[American Institute of Aeronautics and Astronautics 42nd AIAA Plasmadynamics and Lasers Conference - Honolulu, Hawaii ()] 42nd AIAA Plasmadynamics and Lasers Conference - Effect of

American Institute of Aeronautics and Astronautics

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Effect of Impulsive Plasma Discharge in Hypersonic Boundary Layer over Flat Plate

Yasumasa Watanabe1 and Kojiro Suzuki2 The University of Tokyo, Kashiwa, Chiba, 277-8561, Japan

The application of plasma discharge to hypersonic flow control methods has received a good deal of research attention in recent years. As a fundamental study for such methods, direct current plasma discharge in Mach-7 hypersonic flow over flat plate was investigated both with wind tunnel experiments and numerical analyses. Impulsive discharge in a boundary layer over flat plate caused a decrease in the wall pressure around electrodes. For the purpose of clarifying the principal cause of this phenomenon, a numerical analysis was conducted by solving the three-dimensional Navier-Stokes equations with impulsive energy addition to the flow. Numerical results revealed that the pressure oscillates in the vicinity of heated region, which suggests that the fluctuation of surface pressure observed in the experiment could be qualitatively explained as the unsteady response of the flow to the impulsive Joule heating by the discharge.

Nomenclature A = heated region E, F, G = convection terms Ev , Fv , Gv = viscous terms f (t, σ) = profile function for heating rate qJ = heat input per unit volume Qmax = maximum heating rate S = source term σ = representative time period for heating

I. Introduction ERODYNAMIC control is one of the major challenges in supersonic vehicle design. Especially in case of hypersonic vehicles that cruise at a very high speed, it is very important to equip with additional aerodynamic

control devices other than conventional ones such as flaps, in order to ensure redundancy and to enhance reliability during the flight.

Recently, a good deal of research attention has been focused on supersonic/hypersonic flow control using the interactions of plasma discharge with a flow investigation method of improving aerodynamic characteristics and of minimizing drag force1,2. Experimental and computational research by Shang et al.3 investigated method of reducing drag on blunt-nose bodies with plasma counterflow jet injection. Research by Leonov et al.4 focused on the manipulation of shock wave position in front of the air inlet of scramjet engines to improve engine efficiency. Numerical investigation of energy deposition that simulates plasma discharge was conducted by Kremeyer et al.5 and Bisek et al.6 to explore the effects of plasma discharge on aerodynamic characteristics of vehicle body. Hypersonic plasma actuator mechanism by means of glow discharge in the boundary layer was investigated by Shang et al.7 with experiments and computational analysis.

Conventional control surfaces such as flaps have several design constraints in case of hypersonic flights. In order to maintain maneuverability of the vehicle, flaps must be settled far away from the center of gravity. However, surfaces that stretch beyond the shock envelope will interact with the shock wave around the fuselage, eventually

1 Graduate Student, Department of Aeronautics and Astronautics, The University of Tokyo, 5-1-5 Kashiwanoha; [email protected], Student Member AIAA. 2 Professor, Department of Advanced Energy, The University of Tokyo, 5-1-5 Kashiwanoha; [email protected], Senior Member AIAA.

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42nd AIAA Plasmadynamics and Lasers Conference<br> in conjunction with the<br> 18th Internati27 - 30 June 2011, Honolulu, Hawaii

AIAA 2011-3736

Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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causing severe aerodynamic heating at the impingement area. Hence, the position of control surfaces is strictly limited so that they will not protrude from the body. Moreover, mechanically driven parts of flaps occupy significant space below the surface thereby consuming available volume inside the vehicle. In addition, mechanical parts also have small gaps near their hinges, causing undesirable aerodynamic heating that threatens the thermal protection system.

Aerodynamic control devices with plasma discharge are expected to be advantageous over mechanical control surfaces. Firstly, they do not have any moving parts and hence can avoid mechanical failure. Secondly, they will not protrude out of the surface because they can be settled even under the surface, and hence will not interfere with surrounding shock wave. Moreover, the response time of electric actuators is far less than mechanical devices. These actuators can offer (1) lift enhancement8, (2) steering moments9,10 and (3) flow separation control11. In light of these researches, plasma discharge is expected to be a promising candidate for an aerodynamic control device in hypersonic flow.

