Reno99-paper - University of Texas at Austinresearch.ae.utexas.edu/FloImLab/Publications/AIAA-99... · · 2008-04-08of the characteristics of the electrothermal plasma itself

American Institute of Aeronautics and Astronautics1

AIAA-99-0452

EXPERIMENTAL STUDY OF AN UNDEREXPANDED PULSED PLASMA-JET

Jong-Uk Kim,* N. T. Clemens,† and P. L. Varghese‡

Center for Aeromechanics Research,Department of Aerospace Engineering and Engineering Mechanics

The University of Texas at AustinAustin, Texas 78712-1085

Abstract1 2

An investigation has been conducted of thecharacteristics of a highly underexpanded pulsedplasma jet originating from an electrothermal capillarysource. Measurements made include spatially andtemporally-resolved emission spectroscopy, from whichpopulation temperatures and electron number densitieswere derived, and laser schlieren imaging of theprecursor blast wave. The emission measurements weremade at several locations along the jet axis, and atseveral times during the course of the discharge in orderto investigate the development of the jet temperatureand electron density fields. In general it is found thatthe temperature and electron density axial profiles −taken at different times during the discharge − aresimilar when the axial location is normalized by thedistance from the jet exit to the Mach disk. For most ofthe discharge, the population temperatures upstream ofthe Mach disk are about 1.2 eV (14,000 K), but increaseto 2.2 eV (25,000 K) just downstream of the Mach disk.Similarly, the electron number densities are of order1017 cm-3 and 1018 cm-3, for locations upstream anddownstream of the Mach disk, respectively. Analysis ofthe trajectory of the precursor blast wave shows that itdoes not follow the scaling expected for a strong shockresulting from the instantaneous deposition of energy ata point. However, the shock velocity does scale as thesquare root of the deposited energy, in accordance withthe point deposition approximation.

* Postdoctoral Fellow, Member AIAA†Associate Professor, Senior Member AIAA‡ Professor, Senior Member AIAACopyright © 1999 by J. U. Kim et al. Published by theAmerican Institute of Aeronautics and Astronautics, Inc. withpermission.

Introduction

Recently, electrothermal plasma injection has beensuggested as a means to enhance and controlcombustion rates of propellant materials.Electrothermal plasmas are also of interest forapplications in fields such as rocket propulsion,electrothermal-chemical launchers, and hypersonicmass acceleration technology.1-3 Electrothermal-chemical (ETC) gun propulsion uses a pulsed powersystem to generate a plasma, which is then injected intoa chemical propellant to improve gun performance.4-6

In many proposed ETC gun systems the plasma ignitesa solid propellant charge; the total energy may also beaugmented by plasma injection into the gun chamberand/or the barrel. Despite the demonstratedimprovements in gun performance using ETCpropulsion, little is currently known about thefundamental processes involved in plasma-initiatedcombustion of a solid propellant. In fact, little is knownof the characteristics of the electrothermal plasma itself.

Therefore, the primary objective of the currentwork is to investigate the characteristics of a pulsedpolycarbonate capillary plasma that is allowed toexpand freely into the atmosphere. Previous work inour laboratory has shown that the capillary dischargeproduces a transient highly underexpanded jet that lastsfor about 250 µs.7 Temporally-resolved schlierenimaging and temporally- and spatially-resolvedemission spectroscopy were used to investigate theevolution of the structure of plasma jet flow-field, andto determine its composition, temperature and electrondensity. This is a continuation of the work reported inKohel, et al.7 where preliminary emission spectroscopicmeasurements were made for a limited range ofconditions.


