INVESTIGATION OF AN UNDERCRITICAL MICROWAVE DISCHARGE IN AIR FLOW NEAR A BODY AND ITS INFLUENCE ON THE AERODYNAMICS OF THE BODY

Igor I. Esakov, Lev P. Grachev and Kirill V. KhodataevMoscow Radiotechnical Institute RAS, Moscow, Russia

khodata@online.ru

The influence of an energy input to the supersonic flow around a body by means of a microwave discharge has been investigated experimentally and theoretically. The energy input is provided by an attached undercritical microwave discharge operating in a continuous mode. An attached undercritical microwave discharge is initiated at the end of a vibrator placed into a supersonic M=2 air flow. In full accordance with the earlier theoretical predictions, an energy input upstream of the bow shock wave leads to a decrease in the drag force of a blunt body with good efficiency. The experimental and theoretic investigations carried out provide a positive answer to the principal question concerning the possibility of changing the aerodynamic characteristics of a body in a supersonic flow by means of an energy input. The most effective influence can be provided by a microwave discharge because only this type of discharge is able to add energy upstream of the bow shock wave. Numerical models of these processes have been developed and reflect the main features of the experimental results. These numerical models are being used to assist in the interpretation of the experimental results.

Introduction

The rich experience of experimental and theoretical investigations of different types of electric discharges in comparatively high-density gases, performed in Russia, show that electric discharges are able to influence significantly gas dynamic processes.1,2,3,4,5

From the very beginning the main hopes were devoted to microwave (MW) discharges because: 1) they have a good ability to absorb MW energy compared to other kinds of discharges and 2) they can be created without electrodes at any point away from a source by means of a focusing of the MW radiation. Unfortunately, the technology for creating electrodeless discharges is much more expensive, so the majority of experiments on the discharge plasma influence on a gas flow had been performed with usage of the direct-current discharges or high-frequency electrode discharges.

Now, a set of new experiments has been carried out on the investigation of electric discharge plasma in flow action on the aerodynamics of the flown around bodies with usage of the electrode discharges.6,7 The cited experiments have shown the same opportunity to change a state of a gas flow near a body and of aerodynamic forces acting on it. It was found out that these changes at relatively high air density are connected mainly with air heating by the discharge plasma. Application of such method of interaction for solution of real applied problems poses at least two questions. The first question concerns the location of the heat source with respect to the flying vehicle in order to achieve a required

result? And the second is how to most effectively realize the energy addition in the required location?

The first question is a purely gasdynamic one and its answer can be determined within the framework of conventional gas dynamics. Many theoretical investigations have been performed on heat energy input into flow for influencing the drag force on a body in supersonic flow. In particular, the idea of a “hot air spike” has been investigated theoretically. The most representative reviews of these theoretical studies can be found in references8,9. It was determined that:

1) Energy input between bow shock and body surface leads to a small drag force decrease with a poor efficiency3 and

2) Energy input upstream of the bow shock is able to strongly decrease the drag force with very good efficiency.

If the energy input channel is quite thin relative to the body radius, the decrease in aerodynamic drag coefficient Cx can be very significant in supersonic flow. This effect is stronger at higher Mach number. Thus, one sees that a thin hot channel is able to strongly change the structure of the flow around a body.

The second practical problem is very difficult to solve with the application of discharges from electrodes. It can be solved only with application of a gas discharge created by focused radiation, particularly, by MW radiation.

The experiments using discharges from electrodes with direct current or HF sources confirm the theoretical predictions based on the thermal nature of discharge influence.10,11,12 In these cases it is impossible to realize high efficiency of electric

41st Aerospace Sciences Meeting and Exhibit6-9 January 2003, Reno, Nevada

AIAA 2003-529

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energy input into flow, since the region of energy input can’t be created upstream of the shock.

The MW discharge is studied quite well to-day.13,14,15,16,17,18,19,20,21 It is clear now that the MW discharge is most suitable for the goals of plasma aerodynamics since it can be realized in the required location of the flow field near a flying vehicle. It absorbs energy of electromagnetic wave with good efficiency at known conditions, and its location can be electronically controlled.

