Low-temperature supersonic boundary layer control using ... · of magnetic compression circuits. The use of the insulated gate bipolar transistor switch allows reaching high pulse

PHYSICS OF FLUIDS 17, 106102 �2005�

Low-temperature supersonic boundary layer control using repetitivelypulsed magnetohydrodynamic forcing

Munetake Nishihara, Naibo Jiang, J. William Rich, Walter R. Lempert,and Igor V. AdamovichNonequilibrium Thermodynamics Laboratories, Department of Mechanical Engineering,The Ohio State University, Columbus, Ohio 43210

Sivaram GogineniInnovative Scientific Solutions, Inc., Dayton, Ohio 45440

�Received 15 April 2005; accepted 2 August 2005; published online 17 October 2005�

The paper presents results of magnetohydrodynamic �MHD� supersonic boundary layer controlexperiments using repetitively pulsed, short-pulse duration, high-voltage discharges in M =3 flowsof nitrogen and air in the presence of a magnetic field of B=1.5 T. We also have conductedboundary layer flow visualization experiments using laser sheet scattering. Flow visualizationresults show that as the Reynolds number increases, the boundary layer flow becomes much morechaotic, with the spatial scale of temperature fluctuations decreasing. Combined with densityfluctuation spectra measurements using laser differential interferometry �LDI� diagnostics, thisbehavior suggests that boundary layer transition occurs at stagnation pressures of P0

�200–250 Torr. A crossed discharge �pulser+dc sustainer� in M =3 flows of air and nitrogenproduced a stable, diffuse, and uniform plasma, with the time-average dc current up to 1.0 A innitrogen and up to 0.8 A in air. The electrical conductivity and the Hall parameter in these flows areinferred from the current voltage characteristics of the sustainer discharge. LDI measurementsdetected the MHD effect on the ionized boundary layer density fluctuations at these conditions.Retarding Lorentz force applied to M =3 nitrogen, air, and N2–He flows produces an increase of thedensity fluctuation intensity by up to 2 dB �about 25%�, compared to the accelerating force of thesame magnitude. The effect is demonstrated for two possible combinations of the magnetic field andcurrent directions producing the same Lorentz force direction �both for accelerating and retardingforce�. © 2005 American Institute of Physics. �DOI: 10.1063/1.2084227�

I. INTRODUCTION

The use of nonequilibrium �low-temperature� magneto-hydrodynamics �MHD� for supersonic flow control, super-sonic air-breathing propulsion, on-board power generation,and for development of novel hypersonic ground testing fa-cilities continues to attract considerable interest.1–9 Controlof boundary layer transition seems to be a particularly prom-ising application of the MHD supersonic flow control tech-nology, because a relatively weak actuating Lorentz forcemay be sufficient to affect the flow field in the ionizedboundary layer. Indeed, the MHD interaction parameter �i.e.,the ratio of the Lorentz force work to the kinetic energy ofthe flow� for the free stream flow is

IFS =�B2L

�u�

, �1�

where � is the electric conductivity, B is the magnetic field,L is the length scale, � is the flow density, and u� is the freestream flow velocity. From Eq. �1�, it can be seen that forB�3 T, L�0.1 m, u��1000 m/s, and conductivity of��0.1 mho/m �currently achieved in nonequilibrium super-sonic flow plasmas9�, the MHD interaction can be significantonly at very low densities, ��10−4 kg/cm3 �P�0.1 Torr for
near room temperature flows�. On the other hand, for the
1070-6631/2005/17�10�/106102/12/$22.50 17, 10610

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boundary layer flow the interaction parameter can be ex-pressed as follows:10

IBL =�B2L

�u+ =�B2L

�u�

� 2

cf. �2�

In Eq. �2�, u+=u��cf /2 is the friction velocity, and cf /2

�0.03 Rex−0.2 is the flat plate turbulent boundary layer skin

friction coefficient,11 cf /2�10−3 at Rex�107, so that MHDinteraction may become significant at significantly higherdensities, ��3�10−3 kg/cm3 �i.e., at static pressures of afew Torr�. Qualitatively, the delay or acceleration of theweakly ionized boundary layer transition may be achievedby suppression or enhancement of flow instabilities by MHDforcing. This method of boundary layer control can be usedin cold supersonic flows for the purpose of drag and heattransfer leverage, or for the purpose of mixing enhancement.

The above estimates are consistent with successfulboundary layer density fluctuation control experimentsin both low-speed salt water flows �conductivity up to�=3 mho/m, B=0.4 T, L=0.25 m, u�=1–5 m/s,�=1 kg/cm3, cf /2�10−3�12 and in M =3 boundary layerflows weakly ionized by an rf discharge ��0.1 mho/m,u�=500 m/s, B=1.5 T, L=0.05 m, P�10 Torr, cf /2�10−3�.9,13,14 In particular, recent experiments at Ohio

9,13,14
State detected an MHD effect on the level of density
© 2005 American Institute of Physics2-1

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http://dx.doi.org/10.1063/1.2084227

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106102-2 Nishihara et al. Phys. Fluids 17, 106102 �2005�

fluctuations in a supersonic boundary layer weakly ionizedby a transverse rf discharge. In these experiments, retardingLorentz force applied to the flow produced a well-reproduced increase of the density fluctuation intensity by upto 10%-20% �1–2 dB�, compared to the accelerating forceapplied to the same flow. On the other hand, the effect ofJoule heating on the fluctuation spectra was insignificant.The effect was produced for two possible combinations ofthe magnetic field and current directions producing the sameLorentz force direction �both for accelerating and decelerat-ing force�. Finally, the effect was observed to increase withthe rf discharge power, i.e., with the flow conductivity. Ourrecent work14,15 also demonstrated that using supersonic flowionization by high-voltage, short-pulse duration, high repeti-tion rate pulsed discharge instead of rf discharge greatly im-proves plasma stability and allows generating significantlyhigher flow conductivities. However, these experiments haveleft open the question of whether the supersonic boundarylayer under investigation was laminar or turbulent.