Background

Excitation Temperature and Electron Densities ofthe Plasma

The methods most frequently used fordetermination of excitation population temperatures arethe “two-line method” 8-10 and the “Boltzmann plotmethod.”11-14 In the Boltzmann plot method, if therelative intensities of the spectral lines of a givenspecies are measured, the associated excitationtemperature (Texc) can be determined from15-16

ln (Iλ/Agu) = B – Eu / kTexc (1)

where I is the relative intensity of an emission line, λ isthe emission wavelength, A is the spontaneous emissionrate, gu is the statistical weight factor for the excitedstate, Eu is the energy of the excited state, and k isBoltzmann’s constant. The distinct atomic linesobserved in emission from a dense low-temperatureplasma are reasonably well represented by a Lorentzianline shape. This is so because Stark broadening, arisingfrom perturbations of the atomic system by electronsand ions, is the dominant broadening mechanism.17-19

Analysis of Stark broadened profiles is a usefultechnique for determining the electron number densitieswithin the plasma, because the Stark widths give adirect measure of the electron density. Since the Starkeffect is well-characterized in hydrogen and thetransitions fall within a convenient region of the opticalspectrum, the Balmer series is frequently used for lineshape analysis.17 The most frequently measured Balmerline is Hβ (486.1 nm), which occupies a very convenientregion of the spectrum, has a rather characteristic andbroad profile, and is far less sensitive to radiativetransfer effects than Hα.17 However, in the plasmasstudied in this work measurement of the Hβ linewidth iscomplicated by impurity lines in this region of theplasma spectrum. Thus, our line shape analysis focuseson the more prominent Hα line at 656.3 nm. Widths forthe observed Hα lines are determined by a nonlinearleast-squares fit of the recorded lineshapes to aLorentzian function. Instrumental broadening for oursystem is reasonably well characterized by aLorentzian, with a full-width-at-half-maximum(FWHM) of 0.62 nm. Because the convolution of twoLorentzian profiles yields another Lorentzian, theinstrumental broadening is subtracted from themeasured FWHM values to obtain the true Stark-broadened widths.

Plasma-Jet Structure

The plasma jet ejected from the open end of thecapillary forms a highly underexpanded jet with acharacteristic barrel shock structure. In a previousstudy,7 time-resolved visible emission images of theplasma jet were obtained using an ICCD detector. Arepresentative image taken 94 µs after the initiation ofthe discharge is shown in Fig. 1, with a schematicdescription of notable features of quasisteady free jetflow. Expansion waves at the bore exit travel to the jetboundary where they are reflected to form weakcompression waves, which then coalesce into the barrelshock. The barrel shock undergoes an irregularreflection and, in the triple-point downstream from theexit bore, the reflected shock, Mach disk, and slipsurface are formed.20-23 In the shock-bounded, highlyunderexpanded jet flow region, the flow ischaracterized by relatively high Mach numbers (M >>1), low pressures, and low temperatures. Across theMach disk, the flow is decelerated to subsonic velocity,the pressure rises suddenly to atmospheric pressure orabove, and the temperature increases due to shockheating at the Mach disk.20-23

Experimental Approach

Design and Operation of the Pulsed Plasma Source

A schematic diagram of the experimentalarrangement is shown in Fig. 2. The plasma source isgenerated by the rapid discharge of 3.1 kJ of electricalenergy into a polycarbonate (Lexan) capillary. Thisenergy is stored in a 251 µF capacitor charged to amaximum of 5 kV. The capillary is 3 mm in diameter,30 mm long, and is open at one end only. The dischargeis initiated with a thin copper fuse wire (2.5 mil, 64 µm)and ablation and ionization of material from thecapillary surface sustains the discharge. The resultingplasma rapidly expands from the open end of thecapillary and issues into room air. The peak currentthrough the plasma is approximately 4.6 kA for adischarge energy of 3.1 kJ, and the discharge durationis approximately 250 µs. The electrodes are made of acopper-tungsten alloy (30% Cu, 70% W) to resistelectrode erosion. The voltage across the capillary wasmeasured as a function of time using a high voltageprobe (Tektronics P6015A). The current trace wasmeasured using a Rogowski coil and the signal wasintegrated with respect to time to get the total current inthe plasma circuit during the discharge. The Rogowskicoil 24 is magnetically coupled to the current throughthe major loop of the toroid and a voltage signal isinduced in the coil, which is directly proportional to thetime rate of change of the total current of the loop. Themeasured voltage and current waveforms were highly


repeatable, for example the peak current was repeatableto less than 3%.

