NASA Technical Memorandum 86955 

Vacuum Chamber Pressure Effects 

on Thrust Measurements of Low 

Reynolds Number Nozzles 

(NASA-TY-e6S55) VACOUU CHAEEIE PGBSSUEB N85-2 1259 

BEFUCTS CY TBdUST MEASUEBflEllS OF' LOU 

LBYlOLDS AUUBBE BCZZLiiS (6ASA) 12 p 

ilC AQz/EF Aiil CSCL 21H Uncla s 

63/20 14526 

James S. Sovzy, Paul F. Penko, Stanley P. Grisnik, 

and Margaret V. Whalen 

Lewis Research Center 

Cleveland, Ohio 

Prepared for the 

1985 JANNAF Propulsion Meeting 

sponsored by the JANNAF Interagency Propulsion Committee 

San Diego, California, April 9-12, 1985 
VACUUH CWRER PRESSURE EFFECTS 09 THRUST nLASUREnENTS 

OF LOU aErmKos ~tme~~ NOZZLES 

James 5. Sovey, Paul F. Penko. Stanley P. Crisnik, and Ilaqaret Y. Yhalen 

National Aeronautics ad Space Administration 

Lais Research Center 

Cleveland, Ohio 44135 

Tests uere conaucted to investigate the effect of vxue ocility pressure on the pcrfwmUue 

of upall-thruster nozzles. Thrust oasureaents of two conveqing-diveqing nozzles with m a+cr 

ratio of i40 ana an orifice plate flowing unheated nitrogen ana hydrogen uere titen over r ride range 

of vacuum f aci 1 ity pressures ar.a nozzle throat Reyno Ids nubers. In tk keynolas number rum of 

2200 to 12 there was no discernable viscous effect on thrust bela m arpbient-to-total-pn sun f ratio of lo!? In nearly all cases, flow separation occurred at a pressure ratio of abt 10- . thls was the upper limit for obtaining an accurate thrust wasuremmt for conical nol~ie with 

area ratio of 140. 

A, area of nozzle exit plane 

k* nozzle throat area 

d* nozzle throat diaeter 

Fc reasured thrust corrected for the ambient-pressure force 

F, seasirred thrust at finite ambient pressure 

F, vacuum thrust or thrust measured at near-spwe conditions 

g acceleration of gravity 

ISp vacuW specific ilpulse. F,I:~ 

; piass f lo* rate 

Pa arnbient or vacbM facility pressure 

Ye static pressure of flow at nozzle-exit plane 

Po nozzle ChdPlber total pressure 

he throat Reynolds number, 46/d*" 

u nozzle exit velocity 

ratio of specific heats 

r visccrsity at nozzie chamber total temperature 

INTAOWCTION 

North South station-keeping of many satellites is being met using thrusters in the 0.2 to 0.4 

h thrust range. Performance calibration of these thrusters is generally undertaken in vwuu fwilities with ambient pressures in the range of a few hundred microketers of mercury. Relatively high 

propel iant flow rates usually preclude the use of diffusion pups and large cryo-puped facilities 

are not widely available. 

The thrust measured in a finite ambient pressure, assuming uniform properties at the n0ZZle 

exit, is given by 

t, = iu + (Pe - Pa)Ae, (1) 

an9 the thrust in vacuum is 

FV = :U + PeAe. 

Approve9 for public release; distribution is unlimited. 
Therefore the thrust measured in a finite dient pressure corrected to vwum conditions is given ty 

Equation (3) should yield the correct spue-vuw thrust providing that the ratio of Vbient pressure to nozzle inlet total pressure (PaIP ) is suffZcicntly la so that shock waws are not 

present in the nozzle. Furthemre, in tk case of low Reynolds ncsbcr flaw, the Ybient pressure 

ust be sufficiently la so that it us not influence the nozzle flow field. 