Although a great deal of research effort has been contributed to utilize plasma discharge as a hypersonic flow control method, plasma discharge phenomenon in high speed flow is not completely understood due to the complexity of the phenomenon (interaction of plasma with high speed flow and ablation gas) and the scarcity in opportunities for hypersonic wind tunnel experiments. Therefore, in this work, plasma discharge in hypersonic flow was investigated both with wind tunnel experiments and numerical analyses for the purpose of clarifying the essence of the phenomenon for the futuristic application as an aerodynamic control device. In the previous study, it was revealed that a steady arc discharge in a hypersonic boundary layer over flat plate can be qualitatively explained as an effect of Joule heating12. In hypersonic wind tunnel experiments, it was found that the pressure change due to surface plasma discharge is different between that in the steady discharge case and the unsteady one. In this study, an unsteady impulsive discharge in the boundary layer was investigated and compared with the results of steady case in order to understand the phenomenon. Here, research interest was focused on discharge phenomenon in flat-plate boundary layer because it is the simplest model that simulates the plasma discharge on the surface of hypersonic vehicles.

The objectives of this study are 1) to investigate the effect of impulsive direct current (DC) plasma discharge in the boundary layer with hypersonic wind tunnel experiments, 2) to numerically analyze the phenomenon to verify if it can be explained as an effect of impulsive Joule heating, and 3) to compare the results of steady and unsteady discharge.

II. Wind Tunnel Experiments

A. Outline of Wind Tunnel Experiment Hypersonic wind tunnel experiments were

conducted at Kashiwa Hypersonic and High-Temperature Wind Tunnel12, University of Tokyo. The captured view of the wind tunnel is shown in Fig. 1.

The detailed specification for the wind tunnel is shown in Table 1. The facility can offer a hypersonic flow of Mach number 7 and 8. The nozzle exit is 200 mm in diameter and its uniform flow core is 120 mm in diameter. The stagnation pressure is around 950 kPa and the stagnation temperature is 1000 K at maximum.

In this study, flow speed was set to Mach number 7. During the experiment, stagnation pressure of the uniform flow was about 950 kPa and the stagnation temperature ranged from 570 K to 610 K. The detailed experimental test conditions is shown in Table 2.

A flat plate model used in the experiment is illustrated in Fig. 2. Most part of the model is made of Bakelite®, whereas its central part in the vicinity of electrodes is replaced with fine ceramics, which prevents the gas injection from the flat-plate surface caused by the intense heating from the plasma. Two pairs of electrodes are settled at the center of fine ceramics. One at the downstream side, a pair of main electrodes, is used to generate plasma discharge and the other one at the

Figure 1. Kashiwa Hypersonic Wind Tunnel at University of Tokyo.


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upstream side, a pair of high voltage electrodes, is used to ignite and to stabilize plasma in the steady discharge experiment. The electrodes were made of an alloy of copper and tungsten (Cu: 30%, W: 70%) of 5 mm diameter for main electrodes in downstream side and of 3 mm for igniters in upstream side. The electrode in the upstream side was set to a cathode and the other one to an anode since, from the previous study12, this orientation was revealed to be preferable to obtain stable DC plasma discharge in this experimental setup.

A high current DC power supply (Matsusada, PR500-15) was connected to the main electrodes and the imposed voltage between electrodes was 500 V, which is used in both steady discharge experiment and unsteady discharge experiment. A high voltage DC power supply (Matsusada, HEOPS-10P2-LC) of 5 kV was connected to the high voltage electrodes (igniters) to stabilize plasma in the steady discharge experiment and it was not used in the unsteady discharge experiment. The pressure was measured at 4 pressure ports around the electrodes as illustrated in Fig. 2. Pressure measurements were conducted with an accuracy of 10 Pa using Kulite® XCEL-152-035 pressure sensors. Pressure data were captured on a data logger with a sampling rate of 100 samples per second. Flow visualization was carried out by means of Schlieren method with a high speed camera, Phantom® Miro® eX4, at 300 frames per second. A spectroscopic measurement was conducted in the steady discharge experiment using a Czerney-Turner type spectrometer (Hamamatsu, PMA-50) with an optical resolution of 0.40 nm in order to estimate the plasma temperature and to identify chemical compounds in the plasma, which will be explained in the appendix.

