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Review Article

Towards In-Flight Applications? A Review on Dielectric Barrier Discharge-Based Boundary-Layer Control

[+] Author and Article Information
Jochen Kriegseis

Institute of Fluid Mechanics (ISTM),
Karlsruhe Institute of Technology (KIT),
Karlsruhe D-76131, Germany
e-mail: kriegseis@kit.edu

Bernhard Simon

Center of Smart Interfaces (CSI),
Technische Universität Darmstadt,
Griesheim D-64347, Germany
e-mail: simon@csi.tu-darmstadt.de

Sven Grundmann

Department of Fluid Mechanics,
University of Rostock,
Rostock D-18059, Germany
e-mail: sven.grundmann@uni-rostock.de

Manuscript received July 19, 2015; final manuscript received May 4, 2016; published online July 7, 2016. Assoc. Editor: Ardeshir Hanifi.

Appl. Mech. Rev 68(2), 020802 (Jul 07, 2016) (41 pages) Paper No: AMR-15-1083; doi: 10.1115/1.4033570 History: Received July 19, 2015; Revised May 04, 2016

Active control of laminar boundary layers with dielectric barrier discharge (DBD) plasma actuators (PAs) has made considerable progress in the last 15 years. First pioneering experiments have motivated numerous researchers to gain a deeper insight into the underlying working principles and corresponding quantification of the actuator performance. These investigations clearly show the strengths but also the weaknesses of the PA as a flow control device. Presently, the boundary-layer control (BLC) with PAs experiences the transition from lab studies to real flight applications. However, the PA community still struggles with the poor fluid mechanic efficiency and the limited momentum flux of the actuator. This review therefore addresses the question how applicable the actuator is as an energy efficient flow control device for future in-flight applications. Since any successful flow control requires detailed knowledge of the actuator’s control authority, this discussion is built upon a careful and comprehensive summary of performance evaluation measures and the interplay with various changes of thermodynamic and kinematic environmental conditions. Consequently, this review for the first time provides a comprehensive discussion of all required steps for successful DBD-based in-flight flow control spanning from the power supply to the achieved flow-control success in one coherent document.

Copyright © 2016 by ASME
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Jukes, T. N. , and Choi, K.-S. , 2012, “ Dielectric-Barrier-Discharge Vortex Generators: Characterisation and Optimisation for Flow Separation Control,” Exp. Fluids, 52(2), pp. 329–345. [CrossRef]
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Schuele, C. Y. , Corke, T. C. , and Matlis, E. , 2013, “ Control of Stationary Cross-Flow Modes in a Mach 3.5 Boundary Layer Using Patterned Passive and Active Roughness,” J. Fluid Mech., 718(3), pp. 5–38. [CrossRef]
Chernyshev, S. , Kuryachii, A. , Manuilovich, S. , Rusyanov, D. , and Skvortsov, V. , 2013, “ Attenuation of Cross-Flow-Type Instability in Compressible Boundary Layer by Means of Plasma Actuators,” AIAA Paper No. 2013-321.
Dörr, P. C. , and Kloker, M. J. , 2014, “ Transition Control in a Three-Dimensional Boundary-Layer Flow Using Plasma Actuators,” Eighth IUTAM Symposium on Laminar-Turbulent Transition, Rio de Janeiro, Brazil, pp. 469–478.
Dörr, P. C. , and Kloker, M. J. , 2015, “ Stabilisation of a Three-Dimensional Boundary Layer by Base-Flow Manipulation Using Plasma Actuators,” J. Phys. D: Appl. Phys., 48(28), p. 285205. [CrossRef]
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Hanson, R. E. , Bade, K. M. , Belson, B. A. , Lavoie, P. , Naguib, A. M. , and Rowley, C. W. , 2014, “ Feedback Control of Slowly-Varying Transient Growth by an Array of Plasma Actuators,” Phys. Fluids (1994-Present), 26(2), p. 024102. [CrossRef]
Osmokrovic, L. P. , Hanson, R. E. , and Lavoie, P. , 2015, “ Laminar Boundary-Layer Response to Spanwise Periodic Forcing by Dielectric-Barrier-Discharge Plasma-Actuator Arrays,” AIAA J., 53(3), pp. 617–628. [CrossRef]
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Fabbiane, N. , Simon, B. , Fischer, F. , Grundmann, S. , Bagheri, S. , and Henningson, D. S. , 2015, “ On the Role of Adaptivity for Robust Laminar Flow Control,” J. Fluid Mech., 767(3), p. R1.
Kurz, A. , Simon, B. , Tropea, C. , and Grundmann, S. , 2014, “ Active Wave Cancelation Using Plasma Actuators in Flight,” AIAA Paper No. 2014-1249.
Dadfar, R. , Semeraro, O. , Hanifi, A. , and Henningson, D. S. , 2013, “ Output Feedback Control of Blasius Flow With Leading Edge Using Plasma Actuator,” AIAA J., 51(9), pp. 2192–2207. [CrossRef]
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Kurz, A. , Tropea, C. , Grundmann, S. , Forte, M. , Vermeersch, O. , Seraudie, A. , Arnal, D. , Goldin, N. , and King, R. , 2012, “ Transition Delay Using DBD Plasma Actuators in Direct Frequency Mode,” AIAA Paper No. 2012-2945.
Kurz, A. , Grundmann, S. , Tropea, C. , Forte, M. , Seraudie, A. , Vermeersch, O. , Arnal, D. , Goldin, R. , and King, R. , 2013, “ Boundary Layer Transition Control Using DBD Plasma Actuators,” J. AerospaceLab, 1(6), pp. 1–8.
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Choi, K.-S. , Jukes, T. N. , Whalley, R. D. , Feng, L. , Wang, J. , Matsunuma, T. , and Segawa, T. , 2014, “ Plasma Virtual Actuators for Flow Control,” J. Flow Control, Meas. Visualization, 3(1), p. 22. [CrossRef]
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Figures