Experiments have shown that the MW discharge in a streamer form with a developed structure can exist in an electromagnetic (EM) beam even if the level of the field is below the critical value. This type of discharge (undercritical, or loose, discharge) can be initiated by a creation of the breakdown conditions locally (for example by means of resonant metallic vibrator – thin wire with length about half wave-length of radiation).22 This undercritical discharge is possible at a gas pressure of hundreds of Torr. The undercritical MW discharge consists of constantly forming, growing and branching streamer channels. Their typical velocity of growth is 106 cm/s. The creation of such a discharge in a supersonic gas flow does not change its properties relative to that observed for discharges in immovable gas.23

A streamer undercritical MW discharge loses the capability to spread from the initiation point when the undercriticality level is expanded (i.e. lower field strength). A discharge that cannot spread from the initiation point is referred to as an attached (deeply undercritical) discharge. This discharge exists near the edge of the initiator where the MW field is overcritical locally. An attached MW discharge also dissipates EM field energy well and can be sustained in a supersonic gas flow.24 In Fig.1 a photograph is provided of an attached discharge initiated by a vibrator in a supersonic flow with a velocity of several hundred meters per second.

Fig.1. The attached (deep undercritical) streamer MW discharge at a vibrator’s tip in the supersonic flow. The supersonic flow is directed from right to left. Upper - photo of real discharge, bottom – calculated view of the discharge for the same conditions. Pdischarge ≈ 500 W, Vjet= 530 m/s.

This type of discharge creates the thin very hot channel with a diameter on the order of millimeters. The attached MW discharge has many areas of

application, but relative to the subject problem the following is important to note. The usage of attached MW discharge allows:

1) One to perform the experimental verification of the theoretical predictions concerning to the influence of energy input upstream of a bow shock in a supersonic stream; and

2) Because the diameter of the energy deposition zone is comparatively small, the experiment can be run without using an expensive large wind tunnel.

The task formulation

The goals of the undertaken experiments consist in experimental study of the influence of a MW discharge generated plasma on the aerodynamic flow around bodies. Experiments were carried out with the creation of a MW discharge in front of the bow shock wave.

Fig.2. Experimental scheme of ignition of attached (deeply undercritical) MW discharge upstream of a bow shock wave.

The experimental scheme is presented in Fig.2. During these experiments, the total drag force acting the model is measured, so its values in the presence of a discharge and in its absence can be compared. These results are used for a check against the theoretical calculations.

In the experiment, the supersonic stream was created using the jet produced by a Laval nozzle operated in the flooded jet regime. The peculiarity of this type of jet is that its diameter are enough large for experiment, although much less than the length of the jet and of the sizes of the test chamber.

Experimental setup

To realize the experiments, modeling of the influence of the MW discharge on the characteristics of a supersonic flow around bodies, at a small power level, and that is accessible in real laboratory conditions, has resulted in the necessity of using a flooded supersonic jet. The supersonic flow from the Laval nozzle is kept from expansion not by walls of the channel of a conventional wind tunnel, but by the pressure of ambient gas filling the test chamber. The remoteness of walls of the chamber from test area

enables a flow of the MW radiation to penetrate freely into the flow and to couple to the initiator and discharge plasma.

The scheme of the setup is presented in Fig.3. The gasdynamic portion of the setup consists of a test chamber 1, intermediate section 7 with diffuser 6, receiver 8 and pumping equipment 9. The test section 1 is constructed using a metal cylinder 0.7 m in diameter and 1 m length with flat ends. Round windows with flanges are located on the side of the test chamber. Two of them are closed by the quartz glasses for an observation of processes inside the chamber. The chamber's internal surfaces are covered by MW absorbers. The diffuser 6 connects the test chamber 1 with the intermediate section 7 and the receiver 8. The whole volume of the vacuum part of the setup is 4.5 m3. The Laval nozzle 4 and the diffuser 6 are placed horizontally along the test chamber's axis at its opposite flanges. The supersonicflooded jet 5 is created by the leakage of room air through the Laval nozzle 4 into the test chamber 1 after opening the controlled valve 2.

Prior to every test, the test section volume is pumped out to an initial pressure that is equal to the desired static pressure of jet at the nozzle’s outlet.

The diffuser connecting the test chamber with a receiver represents a tube with internal diameter 7 cm and 70 cm length. In the front part it comes to a cone of 22 cm and maximum inlet diameter of 14 cm. The diffuser can move along the system's axis and can be mounted at different distances from the outlet of the Laval nozzle in the range 5 – 50 cm.

Fig.3. Scheme of the setup. 1- test chamber, 2 – inlet valve, 3 – compounding section, 4 –Lavale’s nozzle, 5 – supersonic flooded jet, 6 –diffuser, 7 – intermediate section, 8 – receiver, 9 – pumping system, 10 – MW generator, 11 –radiating horn, 12 – initiating vibrator, 13 –model.