B. Experimental Results The results of the pressure measurement and the flow visualization are shown in Fig. 3 and Fig. 4 respectively.

Table 1. Wind tunnel specification. Mach Number 7, 8

Nozzle Exit 200mm dia. uniform flow core 120mm dia.

Stagnation Pressure Max. 0.95 MPa Stagnation Temperature Max. 1000 K

Unit Reynolds No. 1-2 x 104 (1/cm) Mass Flow Rate Max. 0.39 kg/s Test Duration Max. 60 sec

Reservoir 5 MPa(G), 4m3 (x1) Heater Pebble-Type City Gas Burner

Exhaust Vacuum Tank (7m dia.)

Table 2. Experimental test conditions.

Flow Conditions

Mach Number 7.0 Stagnation Pressure P0, kPa around 950

Stagnation Temperature T0, K 570-610

Power Supply Settings

Maximum allowable voltage, V 500 Maximum allowable current, A 6

Attack angle of the model, deg. 0

a), Geometry (in mm unit). b), Captured view. Figure 2. Flat plate model.


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(a) Pressure change due to steady discharge.

(b) Pressure change due to unsteady discharge. Figure 3. Pressure change induced by plasma discharge.

(a) Steady discharge experiment. (b) Unsteady discharge experiment. Figure 4. Schlieren picture.

Magnify

Separation shock


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In the experiment, the pressure around electrodes increased up to 40% in the case of steady discharge as illustrated in Fig. 3(a). Our previous study12 showed that this pressure rise is qualitatively explained as an effect of Joule heating, subsequent boundary layer separation and resulting separation shock wave (Fig.4(a)). In the case of the unsteady discharge experiment, a pulse discharge was observed three times as indicated in Fig. 3(b). Figure 3(b) also shows that the pressure around electrodes is affected by a pulse discharge and oscillates with an amplitude of 30 Pa at maximum, which is quite different from the steady discharge results. It should also be noted that the pressure decreases due to the pulse discharge. Figure 4 depicts a captured frame of the Schlieren video. Although the high speed camera captures each frame with 3.33-ms interval (300 frames per second), pulse discharge was captured only in one frame. Therefore, the duration of the pulse discharge was estimated to be much less than 3 milliseconds. This estimation doesn’t conflict with the fact that typical duration of pulse discharge with no flow environment is of the order of several ten nano-seconds to some ten microseconds.

In our previous experimental study12, it was clarified that steady DC discharge enhances the pressure around electrodes and the phenomenon can be qualitatively explained as an effect of Joule heating, whereas the cause of the pressure oscillation observed in the experiment with pulse discharge is not quite clear.

For the purpose of clarifying the main cause of the pressure change, a numerical analysis was conducted under the assumption that the principal cause was an impulsive heat addition from the Joule heating to the flow.

III. Numerical Analysis Computational analysis was conducted in order to investigate the dominant factor of the pressure change. In our

previous study12, it was revealed that the Joule heating plays the main role in the steady discharge phenomenon and the experimental result of the surface pressure change and the surface streamlines showed a good agreement with numerical results (Fig. 5).

In light of these results of the steady discharge analysis, it is expected that the unsteady discharge phenomenon

can also be explained as an effect of Joule heating. Therefore, a numerical analysis was conducted in order to verify whether the pressure oscillation in the experiment could be explained as a Joule heating effect.

A. Conditions for Computation Computational domain is illustrated in Fig. 6. Here, the domain is limited only to the right side of the flat plate.

A definition of coordinate axes is also depicted in Fig. 6 with the origin of the coordinate positioned at the center of

(a) Temperature contour on the plane normal to the surface and along the centerline.

(b) Pressure contour on the flat-plate surface (c) Comparison of surface streamlines and

boundary separation area Figure 5. Numerical results of steady discharge phenomenon.


