1159 IEPC-93-126

CHAMBER EFFECTS ON PLUME EXPANSION

FOR A LOW-POWER HYDROGEN ARCJET

Iain D. Boyd*

Cornell University, Ithaca, NY 14853.

Doug R. Beattiet and Mark A. Cappellit

Stanford University, Stanford, CA 94305.

Abstract

Numerical simulations and experimental measure-ments are obtained for the expansion of a low-densitythruster plume into a finite back-pressure. The cence far into the plume flow field of the arc-ignited

thruster employed is a low-power hydrogen arcjet de- thruster. These measurements indicated the presence

veloped by NASA Lewis Research Center. For these of some interference between the plume and the resid-

investigations, the arc is not ignited. The computa- ual gas. There is a requirement to assess these effects

tions are performed with the direct simulation Monte in all plume vacuum facilities.

Carlo method (DSMC). The experimental investiga- Unfortunately, it is quite difficult to estimate such

tion probes the flow using the Raman scattering tech- effects. It is not sufficient to measure the background

nique. The interaction of the expanding plume with pressure in the chamber and feel secure if that value is

the chamber background gas is found to form shock much smaller than the exit pressure predicted by one

waves in both the simulations and experiments. This dimensional analysis of the nozzle flow. The plume

phenomenon is investigated further by increasing the expanding from a typical arcjet is complicated by vis-

background pressure. Direct comparison of the simu- cous and chemical kinetic effects. The flow field istwo-dimensional such that densities at the nozzle exitlation results and experimental measurements is veryimensional such that ensities at the nozzle exit

favorable. centerline may be an order of magnitude higher thanthose at the nozzle lip. In addition, the physical be-

Introduction havior that occurs in the interaction region betweenFor several years, there has been a substantial the plume and the residual gas is not simple. Depend-

amount of research and development in arcjet technol- ing on flow conditions, shock waves may be formed.ogy. Many recent studies have applied sophisticated and the viscous and kinetic effects again become sig-experimental techniques to investigate flow properties nificant.in the nozzle and plume of various arcjet thrusters. In Therefore, a detailed study of the interaction phe-these investigations, the thruster plume expands into nomenon has been undertaken. Experimental inves-a vacuum tank. Of course, due to the finite pump- tigations employing Raman scattering are applied toing speeds of ground-based experimental facilities, the measure number density along the axis of the plume.back pressures obtained are orders of magnitude higher The measurements are carried through the interactionthan orbital flight conditions. There is a real con- region where the thruster plume encounters the resid-cern that measurements taken in such facilities may be ual gas. In addition, detailed Monte Carlo calculationsaffected by the interaction of the expanding thruster of the same flow conditions are performed. These ex-plume with this residual pressure in the test chamber. perimental and numerical techniques are described in

The purpose of this paper is to address this issue the following sections.for a specific thruster operated in the arcjet facilityer lat Stanford University. A previous paper reportedmeasurements obtained using laser induced fluores- Theory

* Assistant Professor. School of Mechanical Spontaneous Raman scattering is an inelastic, lin-

and Aerospace Engineering. ear two-photon scattering process. In this case, an

t Research Assistant. Mechanical Engineering Dept. incident photon scatters off an H2 molecule causingt Assistant Professor. Mechanical Engineering Dept. a change in the molecular quantum state and a corre-

Copyright @1993 by the American Institute of Aeronautics andAstronautics, Inc. All rights reserved.

IEPC-93-126 1160

2 IEPC 93-126

sponding change in the energy of the scattered photon. of about 2800. This value indicates that the flow isThe intensity of the signal is given by: 3 dominated by the effects of thermal relaxation, and

by viscosity in the nozzle boundary layer.

