Feedback Control of Flow Separation Using Plasma Actuator and FBG Sensor

1Research Institute for Energy Conservation, National Institute of Advanced Industrial Science and Technology (AIST), 1-2-1 Namiki, Tsukuba, Ibaraki 305-8564, Japan 2Graduate School of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan 3Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8577, Japan 4Department of Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, UK


Introduction
Various studies have been conducted on the flows induced by dielectric-barrier-discharge (DBD) plasma actuators, since the basic structures and possibilities as a flow control device were shown by Roth et al. [1] and Corke et al. [2].Conventional DBD plasma actuators (named "sheet-type" DBD plasma actuators in this study) consist of a dielectric layer and exposed and encapsulated electrodes.By applying high voltages at radio frequencies between the electrodes, DBD plasma is formed near the edge of the exposed electrode, and then a tangential jet with a strong horizontal velocity component is induced in the vicinity of the surface.The resultant tangential jet is one-directional, irrespective of changes in the polarity of the applied voltage, when the exposed and encapsulated electrodes are arranged asymmetrically in the - cross section, as shown in Figures 1(a) and 1(b).Various studies have been conducted, not only to explain the phenomenon based on the experimental and numerical approaches reported by Shyy et al. [3], Roy and Gaitonde [4], Boeuf and Pitchford [5], Forte et al. [6], Moreau [7], Corke et al. [8], and Nishida et al. [9] but also to show the potential for achieving flow separation control and drag reduction through the use of DBD plasma actuators, as shown by Post and Corke [10], Labergue et al. [11], Asada et al. [12], Segawa et al. [13], Choi et al. [14], Walker and Segawa [15], and Jukes et al. [16].In addition, pulse modulation in DBD plasma actuators, wherein tangential jets are intermittently induced, is remarkable not only for achieving lift enhancement in a variety of airfoils, but also for reducing power consumption.Recent CFD studies using the K computer have tended to reveal a flow separation control mechanism involving pulse modulation, as described in Sato et al. [17].Control of flow separation on airfoils and rotor blades is an important technological consideration for fluid machinery such as aircraft and wind turbines.In addition to the benefits provided by pulse modulation, the detection of flow separation in real time is effective for minimizing the operation time of DBD plasma actuators.The fiber Bragg grating (FBG) flow sensor is a promising device for detecting flow separation, as described in [18][19][20], and integrates well with DBD plasma actuators because it is an optical sensor immune to electromagnetic interference.The application of flow control technologies will expand if DBD plasma actuators can be attached to or embedded in the metallic and three-dimensional surfaces characteristic of actual fluid machinery.Thus far, most research groups have utilized conventional sheet-type DBD plasma actuators as proposed by Roth et al. [1].However, numerous technical problems must be solved in order to attach DBD plasma actuators to the metallic and three-dimensional surfaces encountered in actual situations, as illustrated in Figure 1(b).From a health and safety perspective, it is inadvisable to use exposed high voltage electrodes on an aerodynamic surface.Conversely, if the high voltage is applied to an encapsulated electrode and the exposed electrode is grounded instead, additional insulation must be inserted in order to use the actuators on metallic structures.Turbomachinery in the field is exposed to rain, moist air, and dust that includes conductive particles, so that additional care must be taken to avoid discharges around insulation areas.In addition, extra insulation causes modifications to the surface shape, adds structural weight, and complicates maintenance.
In order to solve the problems connected with sheet-type DBD plasma actuators, effective active flow control stringtype DBD plasma actuators (as illustrated in Figure 2) were developed, as reported in our previous study [19].These consist of metallic wires coated with insulating materials, instead of a dielectric sheet and encapsulated electrode, although additional grounded electrodes (exposed electrodes) such as Cu tapes are necessary when the surfaces to which the wires are attached are composed of insulating materials.In the case of conductive surfaces, the surface itself is chosen as the exposed electrode and connected to ground.As the metallic wires are already coated with insulating materials, they are sufficiently safe for the application of high voltages, although both free ends should be covered to prevent a short circuit.If elastic materials such as silicone resins are chosen as wire insulation, it is possible to put wires on two or threedimensional surfaces.String-type DBD plasma actuators also possess the advantage, in comparison with the sheet-type variety, of being easy to replace in the case of partial damage to the dielectric coating.The flow patterns induced by stringtype DBD plasma actuators vary according to the location of and distance between the metallic wire coated with insulating material and the exposed electrode.
Although string-type DBD plasma actuators and the FBG flow sensor are promising devices for industrial applications, it is necessary to assess their potential in flow conditions similar to those in which fluid machinery is typically operated.In this study, feedback control of transient flow separation, using string-type DBD plasma actuators and an FBG flow sensor, was tested under fluctuating flow conditions, as a preliminary experiment in preparation for use in actual fluid machinery.