Optical Diagnostics

An intensified gated 512-element linear arraydetector (Tracor Northern TN 6143) and a 1/4-mspectrometer (Spex 1681C) were used to obtain time-resolved emission spectra from the pulsed plasma jet.The spectrometer was calibrated using either a Ne orHg standard lamp to obtain absolute wavelength and tofind instrumental broadening (the lamp used dependson what wavelength range the spectrometer is set to). Atungsten filament standard lamp was utilized tocalibrate the relative spectral response of the entireoptical system. The plasma emission was focused by alens onto an optical fiber which transmitted theemission to the spectrometer. The lens and fiber tipwere micrometer-positioned so as to image differentheights along the axis above the exit of the capillary.The spatial resolution along the axis, perpendicular tothe line of sight, was found to be 0.86 ± 0.03 mm, asdetermined by a measurement of the beam waist(FWHM) of a He-Ne laser directed into the oppositeend of the fiber and focused by the same imaging lensabove the plasma device. The temporal resolution of thespectrometer was set by a 1 µs gate on the intensifier ofthe detector array. The temporally- and spatially-resolved plasma spectra were recorded over threewavelength ranges (350 - 470 nm, 465 - 585 nm, and580 - 700 nm). Measurements were made at severalaxial locations along the centerline of the jet, and atdifferent times after the plasma ignition unit wastriggered.

Optical System for Schlieren Imaging of the PlasmaJet

Schlieren imaging is a well established techniquethat enables the visualization of index-of-refractiongradients in a flow field. Figure 3 shows a schematicdiagram of the schlieren system used in our study. Thesecond harmonic (532 nm) of a pulsed Nd:YAG laserwas used as a light source. The pulse duration is 10 ns,which is sufficient to freeze the motion of the flow. Toimprove image quality the beam was spatially filteredby passing it through a 25× microscope objective lenswhich focused the beam onto a 25 µm pinhole. Thelaser pulse was first attenuated (to about 5 µJ per pulse)by reflecting it from three glass flats to avoid burningthe pinhole. The spatial filter was placed at the focus ofthe concave mirror, so that the working section wasilluminated by a collimated beam of light. To protectthe camera from damage the schlieren image wasprojected onto a ground glass target (5.0 mm × 5.0 mm× 1.6 mm). The target was imaged using an intensified

CCD camera (Princeton Instruments ICCD-576,576×384 pixel resolution) fitted with a 105 mm focallength (AF Micro Nikkor) camera lens operated at f/22.To reduce interference from the intense emission fromthe plasma jet, a laser line filter (532 nm, 3 nmbandwidth) was placed in front of the camera lens. Tofurther reduce the background luminosity from theplasma, the second schlieren mirror was placedapproximately 6 m from the plasma source.

Overall Synchronization

One issue involved in conducting the schlierenimaging was being able to obtain a laser pulse at anydesired time delay from the initiation of the discharge.This is problematic because the laser is inherently asynchronous device that operates at 10 Hz, i.e. it cannotbe fired at an arbitrary time. A further complication isthat the laser requires that the flashlamps be triggered165 µs before the Q-switch (which initiates the laserpulse). Our solution was to build a triggering circuitthat, upon the input of a manual trigger, would initiatethe discharge at a user-set time before the next laserpulse is to occur. Since there is a relatively short timedelay between when the discharge is triggered andwhen it physically begins (about 6 µs), and thedischarge itself is over in about 250 µs, these triggeringevents easily take place within the 100 ms between the10 Hz laser pulses. The ICCD camera was synchronizedwith the laser to insure that a laser pulse occurredduring the 280 ns gate width (i.e. integration time) ofthe camera. Only one image was taken per laser shotwith this configuration, and the acquired schlierenimages were transferred to computer memory andwritten to disk for further analysis.

