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AIR FORCE REPORT NO. AEROSPACE REPOHT NO.

SSO-TR66-180TR-66 9f623O-33)-l

Dynamic- Performance of Low Thrust Cold GasReaction Jets in a Vacuum

AUGUST 1966

Prepared by H. GREERAppied Mechanics Division

El Segundo Technical Operationsand D. J. GPJEP

Electronics DivisionEl Segundo Technical Operations

Laboratory OpcrationsAEROSPACE CORPORATION

Prcparcd for BALLISTIC SYSTE'MS AND SPACE SYSTEMS DIVISIONSAIR FORCE SYSTEMS COMMAND

LOS ANGELES AIR FORCE STATIONLos Angclcs. (.ahforni

Air Force Report No. Aerospace Report No.SSD-TR-66- 180 TR-66^9(62 03 - I

DYNAMIC PERFORMANCE OF LOW THRUST COLD GAS

P EAC UiN jETS iN A VACUUM

Prepared by

H. GreerApplied Mechanics Division

El Segundo Technical Operations

and

D. J. GriepElectronics Division

El Segundo Technical Operations

Laboratory OperationsAEROSPACE CORPORATION

E! Segundo, California

August 1966

Prepared for

BAXLLISTIC SYSTIM-S AIND S EA -YSTE DIVI5IONSAIR FORCE SYSTEMS COMMAND

LOS ANGELES AIR FORCE STATIONLrs- Angeles, California

BestAvailable

Copy

FOREWORD

This report is published by the Aerospace Corporation, El Segundo,California, under Air Force Contract No. AF 04(695)-669 and documentsresearch carried out from March 1965 through April 1966. On 27 September1966 this report was submitted to Capt. John T. Aliton, STD, for reviewand approval.

The authors wish to acknowledge the contribution of Mr. Ford Cox,Equipment Analysis Section, who was instrumental in developing and oper-ating the experimental apparatus.

Information in this report is embargoed under the U. S. Export ControlAct of 1949, administered by the Department of Commerce. This reportrnay be released by departments or agencies of the U. S. Government to de-pa:;Aments or agencies of foreign governments with which the United Stateshas di-ense treaty commitments. Vvi-vate individuals or firms must complywith Depsrtment of Commerce expr. t control regulations.

Approved

Ca

W. adcliffdo/irctor ' '.Levin/ DirectorEngineering Selences Subdivision / Guidance and Control SubdivisionApplied Mechanics Division ('Electronics Division

, D. . King, DirectorElectronics Research LaboratoryLaboratories Division

Publication of this report does not crnstitute Air Force approval of thereport's findings or conclusions. It is published only for the exchange andstimulation of ideas.

Approved

J &. AltonCapt, USAFSpace Technology Division

-

ABSTRACT

The pulsed propulsive performance of low-thrust .,-action jetb, typical

of those used for small spacecraft attitude control, is analyzed and com-

pared with the results of laboratory experiments. Five gases, hydrogen,

nitrogen, ammonia, Freori-Q, and Freon-i4, are investigated using a

48 to i expansion ratio nozzle. The transient processes which dominate the

short-pulse or limit-cycle mode of thruster operation are formulated. These

relationships show good correlation with the data. The apparatus, proce-

dures, and techniques required to obtain accurate test results for a low-

thrust, dynamic mode of operation are described. Impulse bit size, gas

consumption, and specific imziulse are characterized in terms of thruster

geometry, gas properties, and command pulse width to provide a basis for

optimum system design. A simplified method for calculati%,g dynamic impulse

bit size, dynam-sic gas consumpi=on, and pulsed specific impulse as a function

of command pulse width i. developed. Finally. the effective performance of

the gases tested is evaluated by a technique which includes the influence of

tank and propellant weights, as well as specific impulse.

II.=

CONTENTS

.ABSRA~'CT .. . . . . . . . . . .* . . . . . . 11JNOMENCLATURE .. . . . . .o. . .. . . . . . . . i

11. INtTRODUT ION .. . . . . . . . . . . . . . . I

II. ANALYTICAL APPROACH......... ........... 03

A. Pressure Transients ................................ 3

B. System Chai-acteristics ......................... 11

C. Performance Losses ............................ l

D. Transient Performance Approximations...................25

E. Performance Comparison.............................. 27

111. EXPERIMENTAL PROGRAM o. . ............. 29

IV. CONCLUSIONS...................................... 39

REFEREN'.ES.......................... o..............41

TABLE

1. Comparison of Performan,- Characteristics.............. 17

-V -

FIGURES

1. Schematic of ExperL ental Apparatus .................. Z

2. Typical Pulse Pressure History ..................... 4

%. Generalized Chamber Pressure Rise .................. 8

4. Chamber Pressure Dtcay Transients .................. 9

5. Dynainic Impulse Bit Correlation ..................... 12

6. Dynamic Gas Consumption Correlation ................. 13

7. Pulsed Specific Impulse Correlation ................... 15

8. Ammonia Evpansion . ........................... 20

9. Reaction Jf:r Cycle with )Yreon-I2 ..................... 21

10. Ammonia Cour4ensate Impingement Pattern ............. 23

1 I. Thrust Stand Avsembl ........... ........... I . . . . 30

12. Undamped Oscillation of Thrust Stand .................. 32

13. Transient Response of Thrust Stand . . . . ............. 32

14. Correlation of Thrust and Chamber Pressurefor Hydrogen ..... .......... . . . . ........ 33

15. Schematic of Command and Computg' Systenr ............. 34

16. Total Impulse Distribution ......... .............. 36

P

NOMENC LATURE

I/a 1 Aa*(Z/yi) /2V

I= (Ata*/Z,)[s),Z'y

a* acoustic velocity

B equivalent orifice -to -nozzle area ratio

A(.1)1/2 (+2(y-i) a,

C d nozzle discharge coefficient

Cf thrust coefficient

II C~ thrust correlation factorf 0v exhaust velocit coefficient

D = diame te r

F = thrust level

g - proportionality constant in Newton's second law

I specific impulse

I ef. effective system specific im~pulse

I tot ~ total impulse

k polytropic exponent

-vii-

I

NOMENC LATURE (cor.,rAxued)