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the flat plate, x axis aligned with the centerline of the surface and z axis settled normal to the surface. The domain under consideration is as follows:

0.06, 0.0 0( , , ) { .03, 00.05 .0 0.04[mm]}x y y zz x! ! ! ! ! !" # (1) A numerical analysis was conducted using three-dimensional Navier-Stokes equations with the source term of

energy addition that simulates Joule heating. In this analysis, in order to simplify the problem, it is assumed that the air is a perfect gas, and the gas is at thermal equilibrium at single temperature. However, the vibrational temperature estimated from the spectroscopic analysis is around 5800K (see the appendix) but the translational temperature is expected to be much less than this value. Numerical analysis results for steady discharge analysis reveals that the maximum temperature is around 1300 K (Fig. 5(a)) Therefore, it should be noted that the actual plasma discharge in the experiment is at non-equilibrium state and the numerical analysis conducted in this work is a very simple analysis in order to understand the essence of the phenomenon.

ˆ ˆˆ ˆ ˆ ˆˆ ( ) ( ) ( ) ˆv v vE E F F G GQ S

xt y z! " ! "!

+ +!

+!

! !=

"

! (2)

Q =

!

!u

!v!wEt

!

"

#######

$

%

&&&&&&&

, E =

!u!u2 + p

!uv!uw

(Et + p)u

!

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########

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%

&&&&&&&&

, Ev =

0! xx

! xy

! xzu! xx + v! xy +w! xz ' qx

!

"

########

$

%

&&&&&&&&

, S =

0000qJ

!

"

#######

$

%

&&&&&&&

(3)

Here, the expression of F or G are omitted but they follow a similar expressions as E . The time integration was made by second-order Runge-Kutta method, the spatial discretization was made by Yee’s Symmetric TVD scheme14 and second-order Central Difference scheme was applied to the discretization of viscous terms.

Conditions for the computation, including the uniform flow condition, were the same as the conditions in the hypersonic wind tunnel experiments. In the actual computation, an initial flow condition was calculated in advance as a flow field over a flat plate without energy addition. In the computation of this initial condition, first-order Matrix-Free Gauss-Seidel implicit time marching method15 was used instead of the second-order time-accurate Runge-Kutta method to save computational resource.

The number of grid points used in the computation was 180 points in x, 80 points in y and 80 points in z direction. The shape of a heat addition is defined as follows:

2 2 2

2 2 2 1.0 0.00 00 0.. ,x y za

y zAb c

! + + ! ! !" #$ $

= % &$ $' (

(4)

where 1.5mm, 1.5mm, 1.0 mma b c= = = (5)

Flow (M=7)

Electrodes

: Heat Addition

x

yz

0.05 mx = ! 0.06 mx =

0.0 my =

0.03 my =

0.0 mz =

0.04 mz =

a), Definition of coordinate. b), Computational grid. Figure 6. Computational domain.


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Here, the heated region A is concentrated at the origin of the coordinate axes because it was revealed, from the past study12, that the result with a concentrated heating region can show a good agreement with the experimental results in the steady state discharge.

The heating rate per unit volume is defined as follows:

) ( , , )

0 ( ,

(

, o or 7

,

) r

m

A

ax

J

x y z A

x y

Qf t

z t

dV

A

q

t

σ

σ σ

⎧∈⎪

⎨⎪

∉ <

=

>⎩

∫ (6)

where Qmax, the maximum heating rate, is obtained by accumulating qJ in the region A. The integral term in Eq. (6) indicates the volume of the region A, and the function f (t, σ) is a profile function for the heating rate. In this study, this function is defined as a Gaussian-like distribution function, namely:

2

2( )) exp,2

(f tt µσ

σ⎡ ⎤−

= −⎢ ⎥⎣ ⎦

(7)

where σ , a deviation of the distribution function, is a representative time period for heating and µ is a certain time when the profile attains a maxima. Here, µ is set to 4σ.