With la Reynolds nubtr (Re) nozzle flow, several investigator^^'^ have found significant 

variation in thrust over a range of vacuum facility pressure from about 1x10'~ to 1 t rr where the 

ramp? f PalPo was wel; below the point dun shocks would be present. Page et al. P and Yoshida 

et 11.9.3 found an appreciable variation in thrust with vwuu ch-r pressure usin) hydrogen and 

rrtnia nsistojets. In their wort, a 17 to 19 percent degradation in thrust occurred dwn tk 

ambient pressure was varied fram about 5x10~ to 1 torr after xcounti 3 for the vlbient pressure 

force over the nozzle exit as ueil as recirculation effects in the vruun chrbtr. Tkir 45 dl 

hydrogen ad amonia resistojets nn operated at throat Reynolds nubtrs of 100 ad 800, respectively. They conjectured that the vicuue chrlwr pressure affected the nozzle f la through the Subsonic boundary layer. 

~othe' did a detailed investigation of lowdeynolds ndr nozzle flow over a Reynolds nrdcr 

range of 50 tc 780. He measured density and tcqtratun distributions in the nozzle fla field using 

an electron-be- method. He also detemined shock patterns and f la separation by f la visualization. His tests were conducted wi4-h unheated nitrogen flowing through two CWI~CII n~zzles, each of 

20' half-angle and area ratio (+/A*) of 66, and each having a different throat diameter. Rothe's 

data showed that at a Reynolds nulber of 50, the flow on the nozzle axis decelerated to sli tly less 

than Uach f at the exit plane. Density profiles at various axial stations in the nozzle $1 f ustrated 

that the flow was fully viscous with no evidence of an inviscid core. At a Reynolds nrrkr of 300, 

the f lor was characterized by a narrow invixid con enveloped by a thick viscous outer layer that 

extended to the ualls. The inviscid core gradually dissipated until it was no longer evident at the 

exit plane. nit flo* on the axis maimd supersonic. 

In investiaatie the effect of a&ient pressure on t flow. Rothe shoed that at a Reynolds hS nubcr of 780, an anbient-to-total-pressure ratio of 3x10- was not enough to maintain full fla in 

the nozzle. A barrel-shaped shock was present upstream of the nozzle exit ad the f low was sepc 

rated from the wall. As the arrbient pressure was raised, the separation point mved further into 

tk nozzle. 

Rothe's ifivestiaation showed that la-Reynolds-nunbcr flow in a converging-diver~ing nozzle is 

characterized by a large subsonic outer region and a nam supersonic core. Hence at la Rewld~ 

nunbers the ambient pressure could conceivably affect the flow through this large subsonic 

and may explain the effect exhibited in Refs. 1 to 3. Rothe's work also showed that as the Reynolds 

nuder was increased, the flow amre closely rescrbled isentropic flow and that shock waves wen 

present when the flow had to adjust to a high anbient pressure. 

To further investigate the effects of adient pressure on low-Reynolds nusbtr nozzle flow and 

the il~plications of testing small thrusters in a finite aabient pressure, tests were conducted with 

several nozzles on unheated nitrogen and hydrogen over a Reynolds nulbcr range of W to 12 000. 

Nozzle thrust was measured at various vrum facility pressures ranging from 3rlO-' co 1 tow. 

The Ateasured alues of thrust corrected for the ambient-pressure force were canparej to the deep- I vacuun (3x10- tow) value in an attenpt to investigate the range of Reynolds nubers where the 

ambient pressure might have a significant effect on thrust as exhibited in Refs. 1 through 3. An 

attempt was also made to irivestiaate the effect of Reynolds nu#&+ on the point where the flow begins 

to separate within the nozzle from the onset of a shock wave. This effort was undertaken to help 

define where thruster test data taken in a finite a6ient pressure can be accurately corrected to 

space-vacuum conditions. 

APPARATUS A10 PfiOtEDURE 

Two convergin+diverging nozzles and an orifice plate were used in the tests. Table I lists 

their dimensions, pressures, and flow rates. Nozzle A was similar to the nozzle on the TRY High 

Performance Electrothema1 Hvdrazine Thruster (H~PEHT)' and had an area ratio of 147. Wozzle B had 

a relatively laroe throat dieter and was operated at nearly the same flow rates as nozzle A to 

achieve lower throat Reynolds n-rs. Nozzle B initially had an area ratio of 140 and was cut down 

to an area ratio of 38 for subsequent tests. The orifice plate had a conical inlet with a 45. 

half-angle. 