Kd empirical decay time ... fac.:.,"r

K choked nozzle flow factor

K r empirical rise time integration factor

M = Mach number

m = molecular weight

N = Knudsen number

N r Reynolds number

P = pressure

R universal gas constant

T temperature

V = volume

v specific volume

W = weight flow rate

w weight

y pressure ratio transformation [i - ( p 2

YOF I - (Pa / PS)1 / 2

Y = ratio of specific hearts

OE = nozzle expansion ratio

efficiency

-viii-

NOMENC LATURE (continued)

8 = timre

p - density

- standard deviation 0. 7631 Xi~l-e rwrigsrs

- dimnensionless time factor =a

SUSSCRIPTS

NIL, aambient

-~ c - cliznbex or t.eznmand

* .d decay

4 e - nozzle exit

I I = final

I = thermal

i initial

n - nozzle

0 orifice

p - polytropic

r - reservoir or rise

s - steady state

t throat

1. INTRODUCTION

The propulsive performance of various gases with a low expansion

ratio (1. 68 to 1) nozzle was reported in Refs. i - 3. In this document,

propulsi~re performance and design r'-lationships for cold gas jet re.,ction

sy-stems which might be used in small epace vehicle attitude -c ontrol applica-

tion are analytically derived and are correlated with the results of va.cuum

experiments using hydrogen, niitrogen, ammonia, F -reon-i2Z, and Fxrecm-14

in a high expansion ratio (48 to 1) nozzle. Theoe relationsips., pr-eviouvly

unavailable in systematic form, provide -the amalytical tool-s needed to desn

low thrust, pulsed, 4cold oas propulsion syvtexns. A simpHifid maeams of

calculating dynamic impulse Int siAze, gas'consumxption, axB specific iraptase

is developed for -use ini preliminary design.

A schematic diagram of the expexinienW, avparatus is sihowmn

Fig. 1. Pressure and-,thrust bistories and -the weight of consumed *as wemre

measured so that specific impulse could be Aeterntined- as A function f [commnand pulse .width. A complete de t cripfion -of the experimenla ram

is presented following a discussion of thie analytical aproach.

4 - -~4~~*4 -

i--w4- -

1- K

G A THRUST STAND (DETAIL 1)G_______ B SUPPLY TANK

C CHECK VALVE0 PRESSURE GAGEE PRESSURE REGULATOR

MF THERMOCOUPLE6SOLENOID VALVEHPRESSURE TRANSDUCER

J LVDT POSITION TRANS-__j DICER (THRUST PICKUP)

~K K THRUST CHAMBER NOZZLEf- L DAMPING FLUID

DEMIL ~ ~ ~ i CANSTSAN TILEVER BEAM AND4 PNEUMATIC FEED

Fig. 1. Sc~'ematic of Experimental Apparatuis

IL ANALYTICAL APPROACH

A. PRESSURE TRANSIENTS

The reaction jet performance is based on a dynamical analysis of the

thrust chamber pressure history. In general, the chamber pressure history

is composed of the steady-state and transient (startup and shutdown) phaIses

illustrated in Fig. 2. In the following analysis, it is shown that the transient

phase causes performance nonlinearities. Design relationships for predicting

and optimizing these nonlinearities are developed.

During startup, the flow rate -through the solenoid supply '0~e orfce

Wexceeds that through the. discharge nozzle W , causing tlp.e4 abr-

pressure P C to build up. The exact expression for the- compressible is_-dntropic

pressure buildup -was given in Ref. 2 as

r. --r

dP ( 1/2! Pc f)

For steady-state operation dP- /do = Oi and P~ /-P. P 'Pr #--, '-Thiviti rtio a-C C

design variable (typically on the order of 0. 99) and- is deteradined by tht"

selection of A0 and At. -

Equati(. (1) cannot be-solved directdy but may bes srpied using

one of three assumptions: (1) the thruster nozzle flow is zero diii g*tirtap;

(2) both nozzles are always choked; (3) the-flow through theorifc,=ur

at constant density. For the case where the thruster -nozzle i4*w is- assumed --

F~2A 4 OR''

........

8,RISE TIME (Pc/rs z 1.0)

STEADY-STATE CHAMBER PRESSURE

AMBIENT PRESSURE

VVE 0- ,CMMANDI ELECTRICAL _ PULSEGdDEATIE(/P:00)DELAY TIME (SOLENOID

ORIFICEOPEN)L0 20 40 60 80 100 120 140 160

TIME, 9(msec)

Fig. 2. Typical Pulse Pressure History

i.4

to be negligible during startup (assumption 1), Eq. (1) becomes

dPc= 2a P (r2 1 /t2[(c +(P)( /y (2)

Integrating Eq. (2) between .the appropriate limits results in

C P y2 [Y ) Y/y] [( )/jB (3)

If both nozzles are assumed always c~ked Jasauznption 2), then Eq. (1)

becomes-

dP Id MO Za 2 (A 0P r/At - P)(4)

which integrates to fi

P/P A /A + 2 - (A /A)].Tc a 0t 0 ot

Assuming constant density orifice flow -(assumption 3), Eq. (1 ecomesi

dPc M 2a, PrL (Pc'/r] 2 a 6)

Equoation (6) can be integrated directly to obtain

2B- 2 y -B B +4

( 2 + 1)/2 (-y 2 _By + 1)i1/2

To solve Eq. (7) explicitly for P /Ps) it is assumed thatB s>4,o

P/P 1 -( +B 2 -2T -T Z 8P P8 (o+B e + ZB(y 0+ B)e - B(8

A comparison of the results obtained with Eqs. (3), (5), and (8) and meas-

ured data indicated better correlation over a wider range of variables when

using Eq. (8). In addition, Eq. (3) is somewhat unwieldy to use, and Eq. (5)

is valid only for A /At >I(rI )

An approximate approach would have been to assume that

[i (PP]l/ ~[I (P/2 P

Lso Eq. (6) integrates to

P B +2)(B BP2je(B+2)T~

*As the equ~ivalent orifice -to -nozzle area ratio B - , the orific e area-

restricts the gas flow (like a throttling orifice) so P cnever reaches P r To

j avoid this condition, B is usually sized > 2.