Results and Discussion

Current, Voltage and Capillary ErosionMeasurements

Figure 4 is a plot of the typical voltage and currenttraces obtained during a discharge with an initialcapacitor voltage of 5.0 kV. The figure shows thecurrent, the voltage across the capacitor, and the voltageacross the capillary. When the discharge is triggered(by closing an ignitron switch), the voltage across thecapacitor decreases rapidly and the voltage across thecapillary increases. If t is the time elapsed from thetriggering of the discharge, a peak voltage of 2.6 kV isinduced across the capillary over the interval0 µs < t ≤ 6 µs, and for t > 6 µs a relatively constantvoltage (≤ 1 kV) was observed and lasts until t = 250 µs.The initial transient voltage spike occurs just prior tothe explosion of the copper wire and the plasma


initiation begins after that time, i.e., the high dischargecurrent causes the fuse-wire to break down within 6 µs.For the 5 kV case the capacitor is completely dischargedin about 250 µs, and the current reaches a peak value of4.6 kA at 115 µs after the start of the discharge.

The explosion of the copper wire provides aconducting vapor, and subsequent ablation andionization of dielectric material from the capillary wallsmaintains the plasma within the capillary as the plasmajet discharges into the atmosphere. The increase of thecapillary exit diameter (φ) due to the erosion of thecapillary bore is shown in Fig. 5. Note that the diameterwas measured only at the bore exit, but it is known thatthe capillary does not erode uniformly, i.e. its diameteris not constant along its length. From Fig. 5 we observethat the mass of the capillary decreases approximatelylinearly with the number of shots. A least-squares fit tothe data shows that approximately 7.6 mg of thecapillary is ablated by every firing. A series ofpreliminary experiments showed that the electronnumber density (ne) in the plasma jet was quitedependent on the capillary bore exit diameter, withlarger diameters leading to lower electron numberdensity. For example, just downstream of the Mach diskand for 5 kV capacitor voltage, ne was found to beapproximately 1×1017 cm-3 and 1.5×1018 cm-3 for φ =5.31 mm and 3.81 mm respectively. In order tominimize this effect each capillary was used for amaximum of 5 shots.

Schlieren Imaging of the Blast Wave

Figures 6(a) and (b) show six sequential schlierenimages of the expanding plasma jet for initial voltagesof 2.5 kV (0.78 kJ) and 5 kV (3.1 kJ). About 30 µs afterthe plasma initiation, the blast wave expands from theexit of the capillary. The blast wave development is anunsteady process comparable to the shock propagationfrom the open end of a shock tube or from the barrel ofa rifle.25 As in the shock tube flow, a nearly sphericalshock wave develops, the expansion regionimmediately adjacent to the bore exit is a Prandtl-Meyer expansion, and the flow expansion is initiallyrestrained by the outer blast wave. It is interesting thatthe index-of-refraction gradients are so large across theblast wave that they completely mask the barrel shockthat exists inside it.

The radius R of the shock, which is assumed to bethe distance from the bore exit to the shock measuredalong the capillary axis, was measured as a function oftime. This is justified by our observation that theposition of the shock is highly repeatable from shot-to-shot. For example, four schlieren images were taken attime t = 50 µs (5 kV initial voltage) and the averagevalue of R was found to be 32.7 mm with a standard

deviation of 0.10 mm. Shock trajectory measurementswere made for image sequences obtained for initialcapacitor voltages of 2.5 kV (Fig. 6a), 3.5 kV (notshown) and 5 kV (Fig. 6b).