The main objectives of the present work are �i� to deter-mine the state of the boundary layer at these conditions usinglaser sheet scattering flow visualization and laser differentialinterferometry �LDI� diagnostics and �ii� to detect the MHDeffect using repetitively pulsed ionization, which may resultin better flow control authority due to producing higher con-ductivities.

II. EXPERIMENT

The experiments have been conducted at the supersonicnonequilibrium plasma/MHD wind tunnel facility at theNonequilibrium Thermodynamics Laboratories.9,13–15

Briefly, this facility generates stable and diffuse supersonicnonequilibrium plasmas flows at M =3–4 in a uniform mag-netic field up to B=2 T, with run durations from tens ofseconds to complete steady state.

The schematic of the supersonic nozzle and a M =3MHD test section is shown in Fig. 1. An aerodynamicallycontoured M =3 supersonic nozzle made of transparentacrylic plastic is connected to a 2 cm�4 cm rectangularcross-section test section 12 cm long with an angle step dif-fuser. The nozzle/test section/diffuser assembly is attached toa vacuum system connected to a 1200 ft3 dump tank pumpedout by an Allis-Chalmers 1300 cfm rotary vane vacuumpump. The minimum pressure in the vacuum system sus-tained by the pump is 35–40 Torr, which necessitates theuse of a supersonic diffuser with the nozzle/test sectionoperated at relatively low stagnation and static pressures�P0=1/3–1 atm, Ptest=7–20 Torr�. The nozzle assembly isequipped with pressure taps measuring plenum pressure aswell as static pressures at the beginning and at the end of thetest section. The nozzle throat dimensions are 20 mm�9.5 mm, which gives a mass flow rate through the testsection of m=15 g/s at P0=1/3 atm.

Two rectangular electrode blocks 5 cm long are flushmounted in the side test section walls �see Fig. 1�. Eachelectrode block, made of mica ceramic, incorporates a singlecopper plate electrode 35 mm wide, 45 mm long, and 3 mm
thick. The electrode edges are rounded using a Rogowski

profile16 to achieve a more uniform electric field distributionbetween the electrodes. To accommodate the electrodes, re-cesses are machined in the ceramic blocks. This creates a2-mm-thick ceramic layer between each electrode and theflow in the test section. On the opposite sides, the electrodesare covered with 2-mm-thick acrylic plates. The gaps be-tween the copper electrodes, the ceramic blocks, and thecover acrylic plates are filled with a self-hardening dielectriccompound to preclude electrode surface exposure to air andprevent corona formation near the high-voltage electrodesurface. Figure 2 shows a photograph of the M =3 test sec-tion. Ionization in the test section is produced using a Chemi-cal Physics Technologies custom designed high-voltage �upto 25–30 kV peak�, short-pulse duration ��10–20 ns�, highrepetition rate �up to 50 kHz� pulsed plasma generator. Theplasma generator produces high-voltage pulses by compress-ing 500 V peak, 1 �s long input pulses using several stagesof magnetic compression circuits. The use of the insulatedgate bipolar transistor switch allows reaching high pulse rep-etition rates. During the pulser operation, current and voltagein the pulsed discharge are measured using a Tektronix

FIG. 1. Schematic of a supersonic nozzle and MHD test section.

FIG. 2. Photographs of an M =3 test section and of a high-voltage pulse
compression unit, mounted above the test section between the magnet poles.

106102-3 Low-temperature supersonic boundary layer control Phys. Fluids 17, 106102 �2005�

P6015A high-voltage probe and a low-capacitance resistivecurrent probe.

Transverse dc electrical current �sustainer current� in thesupersonic flow ionized by the repetitively pulsed dischargeis sustained by applying a dc field �up to 500 V/cm� to two50 mm�20 mm dc electrode blocks flush mounted in thetop and bottom nozzle walls 4 cm apart, perpendicular bothto the flow velocity and to the magnetic field direction, asshown in Fig. 1. The applied dc field, which is far too low toproduce additional ionization in the flow, except in the cath-ode layer, is needed to sustain transverse �MHD� current.The dc electrode blocks are made of boron nitride ceramic,with continuous copper electrodes 45 mm long each. Thetransverse dc field is applied using a DEL 2 kV/3 A powersupply operated in a voltage stabilized mode, with a0.5–2.0 k� ballast. Two inductors 1 mH each were placedin the dc circuit in series with both dc electrodes to attenuatehigh-amplitude current pulses propagation into the dc circuit.Current in the dc sustainer circuit is measured using aTektronix AM503S current probe.

The concept of a pulser-sustainer discharge where ion-ization is generated by a series of high-voltage, short dura-tion breakdown pulses and the current in the decayingplasma between the pulses is sustained by a relatively low dcvoltage was first suggested and demonstrated by Hill in1973.17 A similar approach, a crossed pulser-sustainer dis-charge in a fast subsonic gas flow in a rectangular cross-section channel, has been used for development of a high-power CO2 laser.18 Finally, recently this approach has beenused for studies of MHD effects in supersonic low-temperature flows.19,20

In the present paper, some plasma characterization mea-surements have been done in a M =4 MHD test section withthe same dimensions and the same electrodes as in theM =3 test section. The M =4 contoured nozzle throat dimen-sions are 20 mm�3.2 mm, which gives the mass flow rate
of m=15 g/s at P0=1 atm.

The entire nozzle/test section/diffuser assembly wasplaced between the poles of a GMW water cooled electro-magnet, as shown in Figs. 1 and 2, and attached to a 4 footlong,6 in. diameter PVC vacuum pipe connected to thevacuum system. To improve the pulsed discharge load im-pedance matching, the high-voltage pulse magnetic compres-sion unit was also mounted inside the magnet, above the testsection �see Fig. 2�, and short high-voltage electrode cables�5 cm long� have been used. The magnet can generate asteady-state magnetic field up to B=3.5 T between two cir-cular poles up to 25 cm in diameter. In the present experi-ments, for the distance between the 15 cm diameter poles of6 cm, the magnetic field at maximum current through themagnet coils of 140 A is B=1.8 T. For relatively short rundurations �of the order of tens of seconds�, the magnetic fieldcan be significantly increased by temporarily increasing themagnet current �up to �200 A� and chilling the cooling wa-ter. To preclude external magnetic field penetration into thepulse compression unit, it was placed inside a custom-madesix-layer shell magnetic shield made of a high magnetic per-meability material with a total wall thickness of 1 /2�. Mul-tiple layers are necessary because of the magnetic flux satu-ration in the outermost shield layers in the strong externalmagnetic field. At the B=1.5 T field between the magnetpoles, the field inside the magnetic shield was about20–30 mT. Mounting the pulse compression inside the mag-netic shield also required the use of longer electrode cables�15 cm long�, which adversely affected impedance matching.