In Fig. 3, nor.iimensional solutions of Eq. (8) are presented for

Yo = 0. 86 to 1. 0, B = 1. 0 to 10. 0, and T = 0. 005 to i. 0. Good correlation

between the analysis and the data for five gases (both at sea level and in

vacuum) is noted. These results indicate that the time required to reach

steady-state operation (P c/Ps = i) is significantly reduced by designing the

jet reaction chamber with a small chamber volhune (Vc) and a high (B > 2)

orifice-to-nozzle area ratio.

From Eq. (8). the rise time, or the time required for the pressure

in the thrust chamber to reach steady state (Pc/Ps = i), is expressed by

er = ('B/ai)tn[BAy. + B)] (9)

During shutdown, the orifice valve is closed and the gas accumaulated

in the chamber discharges through the nozzle, The instantaneous chamber

pressure during an isentropic shutdown is given by

dPc/de Zya(P c) (,--)I2y(p )(3y- i )/ 2Y (iO).

Integrating Eq. (10), the pressure ratio at time 0 becomes

l:cPP i - a_ - "lZ I i- )(11)PC / ci Ita( )1Z/-y

with the results as given in Fig. 4.

-7-

%At

.S .. > - - LA > L >zoo >

u - j - 'L js~ ~ tt 68 t

Cc c L< IN 0 (1m)DL actLa-

4)~.k

CC,,

U*4)

3c 4c

d/ '3mfS38d 31VIS-AUV31S 01 MONOVH JO 0I1LVH

OD-

C)~ CLI=I

06.M

00

40 v,

0, d.

0 1w

$4

C~i 4w

T2

(bisd)d '3H1SS38Id I38WVHO

If the decay time 0 d is defined as the time :equired to discharg from

P to Pal then from Eq. (11)

d - ( P s)/a2( - ) (12)

It can be seen that 0d is a functiQn of the gas properties and of Vc /At(chamber characteristic length).

The correlation between the ideal isentropic decay and the experi-

mental results is not quite as good for the "slow" (low sonic speed) gases,

such as the Freons, as for the "fast" gases, e. g., H 2 or NH 3 . These fast

gases discharge so rapidly that the time in which heat transfer ane other

non-isentropic imperfect gas effects can occur is restricted. The behavior

of the more complex, heavy Freon molecules indicates that the decay

transient for these gases follows a polytropic process.

In a polytropic expansion, deviations from isentropic perfect gas

behavior are accounted for by adjusting the ratio of specific heats -Y through

a polytropic efficiency -q to obtain a polytropic exponent k. This relationship

becween k and y in terms of qp is given by

k -y/[y + np(i - -) (13)

IPIIn a vacuum, ai bumed equal to 10-

Pa/P

The thermal expansion efficiency I, is the square root of actual drop in gas

temperature to the ideal ter,.perature change and is related to polytropic

efficiency by

I (P fpi) By /-Y n P-11/

Values of qp were determined from the test results, and the corresponding

values of k and i were calculated. The restilts are listed in Table I for :he

gases tested (except H2 which is so fast that its decay is well described by an

isentropic decay). Better correlation is obtained by use of the polytropic

exponents in the decay transient, as shown in Fig. 4.

B. SYSTEM CHARACTERISTICS

The thrust and nozzle flow transients are readily deterrined from the

chamber pressure history. The dynamic impulse bit size (total impulse per

pulse) and the dynamic gas consumptioft (gas consumed per pulse) are .,

obtained by integrating the rise transient, the steady-state value (ifa >

* and the decay transient of thrust and of gas flow. The thrust correlation,

.factors and nozzle discharge coefficients listed in Table I (e.d disuswsed

under Performance. Losses) were used in the transient analysis to calculate

impulse bit sizf and gas consumption, as functions of command pulse 9.

(defined as the time the valve is open) for the fi".e gases shown in Fiji. 5

and 6. Referring to Fig. 5, the difference be'ween the theoretical-and the___-

measured vai Les is due to the assumption oi an iselitropic Gecay. irwas

found (Ref. 3) that the correlation is improved if a polytropic expansion

-111-

ii

040 0

4 00,

Cl, 0:

CJ

~ I ~: Coxxsql11 3Sn~

a'a

0 0 O

c0

CA 1 I05*4tip

0c4X cm a 1

0z1.00 I''M S

efficiency of about 85%6 is assumed when calculating impulse bit size and

amount of gas e-tonsumed. However, specific impulse is not affected by the

assum~ption of isentropic decay.. and the polytropic approach is unnecessary

for this calculation. Note that in the region of small command puilses

(s < 0 b, oth impulse and consumption are nonlinear functions of comnmandC r

pulse. This nonlinearity, or deviation from the ideal square pulse-\r~ave

(instartaneous rise and decay), is produced by the rise and decay transients

Equations (8) and (iI) provide the designei wt reainshp ew

the, variables so that de sign tradeoff s may be evaluated. For minimum gas

coiisumption at any given command pulse, the transients should be mini-

~ xnizedA or possibly designed to effectively complement each other; i. e. , the

ideal square pulse wave is approached if the integral of the chamber pressure

over the decay time car. be designed to compensate effectively for the initial

difference between the product of the steady-state chamber pressure and] the

rise time and the integral of the chamber pressure over the rise time, i. e.,

P Sshoul~d approach P Er d for an ideal square pulse wave.f c Pd sr c0 Pd

- The dynamic (pulhed) specific impulse for five gases as a function of

e - O_(Fig. 7) w..As obtained by dividing the impulse bit by the weight of gas con-

surned. For %racuum opv.ration, specific impulse is essentially independent

of command p-Ase dtration (unlike I and w) and is close to the steady-statetot

value. Figure 7 indicates good correlation betwveen the analytical and experi-

- ITFor command pulses less th.Avi 20 rnsec, the data becomes nonrepeatablebecause of valve dyniamic limitations at.d increased experimental error.