N,, = NL. 1.n. n (. \ .dJd The Raman excitation source is an Ar+ laser withno \&W /, f 2.0 W in the 487.986 nm line used for this experiment.

where: The laser beam is focused axially into the plume witha beam waist under 100 um (see Fig. 2). Scattered

N,, =number of Raman photons collected light is collected and focused onto a monochromatorfor transition from initial state "i"

entrance slit with an achromatic two-lens system. Theo final s tae f" collection optical axis is perpendicular to the laser po-

NL =number of incident laser photons larization and the direction of laser propagation. TheI =sample length imaged spatial resolution is 4 mm in the axial direction (de-

ni =number density of sattering species termined by the slit height) and 0.1 mm in the radialno direction (determined by the laser beam waist). TheV. =initial vibrational state monochromator is a 1.0 m focal length f/8.7 single-J, =initial rotational stateS =itial rotational state pass Czerny-Turner design with a 1180 line/mm grat-(A),,, =differential Raman cross section forS differential Raman cross section for ing blazed at 500 nm. A long-pass filter is placed be-

transition from state "i" to "f" fore the entrance slit to further reduce the intensity ofdw =collection solid angle collected laser light to negligible levels. The monochro-

The number of scattered photons is linearly propor- g g resolution ofmator slits are 400 /m giving a spectral resolution oftional to the number of incident photons and the den- 0.2 nsity of the scattering species. Spontaneous Raman 0.24 nm.sity of the scattering species. Spontaneous Raman Light is detected at the exit slits by a cooled. lowscattering has the advantage of allowing spatially re- ni photomultiplier tue (PMT) with a dark noisesolved measurements of ground state densities with of 03 out Te PT outp amplifed andan easily interpretable signal. The primary disad- s to continuously gated photon counter. Thevantage is the small scattering cross section (typically monc mator is set at the position of the vi-10-33M M emonochromator is set at the position of the J=1 vi-10- -m2). Measurements here are based on the purely1 ). easurements here are basd on the pel brational transition. Data is collected with the arcjetvibrational transition from v=0 to =1 with J=l. The .

St r fixed, then the arcjet is translated to a new positionvibrational transitions are well separated spectrally and the proess repeated. In this study, data is taken

Sd t = s and the process repeated. In this study, data is takenfrom the laser wavelength and the J=1 state is the

along the arcjet axis from the exit plane to 60 mmmost populated at the low temperatures involved in ai t

downstream. The back pressure is varied from 43 to67 Pa by varying the number of pumps used. Data

Experiment is also taken with the chamber evacuated below 1 Pa

The arcjet considered in the present study is a to give a background signal. Calibration is performed

1 kW class NASA laboratory hydrogen thruster. by filling the chamber with 10 kPa of static H2 and

The converging-diverging nozzle geometry is shown in repeating the scans.

Fig. 1. The nozzle has a 0.635 mm throat diameter The signal recorded is a linear function of the num-

with a 20" half-angle, and an exit to throat area ratio ber density of H2 in the J=1 state. The density is

Sof 225:1. The thruster is operated in a vacuum cham- found by first subtracting the background signal (pri-

ber 1.09 m long and 0.56 m in diameter with optical ac- marily PMT dark noise) from both the data and ref-

cess through 75 mm diameter ports. It is mounted on a erence signals, and then scaling by the known number

two axis translation stage (axial and radial). The tank density of the reference scan:

is evacuated by two Roots blowers backed by mechani- N(flow) - N(back)cal roughing pumps with a total capacity of 1.2 m3s- '. n(J = 1, flow) = N(re) - N(back) x n(J = , ref)This system is capable of maintaining a back pressureof 43±2 Pa with hydrogen flowing. The density of the J=1 state in the reference cell is

The experimental conditions chosen are a cold-flow calculated using a Boltzmann population distributionof 14.1±0.1 mg s - 1 hydrogen with a stagnation tem- for the rotational states, using the energy levels fromperature of 300 K (no arc ignition). These conditions Jennings. 4 The error in density is estimated as onecorrespond to a Reynolds number at the nozzle throat standard deviation, assuming the counts follow a Pois-

1161 IEPC-93-126 IEPC 9326 3IEPC 93-126 3

son distribution. The errors range from 6% at the simulation are specified in terms of pressure and tern-highest densities to 36% at the lowest. perature. It is very difficult to perform an exact sim-

ulation of the chamber residual pressure. It is almostNumerical Investigation certainly not going to be distributed homogeneously