Experimental Setup
A series of experiments was conducted in an opencircuit blow-down wind tunnel with transparent test section (200 mm × 200 mm × 600 mm), as shown in Figure 3.The mean stream velocity ( ∞ ) was varied up to  ∞ = 20 m/s.The leading edge of the NACA0024 airfoil was located 370 mm downstream from the entrance of the test section and at the tunnel midheight.A NACA0024 airfoil (chord length:  = 80 mm; span width:  = 100 mm), composed of ABS plastic and modeled using 3D rapid prototyping (Figure 4), was used to demonstrate feedback control of flow separation.As described in "Introduction," the string-type DBD plasma actuators are possible to attach on metals in principle (see Figure 2), and we are planning to install them in practical fluid machinery which consists of metallic parts, in our future works.In this research, however, it was difficult to construct a NACA0024 airfoil with three-dimensional structure such as cantilever and output shaft made of metals from reasons of technical problems and cost for modeling by the use of a 3D rapid prototyping machinery.As a result, insulative ABS  plastic was chosen as the material of the airfoil.On the other hand, tangential jets can be induced regardless of the material of the airfoil.Therefore, it is considered that control effects of flow separation will be similar even when airfoils made of metals are used.Since flow separation is dependent on the airfoil angles of attack () under steady-state conditions, the airfoil was fixed at  = 12 ∘ in this experiment, and the flow was artificially separated by pivoting the test section wall downstream of the airfoil.In this way, wall oscillation downstream of the airfoil was used to demonstrate feedback International Journal of Aerospace Engineering control of unsteady flow separation.The side wall of the test section near the airfoil suction surface was hinged at 400 mm downstream of the entrance and was pivoted over a range of 0 ∘ ≤  ≤ 16 ∘ , where  is the angle between the pivoting wall and the stationary wall of the test section.By periodically oscillating the plate over a range of 0 ∘ ≤  ≤ 12 ∘ , using a DC motor, the flow separation was artificially enhanced or mitigated up to 1 Hz.DOS (dioctyl sebacate) droplets atomized by a Laskin nozzle to the order of 1 m diameter were introduced into the flow as seeding particles, and the flows around the NACA0024 airfoil were visualized using a 30 mJ/pulse double-pulse Nd:YAG laser (Litron Lasers, NANO S30-15PIV), with flow-image pairs acquired at 3.75 Hz using a cross-correlation camera (TSI Inc., PIVCAM13-8, 1,280 × 1,024 pixel resolution).The velocity vectors in the plane of the - cross section at the midspan of the airfoil and DBD plasma actuator were analyzed using particle image velocimetry (PIV).
The response of feedback control in quiescent flow was estimated by inputting thermal strain and measuring the time delay between the input signal and output response.This was found to be less than 5 ms.In addition, lift () and drag () forces were measured using a three-component force transducer (Kyowa, LSM-B-5NSA37) located outside the test section, as shown in Figure 3.This system has a temperature correction function, so that the temperature drift during the experiments was automatically corrected.The force measurement resolution was stated as 0.001 N in the specifications, but our own calibration using standard weights showed the repeatability of the lift and drag force measurements to be less than 0.01 N.