The system forms an almost homogenous flooded jet with parameters: flow velocity Vjet=528 m/s, density ρ=0.228⋅ρatm, temperature T=0.553⋅Tatm (150 K), static pressure pstat=0.126⋅patm (96 Torr), Mach number M=2.01, jet radius b=1.5 cm, jet length L=50 cm. The equality of the static pressure volumes in jet

and of in the test chamber can be sustained for a test duration of 1-2 s.

The MW discharge part of the setup consists of a MW generator 10, the device for its feeding and the waveguide tract ended by a horn 11.

The main element of the MW source is a magnetron with generated wavelength 12.5 cm. The waveguide outlet has a cross-section 4.5х9 cm2. The output power was calibrated using a calorimetric load (while operating in a continuous mode) and can be controlled in the range of 0.38 - 2.64 kW. The operating system can change the time duration of generation from fractions of a second to continuous operation.

The horn outlet is located 9 cm from the axis of the stream forming the MW radiation, which crosses the stream's axis perpendicularly. The axis of the MW radiation is located at a distance of 6.5 cm downstream of the outlet of the Laval nozzle. The vector of the electric component of the radiation is parallel to the stream's axis.

A photo of the central part of the test chamber is presented on Fig.4.

Fig.4. The central part of the test chamber. 1 –Laval nozzle, 2 – receiving diffuser, 3 –overflowed model, 4 – initiating vibrator, 5 –MW horn, 6 – absorber of a MW radiation, 7 –pressure tube measuring the static pressure in the chamber, 8 – inlet of the balance, 9 – vibrator support.

During the experiments the following characteristics are measured: static pressure at the outlet of the Laval nozzle рstat, air pressure in the test chamber pc, stagnation pressure of the flow at varying distances from the outlet of the Laval nozzle

pstag, stagnation temperature of a flow at different

cross sections Tstag, and the drag force F acting on a model placed into the flow downstream of and on the axis of the discharge wake. All these quantities can be measured as functions of time t starting from themoment of the opening of the valve. In addition, the absolute pressure value pc is measured using a manometer in stationary conditions with an accuracy

±1.5 Torr. The manometer measurement is used for the absolute calibration of the dynamic gauges for pc, pstat and pstag.

The dynamic gauges for the pressure measurements consist of a tube and membrane inductive sensor. The membrane inductive sensor are used as the basis of the dynamic gauges measuring pc, pstat, pstag and F. It is constructed from two closed volumes separated by a membrane. The inductive sensor reacts to the difference of forces acting on the opposite sides of the membrane, which leads to its deflection. The deflection changes the inductance of the arms of the electrical bridge. The signal from the bridge is recorded by an oscilloscope with memory. For measurements of pressure the volume on one side of the membrane is connected to the room atmosphere and other side is connected to the pressure tube. The tube is made of copper with internal and external radii of 0.11 cm and 0.14 cm, respectively. The probe is mounted on a three-coordinate positioning table, so measurements can be made in the stream's cross section and along its axis.

For the measurement of F both volumes of the inductive sensor are vented to the chamber pressurepc, but one side of the membrane is loaded with the measured F. The scheme of the bridge is balanced at F = 0.

For measuring the stagnation temperature Tstag a chromium-capel thermocouple sensor is mounted on the same positioning table in the absence of the pressure tube. The thermocouple is inserted into the same copper tubing used for the pressure measurements. The thermocouple wires are isolated from the tube. The working junction is located in an opening at the outlet end, which is directed towards the flow.

One component balances are located in the inlet cross section of the moveable diffuser. Models placed in the flow are mounted on the balances. All gauges are calibrated with a quite high accuracy.

The flooded jet

A flooded supersonic jet is a quite complicated object, whose behavior depends on many factors. During this experiment the stagnation pressure pstag(t) was measured along the axis of the supersonic stream at different axial locations downstream for the Laval nozzle outlet. Measurements were carried out in two locations: at the point of the crossing of the supersonic stream axis with the MW beam axis (where the initiator of the MW discharge can be located) and at the point where the front edge of the model in experiments is located when investigating the influence of the MW discharge upstream of the bow shock. In the experiments the dependence pc(t) was measured simultaneously with pstag(t). The measurements have shown that the characteristics of the submerged supersonic stream in the test region at pc ≈ pstat differ

little from the characteristics in the outlet plane of the Laval nozzle over a time period of a couple of seconds (< 10%).