The data on shock trajectories for all three voltagesare shown in Fig. 7. The solid line represents a linear fitto the 5.0 kV plasma discharge data. Wilson, et al.26

show that the blast wave trajectories scale as R ~ t(2+β)/5,where β is a parameter related to the rate of energydeposition.27 Instantaneous energy deposition corres-ponds to β = 0, i.e. R ~ t2/5, which is the strongspherical shock solution.28,29 The approximately firstpower dependence of R on t observed experimentally,corresponds to β = 3. Dashed lines corresponding to β= 0 and β = 2 are also shown on Fig. 7. Because energyis being deposited continuously during the discharge itis unsurprising that the β = 0 line does not match thedata. The β = 2 line is shown for comparison withcomputations of Kim and Wilson30 shown below.

From the blast wave trajectories shown in Fig. 7 itcan be seen that the shock velocities are approximatelyconstant with values of 668, 586, and 534 m/s forcharging voltages of 5.0, 3.5, and 2.5 kV respectively. Aplot of the blast wave velocity vs. the square root ofinitial electrical energy (E1/2) is shown in Fig. 8. Thesolid line is the fit to the data. These results show thatthe velocity of the blast wave is approximatelyproportional to E1/2.

From the emission images of Ref. 7, the contactsurface (CS) and Mach disk (MD) locations weremeasured and those results combined with the blastwave position data are shown in Fig. 9. The lines arethe theoretical calculations of Kim and Wilson30 usingthe model of Wilson, et al.26 for the Mach disk andcontact surface and for the blast wave approximation,respectively. One can observe a good agreementbetween the calculation and measurements for theMach disk and contact surface, but there is a biggerdifference in the blast wave trajectory. In the theoreticalmodel, Kim and Wilson use β = 2, to account forcontinuous energy deposition.30 Earlier calculationswith β = 0 showed still larger discrepancy with ourexperimental observations. As noted above, Fig. 7shows that our blast wave velocity data are moreconsistent with β = 3, and computations of blast wavetrajectories with this value would agree better withexperiment. The axial displacement histories (Fig. 9)show that the Mach disk and the contact surface movecontinuously away from the exit bore of the plasma jetuntil they attain a maximum standoff. Then thedirection of the motion is reversed, and the Mach diskretreats upstream towards the capillary. Figure 9 alsoshows that the axial motions of the blast wave and thecontact surface are closely coupled for a relatively longtime. The blast wave and contact surface appears to


separate some time after 70 µs, with the blast wavemoving slightly faster than the contact surface. There isclear separation 160µs after the plasma initiation.

During the interval 0 µs ≤ t ≤ 160 µs the blast waveappears to restrain the flow expansion. At t = 160 µs theMach disk attains its maximum axial distance from theexit. Subsequently, it retreats back toward the bore exitowing to the decrease of the capillary bore pressure asthe discharge terminates.

General Characteristics of the Plasma Spectra

In order to investigate the evolution of thetemperature and electron density fields within theexpanding plasma jet, emission spectra were obtained ata wide range of axial positions and times during thedischarge. For example, emission spectra were acquiredat 7 separate axial locations for 6 different times. It isobserved that the measured plasma emission spectra ata particular x and t are highly repeatable, although thefeatures vary substantially with position and time, as isillustrated in Fig. 10. For convenience we define thenondimensional axial distance, ζ t = x/xm(t), where xm(t)is the vertical distance from the exit bore to the Machdisk at time t. Three typical axial regions are at the exit(ζ t ≈ 0), upstream of the Mach disk (ζ t < 1), anddownstream of the Mach disk (ζ t > 1). Time-resolvedMach disk locations were obtained from previouslyobtained emission images7 and those data points werefitted to obtain a relationship between Mach disklocation and elapsed time. In general, the spectrarecorded near the capillary exit (ζ t ≈ 0) arepredominantly blackbody in nature, with discretefeatures appearing as reversed lines due to self-absorption at the cooler outer edges of the opticallydense plasma. Axial profiles of the populationtemperature in the plasma jet at different times areshown in Fig. 11. It should be noted that the measuredpopulation temperatures have an average standard errorof ± 4,500 K upstream of the Mach disk (ζ t < 1), and ±5,600 K downstream of the Mach disk (ζ t > 1),respectively. During the interval 60 µs ≤ t ≤ 120 µs, theaxial location of the temperature jump movesdownstream. The temperature jump is clearly due to theMach disk, and its location is in good agreement withthe Mach disk location inferred from the visibleemission images taken by Kohel, et al.7 Once thetemperature reaches a maximum just downstream of theMach disk, it apparently decreases further downstream.This is seen from the data obtained at t = 60 and 80 µs.This is probably due to the reacceleration of the flowdownstream of the shock. For 140 µs ≤ t ≤ 160 µs thereis no appreciable axial variation in temperature, and atemperature of about 14,000 K was observed.Temperature distributions along the jet centerline for