The numerical investigation employs the direct sim- throughout the chamber. Also, it is not clear what theulation Monte Carlo method (DSMC). In this tech- temperature of the residual gas will be. For the pur-nique, model particles are simulated in the computer poses of the present investigation, a constant pressureand used to represent the large number of molecules (ps) for the background gas is assumed at each of thein a real gas. These particles undergo translational boundaries. In addition, the residual gas is assumed tomotion and intermolecular collisions. In this manner, be at room temperature (300 K). Particles are intro-the technique has been very successful in simulating duced into the simulation across each boundary withnonequilibrium gas dynamics occurring for low den- properties corresponding to a gas at rest at the condi-sity flows in propulsion and hypersonics. The code tions of the residual gas defined in this manner. Thisemployed in the current study is based on a numer- technique was applied in a previous investigation ofically efficient program designed to execute on Cray helium micro-thrusters, 10 and diffuse shock-like struc-supercomputers. 5 With minor modifications, the same tures were observed in the solutions. However, no ex-code is used in the present study on a Silicon Graph- perimental data was available to assess the validity ofics Indigo work-station. The rate of execution of the the calculated results.code on the work-station is ten times slower than on aCray YMP. In the future, it is planned to optimize the Results and Discussion

DSMC code for improved performance on the scalar First, the DSMC method is applied to model thework-station. hydrogen plume expansion process into a perfect vac-

Application of the DSMC technique to model the uum. This is close to the in-flight operational mode ofnozzle and near-field plume expansion of this unig- the device (although the arc is unignited). Therefore,nited hydrogen arcjet has been reported previously.8 In the boundary conditions are specified with pb=0 Pa.Ref. 6 it was shown that the operating conditions give Contours of number density are shown in Fig. 3.rise to a strong degree of rotational nonequilibrium for The labels correspond to LOG10 number density inexpanding hydrogen. Through comparison with ex- molecules/m 3 . Note that the nozzle exit is aboutperimental measurements of number density and rota- 4.75 mm long. It is clear that the flow is highly di-tional temperature, an accurate model for simulating rected. The variation of density along the plume cen-rotational relaxation of hydrogen was developed. This terline is shown in Fig. 4a. The density decreasesmodel is again employed in the current study. The rapidly by a factor of about 50 at a distance of 10 cmflow field considered begins at the exit plane of the from the nozzle exit. A slower decrease in the trans-nozzle and extends to distances of 10 cm axially and lational temperature is shown in Fig. 4b. Also in-6 cm radially. The calculated results reported in Ref. 6 cluded is the rotational temperature which appears toare employed as an input condition at the nozzle exit be frozen. Note the degree of thermal nonequilibriumplane for the present study. Decoupling the nozzle and that exists at the nozzle exit plane which occurred dur-plume calculations saves a great deal of computational ing the nozzle expansion process. The vacuum simu-expense. The densities in the nozzle flow are orders of lations are the least expensive to compute and requiremagnitude higher than those occurring in the plume, about 3 hours on the work-station.The computational expense of the DSMC method is The lowest value of the residual chamber pressureapproximately proportional to the density of the flow. that can be achieved in the experimental facility isTherefore, it takes much less computer resources to pb=43 Pa. The density and temperatures obtainedperform a plume calculation. The smaller size of the using the DSMC method for this residual pressure con-plume problem allows the simulation to be performed dition are shown in Figs. 5a and 5b respectively. Thein reasonable times on a work-station. The decoupled density profile indicates that complex fluid dynamicsapproach for simulating nozzle and plume flows using processes are at work. A very strong shock wave isthe DSMC technique has been successfully applied in formed at a distance of about 10 mm from the noz-previous investigations.'7- zle exit plane. Behind this shock, the gas expands

The conditions along the outer boundaries of the rapidly again before a second compression is reached.