The differences between the values of the stagnation pressure measured at different locations along the flow and those calculated for an equilibrium flooded jet are quite small.

The internal parameters of the streamer discharge, which define the ignition ability of the discharge, are very difficult to measure. The correct interpretation of the measurement results for the influence of the gas discharge on the aerodynamics of a body in a supersonic flow needs the complete knowledge of the parameters of the unperturbed flooded jet. With this purpose, numerical experiments were also carried out to complement the measurements described above.

n

0 5 10 150

2

4

6

Fig.5. Lines of equal density of the jet in the test region at air pressure in the chamber 60 Torr.

The numerical modeling is carried out using the known system of hydrodynamic equations for a perfect gas with parameter γ = 1.4 using the assumption of azimuthal symmetry and steady state flow.

Fig.6. The calculated longitudinal distribution of stagnation pressure at the jet axis versus air pressure in the test chamber. The air pressure values pointed near curves. The axial distance begins at the nozzle outlet.

Artificial viscosity was used to obtain a continuous solution. The theoretical distributions of the jet parameters at the nozzle outlet, for the

experiment conditions, were used as the boundary conditions.

In Fig.5 the typical spatial density distribution of the supersonic jet injected into the air is shown for a case when the chamber pressure is less than the static pressure of the jet at nozzle outlet. One can see a system of oblique shocks creating the strong variation of a density in the jet. However, the modeling shows that the flooded supersonic jet is quite homogeneous if the surrounding air pressure in the test chamber is about 70-110 Torr, which is approximately equal to the static pressure in the jet at the nozzle outlet (see Fig.6).

Although the nozzle increases the chamber pressure about 15 Torr/s, the jet produces almost homogeneous flow suitable for accurate measurements of the MW discharge influence on model aerodynamics during 1-2 s, which is quite enough for measurements.

The measurements have confirmed the flooded jet operation (see Fig.7).

Fig.7. The dependence of the stagnation pressure on the jet’s axis on the air static pressure in the test chamber. The measured pstag in nozzle’s outlet – dashed line, the measured pstag

at 10 cm from nozzle’s outlet – solid line, pstag at the same point calculated by modeling – solid line with circles, pstag, estimated by Raleigh’s equation – dotted line.

The attached MW discharge in supersonic flow

Based on preliminary experiments and after tests of several vibrator variants, we used in the key experiments the vibrator design that one can see in Fig.1 and Fig.4. The vibrator is integrated into single unit with the fastening bar. Its main part is made of duralumin. The vibrator is rounded at the upstream end with respect to a flow. At the downstream end (away from the Laval nozzle) it has a changeable core. The core is shaped like a sharpened cylinder and is made from nickel-chromium alloy. A core is

tightly inserted into the main body of a vibrator. After burning, the core can be either sharpened again or changed. The streamlined fastening bar is perpendicular to the vibrator axis and is attached in the middle of its length.

The experiments show that the attached discharge can be created in the supersonic jet at the given generator’s power on the back top of the initiator only. The forward top of the vibrator is blunt and correspondingly the electric field on this top is less than the field on the thin back top.

The discharge emission in the photo in Fig.1 is in general recombination radiation, a result of the dissociative recombination. It is seen that the bright region is saturated over its length. The brightest light comes from the top of the vibrator. It is clear that recombination is a maximum in the region with high electron density. At conditions of this process, it partly corresponds to high conductivity where the MW current can exist.

For better understanding of the attached MW discharge, a theoretical model was developed. Earlier modeling of a MW undercritical discharge was developed for static gas.25 The models for undercritical and deep undercritical discharges in a supersonic flow are described in Ref.26,27. The formulation of the current task is the following. The nonsymmetrical vibrator is placed into the supersonic homogeneous flow along its direction. The forward top of the vibrator is blunt and the back top is thin, so the deep undercritical discharge will be created on back top of the vibrator. The influence of the vibrator on the flow is neglected because the vibrator is very thin. The parameters of the flow correspond to the experimental values.

The calculated temporal evolution of the electric field amplitude distribution along the system axis after the MW radiation is initiated is shown in Fig.8. One can see the field rising at the ends of the vibrator.

Fig.8. The spatial-temporal distribution of electric field amplitude |E|/Ecr atm along the vibrator’s axis. The directions of axis z and of the flow velocity are the same. The initiating vibrator is located between –5.95 cm and 0 cm.

