10 fu ′u′ (m2/s2 Hz) fu ′u′ (m2/s2 Hz) 10 100 2 10 10–3 x /D 0.05 0.07 0.10 10–4 –5 10 Forcing frequency –6 5000 10000 15000 20 000 25 000 30000 35000 f (Hz) 10 0 5000 10000 15000 20 000 25 000 30000 35000 f (Hz) FIGURE 15 .24 ... in this chapter, the use of microactuators to alter the characteristics of the shear layer and ultimately the vortical structure has a good potential for success Furthermore, when the edge of the wing is rounded rather than sharp, the specific separation point location will vary with the distance from the wing apex, the flow velocity, and the position of the wing relative to the flow Therefore, a distributed... outward-shift of approximately one vortex © 20 06 by Taylor & Francis Group, LLC Towards MEMS Autonomous Control of Free-shear Flows 40 Re 2. 10 × 105 3.15 × 105 4 .20 × 105 5 .25 × 105 30 20 10 Change of normalized roll moment (%) Change of normalized roll moment (%) 40 0 –10 20 1 5-1 5 0 20 40 60 80 20 10 0 –10 20 100 120 140 ° (a) 30 20 40 60 80 100 120 140 80 100 120 140 ° 40 30 30 Change of normalized... normalized roll moment (%) 0 (b) 20 10 0 –10 20 0 20 40 60 80 10 0 –10 20 100 120 140 ° (c) 20 0 20 40 60 ° (d) FIGURE 15. 12 Actuation effect on delta wing rolling moment for different angles of attack: (a) 20 °; (b) 25 °; (c) 30°; (d) 35° Change of normalized roll moment (%) 60 50 40 30 20 10 0 0×100 Two-sided actuation Sum of the right- and left-sided actuation 2 105 4×105 6×105 8 105 1×106 Re FIGURE 15.13 . actuator. 1.4 mm 2. 0 mm 0.3 mm 8. 6 mm 9.5 mm Silicon rubber, 120 m Parylene C, 1.6 m FIGURE 15.10 Schematic of bubble actuator details. © 20 06 by Taylor & Francis Group, LLC Figures 15.12a and 15.12b 1 4-1 5 © 20 06 by Taylor & Francis Group, LLC 15 Toward MEMS Autonomous Control of Free-Shear Flows 15.1 Introduction 1 5-1 15 .2 Free-Shear Flows: A MEMS Control Perspective 1 5 -2 15.3 Shear-Layer MEMS. MEMS Autonomous Control of Free-shear Flows 1 5-1 1 0 2 4 6 8 10 0 20 40 60 80 100 rms (mV) MEMS shear sensor Wing edge  ° FIGURE 15.4 Distribution of surface-shear stress rms values around the