Open-Loop Control of Flow Separation.
In the present study's string-type DBD plasma actuator, a copper wire coated with PTFE functioned as the actuator (Cu: 0.076 mm in diameter; PTFE: 0.1 mm in thickness; total: 0.3 ± 0.02 mm in diameter).The wire was placed at  = 0.06 mm on the suction surface using double-sided tape, and the surface of the NACA0024 was wrapped in a polyimide sheet of 125 m in thickness.An exposed electrode made of copper film, 35 m in thickness and 80 mm long in the spanwise direction, was attached to the polyimide sheet surface, and DBD plasma was formed near / = 0.05 by applying high voltages using a power supply (PSI Inc., PG1040F).The power consumption of the string-type DBD plasma actuator ( PA ) was estimated using the - Lissajous method, as described in [21].In our previous study, involving instantaneous measurement, a tangential jet with maximum velocity  -max = 0.8 m/s was induced from the leading edge by a sheet-type DBD plasma actuator with a 125 m thick polyimide sheet, through the application of voltage  - = 8.0 kV at frequency   = 9 kHz [15].In this study, however, a higher voltage of  - = 12.0 kV at frequency   = 9 kHz was necessary to achieve  -max = 0.8 m/s from the exposed electrode attached to the NACA0024 airfoil, in quiescent flow, because of the increased distance between the metallic wire and exposed electrode.The  PA of the plasma actuator of 80 mm long in the spanwise direction was estimated to be 2.5 ± 0.4 W (≈31 W/m), as the average of 10 values.
Before conducting feedback control of flow separation, PIV measurements of the instantaneous velocity distributions around the NACA0024 (fixed at  = 12 ∘ ) were conducted under open-loop control conditions, at fixed angles to the wind tunnel side wall between 0 ∘ ≤  ≤ 16 ∘ .The free-stream velocity ( ∞ ), calculated using PIV by averaging 50 velocity distributions near the upstream region of the leading edge, was set at  ∞ = 10 m/s at  = 12 ∘ and  = 0 ∘ , under steady-state conditions.When  ∞ under steadystate conditions was adopted as the characteristic velocity, the Reynolds number and velocity ratio of the tangential jet were Re =  ∞ /] = 5.3 × 10 4 and  -max / ∞ = 0.08, respectively.