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Fig. 1

“Sketch of the airflow behavior generated by plasma-actuator operation: (a) wall-jet formation under quiescent air conditions, and (b) manipulation of an existing boundary layer.” (Reprinted with permission from Kriegseis [38]. Copyright 2011 by Jochen Kriegseis.)

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Fig. 2

“Power flow diagram of plasma-actuator operation.” (Reprinted with permission from Kriegseis et al. [62]. Copyright 2013 by American Institute of Physics.)

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Fig. 3

“ΔCL versus Cμ for the PTL IVL at α=17deg (left). Blowing over a 45 deg inclined flap on a NACA 23015; measured values from Ref. [66] according to Ref. [67] with the blowing slot width as a parameter (right).” (Reprinted from Weier et al. [65] with permission of Springer. Copyright 2003 by Springer Science+Business Media B.V.)

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Fig. 4

Typical coordinate system for and configuration of DBD PAs comprising two electrodes separated by a dielectric and an encapsulation film below the lower electrode. (a) Positive x-displacement—electrode gap. (Reprinted with permission from Bénard et al. [75]. Copyright 2008 by American Institute of Aeronautics and Astronautics, Inc.) (b) Negative x-displacement—electrode overlap. (Reprinted with permission from Joussot et al. [72]. Copyright 2013 by IOP Publishing.) Furthermore, (b) indicates the application of probe capacitors Cp or probe (shunt) resistors R.

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Fig. 5

“Time evolution of discharge current and voltage when the grounded electrode is encapsulated.” (Reprinted with permission from Forte et al. [76]. Copyright 2006 by the authors.)

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Fig. 6

“Emission from the plasma indicates a much more irregular discharge on the positive-going part of the cycle (0.0–0.2 ms in this figure) than on the negative-going part (0.2–0.4 ms).” (Reprinted with permission from Enloe et al. [78].)

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Fig. 7

“High-speed photographs of the DBD discharge in the negative-going (forward) stroke (top) and the positive-going (backward) stroke (bottom).” (Reprinted with permission from Enloe et al. [79].)

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Fig. 8

“Picture of an operating DBD plasma actuator indicating the coordinate system and measurement domain of the light-emission analysis.” (Reprinted with permission from Kriegseis [38]. Copyright 2011 by Jochen Kriegseis.)

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Fig. 9

Typical examples for the length of the plasma extent Δx as function of operating voltage V. (a) “Effect of input voltage on the extent (…) of the plasma discharge edge for SDBD actuator (from Orlov [84] and Orlov et al. [85]).” (Reprinted from Corke et al. [26] with permission of Springer. Copyright 2009 by Springer Science+ Business Media B.V.). (b) “Plasma length Δx as function of voltage V (…) for several frequency f.” (Reprinted with permission from Kriegseis et al. [86]. Copyright 2011 by American Institute of Physics.)