IEPC-93-126 1162

4 IEPC 93-126

This secondary shock-like structure is much weaker, Fig. 7b. The effect of the residual gas is first felt at aand the gas eventually starts to expand again further radial distance of 3 mm from the centerline.downstream. Although not clear in Fig. 5a, a further Consideration is now given to the comparison of theweaker compression occurs at about 70 mm from the numerical results with the measured data. To facilitatenozzle exit plane. These results are consistent with taking high spatial resolution experimental data, onlythe diamond shock patterns observed in larger super- the density in the J=1 rotational state is measured.sonic nozzles. The pressures in the nozzle exit plane These measurements are taken along the plume center-are less than the residual pressure of 43 Pa, thus the line. In the present study, the corresponding numer-nozzle is overexpanded. Actual diamond structure is ical prediction is calculated using the DSMC resultsnot observed in the calculations and this is probably obtained for the total number density and the rota-due to viscous dissipation at the low densities encoun- tional temperature. These are combined in the usualtered. The compression and expansion wave behavior equilibrium relation to determine the number densityis also found in the translational temperature profile in the first rotational level. The numerical and exper-shown in Fig. 5b. The translational mode reaches a imental results are compared in Fig. 8. It should bemaximum after the shock formation at 10 mm from noted that each experimental data point is obtainedthe nozzle exit plane. The subsequent expansion is over a volume that is 4 mm in length axially. Thefollowed by further compression of the temperature measurements resemble the variation in total numberup to and beyond the temperature of the background density shown in Fig. 5a. The agreement between thegas. Extension of the flow field beyond 10 cm axi- two data sets is remarkably good. Although the com-ally would presumably allow the translational mode puted shock location is further from the nozzle exit.to equilibrate with the residual gas. By comparison, the peak value is well predicted. While difficult to dis-the rotational mode undergoes a much slower rate of cern in the experimental data, the secondary compres-relaxation. The rotational temperatures slowly rise sion predicted numerically is not inconsistent with thetowards the equilibrium value. This illustrates the de- measurements. Given the complicated fluid mechan-gree of thermal nonequilibrium that accompanies the ics and physics of these flows, and the uncertainty incomplex flow field structure of these interaction re- the spatial distribution of the residual pressure, thisgions. degree of agreement is very satisfying. The most obvi-

The results shown in Figs. 5a and 5b indicate that ous explanation for the difference in shock location isthe effective test section of flow undisturbed by the that the back pressure in the chamber is not uniform.residual gas only extends along the axis to a distance It is certainly possible that, locally along the axis, theof about 10 mm along the plume centerline. Radially, back pressure may be higher than the value measuredthe influence of the chamber pressure is much stronger experimentally, thus pushing the shock closer to thedue to the reduction in nozzle exit pressure in the ra- nozzle exit. It would be difficult to include this typedial direction. In Fig. 6 contours are shown of the ratio of behavior in the numerical analysis.of pressures computed with pb=0 to those obtained at The results obtained at higher residual pressures inpb= 4 3 Pa. The contour value just less than unity in- the test chamber are now considered. The density anddicates where the residual gas first affects the plume temperature profiles for pb=56 Pa computed along theexpansion process. While the flow along the axis is plume centerline are shown in Figs. 9a and 9b. The

* unaffected to a distance of about 10 mm from the noz- results show the same trends as those obtained for thezle, it is clear that in the radial direction interference lower value of pb. The shock is moved closer to the noz-effects are felt much sooner. Indeed, it appears that zle exit plane, and is now stronger. The peak in trans-there is some interference close to the nozzle lip in the lational temperature is reached sooner. Comparisonnozzle exit plane. This is confirmed in Figs. 7a and 7b with the experimental data shown in Fig. 10 is oncewhich compare the number density and translational again very good. As before, the precise shock loca-temperature profiles computed just downstream of the tion is predicted slightly further downstream than thatnozzle exit plane for the vacuum and pb= 4 3 Pa cases. measured. Finally, the results obtained at the highestFigure 7a indicates that the number density at the back pressure (pb= 6 7 Pa) are shown in Figs. lla, 11b,nozzle exit is only slightly affected by the back pres- and 12. Comparison with the previous figures clearlysure beyond about 4 mm. The translational tempera- illustrates the progressive increase in shock strengthture. however, is much more sensitive as indicated by and movement of the shock closer to the nozzle exit