Thrust measurements were mad on a thrust Stand that consisted of a ~orizontal mounting plate 

supported by four flexure plates.' Force in the horizontal direction either from thrust or application of calibration weights was @asured by a strain-gage load cell. Prf~pellant was fed to the 
thrust stand in a 3.2 m (118 in) dieter, thi~a11, stainless steel tube that acted as a fifth 

flexure. Thrust-stand tares wen highly reproducible and load-cell drift was insignificmt for 

operation with unheated propellmts. The estiamted precision of the thrust easunwnt is rbout 

N.4 #. Tht uncertainty in the thrust rwasurcll~~t ram from t0.5 percent at 75 di to tz.7 percent 

at 22 * which was the rmqe of thrust values for the tests. 

Yindigc effects, or the circulation of gases in the test facility, produced a thrust-stmd 

deflection opposing the dimtion of mtzzle th st. Sow of the thrust stand mrs rpparently act 

as a osailo in the circulating gas enrirant? The windage effect was exzmined by flawing gas 

thrwgh the orifice plate which was located very mar but disconmctd from the thrust stand aounting plate. Thrust stmi deft tions wen mitored, at the fla rates of interest, over a vacuu 

facility pressure ramp of 10' to LO tow. The largest windage effects occurnd at an aient 

pressure of about 0.05 tom. The nuxirul thrust correction for windage was 1.5 percent f r nitrogen 

and 3 percent for hyd-. The windage corrections at ambient pmsur?s less than 1x1OJ torr 

and greater than 0.3 torr were always less than 1 percent. 

Gas flow rates were measured with mass-fla-rate transducers which used a heated capillary tube 

to relate them1 changes to *ass flow rate and the ads heat capacity. The fla tranducers *tn 

calibrated rith either air or nitrogen using a volume displuermt mthod. A fla rate calibration 

for hydrogen was obtained using gas conversion factors supplied by the transducer venoor. Thus a 

greater uncertainty exists in the hydrogen flow rate measurement. 

The chnbCr pressure for nozzle B was directly measured. The chvlbcr pressure for nozzle A was 

assumed to be bete the line pressure ad the mini- chebcr pressure calculated assuaing a 

thrust cnfficient, FvlPoA*, of 1.6. A value of 1.6 was based on analysis and exptrir;cnt fra~ 

Refs. 6 and 7. 

The tests rere conducted in a vxuua chgber measuring 4.6 m in dir~ter by 19 m lang8. The 

puqing systes is corprised of 20 oil liffusion pumps with four lobe-type blowers installed in parallel, for lowed by four rotating piston-type roughing puaps. Vacuum chdcr pressures in the vicinity of the thr:cst stm wen easured rith a hot cattmle ionization gauge for pressu es less than 

3xl(r4 tow, & cold cathode gauge f rm lw4 to 0.2 tcrr, an Alphatron gauge from l(Tf to 0.5 tor., 

and a bourdon-tube gauge fer pressures greater than 0.5 tom. The indicated pressures were corrected for gwge sensitivity to propellant type. The uncertainty in the aabient pressure (Pa) m?+ 

sureant belau 0.5 torr ras estimted to be less than $8 percent. The uncertainty in the pressure 

ratio (PalPo) for nG.:le A was less than *40 percent ana nozzle B, *ZO percent. 

A typirai plot of thrust versus ambient pressure for nozzle A flawing hydrogel is shown in 

Fia. 1. ite men symbols are the direct thrust apasurenpnts, F,, and the solid symbols are Fm 

corrected for the wbient pressure force. 

The aiffusion pumps could maintain operation at pressures up to 4x10-~ torr for 0-1 gls of 

nitrogen 3nd 9x10'~ torr for the 0.03 gls of hydrogen. A fla rate of 0.1 gls of nitrogen cornsponded to a thrust of abwt 70 &. 

