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MARCH 1963 TECHNICAL NOTES AND COMMENTS 715

Photo-

q z q . dFig. 1 Schematic ofthe apparatus

gas stream, thus enabling fluctuations of plasma intensi ty a tfrequencies in excess oflOO-kc/sec to be resolved. In theseinvestigations, both argon and nitrogen gases have been used.

The resul ts show th at two distinct modes of operation oc-curred: 1)a steadily burning arc, characterized by an almostconstant voltage drop between the electrodes, and 2) an

unstable arc, recognizable by large amplitude fluctuationsin the voltage. When argon was being used as the tes t gas,both types of operation were observed, the unstable arcoccurring only a t low mass flow rates. In Fig. 2, traces ofthe arc voltage (Fig. 2a) and current (Fig. 2c) are shown forthe stable arc column, the current trace reflecting a 3Wcpsripple inherent in the power supply which uses three-phaserectification. Also in Fig. 2a IS a trace of th e photodiodeoutput, which may be related to t emperature fluctuations byreference to Fig. 2b. The curves shown in this figure havebeen derived from a knowledge of such transi tion probabilities

T,i 3000

as are currently available (see Ref. 2) . For the nitrogen casediscussed below, similar curves have been interpolated fromdata given b y Keck et aL3considering t he l\r, first and secondpositive bands and the N z+ first negative. These calcula-tions have assumed th e plasma to be in thermal equilibriumand optically thin, both of which conditions are, with otherrelated matters, currently under investigation in the labora-tory of th e Imperia l College ofScience and Technology.$The family ofcurves shown in Fip. 2b illustrates that thefluctuations in relative intensity recorded by the photodiodeare indicative of only small changes in temperature. Spec-troscopic measurements ofthe freestream temperature in-dicate a mean value of4550K (shown in Fig. 2b) for thisoperating condition, which leads to the conclusion that thegas temperature was fluctuating only by approximately+50K.

In passing, it should be noted that for argon at thesetemperatures a change oftwo orders of magnitude in the lightintensity, i.e., the range normally covered by photographicmaterials, would indicate a temperature fluctuation ofonlyabout 15YG. Although this is not an insignificant variation,when examining photographs ofa jet care must be exercisedto avoid concluding that unexposed regions on the film showthe nonexistence ofthe plasma.

The curves ofFig. 3illustrate the difference between thenitrogen operation and the stable argon characteristics dis-cussed previously. The most striking point is the un-steadiness of the arc voltage, which oscillates a t a frequencybetween 2 and 3 kc/sec. Figure 3a shows that the arcvoltage increases from about 40 v t o a peak value in excess of

0 Excitation temperature measurements ofgases in an archeated ind tunnel at reduced pressures ( to be published).

4Fig. 2 Observations ofthe are behavior for argon; = @.I.% Ibjrnin, 7 = 24 v, f = 870 amp; s w e e p spced 011 oscilloscope

traces i s 2.0msec/cm

Tr:3150 650@ 7700

a) b) c)Fig. 3 Ohservaliorisofthearcbehavior for nitrogen;h = 0.180 Ib/min, V = 81.0 v37 = 460 amp; s w e e p sp eed on o ~ ~ i l t o ~ c a ~ p e

traces is 0.2 msecJcm

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716 AIAA JOURNAL VOL. 1, NO. 3

Fig. 4m = 0.128 lb/min,Another mode of the unstable nitrogen operation;= 64 v; sweep speed is 0.1 msec/cm100 v and then falls very suddenly to the initial value;measurements of t he decay time indicate values of t he orderof1.0 psec. This sudden drop in voltage is reflected as apeak in the arc current, seen in the upper t race of Fig. 3c.The lower trace of this figure shows the photodiode output,which indicates that a peak in the light intensity occurs in-phase with the current maxima, although the effects ofdiffusion appear to have broadened the intensity pulse.When operating with nitrogen, the tes t section becomes filledwith a luminous gas, which probably accounts for the apparen tshift of t he intensity curve away from the zero.