1163 IEPC-93-126 IEPC 93-126 5

plane as the back pressure is increased. In all these (Grant NAG3-1451) with Dr. P.F. Penko as techni-simulations, the DSMC shock location prediction is cal monitor is gratefully acknowledged. The work ofslightly further from the nozzle than that observed ex- D.R.B. and M.A.C. was supported in part by NASAperimentally. This gives a trend that is consistent with Lewis Research Center with Dr. F.M. Curran as tech-the idea proposed earlier that the pressure in the cham- nical monitor (Grant NAG3-1040), and by Norton Co.ber may be higher than that indicated by the back (Grant ACH-116820).pressure measurement. The general agreement be-tween calculation and experiment is maintained. For Referencesthe experimental data shown in Fig. 12 it appears that 1 Liebeskind, J.G., Hanson, R.K.. and Cappelli, M.A.,the measurements at the nozzle exit plane are affected "Plume Characteristics of an Arcjet Thruster," AIAAby the back-pressure. Clearly, operation of the facil- Paper 93-2530.ity at higher pressures will produce a flow that is not 2 Beattie, D.R. and Cappelli, M.A., "Molecular Hy-anywhere representative of the plume expanding from drogen Raman Scattering in a Low Power Arcjetthe thruster under flight conditions. Thruster." AIAA Paper 92-3566, Nashville, Tennessee,

The solution times required by the DSMC method July 1992.for the simulations with finite back pressures increase 3 Valentini, J.J., in Laser Spectroscopy and Its Ap-with Pb. For the case of pb=67 Pa, a total of 15 hours plications. edited by L.J. Radziemski et al. (Marcelon the work-station is used. Dekker, Inc., New York, 1987), p. 516.

Conclusions 4 Jennings, D.E., Rahn, L.A. and Owyoung, A..Detailed experimental and numerical results have "Laboratory Measurement of the S(9) Pure Rotation

been obtained for the interaction region of an arcjet Frequency," Astrophysical Journal, Vol. 291, 1985,thruster plume expanding into a finite back pressure. pp. L15-L18.Despite the low densities involved, the characteristic 5 Boyd, I.D., "Vectorization of a Monte Carlo Methodphenomena involving formation of shock and expan- For Nonequilibrium Gas Dynamics," Journal of Com-sion waves are observed. Direct comparison of the ex- putational Physics, Vol. 96, 1991, pp. 411-427.perimental data and numerical results gives very good e Boyd, I.D., Cappelli, M.A., and Beattie, D.R.,agreement along the plume centerline. There are two "Monte Carlo and Experimental Studies of Nozzlesignificant findings from the present study. The first is Flow in a Low-Power Hydrogen Arcjet," AIAA Paper-that for this particular facility, there is a small region 93-2529, Monterey, July 1993.of the plume centerline that is unaffected by the back 7 Boyd, I.D., Penko P.F. Meissner D.L. and DeWittpressure. At the lowest pressures achieved, this region K.J., "Experimental and Numerical Investigations ofextends to 10 mm along the centerline: this is less than K .J., enxri m en t al and umerical Investigations of3 nozzle diameters. It is likely that interference effects Low-Density Nozzle and Plume Flows of Nitrogen,"first occur in the radial direction at a much shorter AIAA JournL Vol. 30, October 1992, pp. 2453-2462.distance from the nozzle. The second important con- 8 Penko, P.F., Boyd, I.D., Meissner, D.L. and DeWitt.clusion is that the DSMC method is a very useful tech- K.J., "Measurement and Analysis of a Small Nozzlenique for estimation of the interference effects for a Plume in Vacuum," Journal of Propulsion and Power,particular facility. The complex fluid mechanics cor- Vol. 9, July 1993, pp. 646-648.bine'd with strong viscous and relaxation effects makes 9 Zelesnik, D., Penko, P.F., and Boyd, I.D., "Ef-modeling of these flows very challenging. The direct fect of Nozzle Geometry on Plume Expansion forcomparisons made in this study with the experimen- Small Thrusters," 23rd International Electric Propul-tal measurements indicate that the DSMC technique sion Conference, Seattle, September 1993.is capable of accurately simulating such complicated 10 Boyd, I.D., Jafry, Y.R. and Vanden Beukel, J., "Par-phenomena. It therefore appears that the method is tide Simulation of Helium Microthrusters," Journal ofcapable of assessing the important question of plume Spacecraft and Rockets (in press).interference effects for similar experimental vacuum fa-cilities.

Acknowledgments

Support by NASA Lewis Research Center for I.D.B.

