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Fast Mixing by Pulse Discharge in High-Speed Flow

Sergey B. Leonov*, Yuri I. Isaenkov†, and Dmitry A. Yarantsev‡ Joint Institute of High Temperature RAS, Moscow, 125412, Russia,

and

Mikhail N. Shneider,§ Princeton University, NJ, USA

This paper presents results of experimental and analytic efforts on the filamentary transversal pulse discharge application for mixing intensification in high-speed airflow. At present, the plasma of electrical discharges in airflow is considered as a quite promising method for flow/flight control and combustion enhancement. In the case of combustion in a high-speed flow several important problems should be solved: fuel ignition by direct heating/active radicals deposition/flow structure modification, mixing in non-premixed flow, flame-holding, etc. Preliminary analysis has shown that the short-pulse repetitive transversal electric discharge is one of the most prospective solutions for the duct with circular cross-section. On the other hand the properties of the filamentary plasma are not well studied under such specific conditions. The effect of fast turbulent expansion of the post-discharge channel in high-speed flow was observed experimentally. The mechanism of the phenomena was described theoretically for quiescent ambient conditions. In this paper it is supposed that effect of fast turbulent expansion of the post-discharge channel is effective for an acceleration of mixing in the non-premixed multi-component flow.

I. Introduction t is apparent now that plasma methods based on electrical discharge generation in a gas flow have practical applications to high-speed flow control. An idea of the method can be formulated in the simplest manner as such:

modification of flow-field structure and thereby changing a pressure distribution and chemical reactions rate by means of bulk force excitation in EM fields. In addition, heat release and active particles deposition with predefined parameters’, location and time can also modify flow.

The realization of the ignition and combustion control in high-speed (M>1) non-premixed flows is one of the most important issues of air-breathing propulsion. Well known methods of the “plasma-assisted combustion” comprise several important approaches: plasma-induced ignition due to chemical activation of oxidant and fuel, combustion of lean mixtures, mixing intensification, flame-holding, burnup completeness, etc. However up to now only a limited number of works is devoted to the problem of fast mixing inflow and/or ignition of non-premixed compositions by electrical discharge treatment [1-8].

Numerous works announce advantages of plasma technology for combustion enhancement. To have successful results it is not enough: the details are important. Unfortunately, specific information available now is not quite sufficient for consideration of the most important mechanisms and, consequently, for the proper choice of the discharge type. Our understanding now is that there is no universal guideline in plasma assistance design and the method of application; each specific situation has to be considered separately. Under these conditions the experimental tests and verification of some analytical predictions are urgently needed. * PhD, Head of Experimental Plasma Aerodynamics Lab, AIAA Associate Fellow, [email protected] . † PhD, Head of Pulse Discharges Lab ‡ PhD Student, Experimental Plasma Aerodynamics Lab. § DSc, Research Scientist, Princeton University, [email protected]

I

14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conference AIAA 2006-8129

Copyright © 2006 by S. Leonov and M. Shneider. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.


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II. Experimental Approach he general scheme of the experiments is shown in Fig.1. The facility consists of gas-dynamic channel, system of the pulse-repetitive feeding (pulse-repetitive discharger PD-60/1.7) and diagnostic equipment. The GD duct includes cylindrical channel D=50-60mm made of ceramics with flush-mounted electrodes. It is equipped with

high-quality optical windows. The diagnostic system includes the Schlieren device with spatial resolution not worse than 0.3mm and temporal resolution about 1us; set of transducers for pressure, temperature, voltage, current, radiation measurements; and spectroscopic system.

The test section has lengthy windows, which are made of quartz glass for observations and leading-out of emission from the discharge zone. The pulse transversal discharge was excited by means of the pulse-frequency power supply made on the base of Tesla coil with impact excitation and inductive-less capacitance. The typical parameters of the tests were the following: air pressure P≈1Bar, flow velocity V=0-500m/s, discharge pulse duration in a range t=40-80ns, maximal voltage, current and power were Umax=120kV, Imax=2kA, Wmax=90MW. Several tests were fulfilled when a residual current of predefined amplitude and duration added to the main pulse. The typical oscillograms of the discharge generation and recalculated power deposition are shown in Fig.2.