Optical access to the flow in the test section is providedusing two 1��1/2� glass windows in the top and bottomwalls of the test section �see Fig. 1�. The MHD effect on asupersonic ionized boundary layer was studied using a laserdifferential interferometry �LDI� diagnostics described ingreater detail in Ref. 21. Briefly, a plane polarized He–Nelaser beam �coherent He–Ne laser, model no. 31-2025� issplit into two circular polarized beams using a Wollaston

FIG. 3. Layout and schematic of theLDI diagnostics.

prism �see Fig. 3� and sent through two different regions in



the supersonic flow in the test section. The reference beam ispassing through the flow along the center line and the probebeam is passing through the boundary layer �see Fig. 3�. Theresultant phase shift between the two beams is proportionalto the average density difference along the two beam paths.Therefore, Fourier transform of the resultant interference sig-nal performed by a Stanford Research Systems �Model SR785� Dynamic Signal Analyzer yields the boundary layerdensity fluctuation spectrum �relative to the reference laserbeam passing through the center line of the flow�. The refer-ence and the probe laser beam diameters, which limit thespatial resolution of the LDI signal, are approximately 2 mmeach. The location of the probe beam can be controlled byrotating the prism. LDI signal acquisition, averaging, andprocessing by the signal analyzer requires a steady-state flowrun time of several seconds, depending on the number ofaverages. Typically, good signal to noise is achieved for theacquisition/processing times of 1–2 s.

As in our previous work,9,13–15 in the present MHDboundary layer control experiments, most LDI measurementsare performed for both accelerating and decelerating Lorentzforce directions. In both of these cases, Lorentz force can begenerated by two possible combinations of the transverse Bfield and the transverse dc electric field directions. Controlruns in a cold supersonic flow without plasmas and in anionized flow without dc electric field applied, i.e., when thetime-averaged Lorentz force is zero, have also been con-ducted. The purpose of this approach was to isolate the MHDeffect, which should depend on the Lorentz force direction,


from the polarity-independent effect of Joule heat. To evalu-ate run-to-run variation of the LDI spectra, several runs �twoto three� have been conducted for each set of conditions.

To visualize the boundary layer flow in the supersonictest section, a separate series of experiments has been con-ducted in air flows without plasmas, with the test sectionmounted outside the magnet. In these experiments, the airflow upstream of the nozzle plenum was seeded with acetonevapor, which condensed into small droplets in the coldM =3 supersonic core flow in the test section but remained inthe vapor state in relatively warm boundary layer flows. Apulsed Nd:YAG laser operated at 10 Hz repetition rate wasused to generate a 1.5 cm wide laser sheet with the aid oftwo cylindrical lenses, which was then brought into the testsection through the two optical access windows, as shown inFig. 4. The laser sheet distance from the test section wallcould be varied by moving a flat mirror �see Fig. 4�. Thelaser light scattered on acetone droplets formed in the flowwas captured through the transparent acrylic test sectionwall, in the direction perpendicular to both the laser sheetand the flow, as shown in Fig. 4. A Princeton InstrumentsPI-Max ICCD camera synchronized with the laser pulses hasbeen used for this purpose.

III. RESULTS AND DISCUSSION

Figure 5 shows laser sheet scattering images of the sidewall boundary layer in M =3 air flows, with the laser sheetpositioned 2 mm from the test section wall. The images

FIG. 4. Schematic of the flow visualization experimentby laser sheet scattering.

FIG. 5. Laser sheet scattering imagesof a boundary layer in M =3 air flows,2 mm away from the test section wall.Left to right, P0=150 Torr, 200 Torr,250 Torr, 350 Torr, and 450 Torr�Reynolds number ranging fromRex=2.7�105 to 8.1�105�.



shown are for stagnation pressures ranging fromP0=150 Torr to 450 Torr. At these conditions, the flowReynolds number ranges from Rex=2.7�105 to 8.1�105

�x=20 cm is the combined length of the supersonic nozzleand the test section, starting from the throat�. To minimizethe amount of laser light scattered off the windows cominginto the camera, the top and bottom of the test section �5 mmdistance from the top and the bottom walls� are masked.Therefore, the images visualize the flow region betweenx=19 and x=21 cm from the nozzle throat and h=5 mm andh=35 mm from the bottom wall. From Fig. 5, it can be seenthat there is a significant warm region near the center planeof the flow with little or no scattering signal, which thereforeappears dark. Regions above and below the center plane areilluminated, which indicates the presence of significantamounts of acetone droplets there and therefore lower tem-perature. The presence of the warm region near the test sec-tion center plane is consistent with the boundary layer bulgedetected by our previous Pitot probe measurements,9,14 alsopredicted by the three–dimensional �3D� compressibleNavier-Stokes flow code.22 One can also see that as the stag-nation pressure and the flow Reynolds number increase, thescattering signal distribution, which essentially maps thetemperature field across the laser sheet, becomes increasinglychaotic, with the spatial scale of temperature variation re-gions �spots� gradually decreasing �see Fig. 5�. At high stag-nation pressures, the center plane boundary layer bulgenearly disintegrates. Similar results are observed for a lasersheet positioned 4 mm from the wall �see Fig. 6�.