IEPC-93-126 1164

6 IEPC 93-12617.4

O 0 30* 20* I a Flow DirectionC6 O ( g A

C o T c

Figure 1: Arcjet nozzle configuration(Dimensions in mm)

Monochromator Long-pass filter

PMT & Preamp Focusing lens

Collimating Lens

Vacuum Chambe r

Arcet thruster

Data AcquisitionComputer

SPhoton Counter

HV Power Supply Laser focusing lenses

Ar Laser

Figure 2: Experimental Apparatus

1165 IEPC-93-126

1 21

C

SIEPC 9 -126

-o 20 -

00 22-0 2 4 6 8 10

Axial distance (cm)

Fig. 3 Contours of number density at a backgroundpressure of 0 Pa.

102210 -....................----------------------------...= o23 - -

.: ttn -- TranslationS------Rotation

1 0 2 1 I -- I 1 0 1 ' '

1020 1 01

0 20 40 60 80 100 0 20 40 60 80 100Axial distance (mm) Axial distance (mm)

Fig. 4a Number density along the plume centerline Fig. 4b Translational and rotational temperaturecomputed with the DSMC method at a background along the plume centerline computed with the DSMCpressure of 0 Pa. method at a background pressure of 0 Pa.

IEPC-93-126 1166

8 IEPC 93-126

20i 500

E16 - 400ho I -- Translation

L .r 30 ------ Rotation5121- 300

8 200

a 4 - 100 - -------E

Z O 00 20 40 60 80 100 0 20 40 60 80 100Axial distance (mm) Axial distance (mm)

Fig. 5a Number density along the plume centerline Fig. 5b Translational and rotational temperaturecomputed with the DSMC method at a background along the plume centerline computed with the DSMCpressure of 43 Pa. method at a background pressure of 43 Pa.

8

0.6 N 6 p 0 Pa

S_0.2 o p=43 Pa2

0.2

0.010o.o -- '--1o-0 1 2 3 4 5S0 Radial distance (mm)

Axial distance (cm)

Fig. 6 Contours of the ratio of pressure obtained at Fig. 7a Comparison of radial profiles for number den-p6=0 Pa to that obtained at pb= 4 3 Pa. sity near the nozzle exit plane obtained in vacuum and

at finite back pressure.400, 14-

1223001 j 4

(D - ; C 0 Expenment= i ii =ToPa J • roS 0 p43 Pa o

finite back pressure, centerline Monte Carlo1 01N200 - 00

. 0E 0S100 Z

0 O'0 1 2 3 4 5 0 20 40 60 80 100

Radial distance (mm) Axial distance (mm)

Fig. 7b Comparison of radial profiles for temperature Fig. 8 Comparison of measured and calculated data fornear the nozzle exit plane obtained in vacuum and at the number density in the J=1 state along the plumefinite back pressure. centerline at a background pressure of 43 Pa.

1167 IEPC-93-126 IEPC 93-126 9

20, 500,

E 16 - 400 I-

o r -Translation.12- 2\ oo 300. ---- Rotation

i 8 - 200

4 100 -'--------- ---

0 00 20 40 60 80 100 0 20 40 60 80 100

Axial distance (mm) Axial distance (mm)Fig. 9a Number density along the plume centerline Fig. 9b Translational and rotational temperaturecomputed with the DSMC method at a background along the plume centerline computed with the DSMCpressure of 43 Pa. method at a background pressure of 43 Pa.

14,1 20120,

12 - "

- °° E 16E 0 Experiment o 6

8 - C Monte Carlo . 120

: o 8-4 0 0

2 -2

0 ' ' ' z 0 20 40 60 80 100 0 20 40 60 80 100

Axial distance (mm) Axial distance (mm)

Fig. 10 Comparison of measured and calculated data Fig. 11a Number density along the plume centerlinefor the number density in the J=1 state along the computed with the DSMC method at a backgroundplume centerline at a background pressure of 56 Pa. pressure of 56 Pa.

400 . 14350 12

S300 -- Translation . o0 ------ Rotation E 10 o Experiment

|~~~C -5 - Monte Carto200 - ., - 2 o

6

0 0': " __0 20 40 60 80 100 0 20 40 60 80 100

Axial distance (mm) Axial distance (mm)

Fig. 11b Translational and rotational temperature Fig. 12 Comparison of measured and calculated dataalong the plume centerline computed with the DSMC for the number density in the J=1 state along themethod at a background pressure of 67 Pa. plume centerline at a background pressure of 67 Pa.

168T

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