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Fig. 10

“Graphical review of published V–P relations.” (Reprinted with permission from Kriegseis [38]. Copyright 2011 by Jochen Kriegseis.)

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Fig. 11

“Typical instantaneous electrical power consumption versus time, for a surface DBD.” (Reprinted with permission from Moreau [23]. Copyright 2007 by IOP Publishing.)

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Fig. 12

Q–V cyclograms (Lissajous figures) of DBDs with typical operating parameters; characteristic quantities such as Vmax, Qmax, and different capacitances. (a) VD with C and Cd: “A QU oscillographic presentation (Lissajous figure).” (Reprinted with permission from Wagner et al. [110]. Copyright 2003 by Elsevier). Note that U denotes the operating voltage in this diagram. (b) SD with C0 and Ceff: “Electircal discharge quantities: QV cyclogram (Lissajous figure) of the DBD as a basis of power consumption PA calculation and effective PA capacitance Ceff derivation.” (Reprinted with permission from Kriegseis et al. [86]. Copyright 2011 by American Institute of Physics.)

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Fig. 13

“(a) Phase relation Δϕ between voltage V and charge Q and (b) electrical efficiency ηE according to definition (7) for various frequencies f and different combinations of HV transformers and actuator lengths (…); vertical dashed lines indicate resonance frequencies for varying operational setups.” (Reprinted with permission from Kriegseis et al. [62]. Copyright 2013 by American Institute of Physics.)

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Fig. 14

“Frequency–current characteristic with different loads at the same exciting power.” (Reprinted with permission from Yang et al. [114]. Copyright 2005 by IOP Publishing.)

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Fig. 15

Resonance frequency fres as function of actuator voltage V for several actuator lengths L: 1IAb =̂ L=0.15 m, 1IBb =̂ L=0.30 m, and 1ICb =̂ L=0.45 m. (Reprinted with permission from Kriegseis et al. [91]. Copyright 2011 by Elsevier.)

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Fig. 17

“Electrical discharge quantities: (a) voltage and capacitance time traces according to Eq. (8), and (b) capacitance histogram with characteristic peaks for C0 and Ceff”; see Fig. 12(b) for the underlying Lissajous figure. (Reprinted with permission from Kriegseis et al. [86]. Copyright 2011 by American Institute of Physics.)

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Fig. 18

“Actuator capacitance Ceff as function of voltage V for several frequencies f.” (Reprinted with permission from Kriegseis et al. [86]. Copyright 2011 by American Institute of Physics.)

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Fig. 19

“Actuator capacitance Ceff as function of plasma length Δx for several frequency f”; cf. Figs. 9(b) and 18. (Reprinted with permission from Kriegseis et al. [86]. Copyright 2011 by American Institute of Physics.)

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Fig. 20

Various diagrams of produced actuator thrust as function of (a) operating parameters, (b) dielectric materials, and (c) geometry parameters. Note that the thrust data in Fig. 20(c) are already normalized with the electric power. This ratio will be introduced as fluid mechanic effectiveness in Sec. 3.3.5. (a) “Actuator thrust measurement compared with other authors. Data reproduced from Refs. [139,140], and [96].” (Reprinted with permission from Ferry and Rovey [141]. Copyright 2011 by Joseph W. Ferry.) (b) “Measured thrust per unit span/g versus rms applied voltage for various dielectric materials.” (Reprinted with permission from Thomas et al. [139]. Copyright 2009 by American Institute of Aeronautics and Astronautics, Inc.). (c) “Momentum transfer to air depends strongly on characteristic dimension of exposed electrode, even though this dimension does not affect bulk properties of the discharge.” (Reprinted with permission from Enloe et al. [90].)

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Fig. 21

“Plasma-actuator thrust as a function of discharge-specific variables for several frequencies f: (a) consumed power PA/L, (b) plasma length Δx, and (c) effective discharge capacitance Ceff/L.” (Reprinted with permission from Kriegseis [38]. Copyright 2011 by Jochen Kriegseis.)