regions as a function ζ t are shown in Fig. 12. Thisfigure shows that all of the profiles are similar whenplotted as a function of the nondimensional axialdistance. This is remarkable because the data representdifferent times during the discharge where the capillarysource conditions would be expected to vary widely.However, regardless of the time (and hence theinstantaneous current), we observe that twotemperatures (upstream and downstream of the Machdisk) can essentially characterize the entire axialprofile, i.e. Texc = 14,000 K for ζ t < 1 and Texc = 25,000K for ζ t > 1.

Electron Density

In order to determine the electron number densitieswe used the results of Gigosos, et al.,31 who havecalculated the Stark widths of the first three lines of theLyman and Balmer series of hydrogen including theimportant contribution of ion-broadening. Theirsimulation results show that the Stark widths do nothave a strong dependence on either the plasmatemperature or atom-ion reduced mass (µ). To obtainelectron number densities, we used the corrected linewidth of Hα and take the plasma temperature to be15,000 K and the reduced mass to be 1.0 amu31

(roughly corresponding to a hydrogen emitter in amixture of heavier ion perturbers).

Figure 13 shows measured electron number density(ne) profiles in the plasma jet at several fixed times. Themeasurements have an estimated uncertainty of 6×1015

cm-3 for ζ t < 1, and 7.5×1015 cm-3 for ζ t > 1 respectively.The jump in the electron density across the Mach disk(to ne ≥ 1×1018 cm-3) is most apparent at early times, 40µs ≤ t ≤ 80 µs. At later times, t >100 µs, electrondensities profiles were relatively flat and the densitieswere relatively small (ne ≈ 0.23×1018 cm-3). The plot ofne as a function of non-dimensional axial distance, ζ t, isshown in Fig. 14. As with the temperature data, theprofiles are seen to be very similar. As expected, weobserve a electron density jump across the Mach disk(ζ t = 1). The measured electron number density rangedfrom 1.7×1017 cm-3 to 5.5×1017 cm-3 upstream of theMach disk. We note that our measurements for electrondensities and temperature in the region of ζ t < 1 are ingood agreement with the time-averaged measurementsof Hankins, et al. near the capillary exit.32 Theymeasured electron densities in the range 2×1017 cm-3 to4.5×1017 cm-3 , with temperature ranging from 8,800 to14,000 K. The emission spectra recorded justdownstream of the Mach disk show a jump in electrondensity to a maximum of about ≈2.0×1018 cm-3. Despitesignificant scatter in the measurements, there appears tobe a trend toward lower electron densities furtherdownstream of the Mach disk.