Fig.1. Principal experimental scheme. Fig.2. Typical oscillograms of pulse discharge generation.

It is known that primary ionization is considered necessary for obtaining a stable breakdown voltage in the discharge gap with sharply non-homogeneous field. Here the initial pre-ionization in the discharge gap was occurred due to appearance of the intensive corona discharge on the electrodes when voltage is tending to the breakdown level. Value of the corona discharge current was measured in a range 5 – 10A at the moment 5ns before breakdown. Light emission reaches the maximum at t = 40ns, then intensity reduces during the 0.6µs. At high level of pressure and fixed 2-electrodes configuration the discharge appears in form of filamentary long spark. The filamentary discharge penetrates cross flow between “hot” electrodes with the speed about V≈107m/s=1cm/ns. The earliest stage of the discharge is visible in the first frame of the Fig.7.

One of the most difficult parameters to be measured is the discharge channel diameter and its dynamics. It is clear that the plasma filament dimensions can be considered by different ways in dependence on which parameter and when is determined. As the result we evaluate that the diameter of high-temperature zone at the maximum of discharge current is about d=0.5mm. At the same time a visible diameter of the plasma channel is d=5-8mm, which corresponds with expanded stage of heated zone.

The plasma temperature was estimated in Tpl=15-17kK on the base of spectroscopic measurements of continuum luminescence. Estimation on the base of deposited energy gives the same result. The initial volume of the discharge channel is about Vol=10-8m3. Specific energy release (specific enthalpy) is about H=108J/kg (up to 25% of the energy is lost due to radiation). Such enthalpy is corresponded to air with the following parameters: temperature T0=16kK, ionization degree α≈0.9, mean conductivity is about σ≈102 (Ohm*cm)-1, channel resistance is R=25Ohm roughly (that is very close to directly measured value). The maximal radius of the heated zone expansion can be also estimated on the base of Sedov’s hypothesis, that the expansion is defined only by integral energy release. By that

T

0,00 0,05 0,10 0,15 0,20-1000

-500

0

500

1000

1500

2000 Current, A Voltage, kVPower, MW

100

50

Time, mcs

VoltageCurrent Power


3

way the maximal radius is equal: ;5

2

0max pl

Er××

=π

where l – is

the length of the channel, p0 – is the external pressure. The estimation gives value rmax≈5mm, which is close to experimental one.

Measurement of the shockwave speed, which is initiated by the spark, and thermal disturbances have been conducted by the Schlieren method (Fig.3). A single-mode laser beam (He-Ne) was used in the experiment. Time delay of the laser ray deviation in respect to the moment of the breakdown was measured at different distances between the line of electrodes gap and the measured beam, and at different speeds of the airflow.

III. Flow Effect on the Discharge Properties (Experiment) he gas flow does not affect on the electrical parameters of single short-pulse discharge if the pulse duration τ less that characteristic gasdynamic time for plasma channel thickness d: τ<d/V; as it correct in considered case. The flow affects on spark gap electric strength and input power for pulse-repetitive mode, consequently, if the

time period T less than gasdynamic time for duct diameter D: T<D/V. In this case the breakdown occurs on the way of “old” plasma channel downstream. As the result the discharge channel locates in undesired place with a reduced power deposition. To prevent such an effect the repetition rate has to be adjusted with flow speed [9-10].

The spark gap electric strength reduction is observed under the pulse-repetitive mode of the breakdown, when time interval between two sequential pulses is insufficient for the complete deionization of the spark gap. It is evidently, that time interval between pulses has to be reduced if the speed of the transversal gas-flow is more then zero through the inter-electrodes gap. It is occurred due to the drifting of the residual plasma under the influence of the airflow. Experiments had been conducted for determining of the residual plasma drift magnitude, which is sufficient for the electrical strength restoring. Conditions of the experiments were the following: pulse repetition rate of f=1kHz and overpressure in the accumulative tank of 1Bar.

It was possible to control breakdown voltage at the different moments of time for the different speed of the airflow correspondingly using a delayed triggering of the measurements. The plot of the electrical strength of the discharge gap versus velocity of the airflow is shown in Fig.4.