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Fig. 22

Normalized wall-jet velocity profiles for various parameter combinations. (a) “Nondimensional velocity profile. Normalized with the maximum velocity Umax and jet half-width δ1/2. The theoretical profiles of the laminar and turbulent wall jet are plotted from Glauert [145]: t = 5 ms.” (Reprinted with permission from Jukes and Choi [146]. Copyright 2006 by American Institute of Aeronautics and Astronautics, Inc.). (b) “Normalized velocity profiles at x = 25 mm downstream of the exposed electrode trailing edge (…); filled symbols for Vpp > 10 kV.” (Reprinted with permission from Murphy et al. [147]. Copyright 2013 by American Institute of Physics). (c) “Nondimensional velocity profiles U/Umax = f(y/y1/2) in the developing region, x = 5, 10, 20, 50, 100, and 150 mm of the plasma-induced wall jet.” (Reprinted with permission from Maden et al. [148]. Copyright 2013 by Elsevier.)

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Fig. 23

Typically applied CV with boundary nomenclature as used in the present work: (a) integral force value F, and (b) force distribution f(x, y). Velocity distribution is sketched with black arrows, and force (distribution) is shaded gray. (Reprinted with permission from Kriegseis et al. [149]. Copyright 2012 by Jochen Kriegseis.)

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Fig. 24

“Plasma-actuator force F/L as a function of operating voltage V; implemented cases 1–6 of the present study appear colored (f = 11 kHz), balance-based data appear gray (∗ explicit weight balance-based measurements of Kriegseis et al. [86]; measurement uncertainty σF < 3%); calculated uncertainties for different PIV-based approaches appear in the legend behind the respective cases.” (Reprinted with permission from Kriegseis et al. [150]. Copyright 2013 by IOP Publishing.)

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Fig. 25

Quasi-steady distributions of the PA body force: (a) and (b) NSE-based horizontal and vertical force components fx(x,y) and fy(x,y), respectively; (c) VE-based horizontal force component fx(x,y); and (d) test of assumption (14) with NSE-based results. The 10% isoline (max[fx]/10) indicates the momentum-transfer domain. (Reprinted with permission from Kriegseis et al. [150]. Copyright 2013 by IOP Publishing.)

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Fig. 26

Phase-averaged body-force distribution fi(x,y,ϕ) and fi(x,y,t∗) summarized and rearranged from Wilke [154] and Benard et al. [157]; for the sake of brevity, only an extract of the published diagrams is shown for comparable phases. The difference between the compared plots in each row is below Δt∗<0.011 (respectively, Δϕ<4deg). (a) “Body-force distributions for various phase angles φ.” (Reprinted with permission from Wilke [154] (translated from German). Copyright 2009 by Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)). Arrows show force vectors f→, and contours show force magnitude |f→|. (b) “Spatial distribution of the electrohydrodynamic volume force, fx(x,t) (…). Scale is given in ×10−3 Nm−3.” (Reprinted with permission from Benard et al. [157]. Copyright 2013 by IOP Publishing). (c) “Spatial distribution of the electrohydrodynamic volume force, fy(x,t) (…). Scale is given in ×10−3 Nm−3.” (Reprinted with permission from [157]. Copyright 2013 by IOP Publishing.)

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Fig. 27

“Time evolution of the electrohydrodynamic body force (horizontal component) by comparison with previous literature.” (Reprinted with permission from Benard et al. [157]. Copyright 2013 by IOP Publishing.) Note that the cited references appear as Debien et al. [133], Wilke [154], and Neumann et al. [158] in the present work.

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Fig. 28

“Plasma length Δx discharge capacitance Ceff: dark markers—estimated momentum-transfer length ΔxF based on the 10% isolines of Fig. 25, and white markers—measured plasma length Δx based on light-emission analysis” (∗: see Ref. [86]). (Reprinted with permission from Kriegseis et al. [150]. Copyright 2013 by IOP Publishing.)

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Fig. 29

Spatiotemporal momentum-transfer domain on the dielectric layer. (a) Induced momentum F̃x(x,ϕ) according to Eq. (17) with ■ =̂ F̃x/F̃x,max=1 and □ =̂ F̃x/F̃x,max=−1. “Normalized x-component of the volume force Fx/Fx,max for a frequency of 1000 Hz as function of x-coordinate and phase angle f, where Fx = f(x,t).” (Reprinted with permission from Wilke [154] (translated from German). Copyright 2009 by Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)). (b) Luminosity of the discharge; note that the 90 deg phase shift between (a) and (b) originates from the chosen definitions of the cycle by Wilke [154] (positive/negative half-cycle) and Enloe et al. [162] (forward/backward stroke). “Surface plot of light output from the plasma as a function of time and chordwise distance, for a single AC cycle of the driving voltage, shown to the left.” (Reprinted with permission from Enloe et al. [162].)