After switching on the MW radiation, a high amplitude electric field arises at the ends of the vibrator. Because the forward end is blunt but the

back end is sharpened, the maximum field at the back end is more than that at forward end, and it exceeds the critical field value. The MW discharge starts at the back end of the initiator. The discharge plasma then flows downstream. The distance of it propagation is limited by plasma decay. The MW field at its far edge is less than the critical field strength and it is not able to ionize air. Ionization only takes place near the back end of the initiator, which means that the discharge can be classified as deep undercritical (or attached).

The field in the region near back end of the vibrator irregularly flashed because the discharge at this place is sparkling and the ionization coefficient is strongly varied. The flow sweeps the ionized air from the vibrator's end so that the conductivity is low at this moment here. The MW conductive current can’t be broken, so the electric field sometimes rises at the end. The peak values of electric field amplitude exceed the critical value so those are high enough for ionization. The summary frequency of ionization, attachment and recombination is positive only near the end of the vibrator.

The second maximum of the electric field moves initially with the boundary of the conducting area. The distance between vibrator’s end and the location of maximum conductivity is approximately 0.5 cm. The plasma boundary, which is defined as the place where the electric conductivity equals to ω/4π (ω -the MW field frequency, s-1), does not move farther than 3-5 cm from vibrator’s end.

Because the overall length is rising, the system comes out of the resonance condition (it follows from the current argument going from zero to ~π/4). This is one of the reasons for the limiting of the MW current. Second reason, main, is the low conductivity of the discharge plasma (compared with metal) and the related ohmic losses. These losses include heating the ionized gas and creating the hot channel.

Fig.9. The total power of the ohmic losses in the plasma Pdischarge related to the power of the MW generator Pgenerator.

The calculations show that a significant part of the MW power is utilized by the discharge and goes into the gas heating (see Fig.9, where a sample calculation is presented). The radiation losses are negligibly small for this discharge. The boundary between the heated channel with low air density and high temperature gas moves moving downstream with the flow.

One of the important peculiarities of the deep undercritical discharge is the tendency to a relaxation instability at relatively low frequencies. If the length of the conducting part of the channel achieves a half wavelength, the local value of the current at vibrator’s end is nearly zero. At this condition the high values of electric field will not rise for low local conductivity and the discharge blows out. When the ionized gas flows far away from the vibrator, the process starts again. This peculiarity, observed sometimes in experiment, needs further complementary investigation.

The simulation provides the possibility to define a simplified model for the heat source and air mixing for adequate gas dynamic calculations and to formulate the task of the creation of a hot channel in the supersonic flooded jet.

The discharge influence on the jet

The stagnation pressure downstream of the attached MW discharge was measured by means of the pressure tube. A photograph of the discharge in the presence of the pressure tube is shown on Fig.10.

Fig.10. Measurement of the stagnation pressure in the discharge wake by Pressure tube.

The typical waveform of the signal from the pressure tube sensor is presented in Fig. 11. It is seen that the stagnation pressure downstream of the discharge is strongly decreased up to half of an unperturbed value.

Fig.11. Stagnation pressure of the flow in the absence (top) and presence (bottom) of the MW discharge. Horizontal scale – 0.2 s/div; vertical scale – 126 Torr/div; initial pressure in the test chamber - pc 0 = 99 Torr.

One can see the shock wave generated by the discharge and the low-density hot channel created by the discharge.

The calculated general view of the jet perturbed by the MW discharge is shown in Fig.12 where the spatial distribution of density is given. The stream flows from left to right (from the nozzle to the diffuser in the real experiment).

Fig.12. The general view of the supersonic flooded jet with local heating.

The jet is flooded into the background gas filling the large volume. The pressure of the background gas approximately equals the static pressure of the jet so the variations of the jet radius are small. This is a good regime for the experiment because the flow is almost homogeneous. In the real experiment this state exists for only a couple of seconds, but the time is quite enough for the all needed measurements.

The discharge identified in Fig.12 by the black line near z-axis creates a shock wave and leads to the hot long channel. The complementary information is given by the surface plots with the spatial distributions of density (Fig.13) and temperature (Fig.14) of the stream in the background air.

Fig.13. The spatial distribution of the density in the flooded jet with channel heated by discharge.

The region near the nozzle outlet of the independent flow limited by a weak compression shock is easily seen. This shock forms the non-diverging flow downstream. The region heated by the discharge is also clearly seen. Behind the discharge a channel with almost fixed radial distribution of a gas parameters is observed.