It is seen that fast reducing of the electrical strength is observed when airflow speed is about 50 m/s. A magnitude of the drift is 5cm at this flow speed and pulse repetition rate 1kHz. It is almost equal to the inter-electrode distance – 5.5cm. The practical result is that if the discharge repetition faster than V/D the power deposition drops in several times.

Flow Modification due to Discharge Generation. As was

noted above we might consider several mechanisms of the short-pulse high-voltage discharge effect on the parameters of gas and flow structure, if it was excited in dense, high-speed flow of air with a fuel. Among of them are the following ones: local superheating of the gas; discharge-induced shock wave, which

increases temperature and pressure locally and intensifies a mixing; photo-dissociation and photo-ionization of air and fuel yields in chemically active radicals production; unsteady artificial separation inflow in disturbed zone that is equal to intensive mixing. The gasdynamic effect of heat deposition by filamentary plasma has been evaluated numerically and proved experimentally as well [10].

The estimations of the photo-dissociation and photo-ionization processes in air due to radiation of the short-pulse high-voltage electrical discharge were done under the following conditions: air at ambient conditions P=1Bar, T0=300K; the temperature in discharge channel is T=16kK that is correlated with energy deposition in about 1.7J; the discharge channel is optically thick; initial diameter of the discharge channel is d=0.5mm, length D=50mm. The direct mechanisms of photo-ionization were taken into account only. A significant absorption of the radiation by air occurs at the wavelength of external source less than λ=186nm due to a strong excitation of Shuman-Runge band of

T

0 50 100 1500

20

40

60

80Breakdown Voltage, kV

Flow Velocity, m/s

P=1Bar, T=300KD=55mm, AirE0=1.7J

Voltage

Fig.4. The effect of breakdown voltage decrease at pulse-repetitive mode.

Fig.3. Scheme of plasma channel arrangement and measurements.


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molecular oxygen O2. At λ=176nm (ε=7.05ev) the absorption spectrum transforms to continuum that leads to dissociation of the oxygen. An effective dissociation of molecular nitrogen N2 begins at λ<140nm. At ε>12.1ev the photo-ionization of oxygen and nitrogen takes place with a large cross-section of process.

It is important that the cross-section of the molecular oxygen and nitrogen excitation and photo-dissociation are decreased with the temperature rise. At the same time the energetic threshold of the effect is slightly fallen due to primary thermal excitation of the molecules. Therefore, under the high-temperature conditions we could expect some increase of the zone of dissociation. Besides of that the excitation of metastable states of molecular oxygen (singlet ∆O2) can be realized effectively. A large share to the dissociation mechanism efficiency can be given by the molecules of any hydrocarbon fuel. The most hydrocarbon substances have the specific dissociation energy in a range εdis=3.95-4.3ev for the reactions of hydrogen detachment: ε−+= − HHCHC yxyx 1 . Such a reaction (free hydrogen appearance) plays a key role in combustion of heavy fuels. From the other side the photo-dissociation of heavy molecules can be executed by the photons with higher wavelength than for air.

The announced analysis is resulted in diameter of photo-exited zone dph≈10mm at p=1Bar in 1us after the discharge. The posterior expansion of the gas increase the value several times.

The thermal distortion, which is generated by the spark, was measured by Schlieren method. It affects on the laser beam during the some time after the shock wave and thermal cavity arrival. Speed of the thermal distortion movement is noticeably lower then one of the shockwave. Oscillogram of the thermal distortions at airflow speed of V=95m/s is shown in the Fig.5. Multiplier photocell responses on the spark emission (first peak) and on the shockwave (second peak) are observed on these oscillograms besides the signal that is caused by the thermal distortion. Arrival time and width of the thermal distortion zone relate to the airflow speed. Dependences of the thermal distortion arrival time t1 and time of the thermal distortion influence on laser ray t2 were obtained experimentally. It allows recalculating the width of disturbed zone and velocity of expansion as well. The result is shown in Fig.6. Some irregularities in experimental data are due to alternation of the plasma channel location. Estimation of the thermal distortion expansion speed gave a value V=100–200m/s at high-speed flow. The data on the base of fast-response pressure transducers have verified the data of Schlieren observations as a whole. Such a value under the ambient air and moderate amplitude of the current was measured as V=10–20 m/s that is compatible with routine theory.