-14-

V =O.183 10 Do 0:040 inl. 0 NH3 '7FREO-12c48 A N2

-ANALYTICAL, IN4CLUOES LOSSES: (BUT NOTCONDENSATION EFFECTS)

50 0 REO 'H

FREOM12

20'0 W- f5

Fig? 7. Pulsed Specjtic Impulse Cqrrelatiohi-

c. ,.osszs

C. MFORMANCE LOSSES

2';.~ The tests in this study were made using a 15-degree half-angle conical

aluminum nozzle with a measured throat diameter Dt of 0. 0188 in. and

an expansion ratio of 48 to 1. The steady-state chamber pressure was

regul1ated to 40 psia; the gas temperature (downstream of the regulator) was

70F, The a'mbient pressure in the vacuum chamber ranged from 300 to

1000 i', depending on the thruster duty cycle.

The perfect gas isentropic flow relktionships wei e used to calculate

the ideal performance (e. g., characteristic velocity, nozzle exit pressure,

and temperature) listed in Table i. The tabulated ideal specific impulse

does not include the effects of nozzle divergence and of the vacumn

chamber pressure. Also listed in . able I are td.e nozzle throat Reynoldsnumber (Nrt fron 10, 000 to 53, 000), the nozzle exit Reynolds number

Wr -from 3, 000 to 18, 000), and the rozzle exit _Knud.en number (Nke from

-3 -30.4 X 10 to 3. 3 X 10 ). Note that all of the gases operate in the coninuum" flow regime (Nk < i0 " 2) and that boundary layer viscous effects are not par-

4ticularly severe (Nrt > 10 ). These effects may become important, however,

if JK tfor operation with values of Nk and Nrt ccnsiderably beyond the limits

indicated.I; The nozzle performance may be characterized by the discharge

coeffici;nt Cd (the ratio of actual weight flow to ideal isentropic weight flow)

and the exhaust velocity coefficient C (the ratio of the average effectiveV

exhaust velocity to the ideal isentroiic exhaust velocity). The ratio of t-he

actual thrust coefficient to the ideal thrust coefficient defines the -thrust-

. 16-

'NO 0 0 , 0- 0 r -, .00 .0.8*4r VN I N 94 %n c a, a , I* on v't V 8

I '8

-. 8' of 4

0 g

0

0 - No A-. 'N N 0 9 ~ - . 9V~

(U aa

'16 ILa

a- ~- w D- 4 liiN8

ILI

correlation factor C, or

Ct f/Cf ideal v Cd 5)

It follows that C is equal to the impulse efficiency, orv

GyC Ct/Cd = I/Iideal

The values of C+ and C d in Table I are based on thrust and flow

measurements taken in the Aerospace Guidance and Control Laboratory.

W The discharge coefficient of the test nozzle averaged abcut 0. 85 for all the

gases except NH3 and Freon-i2. The relatively high Cd of nearly 1. 00 for

these two gases was attributed to the presence of fluid condensate in the

nozzle -flow. The thrust correlation factor was also slightly higher for the

condensable NH 3 and Freo.-Z gases. The average impulse efficiency (CV )

was about 91%. The efficiency of Freon-12 is slightly lower than average.

This is attributed to: heavy molecular weight, uncertainties in thermo-

dynamic properties, and very long transients. Values of C v for NH 3 ranged

from 88 to 95%, depending on the amount of condensation.

A method of correlating the losses associated with small nozzles in

terms of throat Reynolds number and nozzle expansion, ratio (Ref. 6) was

- 1 'This is also the average quoted in Refs. 4 and 5.

1

i .I ________________g-____

investigated. 9 No correlation could be obtained using the present data (a

similar lack of correlation of Cf and Cv in terms of Reynolds number was

reported in Ref. 7). The results indicate that the difference between the

ideal isentropic thrust coefficient and the measured thrust coefficient is a

constant of about 0. 39 (except for NHH3 ) and is independent of the throat.

Reynolds number.

In addition, an analysis of the boundary layer (Ref. 8) was made to

determine its effect on nozzle performance. The effective nozzle expansion

ratios were found to be up to 20% less than the geometric ratios (see Table 1)

with a consequent performance- loss of about 3%. It was estimated that

viscoue losses and changes in the free-stream flow conditions introduced by

the boundary layer would result in about 3% additional losses.- The tatal.

losses, including divergence and vacuum backpressure (but n6t condensatioii),

are estimated to be about 9%.

Isentropic reaction jet expansions of NK- and Freon - 12 are ih6wn.3 6

on Mollier diagrams in Figs, 8 and 9. The ideal expansion en4--pinto9f,--

either gas is well into the two-phase (Uiquid-vapoi) mixture r-egion *oqith*t

a metastable supersaturated condition would be expected to occur in Ate

nozzle. The NH3 expansion not only crosses the saturation line but also

crosses the triple line (solid-liquid-vapor) into a solid-vapox region;

Since incipient condensation of steam is known to occur it the 59 The data in Ref. 6 was obtained for only one gas, H2 , ad atReyild.

numbers generally less than 10, 000, -whereas the values of N -forte ve -rt-

gases tested in the present investigation ranged'from f0, 000. to 53, 00,0.

-19-

PV

r4r:s

50

30

II

a:a'I, I

-f 10 TRIPLE LINE /

as/

03/

0.05 - (TO 0 ISENTROPIC EsFMNSION WITH E 48

200 300 400 500 600 700FM. HAILPY (Atu/Ib)

Fig. B. Ammonia Expansion

-

0 To (2 ISENTROPICEXPANSION WITH f:48

50-

101

a.5

0.5 f

0.1

F0 40 5M 60 70 80"

Fig. 9. Reaction Jet Cycle with Freon-lZ

- 41-,.

liquid or Wilson line (Ref. 9), it is reasonable to assume that highly

hiAer-saturated conditions in the test gases cannot be sustained without

condensation occurring, thus resulting in significant deviation from an ideal

constant-entropy expansion process.

The problem of small nozzie condensation was first observed in the

present study when NH3 and Freon-12 were tested at sea level (Ref. 1).

The existence of liquid condensate in the nozzle dischargc was demonstrated

experimentally (Ref, 3) through hot-wire conductivity measurements and by

photographing the flui i impingement pattern produced on a black matte target

downstream of the nozzle (Fig. 10). Attempts at direct observation of the

condensate droplets in a transparent nozzle through the Tyndall effect

(backscattering of a light beam) were inconclusive, probably because the

droplets in the nozzle were smaller than the wavelength of the light and

were moving at a high velocity (s.'ort residence time). The small size of

the nozzle also hampered direct optical viewing of the condensate.