It has been noticed tha t the nature of the voltage instabilityfor nitrogen changes to tha t shown in Fig. 4when the massflow rat e is reduced. Comparing Fig. 4with Fig. 323, it canbe seen that the voltage follows a similar trend while increas-ing, but instead of falling suddenly from the peak value, itdecreases in a series of steps. Despite the radical change involtage characteristic, the frequency of the fluctuations re-mains almost unaltered.It has been proposed t ha t the arc instability results from a

mechanism indicated in Fig. 5a. The arc initially strikes atposition 1 and then moves down the anode through the sub-sequent positions. This movement results from both thedownstream convection ofthe lower conductivity gas,initially at position I , and the self-induced magnetic forcecaused by the curvature in the current path. For simplicity,any representation of the gas swirl has been omitted; however,the inherent stability of the vortex tends to localize the arcalong the axis of the anode. When the arc reaches position5, the voltage drop along it has increased to a value sufficientlyhigh for breakdown to recur at position I , so tha t th e processis cyclic. Such a behavior is compatible mith the voltagetrace shown in Fig. 3a; however, it cannot explain the modeshown in Fig. 4.An explanation for this mode is that,before breakdown occurs, the arc column between C an d B inFig. Sa itself becomes unstable. This is possible because aradial perturbation ofthe column will produce an outwardmagnetic force, which under unfavorable conditions couldovercome the inward aerodynamic force resulting from the gas

Fig. 5 Proposed arccolumn configurations

swirl. This type of instability could lead to the column con-figuration shown in Fig. 5b. Ifthe amplitude of the wavesshown increases, the arc path will be shortened due to succes-sive earlier contacts with the anode, and avoltage trace similarto th at ofFig. 4 could be expected.

Conclusions

The results of these investigations show that for th is typeof a rc generator it is possible to have a stable arc columnconfiguration for argon. This is contrary to the inferenceof Ref. 1,in which the gas being used was not stipulated.

Stable operation has not yet been achieved when runningwith nitrogen, even though the mass flow, open circuit voltage,and electrode geometry were varied. The measurements ofthe light intensity, taken downstream of the nozzle, indicatethat the sett,lingchamber and nozzle did not smooth the fluc-tuations. Thus, the interpretation of results taken in such afacility must be made with caution, since time-averagedmeasurements for the unsteady flow are not necessarily thesame as those tha t would be measured in a n equivalent steadyflow.

References

1 Dooley, M. T., McGregor, W. K., and Brewer, L. E., Char-acteristics ofthe arc in a Gerdien-type plasma generator, ARSJ.

2 Glennon, B. M. and Wiese, W. L., Bibliography ofatomicprobabilities, Natl. Bur. Standards Monograph 50

Keck, J. C., Camm, J. C., Kivel, B.. and Wentink, T., Ra-Shock tube study ofabsolute in-

32,1392-1394 (1962).

transition(1962).

diation from hot air: Part 11.tensities, Ann. Phys. 7, 1-38 (1959).

Blast-Wave Correlation of Pressures on

Blunt-Nosed Cylinders in Perfect- and

Real-Gas Flows at Hypersonic Speeds

DONALD M. KUEHNNASA Ames Research Cenlei,Moffett Field, Calif .I t is shown that the blast-wave parameter that

includes a function ofthe isentropic exponent y of-

fers the possibility ofcorrelating blunt-nosed cylin-

der pressures obtained by theoretical solutions and

experiment for both perfect and real gases. The re-

sult of the correlation is a single equation, in blast-wave form, which should approximate the pressures

on blunted cylinders in both real and perfect gases

for a wide range of nose drag and Mach number.

HE blast-wave theory has been used in many investiga-T tions to correlate the surface pressures for blunted,stream-aligned cylinders. The parameter ( z / d )/Ma2CD1/2hasbeen used for both perfect an d real gases (e.g., see Refs. 1and2). Pressures on cylinders with different nose-drag coefficientsCD and freestream Mach numbers Ma obtained by themethod of characteristics are correlated in Ref. 1 for each oftwo perrect gases. The parameter worked very well for con-stant isentropic exponent y but is inadequate for correlatingpressures for various values ofy.

The generalized first-order blast-wave theory for axisym-metric flow223contains a parameter for the effects of t he isen-

- I

\ \ \ \ \ \ \ 9 Received by ARS November 13,1962.* Research Scientist.