The schematic of the profile function in Eq. (7) is illustrated in Fig. 7. As a typical duration of pulse discharge is around several ten nano-seconds, the representative time σ was set as

in Table 3, and the settings for maximum heating rate Qmax are also shown in Table 3. Here, the total amount of energy addition is 2.5 x 10-3 J in Case 1 and Case 3 whereas in Case 2, the total energy

is 2.5 x 10-4 J and in Case 4, 2.5 x 10-2 J. During the time marching in each case, pressure values were monitored at 16 points, P1 to P16, in the vicinity of heated region. The exact position of each point is illustrated in Fig. 8. The pressure port #1, #2, #3 and #4 in the experiment corresponds to P5, P10, P11 and P13 respectively.

1f(t,σ)

start heating(t = σ)

stop heating(t = 7σ)

max. heating rate(t = 4σ)

00 4σ t

X

Y

P1 P2 P3 P4 P5 P9 P13 P14 P15 P16

P6 P10P7 P11

P8 P12

X[m]

Y[m]

-0.04 -0.02 0 0.02 0.04 0.060

0.02

0.04

Pressure monitoring point with 3 mm interval in y direction

Pressure monitoring point with 3 mm interval in x direction

Figure 7. Heating profile in time. Figure 8. Pressure monitoring points.

Table 3. Parameter settings. σ, ns Qmax, W

Case 1 100 1000 Case 2 10 1000 Case 3 10 10000 Case 4 10 100000


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B. Results of Numerical Analysis In all cases in Table 3, at the heated region, shock waves were generated and gradually changed into

compression waves. The waves propagated to every direction. The wave propagation speed was larger in the downstream direction. However, the wave stopped moving in the upstream side due to a high speed flow in a boundary layer. The schematics of the wave propagation in case 1 are shown in Fig. 9 with pressure contour diagrams. Here, red arrows indicate the approximate positions of the wave front, i.e. the frontal point of pressure gradient propagation, at the downstream side.

As a result of the occurrence of shock or compression wave, the fluctuation and the decrease in pressure

distribution is induced in the area close to the heated region. The aerodynamic explanation for this pressure decrease is as follows: (1) The temperature of rapidly heated air increases and the subsequent pressure rise occurs and (2) the air suddenly expands and strong density gradient, and shock wave, is formed and propagates in every direction in order to relax the severe density gradient. (3) At a certain point, the large density gradient is relaxed and the pressure and the density gets back to their original value (4) but the shock wave or compression wave keep moving and come to the state of overrelaxation where the pressure can be less than its original value. This imbalance in pressure distribution propagates in the downstream direction as time passes, which could cause time-dependent surface pressure oscillation. In order to see the phenomenon more precisely, the pressure change at each pressure monitoring ports presents some important facts.

Figure 10 shows a pressure change at some selected monitoring ports at which the pressure changed significantly. From Fig. 10, it was revealed that 1) Pressure oscillation can be observed at almost every port in every case. 2) Pressure decreases at some ports in every case, even 70 Pa less than the pressure observed without heating. The pressure change in case 2 along the centerline of the flat plate (corresponding to x-axis) in time is shown in Fig. 11, from which it is clear that the pressure oscillation propagates in downstream side. This oscillation of pressure is probably due to the propagation of pressure perturbation induced by the heating. From Fig. 10, it is also clear that the pressure change attenuates quickly but the time required to attenuate to certain amplitude strongly depends on the parameter σ. The approximate time required for pressure attenuation down to 100-Pa amplitude is shown in Table 4. It should be noted that the heating duration in case 1 is 10 times longer than that of case 2 to 4 and the attenuation times are almost the same in cases 2 to 4. Therefore, the result suggests that the duration required for attenuation depends on the heating time σ but does not depend on the total amount of energy. The time required to

Figure 9. Wave propagation and pressure contour diagrams.

t = 478 ns t = 2.48 µs t = 4.30 µs

t = 7.07 µs t = 11.6 µs


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attenuate is considered to be strongly related to the wave propagation speed. Therefore, the wave speed at the point: x = 3 mm, y = z = 0 mm was estimated from pressure contour. The results are shown in Table 5. Here, the heating time period is the same in cases 2 to 4 but only the total heating energy is different (as shown in Table 3) and the wave speed increases with the increase of the total heating energy. In cases 1 and 2, the heating duration is different and the heating amount is the same, but the wave speed is much larger in the case 1. Therefore, as expected, the wave speed depends not only on the parameter σ, the representative heating duration, but it also depends slightly on the total amount of deposited energy. In case 1, the wave propagates at a supersonic speed. This is because the fluid is heated for a longer duration compared to the other three cases thereby enhancing the wave propagation speed with a high pressure ratio.