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Fig. 30

“Efficiency as a function of the frequency fac and voltage Vapp. For the frequency run, the voltage is kept at a fixed value of 10 kVpp, and for the voltage run, the frequency is kept at a fixed value of 2 kHz.” (Reprinted with permission from Giepman and Kotsonis [163]. Copyright 2011 by American Institute of Physics.)

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Fig. 31

“Efficiency versus electrical power for every thickness.” (Reprinted with permission from Jolibois and Moreau [142]. Copyright 2009 by IEEE.)

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Fig. 32

Fluid mechanic efficiency ηFM∗ (a) and effectiveness ηFM∗ ((b) and (c)) of the PA as a function of power consumption PA for various parameter combinations, where all experiments were conducted with identical actuator construction: (a) ηFMPA diagram, (b) η*FMPA diagram (PIV data), and (c) ηFM∗−PA diagram (balance data). (a) and (b) show the results from explicit determination approaches of identical PIV data [150]; (c) shows the results form explicit thrust measurements [86]. (Reprinted with permission from Kriegseis et al. [62]. Copyright 2013 by American Institute of Physics.)

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Fig. 33

“Experimentally and computationally obtained mean velocity profiles u(y) at selected streamwise locations x; implemented models: Wilke [154] and Albrecht et al. [155], according to Shyy et al. [169] and Suzen et al. [170]; PIV data: Kriegseis [38].” (Reprinted with permission from Maden et al. [167]. Copyright 2012 by Imdat Maden.)

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Fig. 34

“Joint performance diagram showing the results of power consumption PA, plasma length Δx, and characteristic capacitances C0 and Ceff as a function of the pressure level p (Exp1 and Exp2). The respective sets of curves correspond to different airflow velocities U∞=0−100 m/s.” (Reprinted with permission from Kriegseis et al. [179]. Copyright 2014 by American Institute of Physics.)

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Fig. 35

Pressure–thrust interrelation for various pressure levels below and above ambient conditions. (a) “Comparison of thrust measurements with that of Abe and Soni.” (Reprinted with permission from Friz and Rovey [181]. Copyright 2014 by Multi Science Publishing). The references appear as Abe et al. [96] and Soni and Roy [182] in the present work. (b) “Induced force FB versus gauge pressure for input configurations 1, 2, and 3”; 10 kHz/15 kVpp, 13.5 kHz/20 kVpp, and 17 kHz/20.5 kVpp, respectively. (Reprinted with permission from Versailles et al. [45]. Copyright 2009 by P. Versailles, V. Gingras-Gosselin, and H.D. Vo.) (c) “Average thrust as a function of pressure” below [183] and above atmospheric for various voltages. (Reprinted with permission from Valerioti and Corke [184]. Copyright 2012 by American Institute of Aeronautics and Astronautics.)

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Fig. 36

“Net actuator force versus air temperature for input frequency of 9.4 kHz at different voltages.” (Reprinted with permission from Versailles et al. [45]. Copyright 2009 by P. Versailles, V. Gingras-Gosselin, and H.D. Vo.)

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Fig. 37

“Portion of an emission spectrum without airflow and for an isentropic Mach number Mis = 0.7, at frequency 10 kHz, input power 100 W, and voltage U2=2.5 kV.” (Reprinted with permission from Pavon et al. [195]. Copyright 2007 by IOP Publishing.)

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Fig. 38

“Lissajous figures with characteristic discharge quantities under quiescent air conditions and at M = 0.42 characterizing the airflow influence on the electrical discharge performance.” (Reprinted with permission from Kriegseis et al. [196]. Copyright 2012 by American Institute of Physics.)

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Fig. 39

“Relative performance Π¯ϕ and corresponding drop Ψ¯ϕ as a function of airflow speed U∞,M for different pressure levels p (Exp1); - - - denotes respective regression lines Πϕ∗, Ψϕ∗. Note the different ordinate scales in the two rows of diagrams.” (Reprinted with permission from Kriegseis et al. [179]. Copyright 2014 by American Institute of Physics.)