Fig.15. shows the dependencies of the flow parameters along the axis (r=0). It is seen that flow velocity rises behind the heated region but the Mach

number decreases. There the values of stagnation pressure in the cases of absent and presence of discharge are compared. The stagnation pressure is calculated using the Raleigh formula

−−−

−×

×−−⋅−

++

⋅=

11

121

2

12

11

121

1

21

γγγ

γγ

γγ

γγ

γ

M

Mstatp

stagp

where M – local value of Mach number. Note that distribution of stagnation pressure and of dynamic pressure ρV2/2 are almost the same (Fig.15).

Fig.14. The spatial distribution of the temperature in the flooded jet with channel heated by discharge.

Fig.15. The longitudinal distributions of the jet parameters along its axis. Mach number M –1, magnitudes referenced to the nozzle outlet values: double flow velocity – 2, stagnation pressure without discharge -3, with discharge – 4, ρρρρV2 related to nozzle outlet value - 5.

The calculated radius of the hot channel is about 0.3 cm, density is about 0.1 of unperturbed value and the temperature is more 1000 K. The ionization and dissociation coefficients are not higher than 5⋅10-5

and 10-6, respectively. The measurement of stagnation pressure in the jet gives almost the same result.

The drag force reduction

The influence of a deep undercritical discharge placed ahead of the body on the aerodynamic force acting on a body was investigated by means of the balance with the previously mentioned electronic sensor. Mutual positions of experimental elements during experiments are presented in Fig.4. The test were carried out at a MW beam power Pgenerator = 2.1 kW and MW pulse duration of 2 s. Measurements of the drag force were carried out with and without the MW discharge for two values of the distance h from the face of cylindrical model to initiator’s sharpened end, h = 1 and 2 cm, respectively. A photograph of the central part of the test chamber with the discharge acting is shown in Fig. 16.

In Fig.17 waveforms of a signal from the balance read at h = 1 cm are presented. The horizontal scale of the picture is 0.2 s/division, and the vertical one is 56 G/division. The upper waveform corresponds to an absence of a discharge (a) and the lower one corresponds to its presence (b). The first “overshoot” connected with arrival of the supersonic stream to the model is recorded in the waveforms.

Fig. 16. The general view of the discharge with the presence of the model.

The measurements show a strong decreasing of the drag force when the MW discharge is switched on as seen in Fig.17 where the waveforms of the signals from balance are shown with and without the discharge.

One can see that the drag force decreases significantly with the discharge burning. From the waveforms, the maximum decrease is estimated to be a factor of 4. This means that the drag force acting the body in the presence of the discharge constitutes only 25% of the initial drag force recorded without of the discharge.

Analogous waveforms at h = 2 cm are presented in Fig.18. These also show the drag force drop when discharge is burning. However, for this placement of an initiator relative to the model, the force drops by a maximum factor of 2.

The estimate of the drag force by famous equation

F = Cx·(ρ·v2/2) πR2

with the supposition that the aerodynamic coefficient

Cx ≈ 1 for model (cylinder of radius R = 0.35 cm with flat edge) gives for jet’s parameters the value 140 G. The minimum level of a signal obtained without a discharge corresponds to a value 124 G. One can see that it differs from the estimated force is only 11 %. This coincident confirms the accuracy of the measurements once more.

Fig.17. The signal waveforms from the balance sensor recording the temporal dependence of the drag force with a cylindrical model placed in the supersonic flow without of a discharge (a) and with a discharge before the bow shock (b); the horizontal scale 0.2 s/division; the vertical scale 56 G/division). The distance between the vibrator edge and the model is 1 cm.

The efficiency of the energy release usage is estimated using the equation

η = ∆F⋅Vjet/Pdischarge.

Supposing that Pdischarge =(0.2÷0.25)Pgenerator (see Fig.9) gives the value of the efficiency coefficient η = 0.9÷1.13. This agrees quite well with theoretical predictions for the case with the body and hot channel radii approximate equal, such as is the case in our experiment. This means that when body radius more than that of the hot channel, one can expect efficiency will be much more than unity because Cx

will decrease.

Fig.18. The same as in Fig.15, but with the distance between vibrator edge and model is 2 cm.