RESULTS AN0 DISCUSSIOU 

The ratio of measured-to-vacum thrust for the two convergingdi verging 922 les is pteSentcd 

for throat Reynolds nunbers of 70C to 12 000 as a function of PalPo. Since n, d*, P , and Po 

*ere all varied, it was necessary to choose Re and PalPo as the independent variabfes. Measured 

thrust refers to the thrust measured at a particular vacuum chanbtr or anbient pressure. Vacuusl 

thrust is defined as the thrust masured at deep vdcclm (Pa c 5x10-~ torr) . 

For reference, thrust measurements with the orifice plate were taken over a range of dient 

pressures. The aattient pressure had no effect on the thrust measur nts. or nitrogen, the thrust 

varied less than '2 percent over the range of pressure ratios of 10ISCto The thrust was 

nominally 42 nN at a f lo* rate of 0.0786 91s. 

Figures ;! and 3 show the effect of aubient pressure on thrust for nozzle A. Figure 2 shows the 

data taken with hydrogen and Fig. 3 the data with nitrogen. The open symbols are the actual maSurcARnts and the sol id symbols are the measurements corrected for the ambient-pressure force. At 

pressure ratios less than 3x10-~ the ambient-pressure force is negligible. At Reynolds n-rs 

from 2000 to 12 000 there is no discernable viscous effect on thrust below an mbient-to-total pnssure ratio of 1x10-~. Relo* this pressure ratio the corrected thrust is generally within *2 percent of the vacuum thrust. 

In the case where a shock stands in the nozzle, the thrust ratio (F IFv) will be greater 

than 1.0 when Fm is corrected using the actual nozzle exit area. In t6is case, the nozzle has 

an effective area less than the geometrical exit area and F, is thus overccrrected. The criteria 
that was used to determine the onset of flow reparation, or the point where a shock roves into the 

nozzle, was the point *htn F IFv just started to exceed 1.0. This point was considend the upper 

limit for testing a nozzle desjgncd for supersonic operation in space simc the thrust measured at 

higher pressure ratios cannot be corruttd to vuwr conditions. Data at pressure ratios higher 

thrn the point where Fc/Fv > 1.0 wen consequently not cf interest in this investigation. 

From thc solid s 1s in Figs. 2 and 3 it -ars that flow separation sets in at about a 

pressure ratio of t of the Reynolds ntmber. This comlates with Rotk's observc 

tions for flow at a Reynolds nukr of 780. As a point of reference, fro si.ple isentropic-flow 

calculations, a shock will tud at the exit of b nozzle with m ma ratio (&/A*) of 140 at a 1 pwssure ratio of &out 10- . 

Figures 4 and 5 display the ratio of wasu+cd-to-vacuu thrust for nozzle 0 as a function of 

pnssure ratio. For nozzle 0 the Reynolds nubcr ranged from 680 to 37M). In the case of nozzle B 

there is insufficient data to discern any vixws effect on thrust at pressure ratios below the 

point of separation. The vacuu facility could not provide a diffusion-pugcd environrnt at pressun ratios of intenst because of the relatively high flow rates in the nozzle. The point of flow 

separation wars to occur at about the sre point as for the higher Reynolds nubcr flows of 

nozzle A. 

When nozzle 8 was ut 3-1 to m area ratio of M:l, flow separation occurred at a higher pres- S sure ratio, about 3x10- (not shown in the figures). As expected a higher pressure ratio was 

required to cause a shock in the nozzle of lower area ratio. 

Figure 6 contains lost of the data from Figs. 2 to 5 in a plot of thrust ratio versus pressure 

ratio. Also shown is the is tropic-flow c lculation of FdFv as a functim of PalPo for an 

area ratio of 140. For lJ< PalPo < lr3, the calculated values of F IF are generally 4 to 

9 percent higher than the measured values. The difference bet- the caTcu!ated and rasu 

may be attributed to the relatively large uncertainty in P 1 . At values of PaIP -> 10-p?lucr 

shock stands in the nozzle and the isentropic calculation o# ~JF, is no longer va?ld as the calculation ws not carried through a shock. 