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Fig. 40

“Electrohydrodynamic number NEHD versus airflow velocity U0 for different discharge locations: 0.1, 0.25, 0.5, and 1 mm from the plate wall.” (Reprinted with permission from Moreau et al. [198]. Copyright 2006 by Elsevier.)

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Fig. 41

“High-speed influence on the relative plasma-actuator performance ΠPA and corresponding drop ΨPA (Exp1, Exp2, Exp4, Exp5, and Exp6): (a) as a function of freestream velocity U∞ and Mach number M (Π,Ψ–M,U∞ diagram) and (b) as a function of the scaling number K=U∞/vd (Π,Ψ–K diagram).” (Reprinted with permission from [196]. Copyright 2012 by American Institute of Physics.)

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Fig. 42

“Sketch of experimental setup; detailed view of electrical plasma-actuator setup comprising function generator (FG), PS, high voltage (HV) transformer, notebook (NB), and plasma actuator.” (Reprinted with permission from Kriegseis et al. [204]. Copyright 2011 by the authors.)

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Fig. 43

“(a) Consumed power, (b) effective capacitance, and (c) cold capacitance with time for Va=4,6, and 8 kV for the 0.18 mm thick Kapton tape actuators (fa = 4 kHz).” (Reprinted with permission from Hanson et al. [68]. Copyright 2014 by American Institute of Physics.)

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Fig. 44

“Actuator power consumption at (a) increasing pressure and (b) variable humidity.” (Reprinted with permission from Duchmann et al. [206]. Copyright 2014 by Alexander Duchmann.)

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Fig. 45

Closed-loop control of actuator power: humidity variation in horizontal flight beneath cloud base, P¯=25 W/m. (Reprinted with permission from Duchmann et al. [206]. Copyright 2014 by Alexander Duchmann.)

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Fig. 46

“Illustrations of the burst, superposition, and ring modulations.” (Reprinted with permission from Benard and Moreau [208]. Copyright 2010 by IOP Publishing.)

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Fig. 47

“Operating modes for the plasma actuator in relation to a TS wave signal (a): continuous mode (b), active wave cancelation (c), and hybrid mode (d). Shown are (qualitatively) the operating voltage (black) and the momentum production over time (red).” (Reprinted with permission from Kurz et al. [211]. Copyright 2013 by Springer-Verlag.)

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Fig. 48

AWC setup on a flat plate. (Reprinted with permission from Grundmann and Tropea [49]. Copyright 2009 by Elsevier.)

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Fig. 49

“Shape factor development with and without control for the LDA measurements.” (Reprinted with permission from Grundmann and Tropea [49]. Copyright 2009 by Elsevier.)

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Fig. 50

“Ionic wind effect on laminar boundary layer at x/c=30%.” (Reprinted with permission from Séraudie et al. [50]. Copyright 2011 by ONERA.)

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Fig. 51

“Transition delay on the model upper side depending on the high voltage supply.” (Reprinted with permission from Séraudie et al. [50]. Copyright 2011 by ONERA.)

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Fig. 52

“Velocity fluctuation distributions along the flat plate at a constant nondimensional height (y/δ99=04) for the natural and manipulated boundary layers (VHV=10 kV).” (Reprinted with permission from Joussot et al. [215]. Copyright 2013 by Inderscience.)

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Fig. 53

“Transition positions as a function of actuator placement and array permutation, T=15.6 N/m (PA=64.4 W/m), U∞=20 m/s.” (Reprinted with permission from Duchmann [207]. Copyright 2012 by Alexander Duchmann.)

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Fig. 54

“Hot-wire standard deviation σU along the flat plate as a function of actuator thrust T.” (Reprinted with permission from Duchmann [207]. Copyright 2012 by Alexander Duchmann.)

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Fig. 55

“Shape factor evolution measured by hot wire and PIV compared to the numerical boundary-layer solution.” (Reprinted with permission from Duchmann et al. [219]. Copyright 2013 by Springer-Verlag.)

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Fig. 56

“Comparison of the wall parallel amplitude distributions û/U∞ at a frequency of 250 Hz between the (a) reference case and the (b) boundary-layer stabilization.” (Reprinted with permission from Widmann et al. [220]. Copyright 2013 by the authors.)