Scattering images obtained with the laser sheet posi-tioned farther away from the wall �6 mm and 8 mm�, shownin Figs. 7 and 8, respectively, demonstrate the presence of afew warm spots near the center plane of the flow �at 6 mm�or none at all �at 8 mm�. This is again in good agreementwith our previous Pitot probe and schlierenmeasurements,9,13,14 which both indicate the boundary layerthickness of approximately 6 mm, with maximum thicknessnear the center plane. Summarizing, the flow visualizationresults shown in Figs. 5–8 are consistent with the Pitot probeand schlieren data and lead us to conclude that as the flowReynolds number increases, the boundary layer flow be-comes less regular and more chaotic, with the density fluc-tuation spatial scale decreasing. This suggests characterizingthe boundary layer in the stagnation pressure range ofP0=150 Torr to 450 Torr as transitional from laminar at thelower stagnation pressures to turbulent at the higher stagna-
tion pressures.

LDI spectra in M =3 air flows without plasmas havebeen measured in the same stagnation pressure range,P0=150–500 Torr. Figures 9 and 10 plot the spectra mea-sured with the probe laser beam located 2 mm and 4 mmfrom the test section wall, i.e., at the conditions of Fig. 5 andFig. 6, respectively. Note that due to the finite He–Ne laserbeam diameters, the LDI signal is actually collected fromregions 2±1 mm and 4±1 mm from the wall, respectively. Itcan be seen that although the flow scattering images changequite significantly as the stagnation pressure is increased �seeFigs. 5 and 6�, the overall shape of the LDI spectra, with anextended plateau and a steep roll-off at high frequencies,does not exhibit such dramatic changes �see Figs. 9 and 10�.Therefore, compared to laser scattering flow visualization,detection of turbulent transition based on the interpretationof LDI spectra alone is somewhat problematic. However, thebehavior of the LDI signal intensity at 10 kHz �i.e., in theplateau region of the spectra�, plotted versus stagnation pres-sure in Figs. 11 and 12 and showing a steep increase up toP0�200–250 Torr with subsequent leveling off, appearsmore systematic. Based on both the laser scattering imagesshown in Figs. 5 and 6 and the LDI signal plotted in Figs. 11and 12, we conclude that turbulent transition in the M =3boundary layers on the side walls occurs at stagnation pres-sures of P0�200–250 Torr.

Figure 13 shows photographs of crossed discharges�repetitively pulsed discharge+dc sustainer discharge� inM =4 flows of nitrogen �at B=0� and air �at B=1.5 T� at

FIG. 7. Laser sheet scattering images of a boundary layer in M =3 air flows,6 mm away from the test section wall. Left to right, P0=250 Torr and

FIG. 6. Laser sheet scattering imagesof a boundary layer in M =3 air flows,4 mm away from the test section wall.Left to right, P0=170 Torr, 200 Torr,250 Torr, 350 Torr, and 450 Torr.�Reynolds number ranging fromRex=3.1�105 to 8.1�105�.

500 Torr.



P0=1 atm. In both cases, the pulse repetition rate isv=40 kHz. Visual observation of the pulsed/dc dischargesshowed that in both cases the plasma is stable and uniform,without the “hot spots” appearing in the test section corners,which occurred in transverse rf discharge in supersonicflows.9,13 Figures 14 and 15 show single pulse voltage oscil-lograms in M =4 nitrogen flows at P0=1 atm, Ptest=10 Torr,and in M =3 nitrogen flows at P0=250 Torr, Ptest=7 Torr,respectively, at different values of the magnetic field. FromFig. 14, it can be seen that using longer electrode cables�15 cm long instead of 5 cm long� noticeably reduced theoutput pulse amplitude, from nearly 20 kV to about 15 kV.In addition, applying a 1.5 T magnetic field resulted in dis-tortion of the pulse due to partial field penetration throughthe magnetic shield, and in further amplitude reduction toabout 11 kV. In M =3 flows, the pulse amplitude remainednearly the same, approximately 15 kV, for the fields up toB=1.25 T �see Fig. 15�. At B=1.5 T, the peak voltage wasreduced to about 12 kV, with pulse duration �full width at

FIG. 8. Laser sheet scattering images of a boundary layer in M =3 air flows,8 mm away from the test section wall. Left to right, P0=250 Torr and500 Torr.

FIG. 9. LDI spectra of M =3 air flows at different plenum pressures. The
LDI probe beam is 2 mm away from the wall.

half-maximum �FWHM�� approximately 30 ns, again due tomagnetic field penetration through the shield.

Figure 16 shows oscillograms of voltage and current be-tween the dc sustainer �MHD� electrodes in a pulse-ionizedM =3 nitrogen flow at P0=250 Torr, Ptest=7.5 Torr,B=1.5 T, dc power supply voltage of UPS=2 kV, and ballastresistor of R=1 k�. Since the dc power supply operates inthe voltage stabilized mode, the voltage between the dc elec-trodes is U=UPS−IR, where I is the sustainer current. In thisfigure, the current pulse produced during the high-voltagepulses is not resolved. It can be seen that the peak MHDcurrent reaches about I=1.25 A after each pulse, with thesubsequent fall-off in a decaying plasma between the pulses,to a minimum value of about I=0.5 A. Note that the plasma

FIG. 10. LDI spectra of M =3 air flows at different plenum pressures. TheLDI probe beam is 4 mm away from the wall.

FIG. 11. LDI signal intensity at a 10 kHz frequency as a function of plenumpressure for the conditions of Fig. 9 �the probe beam is 2 mm away from the
wall�.


does not fully decay between the pulses. The time-averagedcurrent and voltage at these conditions are �U=1.27 kV and�I=0.73 A. The time-averaged dc power coupled to the ni-trogen flow at these conditions is quite substantial, about1 kW, which in the case of instant thermalization wouldresult in the estimated flow temperature rise of about�T=60 K, from the baseline core flow temperature atM =2.9 of T=110 K. However, at the reduced electric fieldin the sustainer discharge of E /N=3�10−16 V cm2 �based onthe initial core flow temperature�, more than 90% of the sus-tainer discharge input power goes to vibrational excitation ofnitrogen,23 whose vibrational relaxation rate is extremelyslow.24 The slow vibrational relaxation rate locks up the en-ergy stored in nitrogen vibrations and makes the supersonicflow essentially frozen. At similar discharge conditions indry air, in spite of a high-energy fraction input into vibra-tional excitation of nitrogen,23 vibrational relaxation of N2 ismuch more rapid, primarily on O atoms produced in theplasma,24 which would result in a more significant Jouleheating of the flow.