The present theoretical treatment of nucleation and droplet growth

during condensation from vapor (i. e., the disappearance of vapor molecules

and~~~~~ th orcie .n so i) appears unable to produce

definitive quantitative results. One major difficulty concerns nucleation

kinetics cr the reactions (and rates) by which vapor molecules combine to

form droplets (Refs. 10 - 16). The treatment of the influence of foreign

I impurities, e.g., dust or ions, which provide heterogeneous nuclei and

the pulsed or dynamic mode of operation introduces another transient con-

sideration. Even for steady-state oparation, the small nozzle size and the

- - - -

- -4 1-

fK~ -

I F--I LI

4t.~

Fig. 10. Ammonia Condensate linpingement Pattern -<-4--u

- - C,

-c -c

* - C> -

-'<B->23-

S- v

;:-:P

abort - 15) involVed (ipee :$t resent theoreiical

-N '~ah the pr~oblem'of detenihing. #he iffoFt 6f flow condensation on

nozZle .#rfbtmice has bieen recognized for 40 yiv'rb (Ref. 17), the experi-

maentia work in homogeneous nucleation and condensation is apparently meager,

partic 4rly with respect to pulsed flow in very small nozzles.~ Most of the

*1 previeui experimental work has been done using, saturated water in large

Ot _t nxleis (Refs. 9, and 1,6i - 20) or in cloud chambers (Ref. 21). The qualita-

tive inditiis are that the actual'flow is somewhat greater than would be

theor~ticaly expected. In the present study, the observed increase in Cd4d

for the N~H 3 -an Freon-1Z was attributed to the presence of fluid condensate.

Theoretic~al methods (Refs. 22 and 23) for calculating the condensation

losses were examined. These res'ilts indicate from 3 to 7% additional per-

formnance loss for two-phase expansion due to: energy transfer between vaporIand droplets (a part of which is lost by dispersion); the appearance of super -

cooled states and impact (shock) condensation; and- (possibly) lack of tin-e

for interphase thermal equilibrium.

In summary, because the effects of condensing vapors on small nozzle

expansion processes are presently not well understood, additional

_7*Accurate measurements are usually difficult to obtain with smaall nozzles

(D+ < 100 mils), e. g. , measurement of At may be in error by 10%. Also,

microscopic difference-s in construction could alter the nozzle flow

I characteristics.

.24-

study is required in order to establish accuL te means of performance analysis

and characterization.

D. TRANSIENT PERFORMANCE APPROXIMATIONS

When the rise and decay thrust and flow rate transients are integrated,

it is possible to define time integration factors so that

der

r

Using these empirical factors, d ynaic iripulse bit siz&e, dynmc gas con- F:s r

surnption, and pulseQ specific impulse can be obtained from the follow ing

approximate relationships. . - - .. !U ing thse emiita atrhemiciplebi ie ywncSol

For 0 <5 0 r

'to t CfAtPs(KrOr + do-d( }c/o r ) -

- For -e> OR 19)

P - [2 + ( Or

- - -IZ~XI HIP

Gas -,nuMPLon

For 0 : Oc r

n- ~ + Ic.6i (8Oc/r(20)

For 0C0r

w= KAPrK + (O O + Kde

where

K choked nozzle flow factorn

,:a* [2/ (. + j)](Y+I)'/ (Y i- +LI~Y - i'RT

For the gases tested in this study, values of Kr U. 69 and

K = 0. 0685 were found to provide good correlation with the measured data.0

Comparison of these approximate results with those obtained with the

isentropic analysis, the polytropic analysis, and the data are shown in

Figs.5 - 7.

Specific Impulse

The specific impulse is the ratio of Eq. (9) to Eq. (20), cr simply

fCfAt.P cde Cf

0.1 3 was found to provide good correlation with an isentrapic decay,

where;'s Kd 0. 0683 correlated with the polytrapic decay process.

-d

-26-

It is noted from Eq. (2i) that specific impulse is theoretically constant and

independent of command pulse 6c

E. PERFORMANCE COMPARISON

Although specific Li.-pulse is the most important single zueasure of pro-

pulsive performance, other factors become important for system desig~i

As pointed out in Ref. 24, conuidera-,:ion should be given to the propellant

density and associated tankage weight This may be accomplished by deftn-

ing effective system specific impulse as the ratio of delivered total impulse

to the combined propellant and minimum spherical tankage weight. Thus

Ie I1/ [i+ 1. 5VP(P/W)]

where- -

P = the propellant storage pressure (typically 3500 psia)-

v = the propellant specific 'Volume

Walrt the ratio of tank density to working stress =3. 25 X 1_0-5 ft 4 fori

titanium with a safety factor of 2. -

This technique was applied to the measured -value* of specific- 4 pple

for the five gases tested. The results are listed in table 1. The coa~njiable-

gas ti, NH 3and Freon -12, were avts..med stored as liqttids at their room,temperature vapor pressures of 130 and 85 psia, respectively, ai% .,~ (18)

was mrodiiflect i acctunt ior minimum gage tanks, based on actual spzcecraft

e ~ ,~ 6s A 'I-I ed t"-t 6Ui e basis of specific impulse, H-2 -ha the highest

"orit-i-'aylt MD sec", iir4& on the basis of effective system specifi!

- peo~znne_(13 sec). 0 the basis of effective

~Ae-iic~ff~i"s~~ aathei hest performrance (75 sec) and Freon- 12

"Ot tMe N1 at -s2 .13:v a 'weit pnalty for the heat of

[2

vaporization of NH 3 and Freon-12 was not included in the Table I perform-

alice values. (In the laboratory this heat was provided by the heat capacity

or the apparatus.) In the case of NH3 , about 500 Btu/lb are required for

vaporization. This heat would either have to be supplied from the heat

- -- capacity of the spacecraft or from an external source, depending on the

application. The final selection of one propellant over another would depend

on the results of a detailed design study for a specific mission.

-28I

~1

III. EXPERIMENTAL PROG;RAM,'

The experimental apparatus shown in Fig.: I incfudeu'arglt~ cl-

gas pneumatic system, a thrust stand, and an -electronic dw~fiman4t and

computer system.