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Fig. 57

Phase velocity evolution of a TS wave downstream of a DBD PA at x = 0.5 m. (Reprinted with permission from Duchmann et al. [221]. Copyright 2010 by Springer Science + Business Media B.V.)

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Fig. 58

“Comparison between wave amplitude evolutions from direct numerical simulation (DNS) and linear stability analysis (LSA) for Blasius boundary-layer flow subjected to DBD forcing at x1=0.325 m and x2=0.425 m.” (Reprinted with permission from Duchmann [207]. Copyright 2012 by Alexander Duchmann.)

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Fig. 59

“A comparison of the critical Reynolds numbers of the different instabilities compared to γ for η = 1.” (Reprinted from Riherd et al. [226] with permission of Springer. Copyright 2014 by Springer Science + Business Media B.V.)

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Fig. 60

“Standard deviation of the hot-wire signals at the wall (y=0 mm) under varying flight states, DBD on/off at T=13.4 mN/m (P=54.2 W/m).” (Reprinted with permission from Duchmann [207]. Copyright 2012 by Alexander Duchmann.)

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Fig. 61

Infrared measurements of in-flight measurements for detection of laminar turbulent transition: (a) PA off and (b) PA on. (Reprinted with permission from Simon et al. [227]. Copyright 2016 by Springer International Publishing.)

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Fig. 62

“Time-mean skin-friction distributions and experimental data of Ref. [231] for the forward-facing step.” (Reprinted with permission from Rizzetta and Visbal [230].)

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Fig. 63

Flat-plate setup for vortex generation in laminar boundary layers. (Reprinted with permission from Barckmann et al. [236]. Copyright 2013 by the authors.)

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Fig. 64

“Boundary-layer profiles (dotted lines) and TS waves (solid lines) in low-speed streak (○) and high-speed streak (□) compared to the case without actuation (no symbol): (a) 5.1 kV, 20% DC, P = 0.95 W per vortex, and (b) 5.1 kV, 40% DC, P = 0.95W per vortex.” (Reprinted with permission from Barckmann et al. [236]. Copyright 2013 by the authors.)

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Fig. 65

“Streamwise velocity isocontours around DBD-VG2 in a laminar boundary layer: 0≤U/U∞≤1 in 0.1 increments (light to dark). Vortex isosurface: λ2=−6.5×104 (dark gray). The DBD-VG upper electrode is marked by a black box.” (Reprinted with permission from Jukes and Choi [151]. Copyright 2013 by Cambridge University Press.)

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Fig. 66

Control of CFVs “(10% isosurface, f10%=0.084, dark): (a) steady CFVs to be controlled, body force off, (b) only body force, and (c) controlled CFVs. A rotated reference system with x0=2.5, z0=−0.04, and Φr=45deg is used.” (Reprinted with permission from Dörr and Kloker [242]. Copyright 2014 by the authors.)

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Fig. 67

“Photograph of the plasma actuator cone tip (left). Largest magnification view of the edge of the copper plating showing the ‘comb’ electrode arrangement to excite m = 68 stationary cross-flow modes (right).” (Reprinted from Schuele et al. [240] with permission of Cambridge University Press. Copyright 2013 by Cambridge University Press.)

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Fig. 68

“Wall-normal-averaged spanwise-wavenumber power spectrum Φu¯ at x=450 mm for (a) actuator A, (b) actuator B, and (c) actuator C.” (Reprinted from Hanson et al. [245] with permission of Springer. Copyright 2010 by Springer Science + Business Media B.V.)

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Fig. 69

“Contour plots of the disturbance velocity for (a) the uncontrolled flow with k=1.25 mm and (b) the controlled flow. Wall-normal disturbance energy profiles are shown for the first three modes for (c) the uncontrolled and (d) the controlled flows.” (Reprinted with permission from Hanson et al. [247]. Copyright 2014 by American Institute of Physics.)

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Fig. 70

Streak generation by DBD PA arrays: (a) “schematic of PA arrays with angled electrodes and electrical setup for measuring PA power consumption,” and (b) “total disturbance energy with respect to actuator power consumption; the regression represents urms2∝Pa1.98.” (Reprinted with permission from Osmokrovic et al. [248]. Copyright 2014 by P. Lavoie.)

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Fig. 71

“Downstream development of u′RMS at a wall-normal position of y = 1.5 mm for the base flow, AWC, continuous mode, and hybrid mode at 8 kVpp.” (Reprinted with permission from Kurz et al. [211]. Copyright 2013 by Springer-Verlag.)

