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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
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
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-
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.
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 -'
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 .. -: -
AEROSPACE CORPORATION
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entitled "Dynamic Performance of Low Thrust Cold Gas Reaction
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