The -old-gas pneumatic system consists* of~a pressure ve&iWAr pWr1:6

pellant storage, a 0 to 400 psi pressure gage, a thermhocouple te ta r

monitor, a pressure regulator adjustable from0t 10pi and aj n~

sure monitor gagze. *hntes.-ris-oe~e.n NZ, or F

pressure and temperature measurema~ht r t4t dej rznine pr~Ui~~

fm xZ _ -;;,8,mass co iupin 1-o er#(f 8 ~.. .*

system is operated with anhydrouzs -NH., -or Frooo ih4. i~a.fe

accurately weighed before aild after a test to detrn-Ane jnss

during ihfe te s k. A typical test conis~ts of-ee~~-

command pulses. -. ~-

The thrust measurement apparar.Fg 1haano n -

the end of a short length-of tubing -to servi- theidm fuink A

feed line and a cantilever. beam iprini,4 When thriusti.pra

is displaced in an amount. proportional to ttrust~a~d X do

of the beam is sensed b6y -a potition trantduce,.- alid

portional to the positioin (thrust leyel):i et~4 ~~ ot

is provided through th6 *hearing action -of -a fbq Itnw1~tt* t~

fluid. A high, natural frequency of the cantilever beam and nozz~le asikeibly

(250 cps) is necessa-ry to provide adeqtiate dynamic response for -the thrust'

transients.

.0

4

C,,

$4

E-i

.4

-30-

The natural frequency of the thrust measurement fixture.was veriftcd

experimentally by two methods, The first was displacement of the beam by

a discharge of gas from the pneumatic system through the nozzle. The natural

f requenc ie s of the fixture. both with and without damping fluid, viere dis Played

on the oscilloscope and photographed. A photograph of the undamnped oscilla-

tion is shown in F* 4Z. - The spr iaditw±wa 'dit~qip g a coaxial saole-

noid valve in ruck ebt a thro'Vg4 the

valve and imping tiii itfr* ilbicw su ting dispae-

merit of the fitrC It-M~sigICSg

011 z. N_.

13 is a phtgal W rCXi4

such an external force. The thrust -stand dynamic response is morel-h4'

adequate for the rise times encountered, as evidenced by the correlation. Oi -

thrust and preasure traces in Fig. 14. (A pressure trarrsducer-with-.'

1200 cps acoustic frequency was usied to monitor pressure. ) .

The thruet stand was calibrated in two ways: ()using a Sclier"<

Turnico force gauge and providing a scale factor in terms oi vol'66, oud

of force; (2) orienting the thrust stand so that the beam was. subjected to a

i gloading. Test weights were then placed on the cantilever-baad

cdrrelatijon of force ve~rsus electrical -output (deflectionj was lna Bt-

methods were in exceilent agreement.-

A schematic of the comimand and comnputer system is shoWn in Wit. i5.

A preset counter or clock was used to fix the repetition rate Qftbe command

I ,- - -~

-.~ 10 j.Imsec ELECTRICALCOMMANO PULSE

~~1 Fig. 14. Correlation of Thrust and Cham~ber Pressur'efor Hydrogen. (steady-state thrust = 0. 0146 1b;steady-state chamber pressure 40 psia;I commxand pulse =50 msec)

Kj -32-

2 mlb

2-MvSec -

Fig. 12. U~ndamped Oscillation 6f Thruast Stand

V

5 m~b

Fig. 13. Transient Response of Thrust Stand Usinx External -

Forcing Function Input.

- gA_ ~

__ ____________TIME

WAEFRM POINT® OUTPUT OF THRUST STAND

(I CUNTI WAEOM+ON

WAVEORM OIN PRESET COUNTER GATING COMMANDS

POINT

THRSTCOUNTM+ REVERSIBLESTAND COUNTER

ELECTRONICS POINT (TTA IMPULSE)

PULSING CMAD PEETO SOLENOID COUNTERVALVE ELECTRONICS CLOCK

Fig. 15. Schematic of Command and Compter System

-34-

pulses, and a digital counter recorded the number of cycles or pulses applied

to the solenoid valve. The output of the thrust transducer was amplified,

demodulated, and fed to the voltage-to-frequency converter. -The output of

the converter was fed into a reversible counter which was used to integrate

the thrust profile ana thus obtain the total impulse per pulse (impulse bit size).

The reversible counter computed the impulse bit including drift or offset dur-

ing a time increment At. Then, the counter totalled the integrated offset and

drift for an equal time increment At and obtained the difference between the

two values to provide a direct readout of total impulse. The reversible

counter provided improved accuracy over the two separite counters pre- -

viously used (Ref. 3) for the same function by eliminting aly errors due to

differences in timing sensitivity between individual counters.

The specific impulse was obtained by, dividing the total impulse by the

gas consumed as measured over a large number of command- plses (>1000).

The solenoid valve closing time was adjusted to equal the valve opening time

by valve driver circuitry modifications (Ref. 29). Therefore, this configura-

tion resulted in a valve open time equal to the electrical command pulse width,

with a 3. 5-msec delay relative to the command pulse.

To complete the experimental evaluation, the repeatability of impulse

bit size was verified. Two thQucand 2O-msec command pulses were applied

to the solenoid valve, and the total impulse of each pulse was recorded. The

M trihitinn pInt nf ths- iru e.ta. rig. I& inedicatfsa -rho ewi-dolsbvt+ '*bl

of impulse bit siza.

An estimated error analysis of the experimental -configuration was made.

This analysis included the effects of mass measurement errors, limited

-35 S -'

7--4

C>

40".

bC

L b 4

-36-

dynamic response of the thrust fixture, calibration errors, and electronic

errors. The error estimate took into account the variation in experimental

measurement accuracy with conn4t pulse width and with the propellant

used. The average error for all propellants and command pulse widths is

approximately 5%, the typical spread of measured data points. Table I

presents the estimated measurement error associated with each pro e'l-l

for command pulse durations of 20 and 200 mset. The predicted meaturement

accuracy of 5% correlates well with the experimental data. In Fir. 7 for

example, 80% of the experimentally measured data lies within 5% of the

theoretical predictions.