Flow Separation Detection with Open-Loop Control of Flow
Separation.An FBG strain measurement system, which can precisely detect minute elastic deformation of an optical fiber, was used to detect flow separation.FBG sensors are generally used, in various research fields such as architecture and civil engineering, for measurement of structural distortion, as described in [22].As shown in Figure 7, approximately 2,000 gratings are installed in the core of the optical fiber (less than 10 m in diameter) in a section of the FBG sensor.A broadband laser with wavelengths ranging from 1,500 to 1,590 nm is shone down the core of optical fiber, and light is reflected from the grating with a wavelength corresponding to the Bragg wavelength,   = 2 0 Λ, where  0 is the fiber refractive index and Λ is the grating interval.forces (mechanical or thermal), a shift is detected in the reflected wavelength, enabling measurement of the strain near the root of the cantilever beam.In this way, multiple sensors with different grating intervals (Λ 1 , Λ 2 , . . ., Λ  ) can be introduced into the same optical fiber, in series, simply by varying the nominal wavelength of the respective gratings ( 1 ,  2 , . . .,   ).In this study, fluctuations in the Bragg wavelength were measured at a maximum sampling rate of   = 1 kHz, using an FBG sensor system (Micron Optics sm130).Control signals for the DBD plasma actuators were operated in real time using LabVIEW coded software.
There was a concern that the Bragg wavelength shifts would be affected by the slightly heated air advected from the surface near the exposed electrode generating DBD, when the FBG sensor was attached to the suction surface of the airfoil.Thus, as a countermeasure, the FBG was attempted to be attached to the structure modeled in the pressure surface of the NACA0024 in our previous study [18].Figures 8(a)-8(c) show the basic structure of the FBG flow sensor here employed for flow separation detection.An optical fiber (outer diameter: 250 m) was inserted into the hollow NACA0024 airfoil.The cantilever, a monocoque structure modeled in the pressure surface of the airfoil, was 10 mm wide by 43 mm long by 0.5 mm thick.The cantilever root was located at  = 0.53, and the cantilever tip protruded 5 mm beyond the trailing edge of the airfoil.In the primary FBG flow sensor, the grating section is located near the exterior surface of the cantilever root, as illustrated in Figure 8(b).Figure 9(a) shows the time-series of Bragg wavelength fluctuations for 20 seconds under PA-OFF conditions.It was confirmed that there were regions with relatively larger amplitude of   in approximately 4 s intervals when the movable section of the wind tunnel was oscillated at   = 0.27 Hz.The   fluctuations with wall oscillation are analyzed in detail below; however, it was concluded that the FBG sensor detected strains at the cantilever root, through vibration of the tip where the wake flow occurred during flow separation.However, the intermediate   value was found to be constant, at roughly 1540.08 nm.On the other hand, under PA-ON conditions,   tended to gradually increase over time, as shown in Figure 9(b).It was found that the heating of the jets, caused by the operation of the plasma actuator, affected flow separation detection, even when the FBG sensor was attached (as in Figure 8(b)) to the exterior surface of the cantilever modeled in the pressure surface of the NACA0024.
Here we discuss a possibility of this phenomenon.Heated air by DBD plasma is mostly carried in the vicinity of the suction surface by the main flow.On the other hand, the exposed electrode and polyimide film (insulation layer) illustrated in Figure 4 are also heated by DBD plasma and temperature around the leading edge can rise gradually by thermal conduction.As a results, it is possible that air which flows on the pressure surface is also heated slightly near the leading edge and the Bragg wavelength reflected from a FBG sensor shifts over time by the thermal effect in the case of location of the FEB sensor attached to the exterior surface of the cantilever.
Consequently, the fiber optic was attached (as in Figure 8(c)) to the interior surface of the cantilever, in the streamwise direction, to minimize the thermal effects of the DBD plasma.The grating section of the FBG sensor was mounted across the cantilever root in the region of 0.44 < / < 0.57.In this FBG flow detection system, the cantilever was streamlined according to the airfoil shape, so that it fit smoothly against the pressure surface of the airfoil.The   fluctuations were measured under the flow conditions shown in Figure 6.The   measurements were conducted for 10 seconds at a sampling frequency of   = 1 kHz.The string-type DBD plasma actuator was operated between 4.0 ≤ t ≤ 6.5 s.When the tangential jets were induced (in PA-ON), the amplitude of the   fluctuations dramatically decreased in comparison to the PA-OFF conditions.The standard deviation in the Bragg wavelength (   ) under PA-OFF and PA-ON, as a function of , is plotted in Figure 10(b).In the case of PA-OFF,   tended to decrease with increasing .It should be noted that    at  ≤ 4 ∘ was significantly higher than    at  ≥ 6 ∘ .These characteristics are consistent with the PIV results, which showed that flow separation clearly occurred at  ≤ 4 ∘ .When flow separation occurs near the airfoil, the fluid motion near the trailing edge becomes unsteady.Therefore, the amplitude of tip deflection in the cantilever beam is greater than in the case of attached flow.In the present study, when the DBD plasma actuator was activated and tangential jets were induced from / = 0.05,    was immediately reduced to less than 0.003 nm at every .This implies that flow separation was successfully mitigated.
In conjunction with the acquisition of Bragg wavelength shift data, the drag () and lift () forces were measured (Figure 11), using a three-component force balance system, under the same conditions as in Figures 6 and 10, in order to compare the results with those obtained using PIV and the FBG sensor.The standard deviations in  and  over 2.0 s were adopted as error bars under PA-ON and PA-OFF, respectively.It is remarkable that  decreased more than 20% and  increased by 200% to 300%, when flow separation was mitigated by the string-type DBD plasma actuator.With larger , the effects of flow control were reduced, though  and  were both slightly improved with the use of the stringtype DBD plasma actuator.Based on the results obtained in the open-loop control of flow separation, the string-type DBD plasma actuator used in this study is considered to be a promising device for mitigating flow separation under lower  conditions, and closed-loop control of flow separation is possible by setting a threshold value of    = 0.0028 for inducing the tangential jets.