In every case, the pressure value at port P9, the one positioned just downstream of the heated area, behaves significantly higher compared with other ones. Hence, the maximum pressure values at P9 were compared in Fig. 12. From Fig. 12, it was shown that the maximum pressure strongly depends on the total amount of deposited energy whereas it is concluded that, by comparing the values of Case 1 and Case 3, the maximum pressure does not depend on the parameter σ.

a), Case 1 b), Case 2

c), Case 3 d), Case 4 Figure 10. Pressure change at each monitoring port.


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Table 4. Wave attenuation time.

Approximate Time required to Attenuate, microsecond

Case 1 20 Case 2 150 Case 3 150 Case 4 150

Table 5. Wave speed at x = 3 mm.

Propagation Speed, m/s

Approximate Propagation Mach

Number

Case 1 951 1.5 Case 2 65 0.18 Case 3 104 0.23 Case 4 249 0.39

(a) Pressure change with constant heating energy. (b) Pressure change with constant heating time. Figure 12. Maximum pressure at port P9.

Figure 11. Pressure change in time along the centerline(Case 2, x-t-P diagram).


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These results indicate that 1) Maximum pressure observed just downstream of heated region depends on the total amount of deposited energy

Qtotal but not on the heating duration σ. 2) The time required for the attenuation depends on σ but not on Qmax. 3) The wave propagation speed at downstream side strongly depends on σ and slightly depends on Qmax.

Numerical results suggest that the pressure around electrodes can decrease due to an aerodynamic effect without

considering any magnetohydordynamic effects. In the wind tunnel experiment, the pressure decrease persisted for about 1 second whereas the duration of pressure change suggested by the numerical results is less than 150 microseconds. However, in the experiment, there existed the pressure pipe of about 10 cm long that connects the pressure ports and corresponding pressure sensors. It would be possible that the actual pressure signals at each port are averaged and there are some time delays that prevent the time-accurate pressure measurements. Therefore, the pressure change observed in the numerical results suggests that the pressure oscillation in the experiment could be the effect of impulsive heating to the flow.

IV. Conclusion Hypersonic wind tunnel experiments and numerical analyses were conducted to investigate the effect of pulse

discharge in a hypersonic boundary layer over flat plate. The experiments showed that in the region close to electrodes and just after the pulse discharge, the pressure oscillates with an amplitude of 30 Pa at maximum. For the purpose of exploring the principal cause of the pressure change, a numerical analysis was conducted with heat addition to Navier-Stokes equations that simulates Joule heating effect to the flow. As a result of the analysis, it was revealed that the shock wave is generated due to the impulsive heating. The generated wave propagates in the downstream direction, which causes the pressure oscillation. Numerical results also suggest that the pressure decrease observed in the experiment could be the effect of Joule heating to the flow.

Appendix Spectroscopic measurement was conducted to evaluate the vibrational temperature of nitrogen molecules using

spectrum-fitting method. In this method, plasma discharge was assumed to be thermal nonequilibrium, composed only of nitrogen molecules. In order to calculate the theoretical spectra, SPRADIAN code16 was employed. A measured spectrograph is shown in Fig. 13 and the fitting result is shown in Fig. 14.

The vibrational temperature was estimated to be around 5800K. In the experiment, the plasma in hypersonic flow

with low static pressure is expected to be at thermal nonequilibrium state, and hence its translational temperature is considered to be much less than the measured vibrational temperature.

Figure 13. Spectrogram of plasma. Figure 14. Spectrum fitting result.