It is necessary to note the following. The estimation is performed supposing constant Cx. But if the channel is quite thin relative to the body radius,

the coefficient Cx can be much smaller than usual. The thin hot channel is able to strongly change the structure of a flow around body. This effect was studied by many authors. The last complete investigation of the energy addition before bow shock of overflowed sphere was performed in Ref.28

numerically in 2-D approximation. It has been proved that if the energy addition inside the region with sizes that are much less than overflowed spherical body and placed before the shock this addition is able to decrease the drag force significantly with high efficiency. The decreasing of drag force can be interpreted as a decreasing of coefficient Cx because of the trapped vortexes erected between heated region and the spherical body. The larger the distance from the body to the energy addition, the higher the efficiency of the influence.

Summary

The experimental and theoretic investigations conducted give assurance to the positive answer on the principal question about changing the aerodynamic characteristics of a body in a supersonic flow by means of a heat energy input provided by an undercritical MW discharge.

The scheme of investigations for modeling the aerodynamics with electromagnetic energy release in the regions before a bow shock wave was experimentally realized using a MW discharge. The flow was produced by supersonic flooded jet of 3 cm diameter, 500 m/s velocity and Mach number 2. The energy input was provided by a MW discharge operating in the continuous regime. The usage of an attached MW discharge allows one to create a discharge with a MW field level 60 times lower than the critical breakdown level. So the MW generator with a power of 2 kW was enough for the experiments.

In full accordance with the theoretical predictions, the energy release before a bow shock by means of a MW discharge can be used with high efficiency for drag reduction of a blunt body.

The developed numerical models, quite well reflecting the main features of the studied processes, support the experiment and help to interpret them.

Together with previous success concerning fuel ignition by a MW discharge24,26, it opens the way for realization of the ideas of external combustion in super- and hypersonic flows.

Acknowledgment

Authors sincerely thank Dr. Reginald J. Exton for constant interest to the work and for fruitful discussions and support and Dr. David VanWie for useful remarks.

References

1 K.V.Khodataev. Gas dynamic processes in extra high power high frequency discharge plasma.Proc. of the ICPIG-XX (1991, Piza, France), Invited papers, pp. 207-217.

2 K.V.Khodataev. Physics of the Undercritical Microwave Discharge and Its Influence on the Supersonic Aerodynamics and Shock Waves. Proc. of Workshop on Weakly Ionized Gases. USAF Academy, Colorado 9-13 June 1997, v. 1, pp. L-1 -L-12.

3 K.V.Khodataev. The plasma effects in air dynamics. The gas discharge theory model in aerodynamic calculations. Proc. supplement of 2nd

Weakly Ionized Gases Workshop. Waterside Marriott Hotel, Norfolk, Virginia, USA, 24-25 April, 1998, pp. 309-338.

4 V.V.Vitkovitskiy, L.P.Grachev et al. Investigation of the unstationary overflow of a body by the supersonic air stream heated by longitudinal electromagnetic discharge. Teplofizika vysokikh temperatur. 1990. Т.28. № 6.

5 L.P.Grachev, N.N.Gritsov, I.I.Esakov et al. The transversal discharge in the supersonic air jet. Jurnal Tehnicheskoy fiziki.. 1991. Т.61. Вып.9.

6 V.L.Bychkov, L.P.Grachev, I.I.Esakov, K.V.Khodataev et al. Computational and experimental investigation of the supersonic overflow of a blunt body by air stream in the presence of the longitudinal electric discharge. Preprint of The Keldysh Institute of Applied Mathematics RAS, № 27. Moscow. 1997.

7 A.Yu.Gridin, B.G.Efimov et. al. Computational and experimental investigation of the supersonic overflow of a blunt body with the needle at presence of the discharge in its forward part. Preprint of The Keldysh Institute of Applied Mathematics RAS №19. Moscow. 1995.

8 G.G.Chernyi. The impact of electromagnetic energy addition to air near the flying body on its aerodynamic characteristics (Russian contribution).Proc. of 2nd Weakly ionized Gases Workshop, April 24-25 1998, Norfolk VA, USA pp. 1-31.

9 D.W.Riggins, H.F.Nelson, E.Jonson. Blunt body wave drag reduction using focused energy deposition. Proc.supplement of 2nd Weakly ionized Gases Workshop, April 24-25 1998, Norfolk VA, USA pp. 365-386.

10 N.K.Makashev. The first results and conclusions in “Plasma Aerodynamics”. Proc. of Workshop on Weakly Ionized Gases. 9-13 June 1997. Colorado, USA. Section F.

11 Y.E.Kuznetsov et al. Results of experimental investigations in wind tunnels of the electric discharge influence on aerodynamic drag and flow over models. Proc. of Workshop on Weakly Ionized

Gases. USAF Academy, Colorado 9-13 June 1997, v. 1, section H.