Closed-Loop Control of Flow Separation around the NACA002 with Periodic Wall Oscillation.
To assess the effectiveness of the flow separation control system with DBD plasma actuator and FBG flow sensor, a demonstration of closed-loop control with periodic flow separation was   12(a) shows the flowchart for the closedloop control of flow separation conducted in the study.The wind tunnel side wall was periodically oscillated (back and forth) from 0 to 12 ∘ by a stepping motor at frequency   ≈ 0.42 Hz, which periodically promoted (or mitigated) flow separation over time.As reported in the previous section, flow separation was confirmed at  ≤ 4 ∘ when the pivoting wall was stationary.Figure 12(b) shows the  time-series, running    , , and  fluctuations for 10 s.The running    was a standard deviation of   , calculated for a sampling duration of Δ STD = 0.05 s in real time.Since the sampling frequency of   was   = 1kHz, the running    at a given time was evaluated using the past 50 values for   .Their parameters were found to vary periodically according to the wall oscillation, at approximately 2.4 s intervals, which was roughly compatible with 1/  .As with the stationary results (Figure 10(b)), it was considered that flow separation occurred in the region of  ≤ 4 ∘ , with dynamic movement of the side wall, because the running    in Figure 12(b) is larger than  = 0.0028.Figure 13 shows a series of instantaneous velocity distributions (1/3.75 ≈ 0.27 s intervals) measured by PIV, with periodic wall oscillation under PA-OFF conditions.It was also confirmed that the main flow was separated dynamically from the NACA0024 airfoil in sync with the wall oscillation.
In order to evaluate the flow separation control effects of the feedback system, tangential jets were induced from the exposed electrode of the string-type DBD plasma actuator for a certain duration (  ), once the running    crossed the threshold value shown in Figure 14(a).Although the flow conditions around the NACA0024 were slightly different with wall oscillation than those observed when the angle of the pivoting wall remained constant, due to the influence of largescale vortices on the wake flow,  = 0.0028 nm was adopted as the threshold for inducing tangential jets with the stringtype DBD plasma actuator.With the periodic wall oscillation shown in Figure 14(b), the lift and drag forces were measured in parallel with evaluation of the running    for Δ STD = 0.05 s. Figure 14(c) shows the time-series for  and  over 10 s, when the jets induced by the DBD plasma actuator were injected for Δ  = 0.3 s beginning when    crossed the 0.0028 threshold (dotted line).In the light-blue areas of Figure 14(c), 5 V DC (TTL) was inputted to the power supply, and a voltage of  - = 12.0 kV with   = 9kHz was applied to the string-type DBD plasma actuator (PA-ON).In comparison with Figure 12(b), we can see an overall reduction in the amplitude of    .In addition, it is remarkable that  increases immediately when    exceeds , and then    returns to below .On the other hand, the drag force shows little variation in comparison with the lift force due to the low initial values of .
The appearance probability (  ) of    ≥ 0.0028, defined as   = (data point numbers larger than )/(total measurement point numbers), was calculated as a parameter of the flow control effect.In the case of PA-OFF, it was estimated as   ≈ 0.39, in contrast to the value of   ≈ 0.12 for PA-ON, with Δ STD = 0.05 s and Δ  = 0.3 s (Figure 16).This indicated that flow separation was mitigated by 70% using this closed-loop control strategy, a result supported by the International Journal of Aerospace Engineering PIV analysis, as shown in Figure 15.Since the TTL signal was not outputted until a value of    ≥ 0.0028 was determined, flow separation occasionally occurred but was immediately mitigated by the jet injections.
Figure 15(f), for example, shows the velocity distributions just before flow control in response to flow separation being observed around the NACA0024.Only 1/3.75 s ≈ 0.27 s later; however, flow separation was immediately mitigated by feedback control (Figure 15(g)).As shown in Figure 16,   was evaluated for Δ  , varying over a range of 0.02 ≤   ≤ 0.5 s, in terms of two durations (Δ STD = 0.02 s and 0.05 s) used for calculating the running standard deviations in the Bragg wavelength.It was confirmed that flow separation was effectively mitigated by reducing Δ STD and increasing Δ  .In order to compare the flow control effect of the feedback system, open-loop control of flow separation was performed with periodic wall oscillation (Figure 17).Tangential jets induced by the string-type DBD plasma actuator were continuously injected over 3.0 ≤  ≤ 9.0 s.It is remarkable that the running    , as calculated for Δ STD = 0.05 s in real time, was clearly reduced to less than  = 0.0028 during PA-ON, and the lift force varied with the opposite phase of wall oscillation.In addition, the lift force values were significantly greater than those under PA-OFF.The velocity distributions with open-loop control of flow separation were measured using PIV (Figure 18), and it was found that the flows around the NACA0024 hugged the suction surface, with exception of the situation shown in Figure 18(a), where the velocity Based on the above results, it is considered that openloop control of flow separation is a promising method for mitigating flow separation under PA-ON conditions, in comparison with closed-loop control.However, the electric power required for operating plasma actuators can also be wasted since jets are injected even when the flow is hugging the airfoil.In this respect, feedback control of flow separation is more effective, because here the DBD plasma actuator operates only when flow conditions are determined to include flow separation.On the minus side, however, the flows around the airfoil occasionally separate (as shown in Figure 15(f)), because the system does not operate until flow separation is detected.The determinations of Δ STD and Δ  are additional technical issues.When Δ STD is greatly reduced, there is fear that the probability of erroneous determination will increase due to the detection of spiky noise in   and increasing Δ  will finally result in continuous operation of the plasma actuator and a corresponding increase in power consumption.Therefore, appropriate Δ STD and Δ  values should be chosen in response to actual flow conditions, such as the typical frequency and fluctuation band of flow separation.