Figure 17 shows sustainer �MHD� currents in M =3 dryair flows at P0=250 Torr, Ptest=7.5 Torr, dc power supplyvoltage of UPS=1.6 kV, and ballast resistor of R=1 k�. The

FIG. 12. LDI signal intensity at a 10 kHz frequency as a function of plenumpressure for the conditions of Fig. 10 �the probe beam is 4 mm away fromthe wall�.

FIG. 13. Photographs of pulsed discharges in M =4 flows at P0=760 Torr,Ptest=10 Torr, pulse repetition rate 40 kHz. Left: nitrogen, B=0; right: air,B=1.5 T. The discharge is seen at an oblique angle, looking in the direction
of the flow.

current oscillograms are shown at different values of themagnetic field. It can be seen that the current decay rate indry air is similar to that of nitrogen �compare Figs. 16 and17�. One can also see that the current decreases as the mag-netic field is increased. This occurs due to the Hall effect,which in the case of continuous MHD electrodes generatesthe axial and reduces the transverse current component.25 Forthe high values of the MHD loading parameter, K=Ey /uBz

�40, at the present conditions, the transverse and axial cur-rent components are given as follows:

Iy =�

1 + �2EyA, Ix = ��

1 + �2EyA . �3�

In Eqs. �3�, � is the scalar electric conductivity, A=10 cm2

is the total surface area of the dc electrodes, and�=eBz /meven is the Hall parameter, i.e., the ratio of the elec-tron cyclotron frequency, eBz /me, to the electron-neutral col-lision frequency, ven. Transverse electric field in Eqs. �3� canbe estimated as Ey �U−Uc� /h, where U=UPS−IR, Uc is thecathode voltage fall, and h=4 cm is the test section height.

FIG. 14. Single-pulse voltage oscillograms in M =4 nitrogen flows atP0=1 atm, Ptest=10 Torr, for different values of magnetic field.

FIG. 15. Single-pulse voltage oscillograms in M =3 nitrogen flows at
P0=250 Torr, Ptest=7 Torr, for different values of magnetic field.


From Eqs. �3�, one can also obtain the following expressionfor the current voltage characteristic of the MHD sustainerdischarge:

I = �Ix2 + Iy

2 =�

�1 + �2�U − Uc�

A

h= �EeffA , �4�

where Eeff=Ey /�1+�2 is the effective electric field. Sincethe flow conductivity, generated by the repetitively pulseddischarge, is independent of the dc sustainer voltage, Eq. �4�shows that the conductivity and the Hall parameter can bedetermined by measuring current voltage characteristics of

FIG. 16. dc sustainer voltage and current oscillograms in a crosseddischarge �pulser+dc� in a M =3 flow of nitrogen. P0=250 Torr,Ptest=7.5 Torr, pulse repetition rate 40 kHz. Udc=2 kV, R=1 k�,B=1.5 T.

FIG. 17. Current oscillograms in a crossed discharge �pulser+dc� in aM =3 flow of dry air for different values of magnetic field. P0=250 Torr,
Ptest=7.5 Torr, pulse repetition rate 40 kHz. Udc=1.6 kV, R=1 k�.

the non-self-sustained dc discharge at different values of themagnetic field.

Figures 18 and 19 show current voltage characteristics ofthe MHD sustainer discharge in M =3 flows of nitrogen anddry air at P0=250 Torr and Ptest=7.5 Torr. It can be seenthat at low voltages, the sustainer current remains very lowand nearly independent of the applied voltage, while at highvoltages the current exhibits linear voltage dependence, asexpected for the constant conductivity plasma. Basically, ifthe applied voltage is low, the voltage across the cathodelayer of the discharge is insufficient to accelerate ions towardthe cathode, release enough secondary electrons from thecathode surface, and sustain a significant current, even at theconditions when the conductivity in the positive column of

FIG. 18. Current voltage characteristics of the sustainer discharge in M =3flows of nitrogen at different values of magnetic field. P0=250 Torr,Ptest=7.5 Torr, pulse repetition rate 40 kHz.

FIG. 19. Current voltage characteristics of the sustainer discharge in M =3flows of dry air at different values of magnetic field. P0=250 Torr,
Ptest=7.5 Torr, pulse repetition rate 40 kHz.


the discharge is high. The cathode voltage falls for differentB fields were determined from the x-axis intercept of thelinear slope of the current voltage characteristics, as shownin Figs. 18 and 19. At the absence of magnetic field, thecathode falls in nitrogen and in air are Uc=260±50 V andUc=350±50 V, which is close to the normal self-sustainedglow discharge cathode fall, 208 V in nitrogen and 370 V inair �both for copper cathode�.23 This result is not surprisingsince at the present conditions external ionization by high-voltage pulses is generated outside of the cathode layer, i.e.,a few mm away from both dc sustainer electrodes. Indeed, ascan be seen from the schematic in Fig. 1, the pulsed dis-charge electrodes do not extend all the way to the top andbottom test section walls �the pulsed electrode height is35 mm while the test section height at the electrode locationis 41 mm�. Because of this, external ionization is not likelyto affect the well-known cathode layer self-sustainingcriterion,23

d = ln�1 + 1/� , �5�

which is still satisfied due to Townsend ionization. In Eq. �5�, is the Townsend ionization coefficient, d is the cathodelayer thickness, and is the secondary emission coefficientfrom the cathode. Therefore, the cathode voltage fall valuesmeasured at the present conditions should be close to theresults in self-sustained glow discharges.