Conclusions

In this study, we have made temporally- andspatially-resolved emission spectroscopicmeasurements of a pulsed plasma jet produced by acapillary discharge issuing into room air. Temperatureand electron number density axial profiles wereobtained at several times throughout the discharge.Results show that the plasma temperature and electrondensity jump across the Mach disk, as expected.Furthermore, regardless of the time within thedischarge, the temperatures are approximately 25,000 Kand 14,000 K, respectively downstream and upstreamof the Mach disk and the corresponding electrondensities are ≥ 1.0×1018 cm-3 and ≈2.5×1017 cm-3. Inaddition, we have measured the trajectory of the blastwave using the schlieren imaging technique atdischarge energies of 0.78, 1.5 and 3.1 kJ. The resultswere compared to previous results for the contactsurface and Mach disk. The results show that the blastwave and contact surface moved together until about160 µs after the plasma initiation. Approximately 160µs after plasma initiation the supersonic expansion hasgrown to its maximum downrange extension, and thebarrel shock structure is fully established. At later timesthe blast wave decouples from the driving core jet flow,and the constraint by the outer blast wave diminishes asthe barrel shock retreats towards the capillary exit. Themotion of the blast wave from a 5.0 kV (3.1 kJ)discharge, did not scale as expected for a strong shockresulting from instantaneous energy deposition at apoint. However, in accordance with the instantaneouspoint deposition model, the velocity of the blast wavescales as the square root of the dissipated energy andshows maximum velocity (668 m/s) for the 3.1 kJ case.

Acknowledgements

This study was supported by the Institute forAdvanced Technology (IAT) at The University ofTexas at Austin.

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Fig. 1 Schematic diagram of principal features of a quasisteady free jet (above). Short duration (250 ns) image7 ofplasma jet emission (below): (a) exit bore, (b) Prandtl-Meyer expansion (Mach cone), (c) barrel shock, (d) Triple-point, (e) Mach disk, (f) Reflected shock, (g) Contact surface, (h) Jet boundary, respectively; xm is the Mach disklocation.

ab

d

c

fe

g

h

xm

ContactSurface

Blast Wave

Mach Disk

Barrel Shock

Capillary Bore


Fig. 2 Schematic diagram of experimental setup for acquiring emission images and temporally- and spatially-resolved spectra of the plasma jet.

Detector GatingICCD Detector

Image out

Fiber Optics

PlasmaSource

PFN

Pulse Forming Network

DelayGenerator

PlasmaInitiationTrigger

PC

Tracor-NorthernController

Interface

Gating

Spectra Data

Spectro-graph

FG-100 Pulser &ICCD Detector Controller


Fig. 3 Schematic diagram of the experimental setup for Schlieren imaging of the plasma jet.

Manual Firing Switch

DigitalSignalGenerator

Nd:Yag

PFN

DigitalSignalGenerator Digital

O.S.C.

Flat Glass

MicroscopeObjective

Spatial Filter

Concave Mirrors

Plasma-JetFacility

Plane Mirrors

Knife Edge

Ground Glass

Laser Line Filter(532 nm, 3 nm bandpass)

ICCD Camera576x384

Trigger-Gate

PC

FG-100 Pulser &Controller

K

Q

Interface1 m

1 m

4 m


Fig. 4 Typical voltage and current traces obtained during a firing of the plasma jet for an initial capacitor voltage of5.0 kV.

Fig. 5 Changes of the capillary exit diameter and mass with respect to number of firings.

-2000

-1000

0

1000

2000

3000

4000

5000

6000

-3000

-2000

-1000

0

1000

2000

3000

4000

5000

-100 0 100 200 300 400 500

voltage across capacitorvoltage across capillary

current

Vol

tage

(V) C

urrent (A)

Time, t (µs)

7.2

7.25

7.3

7.35

7.4

7.45

7.5

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

0 4 8 12 16 20 24 28 32

mass of the capillary

capillary diameter

Mas

s of

Cap

illar

y (g

)

Capillary E

xit Bore D

ia. φ (mm

)

Number of Firings at 5 kV


Fig. 6(a) Schlieren image of plasma jet from 2.5 kVdischarge

t1 = 34 µs t4 = 94 µs

t2 = 50 µs t5 = 114 µs

t3 = 71 µs t6 = 156 µs


Fig. 6(b) Schlieren image of plasma jet from 5.0 kV discharge.

t1 = 34 µs t4 = 94 µs

t2 = 50 µs t5 = 114 µs

t3 = 71 µs t6 = 156 µs


Fig. 7 Experimental data for time-dependence of blast wave radius (R) for three discharge conditions. The solid lineis a linear fit to the 5.0 kV discharge data. This corresponds to energy deposition rate parameter, β = 3 (see text).Other lines correspond to β = 0 (instantaneous energy deposition, R ∝ t2/5) and β = 2.