During the course of the experiments, a leakage problem became

apparent when testing H2 . Because of the low molecular weight of H2 (see

Table I), a leak of only 1. 25 X 10" lb of gas while obtaining a data point

would produce a 20% error in me ured specific impulse. The same quantity,

of leaking N2 would result in ;, 5% error iu specific impulse. It was found fthat the leak was caused by thc O-ring used to seal the nozzle in the no'zle

block and could have been prevented by careful installation.

An additional problem was encountered during the H2 expecrimentis.

Significant variations in specific impulse were observed during the initial

testN. Subsequent investigation revealld that these variations were due-to, -the ffets f gseos contamination occurring during the fillinp of thi7 ro-:

theeffctsof aeF-pellanx- tank. Normally, when the propellants were changed : ;.g. , chfiani-lg

fro N o H), the complete pneumatic system was evacuated using a7'

vacuum pump to remove residual gasei. . Then the propellant tayik was filled

with the new gas. However, ambient air in the 4-ft long fill hose had rot

been considered. Calculatiezs indicated that the error in s 4cific impulse

introduced by the cont".mination of H2 with trapped air could be as large as

, .. Z,=-2076 due to the change in the average gas molecular weight. This conclusion

was experimenta"_'Y ie -_fied. The propellant loading procedure was then

modified to include a vacuum purge of the propellant fill line as we .as of

the pneumatic system.

n!

'I

--

; .. 38-

-i ___________

IV. CONCLUSIONS

Accurate predictions of impulse bit size, gas consumption, and effective

specific impulse can be made using the gas cqfnamical relationships ,given for

the transient pressure histories. These relationships constit-e an'effectie

analytical tool for optimizing system performance 1.r a given cortiol

z .rement.

Both the gas consumed and the impulse bit size are nonlinear functions

con-ma.id pulses for small pulses but become linear when steady-etate

chaaw, v; essure is reached. The nonlinearity, or deviation from the ideal

square pulse-wave, is due to the rise and decay transients.- For minimum

gas consumption at a given command pulse, the transients can be mcnimized

by proper design so that the rise transient effects are essentally offsetby

the decay transient effects. A simplified approach to transient performance

determination given by Eqs. (19) through (21) can be used for preliminary

design purposes.

The pulsed vacuum specific impulse is essentially independent of

command pulse width and is close to the steady.state value, A loss of f-orn

5 to 10% in specific inmpulse was observed for command pulses less than

20 msec. This d.zgradation is attributed to the increasing dominance of

solenoid valve dynamics. Because of incieasing interest in small pulse-

width performance (<20 msec), additional study in this area is required in

order to characterize solenoid valve dynamic effects on performance.

-E9

39~

This isr-ag coefficient of tenozzetested averagdabout W4forall the gases except NH 3 and Freon-1.2. The average impulse efficienc~y was

iabout 9 176. No co-'relarion of the nozzle losses could be obtained in terms of

Reynolds number. Thu results indicate a constant loss in ideal isentropic

thrust coefficient of approximately 0. 39 (except for condensing gases, NH 3

" and Freon-12). Additional study is warranted on the subject of small n')zzle

/.. Jexpansion processes and on the performnance' effects of condensing vapors.

I On the basis of specific impulse alone, H2 .s h o w s the highest perform-

Zt • - .

;i ance. If propellant and tank weights are considered, then NH 3 has the highest

effective systen specific impulse. Sin e e NH was assumed to be stored

I NH3

as a liquid, the effect of the required heat of vaporization would have to be

considered in spacecraft design applications. The final selection of pro-

pellant should be based on a detailed study of the specific mission require-

• ments.

4

exaso rcse n ntepro{ac fet fcnesn aos

On te bsisof peciic mpuse l-4 H .hw h ihs efr.

ane1fpoeln n akwihsaecnieete H a h ihs

REFERENCES

1. Griep, D. J. , "Experimental performance of anhydrous ammonia,"

Aerospace Corp. TDR-469(5230-33)-i (12 October 1964).

2. -Treer, H. , "Analytical iaivestigation of nitrogen jet reaction control

systems," Aerospace Corp. TDR-469(5560-30)-1 (30 November 0-.4).

3. Greer, H. and Griep, D. J., "Low-thrust reaction jet performance,"4

Aerospace Corp TDR-469(5230.-33)-Z (August 1965).

4. Sutton, G. P., Rocket Prolpulsicin Elements (U. Wiley& Sons, Inc.,

New York, 1956), Znd ed. , p. 77.

5. Sutherland, G. S. and Macs, M. E., "A review of micro-rocket tech-

-6noiogi: 10 to ti-lb thrust, " AIAA Paper No. 65 -5201f 14 June 1965).

6. Spisz, E. W. , Bri izck, P. F. ,- and Sack, J. R., "Thrust coefficients

of low-thru,-t nozzles,' NASA Lewis Research Center, TN D-3056

(October 1965).

7. Tinling, B. E., "Measured steady-state perfozmance of wat er vapor

jets for use in space vehicle attitude control systems," NAS4A. mes

Research Center, TN D-1302 (May 1962).

8. Schlichting, H., Boundary Layer Theory (Pergamon Pre.-s, New York,

1955), pp. 281-297.

9. Yellu,.t, J. I. and Holland, C. K., "Condensation in diverging itozzles,"

Trans. ASME, Vol. FSP-59-5, 161-183 (1937).

10. Hischefelder, J. 0. , Curtiss, C. F., an~d Bird, -R. B., Mo lecu~lar

Theory of Gases and Liquids (J. Wiley& Sons, Inc., New York, 1964),

pp. 377-390,~ 405-407.

.41-

°g

11 . Frenkel, J. Kinetc Theory of Liquids (Dover Publications, Inc., New

York, 1955), pp. 365-413.

ito _i,5c -- 12. Courtney, W. G., "Condensation in Nozzles," Ninth Symposium on

Combustion (Academic Press, Inc. , New York, 1963), pp. 811-826.

13. Wegener, P. P., "Condensation Phenomena in Nozzles" Heterogeneous

Combustion, edited by H. G. Wolfhard, et al. (Academic Press, Inc.,

New York, 1964), pp, 701-724.