COllCLUDIffi REMARKS 

Thrust measurements of two converging-diverging nozzles and an orifice plate flowing unheated 

nitrogen and hydrogen were taken over a wide range of vacuun facility pressures and nozzle-throat 

Reynolds mrabtrs. The purpose of the tests was to investigate the effect of vacuu fdci lity pressure as a function of Reynolds nubcr on the performance of small nozzles designcd to operate in 

spwe vacuurs. 

In the Re) iolds nuslber range of 2200 to 12 000 t re was no discernable viscous effect on hS thrust &?a an adient-to-total pressure r tio of 10- . In nearly all cases, flow separation 

occurred at a pressure ratio of about IxIO-~ This was the upper limit for obtaining an accurate 

thrust Ileasur~et with the conical nozzles iaving an area ratio of 140. Tests with a nozzle of 

smaller area rarl- moved this point to a slightly higher pressure ratio since a hightr aditnt pressure would be required to cause a shock to move into the nozzle. 

Further investigaticn of the viscous effect on thrust will require that additional tests be 

performed using heated fiow at loaer flow rates to achieve 1-r Reynolds nubers and ambient pnssures than reported in this paper. The sensitivity of flow separation to nozzle area ratio and 

contour is also of interest, and further testina is required to fully understand that inportant 

relationship. 

REFEREKES 

1. Page, Russell J., et al.: Life Test of Six High Tcnperature Resistojets. AIM Paper 69-294, 

Mar. 1969. 

2. Yoshida, R.Y., et al.: Resistojet Thruster Life Tests and High Vacuum Performance. 

(THC-S-974, Marquardt Corp. ; NASA Contract NAS1-8090. ) NASA CR-66970, 1970. 

3. Yoshida, Ronald Y.; Halbach, Carl R.; and Hill, C. Scott: Life Test Sumnary and High-Vacuun 

Tests of 10-mlb Resistojets. J. Spacecr. Rockets, vol. 8, no. 4, Apr. 1971, pp. 414-416. 

4. Rothe, Dietmar E.: Electron-Bean Studies of Viscous Flow in Supersonic Nozzles. AIM J. vol. 

9, no. 5, May 1971. pp. 804-811. 

5. Zafran, S.; and Jackson, 0.: Electrothennal Thruster Diagnostics, Vol. 11. 

(TRU-39152-6012-UE-(10-Vo1-2. TRW; NASA Contract MS3-23265.1 NASA CR-168174-Vot-2, 1983. 
6. Spisz, Ernie Y.; Brinich, Paul F.; and Jack, John R.: Thrust Coefficients of Lor-Thrust 

Uozzles. NASA TN-lr-30%. 1965. 

7. R 1 J.: Saw Numerical Results on Viscous Lor-Dcnsi+v Ilozzle Flon in the SlenderChmnel Approximation. AIM J., vol. 9, no. 5, Nay 1971. pp. 811-820. 

8. Finke, Robert C.; Holes Arthur 0.; and Keller, Thomas A.: Spwt Environent Facility for 

Elutric Propulsion Systeas Research. MSA TN-D-2774, 1%5. 
TABLE I. - THRUSTER AND ORIFICE PLATE PARMTERS 

a~ Line pressure. 

b~h&nber pressure. 

CAnmonia. 

Nozzle A 

Nozzle 6 

Orif ice 

resistojet 

Throat 

dia, nm 

0.64 

2.06 

Area 

ratio 

147 

140.38 

Nozzle 

half 

angle 

21' 

20' 

1 

37 

a5.8 

al~.~ 

a13.4 

a34.5 

Hydrogen Nitrogen 

Pressure. 

NIC~~ 

a10.7 

Pressuf. 