The present measurements show that both in nitrogenand air, the cathode fall increases with the magnetic field, upto Uc=500±50 V and Uc=520±50 V at B=1.5 T in nitro-gen and air, respectively �see Figs. 18 and 19�. This result isconsistent with the electrical breakdown theory in crossedelectric and magnetic fields,26 which predicts breakdownvoltage to increase with the magnetic field because of theHall effect,

U =C · Nd�1 + �2

ln�Nd�1 + �2� + ln� A

ln�1 + 1/��. �6�

In Eq. �6�, N is the number density, d is the breakdown gap,� is the Hall parameter, and A and C are constants in theexpression for the Townsend ionization coefficient in thecrossed E and B fields,26

N= A�1 + �2 exp�−

C�1 + �2

E/N� . �7�

Equation �6�, applied to the cathode layer of the discharge �inwhich case d is the cathode layer thickness�, shows that thecathode voltage fall, Uc, should increase with the Hall pa-rameter �, i.e., with the magnetic field. Note that Eq. �6�,which can be easily obtained from Eqs. �5� and �7�, is ingood agreement with experimental measurements of break-down voltages in crossed fields in nitrogen.27

The electrical conductivity of the flow was found fromthe linear slope of the current voltage characteristics atB=0 �i.e., at �=0� using Eq. �4�, �=0.073 mho/m in nitro-gen and �=0.072 mho/m in air. Finally, assuming that theconductivity is independent of the magnetic field, the Hall
parameter was determined from the current-voltage charac-

teristics of Figs. 18 and 19 and Eq. �4�. From Eq. �4�, it canbe seen that sustaining the same current at different magneticfields requires the effective reduced electric field, �E /N�eff

U−Uc /h�1+�2, to be the same. Using this procedure, theHall parameter was calculated for �E /N�eff= �0.6–1.2��10−16 V cm2 �this corresponds to U−Uc�200–400 V atB=0 and U−Uc�400–800 V at B=1.5 T�. In this range of�E /N�eff values, the electron-neutral collision frequency innitrogen or air, predicted by solving the Boltzmann equationfor electrons, varies by about 20%. This gives �=1.2±0.12at B=0.75 T and �=1.8±0.35 at B=1.5 T in nitrogen, and�=2.5±0.4 at B=1.5 T in air. The less than linear increaseof the Hall parameter with the magnetic field in nitrogensuggests that the flow conductivity may not remain constantas the magnetic field is increased. The present conductivityand Hall parameter measurements are more accurate than ourprevious results,9,14,28 since in our previous work systematicmeasurements of the current voltage characteristics and ofthe cathode voltage fall were not conducted. In addition, inour previous experiments9,28 the transverse rf discharge ge-ometry was rather complicated, which made discharge char-acterization difficult.

Recently, Faraday current in a crossed pulser-sustainerdischarge in a M =3 supersonic air flow at P=10 Torr hasbeen measured in the presence of a B=5 T magnetic field.19

In these measurements, the peak dc sustainer current did notexceed 1.1 mA, which is about three orders of magnitudelower that the present results shown in Figs. 16–19. Such adramatic difference is most likely due to rather low dc volt-ages used in Ref. 19, up to U=300 V, which is below thecathode voltage fall measured in the present experiments,Uc=520±50 V at B=1.5 T. At these low voltages, the sus-tainer current measured in the present work was also verylow �see Figs. 18 and 19�. Again, from Figs. 18 and 19 it canbe seen that the cathode voltage fall increases with the mag-netic field, which would require applying increasingly higherdc voltages to draw significant sustainer currents at highermagnetic fields. Also, the surface area of the sustainer elec-trodes used in Ref. 19 was significantly smaller than in thepresent work.

Figure 20 shows the LDI spectra in M =3 flows of nitro-gen at the plenum pressure of P0=250 Torr, magnetic fieldB=1.5 T, sustainer voltage UPS=2 kV, and the LDI probebeam placed 6 mm from the wall, i.e., near the outer edge ofthe boundary layer �see Figs. 5–8�. The two groups of spec-tra shown are for the ballast resistor of R=1 k� �time-averaged MHD current of �I=0.65 A� and R=0.5 k� ��I=0.94 A�, both for accelerating and retarding Lorentz forcedirections. It can be seen that at the lower MHD current,there is almost no effect of the Lorentz force polarity on thedensity fluctuations, while at the higher MHD current, theretarding force results in higher density fluctuation intensityin the frequency range of 2–40 kHz, up to 2 dB �about25%�. For both accelerating and retarding force, the resultsof two successive runs are shown to demonstrate the run-to-run reproducibility of the observed effect, which appears toincrease with the MHD current.

Figure 21 shows the LDI spectra in M =3 dry air flows at
the same conditions as the high-current regime of Fig. 20,


i.e., at R=0.5 k�, �I=0.78 A. In this case, the four spectrashown correspond to four possible combinations of the MHDcurrent and the magnetic field vectors, j and B, two of whichcorrespond to the accelerating Lorentz force and the othertwo to the retarding Lorentz force, F= jÃB. This has beendone by switching the dc power supply polarity and/or themagnet power supply polarity. One can see that both retard-ing force combinations produce significantly higher densityfluctuation intensities in the frequency range of 2–40 kHzcompared to both accelerating force combinations, again upto 2 dB.

Figures 20 and 21 also show LDI spectra measured withthe pulsed power supply operating but with the dc sustainervoltage turned off, i.e., when there was no MHD force ap-plied to the flow. It can be seen that at these conditions thedensity fluctuation spectra are very close to the spectra mea-

FIG. 20. LDI spectra in a crossed discharge in an M =3 flow of nitrogen, fordifferent Lorentz force directions and ballast resistances �MHD currents�.

FIG. 21. LDI spectra in a crossed discharge in an M =3 flow of dry air, fordifferent Lorentz force directions. Both accelerating and retarding jÃBforce directions are created by two different combinations of j and B
vectors.

sured with the accelerating MHD force applied. It was alsofound that the LDI spectra measured in both nitrogen and airflows without plasmas �i.e., with both power supplies turnedoff� are nearly identical to the spectra with only the pulseroperating. These results show that in both cases the effect onthe density fluctuations is detected only when the retardingMHD force is applied to the flow, as well as provide strongevidence that the observed effect is indeed due to Lorentzforce, not Joule heating of the flow.