Future Works on Feedback Control of Flow Separation for
Applying to Fluid Machinery.The feedback control of flow separation by means of string-type DBD plasma actuator and FBG flow sensor is a promising technology to realize enlargements of energy efficiency in fluid machineries which work in unsteady flow, as demonstrated by Jukes [23].For example, this technology is applicable for wind turbines because wind conditions change by the minute in the field.Since flow separations occur occasionally, the closed-loop control system has a beneficial effect on mitigations of flow separation.At present, we are developing to fit these technologies on a 1 kW-class wind turbine (Figure 19) in order to demonstrate a feedback control of flow separation in the natural environment.The copper wire coated with PTFE was attached to a cupper tape which was glued on the suction surface of the turbine made of a carbon-fiberreinforced plastic (CFRP).As shown in Figure 19, stringtype DBD plasma actuators was suitable for applying on 3D-shaped turbine blades although it was difficult in case of using conventional sheet-type DBD plasma actuators.By applying high voltages at radio frequencies, DBD plasma is found over the entire length of the wire as shown in Figure 19(c).It is suspected that CFRP has slight conductivity, but it is possible to prevent a short circuit because the metallic wire is previously insulated except for both free ends.This characteristic is an additional advantage of string-type DBD plasma actuators.
On the other hand, a FBG flow sensor will be constructed in the pressure surface side of turbine blade for constructing feedback control system.Therefore, a fiber optic rotary joint (FORJ), which can transfers a broadband laser and Bragg wavelength between the stationary location and FBG flow sensor, has been developed in conjunction with a power transmission system for controlling actuators from the stationary location.In our future works, quantitative evaluations of control effects will be carried out by using combining developed elements in the wind turbine system.algorithm (threshold, moving average scheme).In terms of control effect parameters, it was also confirmed that shorter duration for calculating the running standard deviations in Bragg wavelength (Δ STD ) and longer duration for inducing tangential jets (Δ  ) increased the likelihood of successful flow control, but it is necessary to optimize the control effect for energy efficiency.Finally, it is considered that closed-loop control of flow separation is promising for the significantly varying flow conditions typically found in fluid machinery such as aircraft and wind turbines.Therefore, in future, the proposed system will be tested under flow conditions simulating real-world environment.

2 InternationalFigure 1 :
Figure 1: Conventional sheet-type DBD plasma actuator.(a) Picture of sheet-type DBD plasma actuator; (b) an illustration of technical problems for use of sheet-type DBD plasma actuator in actual situations.