Fig. 8 Dependence of blast wave velocity on initial electrical energy.

300

350

400

450

500

550

600

650

700

0 0.5 1 1.5 2

measured valuesacoustic limit

Sho

ck V

eloc

ity ,

U (m

/s)

[ E (kJ) ]1/2

20

30

40

50

60

708090

100

30 40 50 60 70 80 90 100 200

2.5 kV, U = 534 m/s3.5 kV, U = 586 m/s5.0 kV, U = 668 m/s

R ~ t(2+β/5 (β = 0, β = 2)

Rad

ius,

R (m

m)

Time, t (µs)

β = 0

β = 3

β = 2


Fig. 9 Experimental axial trajectories (symbols) of the blast wave (BW), contact surface (CS) and Mach disk (MD)and comparison with computations (lines) of Kim and Wilson30 for β = 2. D is the exit diameter of the capillary.

0 5 10 15 20 25 30 35 401

10

100

Mach Disk (MD)Contact Surface (CS)Blast Wave (BW)BW (β=2, Wilson, et al.)CS (Wilson, et al.)MD (Wilson, et al.)J

x/D

Tim

e, t

(µs)


Fig. 10 Temporally- and spatially- resolved emission spectra from the pulsed plasma jet (a) 160 µs (a), and (b) 90µs for a 5.0 kV discharge.

(a)

(b)

0

2000

4000

6000

8000

1 104

1.2 104

1.4 104

1.6 104

580 600 620 640 660 680 700

a. 160 µs, 0 mm, ζt = 0

b. 160 µs, 22 mm, ζt = 0.51

c. 160 µs, 36 mm, ζt =0.84

Inte

nsity

(a.u

.)

Wavelength ( λ/nm)

a

c

b

0

5000

1 104

1.5 104

2 104

2.5 104

480 500 520 540 560 580

a. 90 µs, 0 mm, ζt = 0

b. 90 µs, 22 mm, ζt = 0.68

c. 90 µs, 36 mm, ζt = 1.12

Inte

nsity

(a.u

.)

Wavelength ( λ/nm)

a

b

c


Fig. 11 Axial temperature profiles in a 5.0 kV discharge at several times.

Fig. 12 Variation of plasma temperature with non-dimensional axial position, ζ t

12000

14000

16000

18000

20000

22000

24000

26000

5 10 15 20 25 30 35 40 45

60 µs80 µs100 µs120 µs140 µs160 µs

Tem

pera

ture

, T (K

)

Axial Distance, X (mm)

10000

15000

20000

25000

30000

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

x = 10 mmx = 15 mmx = 20 mmx = 25 mmx = 30 mmx = 35 mmx = 40 mm

Tem

pera

ture

, T (K

)

Reduced Variable, ζt


Fig. 13 Axial electron density profiles in a 5.0 kV discharge at several times.

Fig. 14 Variation of electron density with non-dimensional axial position, ζ t

0

5 1017

1 1018

1.5 1018

2 1018

5 10 15 20 25 30 35 40

40 µs60 µs80 µs100 µs120 µs140 µs160 µs180 µs190 µs

Ele

ctro

n D

ensi

ty, n

e(cm

-3)

Axial Distance, X (mm)

0

5 1017

1 1018

1.5 1018

2 1018

2.5 1018

0 0.5 1 1.5 2

ζτ < 1

ζτ > 1

data fitdata fitζ

τ = 1

Ele

ctro

n D

ensi

ty, n

e (c

m-3

)

Reduced Variable ( ζτ= x/x

M)

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Reno99-paper - University of Texas at Austinresearch.ae.utexas.edu/FloImLab/Publications/AIAA-99... · · 2008-04-08of the characteristics of the electrothermal plasma itself