Qualitatively, the observed density fluctuation increaseby the retarding Lorentz force appears to be consistent withthe results of turbulence measurements in a M =3 turbulentboundary layer in the presence of an adverse pressuregradient,29 which showed that at these conditions the turbu-lence intensity, u�2 ,v�2, and turbulent shear stress, u�v�, areall significantly amplified. However, the authors of Ref. 29suggest that these results should be interpreted with caution.Indeed, turbulence measurements in a M =3 turbulent bound-ary layer in a rapid expansion flow �i.e., in the presence of anaccelerating pressure gradient�30 showed that although theturbulence intensity, u�2, at these conditions is significantlyreduced, the mass flux fluctuations, ��u�, remain unchanged,which suggests that density fluctuations, ��, are also unlikelyto change. Interestingly enough, in the present work we alsohave not found any detectable effect of accelerating Lorentzforce on the density fluctuations.

In the present measurements, the highest time-averagedMHD sustainer currents, exceeding 1 A, were detected inM =3 flows of N2–He mixtures. Figure 22 shows the densityfluctuations spectra in M =3 flows of an 80% N2–20% Hemixture, at P0=250 Torr, magnetic field B=1.5 T, sustainervoltage UPS=2 kV, and R=0.5 k�. At these conditions, thetime-averaged MHD current was �I=1.02 A for the acceler-ating Lorentz force and �I=1.14–1.17 A for the retardingforce. The LDI spectra shown in Fig. 22 have been measuredat two different distances from the test section wall, 6 mm

FIG. 22. LDI spectra in a crossed discharge in an M =3 flow of an 80%nitrogen–20% helium mixture, for different Lorentz force directions andLDI probe beam locations.

and 4 mm. Again, in both of these cases, the results are con-



sistent with measurements in nitrogen and air, i.e., the den-sity fluctuation intensity is noticeably higher �by up to 2 dB�for the retarding Lorentz force. This final series of measure-ments demonstrate that the MHD effect on the density fluc-tuations is detected at multiple locations across the boundarylayer.

IV. SUMMARY AND FUTURE WORK

This paper presents results of supersonic boundary layerflow visualization experiments using laser sheet scattering,as well as MHD boundary layer control experiments usingrepetitively pulsed, short-pulse duration, high-voltage dis-charge in M =3 flows of nitrogen and air in the presence ofmagnetic field of B=1.5 T. Laser sheet scattering experi-ments using flow seeding with acetone vapor showed thatside wall boundary layers in the supersonic test section areconsiderably thicker near the center plane of the flow.Boundary layer thickness determined from the flow visual-ization is consistent with previous Pitot probe and schlierenmeasurements. The flow visualization results also show thatas the stagnation pressure increases from P0

=150 Torr to 450 Torr, for Reynolds number ranging fromRex=2.7�105 to 8.1�105, the boundary layer flow becomesmuch more chaotic, with the spatial scale of temperaturefluctuations decreasing. Combined with the results of densityfluctuation spectra measurements using the laser differentialinterferometry �LDI� diagnostics, this behavior suggests thatboundary layer turbulent transition occurs at stagnation pres-sures of P0�200–250 Torr.

Operation of a crossed discharge �pulser+dc sustainer�in M =3 flows of air and nitrogen at the pulse repetition rateof 40 kHz demonstrated that such discharge produces astable, diffuse, and uniform plasma. The peak voltage in therepetitively pulsed discharge used for supersonic flow ioniza-tion in the present experiments is about 12 kV, with a volt-age pulse duration �FWHM� of approximately 30 ns. Both innitrogen and in dry air, the plasma does not fully decay be-tween the ionizing high-voltage pulses. The time-average dccurrent achieved in such discharges is up to 1.0 A in nitrogen�conductivity of �=0.073 mho/m� and up to 0.8 A in air��=0.072 mho/m�. The electrical conductivity and the Hallparameter in nitrogen and air flows are inferred from thecurrent voltage characteristics of the sustainer discharge.These results demonstrate the feasibility of the use of therepetitively pulsed discharge as an efficient and stable ion-ization source sustaining electrical conductivity in super-sonic nonequilibrium MHD flows.

LDI measurements detected an MHD effect on the ion-ized boundary layer density fluctuations at these conditions.In particular, retarding Lorentz force applied to M =3 nitro-gen, air, and N2–He flows produces an increase of the den-sity fluctuation intensity by up to 2 dB �about 25%�, com-pared to the accelerating force of the same magnitudeapplied to the same flow. The effect is demonstrated for twopossible combinations of the magnetic field and transversecurrent directions producing the same Lorentz force direction�both for accelerating and retarding force�. Comparison with
the LDI spectra measured with no MHD force applied

showed that the effect on the density fluctuations is producedonly by the retarding Lorentz force, while the Joule heateffect appears insignificant.

In future work, the main thrust will be to improve theflow quality in the MHD test section. This will include de-sign and manufacturing of two new M =3 and M =4 testsections with the contoured nozzle walls, as well as anglestep diffuser walls being the side walls of the test section�instead of top and bottom walls in the present design�. Inthis new design, small divergence angle will also be intro-duced between the side walls to provide boundary layer re-lief. These changes are expected to considerably reduce thesecondary cross flow producing bulges in the side wallboundary layers. Finally, since seeding the flow with acetonevapor is not feasible in the presence of plasmas in the testsection, a long-term objective is also to develop in situboundary layer flow visualization diagnostics, which can beused to characterize the state of the boundary layer duringthe MHD forcing. A promising possibility in this respect isseeding the flow with nitric oxide and using laser sheet NOLIF on the 226 nm NO�X2�, v=0→A2�, v=0� -band tran-sition to map the flow temperature field.

ACKNOWLEDGMENTS

This research has been supported AFOSR Grant No.F49620-02-1-0164, and Phase II SBIR Grant No. F33615-01-C-3112 of Air Vehicles Directorate of AFRL. We wouldlike to thank Dr. Roger L. Kimmel for numerous helpfuldiscussions. We would also like to express our sincere grati-tude to Fiodar Pliavaka and Syarhei Harbatau from ChemicalPhysics Technologies for continuing support and collabora-tion, as well as for their help in setting up and operating thepulsed power supply.

1I. V. Adamovich, J. W. Rich, and G. L. Nelson, “Feasibility study ofmagneto-hydrodynamics acceleration of unseeded and seeded air flows,”AIAA J. 36, 590 �1998�.

2V. L. Fraishtadt, A. L. Kuranov, and E. G. Sheikin, “Use of MHD systemsin hypersonic aircraft,” Tech. Phys. 43, 1309 �1998�.