Figure 2 :
Figure 2: Basic structures and velocity distributions of string-type DBD plasma actuator designed by Segawa et al. [19].(a) One-directional tangential jet is induced by embedding a metallic wire coated with insulation materials in insulation material.(b) The surface itself can be chosen as the exposed electrode when the wire is attached on surface of conductive material.

Figure 3 :
Figure 3: Schematic illustration of experimental setup.The side wall of the test section near the airfoil suction surface is hinged at 400 mm downstream of the entrance and can be pivoted over a range of 0 ∘ ≤  ≤ 16 ∘ .

Figure 4 :
Figure 4: String-type DBD plasma actuator constructed in suction surface near the leading edge of NACA0024.

Figure 5 (
a) shows the electric circuit diagram, in which the plasma actuators (capacitance:  PA ) and an additional capacitor (capacitance:   = 22 pF) were connected in series.When voltages of  PA and   are applied to the plasma actuator and additional capacitor, the respective electric charges ( PA and   ) are equal:  PA =   =  PA  PA =     .Therefore,  PA can be evaluated in terms of   by measuring   , since   = 22 pF is known.The - Lissajous figure can be plotted by measuring  PA using a high voltage probe, and  PA is calculated as the product of   ×   , which is the area encompassed by the Lissajous figure, as shown in Figure 5(b).

Figure 5 :Figure 6 :
Figure 5: Power consumption evaluation ( PA ) of string-type DBD plasma actuator by means of - Lissajous method.(a) Electric circuit diagram; (b) - Lissajous figure by applying  - = 12.0 kV at frequency   = 9 kHz. PA is calculated as the product of   ×   .

Figure 7 :
Figure 7: Schematic diagram of strain measurement method by FBG sensor.

Figure 8 :Figure 9 :
Figure 8: Schematic illustrations of FBG flow sensor constructed in pressure surface of NACA0024.(a) An optical fiber is inserted in the inside of hollow NACA0024 airfoil.Detections of flow separation are tried by attaching the FBG sensor (b) on exterior surface of cantilever and (c) on interior surface of cantilever.

Figure 10 :Figure 11 :
Figure 10: (a)   fluctuations under PA-OFF and PA-ON which are detected by FBG sensor attached to interior surface of cantilever (Figure 8(c)).(b) Standard deviations of Bragg wavelength (   ) as a function of .

Figure 12 :
Figure 12: (a) Flowchart for the closed-loop control of flow separation.(b)  time-series, running    , , and  fluctuations for 10 s.The running    at a given time was evaluated using the past 50 values for   .Flow separation occurs in the region of  ≤ 4 ∘ when the running    is larger than  = 0.0028.

Figure 13 :
Figure 13: A series of instantaneous velocity distributions (1/3.75 ≈ 0.27 s intervals) measured by PIV, with periodic wall oscillation under PA-OFF conditions.The main flow was separated dynamically from the NACA0024 airfoil in sync with the wall oscillation.

Figure 14 :
Figure 14: Flow separation control effects of the feedback system under periodic wall oscillation.(a) Duration (  ) for inducing tangential jets from the exposed electrode of the string-type DBD plasma actuator, once the running    crossed the threshold value.(b)  variations under periodic wall oscillation.(c) Time-series for TTL,    , , and  over 10 s in case of Δ STD = 0.05 s.Jets induced by the DBD plasma actuator are injected for Δ  = 0.3 s beginning when    crossed . increases immediately when    exceeds , and then    returns to below .

Figure 15 :
Figure 15: A series of instantaneous velocity distributions (1/3.75 ≈ 0.27 s intervals) measured by PIV, with periodic wall oscillation under PA-ON conditions.Flow separation was mitigated by 70% using this closed-loop control strategy.

Figure 18 :
Figure 18: A series of velocity distributions with open-loop control of flow separation measured by PIV (1/3.75 ≈ 0.27 s intervals) with periodic wall oscillation.Flows around the NACA0024 hugged the suction surface, with exception of the situation under PA-OFF conditions (a), which is just before PA-ON.