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Fig. 72

“Compensator schemes for static (LQG) (a) and adaptive (fxLMS) (b) strategies. The measurements by the error sensor z are used by the fxLMS algorithm to adapt to the current flow conditions. The gray lines indicate the input–output relations required to be modeled by each strategy.” (Reprinted with permission from Fabbiane et al. [258]. Copyright 2015 by Cambridge University Press.)

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Fig. 73

“Hybrid mode—spectra of hot-wire signals: (a) 2 at x/c = 0.38, and (b) 3 at x/c = 0.47.” (Reprinted with permission from Kurz et al. [259]. Copyright 2014 by Armin Kurz, Bernhard Simon, TU Darmstadt.)

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Fig. 74

“Results of phase-locked PIV measurements with two cameras for hybrid operation mode: (a) TS wave Φ  = 0 deg and (b) wave damping with hybrid operation mode.” (Reprinted with permission from Widmann et al. [220]. Copyright 2013 by the authors.)

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Fig. 75

“Experimental time-averaged power spectral density (PSD) functions for z(t). The flow is excited by a white-noise signal d(t). The top axis reports the nondimensional frequency F=(2πν/U∞2)f. The Reynolds number at the error sensor location is Rex,z=375×103.” (Reprinted with permission from Fabbiane et al. [258]. Copyright 2015 by Cambridge University Press.)

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Fig. 76

“Effect of wind tunnel speed variation ΔUWT on the performance indicator Z. The solid line depicts the DNS data shifted to fit the experimental curve. The flow is excited by the disturbance source operated with a white-noise signal d(t).” (Reprinted with permission from Fabbiane et al. [258]. Copyright 2015 by Cambridge University Press.)

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Fig. 77

“(a) Signal measured by the error sensor and (b) respective body force actuation value for different body force lengths l (F = 86).” (Reprinted with permission from Kotsonis et al. [262]. Copyright 2013 by Marios Kotsonis.)

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Fig. 78

“Stability of the fxLMS control algorithm with constant Ĥec,UWT at different UWT.” (Reprinted with permission from Simon et al. [263]. Copyright 2015 by Elsevier.)

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Fig. 79

“Measured and scaled/stretched secondary path model Ĥec for different wind tunnel velocities based on a reference UWT,ref=12 m/s.” (Reprinted with permission from Simon et al. [263]. Copyright 2015 by Elsevier.)

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Fig. 80

“Percentage reduction in streamwise velocity cancelation averaged along wall-normal direction for cases D (a) and E (b) is shown. The white dots indicate the location of sensors C1 and C2 and actuators B2.” (Reprinted from Dadfar et al. [265] with permission of Springer. Copyright 2014 by Springer Science + Business Media B.V.)

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Fig. 81

“RMS value of a hot-wire signal along the chord of the airfoil for the base flow, with excitation and with closed-loop control (α=2deg and U∞=7 m/s).” (Reprinted with permission from Kurz et al. [267]. Copyright 2013 by ONERA.)

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Fig. 82

“Fluctuating streamwise ((a)–(c)) velocity in the x–z plane of the turbulent boundary layer at y+=5 showing (a) no-control data, (b) unidirectional spanwise traveling waves at 3/4T+, and (c) bidirectional spanwise traveling waves at 3/4T+. Scaled with canonical μτ.” (Reprinted with permission from Whalley et al. [238]. Copyright 2014 by the authors.)

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Fig. 83

Friction coefficient Cf in streamwise direction x for different nondimensionalized forcing amplitudes Dc. (Reprinted with permission from Li et al. [273]. Copyright 2015 by Elsevier).

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Fig. 84

“Spanwise variation of scaled streamwise component mean velocity downstream of PSVG array (40 kV case); surface electrode location indicated on abscissa.” (Reprinted with permission from Wicks et al. [275]. Copyright 2015 by American Institute of Aeronautics and Astronautics, Inc.)

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Fig. 85

“Measured variation of ω¯x with actuator applied voltage for L=λ=2.53 cm (1  in.) and U∞=20 m/s.” (Reprinted with permission from Wicks et al. [275]. Copyright 2015 by American Institute of Aeronautics and Astronautics, Inc.) Note that E denotes the operating voltage in this diagram.

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