12 V.Skvortsov et al. Investigation of aerodynamic effects at electric discharge creation on the models of different geometry. Proc. of the 2nd

Workshop on magneto-plasma aerodynamics in aerospace applications. April 5-7, 2000. Moscow, Russia. pp. 102-106.

13 L.P.Grachev, I.I.Esakov, K.V.Khodataev et al The electrodeless discharge in air at median pressure. Zurnal Tehnicheskoy Fiziki. 1988.Т.55. v2.. pp. 389-391

14 L.P.Grachev, I.I.Esakov, G.I.Mishin, K.V.Khodataev, V.V.Tsyplenkov. Evolution of structure of a gas discharge at a microwave focus as a function of pressure. Tech. Phys. 39(1), January 1994, pp. 40-48

15 L.P.Grachev, I.I.Esakov, G.I.Mishin, M.Yu.Nikitin, K.V.Khodataev. The electrodeless discharge in air under moderate pressure Jurnal Tehnicheskoy Fisiki, vol.55, is. 2 (1985), p.389-391

16 L.P.Grachev, I.I.Esakov, G.I.Mishin, K.V.Khodataev, V.V.Tsyplenkov. Evolution of structure of a gas discharge at a microwave focus as a function of pressure. Tech. Phys. Lett 39(1), January 1994, pp. 40-48

17 L.P.Grachev, I.I.Esakov, K.V.Khodataev The development peculiarities of pulse UHF discharges in quasioptical radiation beam in different gases. Jurnal Tehnicheskoy Fisiki 1998, v.68,No.4, pp. 33-36.

18 L.P.Grachev, I.I.Esakov, et al. The development dynamics of the spatial structure of the electrodeless discharge Jurnal Tehnicheskoy Fisiki, vol.59, is.10 (1989), p.149-154

19 L.P.Grachev, I.I.Esakov, G.I.Mishin, K.V.Khodataev. The development stages of the electrodeless microwave discharge Jurnal Tehnicheskoy Fisiki, vol.66, is.7 (1996), p.32-45

20 L.P.Grachev, I.I.Esakov, K.V.Khodataev et al. Dependence of evolution of a gas discharge in microwave beam focus on pressure. Jurnal Tehnicheskoy Fisiki, 1994, v.64, No.1, pp.74-88.

21 L.P.Grachev, I.I.Esakov, G.I.Mishin, K.V.Khodataev. The high-frequency air breakdown in presence of vibrator Jurnal Tehnicheskoy Fisiki, vol.65, is.7 (1995), p.60-67

22 L.P.Grachev, I.I.Esakov, G.I.Mishin, K.V.Khodataev, The high-frequency air breakdown at presence of the vibrator. Zurnal technicheskoy Fiziki. 1995.Vol.65. No.7. pp.60-67.

23 L.P.Grachev, I.I.Esakov, K.V.Khodataev, The streamer UHF discharge in a supersonic air flow.Zurnal technicheskoy Fiziki.. 1999. Vol.69. No.11. С.14-18.

24 I.Esakov, L. Grachev, and K. Khodataev, Moscow Radio Technical Inst., Moscow, Russia; D. VanWie, Johns Hopkins Univ., Laurel, MD, USA.

Investigation of Subcritical Microwave Streamer Discharge for Jet Engine Fuel Ignition. 4th Weakly Ionized Gases (WIG) Workshop. Anaheim, California. 11-14 Jun 2001. AIAA-2001-2939

25 K.V.Khodataev. Physics of super undercritical streamer discharge in UHF electromagnetic wave. Proc. XXIII ICPIG, 17-22 July 1997, Toulouse-France, Contributed papers, IV-24.

26 K. Khodataev. The Ignition of the Combustion and Detonation by the Undercritical Microwave Discharge. 4th Weakly Ionized Gases (WIG) Workshop. Anaheim, California. 11-14 Jun 2001. AIAA-2001-2941.

27 K. V.Khodataev. The numerical modeling of the air supersonic flooded jet with deep undercritical microwave discharge. Proc. of The 4th Workshop on Magneto-plasma Aerodynamics in Aerospace Applications. 6-11 April 2002, Moscow, Russia.

28 V.A.Levin et al. Influence of energy input by Electric discharge on supersonic flows around body. Proceedings of 2-nd Weakly Ionized Gases Workshop (Norfolk, VA, April 24-25, 1998), pp. 201-231.