3C. Park, U. B. Mehta, and D. W. Bogdanoff, “Magnetohydrodynamic en-ergy bypass Scramjet performance with real gas effects,” J. Propul. Power17, 1049 �2001�.

4S. O. Macheret, M. N. Shneider, R. B. Miles, and R. J. Lipinski, “Electronbeam generated plasmas in hypersonic MHD channels,” AIAA J. 39, 1127�2001�.

5S. O. Macheret, M. N. Shneider, and R. B. Miles, “Magnetohydrodynamiccontrol of hypesonic flow and Scramjet inlets using electron beam ioniza-tion,” AIAA J. 40, 74 �2002�.

6S. O. Macheret, M. N. Shneider, and R. B. Miles, “MHD power extractionfrom cold hypersonic air flow with external ionizers,” J. Propul. Power18, 424 �2002�.

7A. L. Kuranov and E. G. Sheikin, “Magnetohydrodynamic control onhypersonic aircraft under ‘Ajax’ concept,” J. Spacecr. Rockets 40, 174�2003�.

8S. V. Bobashev, Yu. P. Golovachov, and D. M. Van Wie, “Deceleration ofsupersonic plasma flow by an applied magnetic field,” J. Propul. Power19, 538 �2003�.

9R. Meyer, M. Nishihara, A. Hicks, N. Chintala, M. Cundy, W. R. Lempert,I. V. Adamovich, and S. Gogineni, “Measurements of flow conductivityand density fluctuations in supersonic nonequilibrium MHD flows,” AIAAJ. 43, No. 9, 1923 �2005�.

10P. Palm, R. Meyer, E. Ploenjes, A. Bezant, I. V. Adamovich, J. W. Rich,and S. Gogineni, “MHD effect on a supersonic weakly ionized flow,”
AIAA Pap. 2002–2246 �2002�.


11H. Schlichting, Boundary Layer Theory �McGraw-Hill, New York, 1968�.12C. Henoch and J. Stace, “Experimental investigation of a salt water tur-

bulent boundary layer modified by an applied streamwise magnetohydro-dynamic body force,” Phys. Fluids 7, 1371 �1995�.

13R. Meyer, N. Chintala, B. Bystricky, A. Hicks, M. Cundy, W. R. Lempert,and I. V. Adamovich, “Lorentz force effect on a supersonic ionized bound-ary layer,” AIAA Pap. 2004–0510 �2004�.

14M. Nishihara, R. Meyer, M. Cundy, W. R. Lempert, and I. V. Adamovich,“Development and operation of a supersonic nonequilibrium MHD chan-nel,” AIAA Pap. 2004–2441 �2004�.

15M. Nishihara, N. Jiang, W. R. Lempert, I. V. Adamovich, and S. Gogineni,“MHD supersonic boundary layer control using pulsed discharge ioniza-tion,” AIAA Pap. 2005–1341 �2005�.

16J. D. Cobine, Gaseous Conductors: Theory and Engineering Applications�Dover, New York, 1958�.

17A. E. Hill, “Continuous uniform excitation of medium-pressure CO2 laserplasmas by means of controlled avalanche ionization,” Appl. Phys. Lett.22, 670 �1973�.

18N. A. Generalov, V. P. Zimakov, V. D. Kosynkin, Yu. P. Raizer, and D. I.Roitenburg, “Method for significantly increasing the stability limit of thedischarge in fast-flow large-volume lasers,” Sov. Tech. Phys. Lett. 1, 201�1975�.

19R. C. Murray, S. H. Zaidi, M. R. Carraro, L. M. Vasilyak, M. N. Shneider,S. O. Macheret, and R. B. Miles, “Investigation of a Mach 3 cold air MHDchannel,” AIAA Pap. 2003–4282 �2003�.

20R. C. Murray, S. H. Zaidi, M. R. Carraro, L. M. Vasilyak, M. N. Shneider,
S. O. Macheret, and R. B. Miles, “Observation of MHD effects with

nonequilibrium ionization in cold supersonic air flows,” AIAA Pap. 2004–1025 �2004�.

21T. R. Salyer, S. H. Collicott, and S. P. Schneider, “Feedback stabilizedlaser differential interferometry for supersonic blunt body receptivity ex-periments,” AIAA Pap. 2000–0846 �2000�.

22P. Rawat, X. Zhong, V. Singh, and S. Gogineni, “Numerical simulation ofsecondary flow in a weakly ionized supersonic flow with applied electro-magnetic field,” AIAA Pap. 2005–5050 �2005�.

23Yu. P. Raizer, Gas Discharge Physics �Springer-Verlag, Berlin, 1991�.24B. F. Gordiets, V. A. Osipov, and L. A. Shelepin, Kinetic Processes in

Gases and Molecular Lasers �Gordon and Breach, London, 1988�.25R. J. Rosa, Magnetohydrodynamic Energy Conversion �McGraw-Hill,

New York, 1968�.26A. E. D. Heylen, “Electrical ionization and breakdown of gases in a

crossed magnetic field,” IEE Proc., Part A: Phys. Sci., Meas. Instrum.,Manage. Educ. 127, 221 �1980�.

27C. L. Dargan and A. E. D. Heylen, “Uniform-field sparking voltages ofgases in crossed magnetic fields,” IEE Proc. F, Commun. Radar SignalProcess. 115, 1034 �1968�.

28R. Meyer, B. McEldowney, N. Chintala, and I. V. Adamovich, “Measure-ments of electrical parameters of a supersonic nonequilibrium MHD chan-nel,” AIAA Pap. 2003–4279 �2003�.

29E. M. Fernando and A. J. Smits, “A supersonic turbulent boundary layer inan adverse pressure gradient,” J. Fluid Mech. 211, 285 �1990�.

30D. R. Smith and A. J. Smits, “The rapid expansion of a turbulent boundary
layer in a supersonic flow,” Theor. Comput. Fluid Dyn. 2, 319 �1991�.

Low-temperature supersonic boundary layer control using ... · of magnetic compression circuits. The use of the insulated gate bipolar transistor switch allows reaching high pulse

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