14. Feder, 3., et al., "Homogeneous Nucleation in Condensation','

Heterogeneous Combustion (Academic Press, Inc., New York, 7I9r64),

pp. 64,7-675.

15. Andres, R. P. and Boudart, M., "Time lag in multistage kinetics,"

3. Chem. Phys. 42 (6), 2057-2064 (March 1965).

16. Hill, P. G. , "Homogeneous nucleation of supersaturated water vapor in

I nozzles, " MIT Gas Turbine Lab. Report No. 78 (January 1965).

17. Stodola, A. and Lowenstein, L. C., Steam and Gas Turbines,

(McGraw-Hill, Inc. , New Yprk, 1945), Znd printing, p. 312.

18. Benjamin, M. W. and Miller, J, G., "Flow of water through throttling

orifices, " Trans. ASME, 419-429 (July 1941).

1 "19. Bailey, J., "Metastable flow of saturated water, " Trans. ASME 73

- ( i), 1109-4116 (November 1951).

20. o ,cener, P. P. and Fouring, A, A. , "Experiments on condensation ofIwater by homogeneous nucleation in nozzles, Phys. Fluids 7

4vapor (3),

-42

21. Allard, E. F. and Kassner, J. L., "New cloud-chamber method for

the determination of homogeneous nucleation rates, "J. Chem. Phys.

42 (4), 1401-1405 (February 1965).

22. Smigielski, J., "Monodimensional adiabatic flow of a two-phase

medium, AGSC Wright Field Report FTD-TT-63-378 (1963).

23. Kliegel, R., "Gas Particle Nozzle Flows, " Ninth Simposium on

Combustion (Academic Press, Inc., New York, 1963), pp. 811-826.

24. Lowi, A., "Spacecraft jet reaction control, " Aerospace Corp.,

TOR-469(5560-10)-2 (July 1962).

25. Kubin, R. F. and Presley, L. L., "Thermodynamic properties and

Mollier chart for hydrogen for 300 * to 20, 000' K, NASA Ames Research

Center, SP-3002 (t964).

26. Dean, J. W., "A tabulation of the thermodynamics properties of

normal hydrogen from low temperatures to 540 OR and from 10 to

1500 psia, " NBS Tech. Note 120 A (June 1962).

27. Din, F., Thermodynamic Functions of Gases (Butterworths, Ltd.,

London, England, 1961) Vol. 3.

28. "Thermodynamic properties of Freon-14," E. I. DuPont Co., Bulletin

T-14 (1961).

29. Griep, D. J., "Electronics program: satellite attitude control system

experiments' Aerospace Corp. TDR-269(4250-32)-2 (15 May 1964).

-43-

UJNCLASS IFIEDSecurity Classification

DOCUMENT COTRLTLE-_&

DYNAMIC PERFORMANCE OF LOW THRUST GOLD GAS REACTION JETSIN A VACUUM

4 DESCRIPTIVE NOTES (Type of report and Inclusive datao)

5 AUTHOR(S) (Last name, first name. initial) 4

Greer, Harold and Griep, Da-Ad J.

6 REPO PIT DATE 7e. TOTAL NO. 0OF PAS1398 480

August 196680. CONTRACT OR GRANT NO. . NG.~'R,,r144*tS

AF 04(695)-60'9 TR-66(63O fb. PROJECT No.

'~~~~PR 'to(3) (A tar 'i~sernum~b I nybeal4r

d, SD TR-6&.46010 AVA I LABILITY /LIMITATION NOTICE$

This docun.ent is subject to special export controls andA each trananattafto £oreia 0 o'rmente or foreign nationals may -be made only with prior avipr' A 7

ofSSSD RT)._____________ ___

I1I SUPPLEMENTARY NOTES 19. SPORtING MILITARIY ACTI~tTY

Space Systems DivisionAir Force Systemns Command

-__________Los Angeles, Califo -rda13 ABSTRACT

The pulsed propulsire performance of low-thrust reaction jets, typical ofthose used for small spacecraft attitude control, is arnalyzeA and compared-with the results of laboratory experiments. Five gases, hydrogen, nitrogen.^ammonia, Freon-12, and Freon-14, are Investigated using a 48 to I expansionratio nozzle. The transient processes which %lorhinate the short-pulsi6 o rlimit-cycle mode of thruster operation are formulated. These relationshipsshow good correlation with the data. The apparatus, procedures, andtechniques required to obtain accurate test results for a low-thrust, dynanic

Smode of operation are described. Impulse bit size, gas consumption, and'specific impulse are characterized in terms of thruster geometry, gasproperties, and command pulse width to provide a basis for 0-ptimum systemdesign. A simplified method for calculating dynamic impulse bit size,dynamic gas consum~ption, and pulsed specific impulse as a function. of

~ ~ ~~0 A ""~-d IN"=11hr #+o tpffpr-tiA n tform~anej ofthe gases tested is evaluate,! lwi a technique which includes the irflulirce of

Itank and propellant weights, as well as specific impulse,

Dor-ACS:S41 LE) _43Ur , i TE

UNCLASSIFIED-Security Classification ___________________

14.KEY WORtIS

Low Thrust PropulsionRe rtion JetsPerformance of Reaction JetsDynamics of Low Thrust JetsTransient Performance of Reaction JetsAttitude Control PropulsionTransient Impulse AnalysisCoid Gas Propulsive PerformanceSpecific Impulse of Various GasesCold Gas Propulsionqae Dynamics of Attitude Control MotorsPulsed Performance of Peaction JetsPulsed Attitude Control PropulsionInert Gas Reaction JetsSpacecraft Vernier Motor PerformanceSmill Pulse Width PerformanceMeasurement of Low Thrust Dynamics

-A ~ Abstract (Contiatcd)

UNLSSFEC .. -: -

INFORMATION

mw w mw -W w w w mr W W W

1W - -

AEROSPACE CORPORATION

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LPlease make the following pen and ink ci'anges to subject report,

entitled "Dynamic Performance of Low Thrust Cold Gas Reaction

Jets in a Vacuum," by H. Greer and D. J. Griep:

1. In the Foreword, please strike out the entire paragraph beginning

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2. Strike out and replace the distribution statement on the title page

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