Fig.5. Schlieren signal under SW and thermal distortion. Fig.6. Plasma disturbance expansion due to time.

In such a way the analysis of experimental data gives some not obvious results concerning the size of disturbed zone under high-speed flow. The Fig.10 shows a recalculated value of the disturbed zone “diameter” (actually, that it is not circular) in dependence on the time after the discharge pulse. An observation of this graph allows us to conclude two important things: the diameter of the plasma zone after the fast expansion is about d=10mm, and the mean “velocity” of the plasma disturbances expansion on the radial direction is more than V=100m/s under the conditions of high-speed airflow in this experiment. The first conclusion is in good agreement with estimated value on the base of Sedov’s formalism. The second conclusion proves the hypothesis of unsteady expansion instead the mechanism of thermal diffusion.


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IV. Fast Mixing by After-Spark Movement of the Medium he visualization of the plasma filament in ambient conditions and high-speed flow was done by means of fast camera, Schlieren method and line-scan (streak) camera. The thermal distortion, which is generated by the spark, was measured by Schlieren method and Schlieren-streak method based on disturbance of thin laser beam

layer recorded by fast line-scan camera. The after-spark channel development with time is shown in Figure 7, where a strong turbulent motion can be seen after several tens of microseconds. Note that the turbulence leads to a rapid expansion of the after-spark channel and thus it has got the potential for fast mixing of the gaseous composition. This effect can be augmented by high speed flow in the channel.

Fig.7. After-spark expanding channel with delay time from 0 to 500us.

The sample of Schlieren streak record is shown in Fig.8. The plane of cutting was perpendicular to the current direction and crossed the after-spark channel on centerline. Each line was exposed during 20us. To recognize the beginning of lateral jets development the initial stage of the channel expansion was stabilized by small residual current during 200us. As it can be recognized easily the turbulence leads to fast increase of the disturbed zone effective radius.

The theory of this phenomenon is developed by M.

Shneider [11-13] of Princeton University. In this model, for the first time, the strong dependence of the gas cooling process characteristics on a relatively small

residual DC current in the channel was demonstrated. It was shown that each current pulse has its corresponding critical value of the residual current which stabilizes the cooling channel under the quasi-stationary arc conditions.

Interaction of the pulsed arc with a gas flow strongly depends on the arc decay time. It is a well-known fact that turbulent gas motion develops in a cooling post discharge channel, creating far more rapid heat transfer than molecular heat conduction, so that the rates of cooling and expansion of the channel increase dramatically. This arising turbulent motion can essentially enhance the rate of fuel-gas mixing, which may control the mixing rate in ramjet or scramjet engines. A simple theoretical model of the cooling of a post-discharge channel in a gas has been proposed, taking into account the generation of turbulence and its influence on the channel cooling and expansion process [7-8]. In the present article we are applying a modified model of the pulsed discharge evolution and after-spark channel decay in the gas flow with carrying out a self-consistent analysis of the entire process of the spark discharge and subsequent cooling of the post-discharge channel with allowance for the generation and dissipation of turbulent motion of the gas. Model is based on the standard equations of one-dimensional gasdynamics and equation of state with Joule heating by the current pulse and heat losses due to the radiation transfer and molecular and turbulent heat conductivities. Similarly to [14], we take into account the velocity pulsations only. We operate with the averaged values of the rest of the macroscopic parameters, for which the root-mean-square values obey

T

Fig.8. After-spark expanding channel by Schlieren-streak technique.


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1/~// 222 <<′′>>′ TTuu ρρ . Below, we are going to drop the line over the averaged values. The characteristics of the macroscopic parameters are assumed to be distributed homogeneously across the cross-section of the channel. The corresponding kinetic energy of the turbulent pulsations per unit mass of gas is

∫≈′′=)(

02/2/

tr

TiiT

ch

rdrWuuK ρπ , where WT is the total kinetic energy of the turbulent pulsations per channel unit

length. The turbulent viscosity coefficient Tη , by analogy with the gas kinetic theory, can be represented in the form