Nlc 

a10.4 

Flow rate 

~lgls 

9.8 

9.8 a5.6 ! 38.3 

19.6 a10.4 78.6 

27.1 134 104 

Flaq;:te 

38.3 

78.6 

104 

a19.5 

a26.8 

a20.3 :::: a26.6 

6.9 C13.9 

"0.50 

h.01 

"1.41 

a.c30.4 

9.8 b0.55 36.3 

19.6 b1.09 78.6 

27.1 
C NOZZLE A, 

55 HYDROGEN PROPE UANT I 

I 

0.1 

c 

1 10 100 lmo 

PASCAL 

Z 

E 

g 45 3 

oc 

I m! 40 

35 

Figure 1. - Typical pld d measured thrust versus vacuum 

facility pressure. 

7jFC \Fm '-4 

i I I 1 

VACUUM VACUUM THROAT 

THRUST, SPECIFIC REYNOUIS 

mN IMPULSE, NUMBER 

s 

0 70.2 264 6100 

0 49.2 256 4400 

1x104 1~10-3 1~10-2 1~10-1 1 10 ~UI 

VACUUM FACILITY PRESSURE, torr 

0.6 

1~10-7 1~10-6 1~10-5 1x10-4 1~10-3 3x10-2 1x10-1 

RATIO OF VACUUM FACILITY PRESSURE TO THRUSTER 

CHAMBER PRESSURE 

Figure 2. - Effect of vacuum facility pressure on thrust for 

nozzle A using hydrogen. 
VACUUM VACUWH THROAT 

THRUST, SPECIFIC REYNOUIS 

mN IMPULSE, NUMBER 

s 

o 75.1 n 12000 

0 547 74 9000 

a6 

1~1~-7 1~10-6 1~10-5 1~10-4 1~10-3 1~10-2 1~10-1 

RATIO OF VACUUM FACILITY PRESSURE TO THRUSTER 

CHAMBER PRESSURE 

Fiqire 3. - Effect d vacuum facility pressure on thrust for 

nozzle A using nitrogen. 

VACUUM VACUUM THRWT 

THRUST, SPECIFIC REYNOLDS 

mN IMPULSE, NUMBER 

5 

0 648 247 1900 

0 4aC 243 1400 

0 22.0 230 680 

0.6 "'7 1x10-6 1xl0-~ ~XIO-~ IX~O-~ 1~10'~ '.1~10-I 

RATIO OF VACUUM FACILITY PRESSURE TO 

THRUSTER CHAMBER PRESSURE 

Figure 4 - Effect of vacuum facility pressure on thrust 

for nozzle B using hydrogen. 
VACUUM VACUUM THROAT 

THRUST, SPECIFIC REYNOLDS 

mN IMPULSE, NUMBER 

S 

0 747 73.0 3700 

o 27.0 71.9 1m r 

-I FclFV -# r 

/' 

0 F 

a 

CL * 0.9 V) 

3 

e 

I 

C 

0.8 

0.7 

1x10-~ 1x10-~ 1x10-~ 1x10-~ 1x10-~ 

RATIO OF VACUUM FACILITY PRESSURE TO THRUSTER 

CHAMBER PRESSURE 

Figure 5. - Effect of vacuum facility pressure on thrust 

for nozzle B using nitrogen. 
NOZZLE VACUUM 

THRUST, 

mN 

'42s "'2 

0 A 70, 75 

0 A 49, 57 

0 A 24, 28 

B 65, 75 

b B 47, -- 

0 B 22, 27 

THROAT 

REYNOLDS 

NUMBER, 

'42, N;! 

6100, 12000 

4400, 9000 

2200, 4400 

19iI0, 3700 

1400, ---- 

680, lux) 

OPEN SYMBOLS DENOTE HYDROGEN 

SOUD SYMBOLS DENOTE NITROGEN 

ONE DIMENSIONAL 

5 a 0.6 

1x10'7 1x10-6 1x10-5 ~XIO-~ 1x10-3 1x10'2 1x10'1 

RATIO OF VACUUM FACILITY PRESSURE TO THRUSlER 

CHAMBER PRESSURE 

Figure 6 -Comparison of thrust ratio for various thrusters 

and propellants.