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References 1Shang, J. S., Surzhikov, S. T., Kimmel, R., Gaitonde, D., Menart, J., and Hayes, J., “Mechanisms of Plasma Actuators for

Hypersonic Flow Control,” Progress in Aerospace Sciences, Vol. 41, No. 8, 2005, pp. 642–668. 2Fomin, V. M., Tretyakov, P. K., and Taran, J.-P., “Flow Control Using Various Plasma and Aerodynamic Approaches,”

Aerospace Science and Technology, Vol. 8, No. 5, 2004, pp. 411-421. 3Shang, J. S., Hayes, J., and Menart, J., “Hypersonic Flow over a Blunt Body with Plasma Injection,” Journal of Spacecraft

and Rockets, Vol. 39, No. 3, 2002, pp. 367-375. 4Leonov, S., Bityurin, V., Savelkin, K., Yarantsev, D., “Effect of Electrical Discharge on Separation Processes and Shocks

Position in Supersonic Airflow,” AIAA Paper 2002-0355, 2002. 5Kremeyer, K., Sebastian, K., and Shu, C.-W., “Computational Study of Shock Mitigation and Drag Reduction by Pulsed

Energy Lines,” AIAA Journal, Vol. 44, No. 8, 2006, pp. 1720-1731. 6Bisek, N. J., Boyd, I. D., Poggie, J., “Numerical Study of Plasma-Assisted Aerodynamic Control for Hypersonic Vehicles,”

Journal of Spacecraft and Rockets, Vol. 46, No. 3, 2009, pp. 568-576. 7Shang, J. S., Kimmel, R. L., Menart, J., and Surzhikov, S. T., “Hypersonic Flow Control Using Surface Plasma Actuator,”

Journal of Propulsion and Power, Vol. 24, No. 5, 2008, pp. 923-934. 8Menart, J., Stanfield, S., Shang, J., Kimmel, R., and Hayes, J., “Study of Plasma Electrode Arrangements for Optimum Lift

in a Mach 5 Flow,” AIAA Paper 06-1172, Jan. 2006. 9Gnemmi, P., Charon, R., Dupéroux, J.-P., and George, A., “Feasibility Study for Steering a Supersonic Projectile by a

Plasma Actuator,” AIAA Journal, Vol. 46, No. 6, 2008, pp. 1308–1317. 10Gnemmi, P., Rey, C., “Plasma Actuation for the Control of a Supersonic Projectile,” Journal of Spacecraft and Rockets,

Vol. 46, No. 5, 2009, pp. 989-998. 11 Menart, J., Stanfield, S., Shang, J., Kimmel, R., and Hayes, J., “Study of Plasma Electrode Arrangements for Optimum Lift

in a Mach 5 Flow,” AIAA Paper 06-1172, Jan. 2006. 12Watanabe, Y., Imamura, O., Suzuki, K., “Effects of Plasma Discharge on Hypersonic Flow over Flat Plate,” AIAA Paper

2010-4761, 2010. 13Kashiwa Wind Tunnel Working Group., “UT-Kashiwa Hypersonic and High-Temperature Wind Tunnel,” URL:

http://daedalus.k.u-tokyo.ac.jp/wt/wt_index.htm [cited 10 July 2008]. 14Yee, H.C., A class of High-Resolution Explicit and Implicit Shock-Capturing Method, Von Karman Institute for Fluid

Dynamics Lecture Series, 1989-04. 15Shima, E, “A Simple Implicit Scheme for Structured/Unstructured CFD”, 29th Fluid Dynamics Conference/Aerospace

Numerical Simulation Symposium, Paper No. 2C9, pp.325-328, 1997. (in Japanese) 16Fujita, K., Mizuno, M., Ishida, K., and Ito, T., “Spectroscopic Flow Evaluation in Inductively Coupled Plasma Wind

Tunnel,” Journal of Thermophysics and Heat Transfer, Vol.22, No.4, pp.685-694, (2008).

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[American Institute of Aeronautics and Astronautics 42nd AIAA Plasmadynamics and Lasers Conference - Honolulu, Hawaii ()] 42nd AIAA Plasmadynamics and Lasers Conference - Effect of