TT LTvρη = , where vT and LT are the typical scales for the turbulent velocity and length, correspondingly. It makes

sense to assume that TKcuc 2v 12

1T ≈′= and chT rcL 2= , where с1 and с2 are numerical coefficients of the order of unity, which need to be adjusted to achieve the best agreement of the calculation results with the experiment, )(trch - after spark channel radius. According to Bossinesque hypothesis, the heat transfer occurs via the combined effect of the molecular transport and far more effective turbulent transport processes

rTrTqqq effTT ∂∂λ∂∂λλλ //)( −=+−=+= ,

where effλ λ , TTpT c Pr/ηλ ≈ are the corresponding effective thermal, molecular and turbulent thermal

conductivities; 1Pr ≈T is the turbulent Prandtl number. The gas flow outside the cooling channel is laminar. During the cooling process the kinetic energy of the

radial flow transforms into the kinetic energy of the turbulent pulsations (with the exception of a certain part of it transforming into heat at the expense of viscosity). As was shown in the previous section, the conditions that are conducive to the hydrodynamic instability development at the channel boundary are set when the boundary moves radially back and the channel pressure rises from its minimal value to the atmospheric level. Therefore, we suppose that the influx of the kinetic energy of the turbulent pulsations into a channel of unit length begins simultaneously with the boundary radial movement back to the center and is governed by the equation [14, 15]

0 ,)(22/))(()(20

2 <+∫Ω−⋅+Λ= chn

r

nchnchchT rurdrurutrrWch

&&& ρνπρπ ,

where )(, chnch rur& are the velocities of channel boundary and the cold gas flow through a relatively stationary axis; the term )(tΛ takes into account the delay of the turbulent flow in the channel. The term

chT rkKkuk /2 ,2 222 πνν ≈≈′≈Ω takes into account the turbulent kinetic energy dissipation into heat because of the viscosity with a coefficient of kinematic viscosity )(Tν .

An example dynamics of the axis temperature, the channel radius, rch, and the turbulent heat conductivity in the after-spark channel for the current pulse )/exp()2cos( aa tftII τπ −= , with aI =1 kA, f=100 kHz, aτ =0.1 µ s, and the pulse duration, timp=5µs are shown in Fig.9.

Fig.9. Calculated temperature on the axis of the cooling down after-spark channel with not accounting for the turbulence motion in the channel (‘laminar’ cooling) and with accounting for the turbulent motion developed in the channel and the channel radius – b. Air, p0 =1Bar; initial flow velocity u=0.

0 2x10-4 4x10-4 6x10-4 8x10-4 1x10-3

2000

4000

6000

8000

10000

0 2x10-4 4x10-4 6x10-4 8x10-4 1x100,0

0,5

1,0

1,5

turbulent cooling

laminar cooling

a

t, sec

turbulent

laminar

b

r ch, c

m

t, sec


7

The Fig. 10 shows the increase of maximum and minimum values of the channel radius with time due to experiments and theory. The theoretical model estimation of the channel radius is the solid blue line plotted in Figure 10.

As it can be considered the velocity of the after-spark channel expansion exceeds conventional values in several times. This effect can be critically important to enhance mixing processes in high-speed flow. The high-speed combustors, designed by conventional way, supposes a quite short time for the components’ mixing τmix<1ms that is defined by limited length of gasdynamic duct. The Figs. 6 and 10 demonstrate an ability of pulse discharge to provide the proper rate of mixing process.

Fig. 10. Expanding channel radius (maximum and minimum). The experiment vs theoretical estimations.

V. Conclusion xperimental and theoretical results presented in this work demonstrate that turbulent motion arising in the after-spark channel can essentially enhance the rate of fuel-gas mixing, which may control the mixing rate in engines with high-speed gas flow.

To develop a more rigorous theory for the after-spark evolution in the gas flow, we plan to carry out comprehensive experimental investigations of the post-discharge stage in high-speed flow to obtain more information about the values of electrical, gas dynamical and thermodynamical parameters of a decaying channel in air and two-phase compositions as well. It may be supposed also that their relationship with the time characteristics of a passed discharge current and bulk flow parameters are critically important for the mixing acceleration.

The authors express their gratitude to Mr. Konstantin Savelkin of IVTAN for valuable assistance in experimental work.

Some part of the work was funded in 2001-2004 by Program #20 of Presidium of RAS (coordinator Acad. Goremir Cherny).

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