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I oilIOGIN a I 'di &C I V Cooeef uter I. REPORT 99CUPTIV CI.A0611PIC Avt@NPrinceton University UnclassifiedDepartment of Aorospacc & Mechanical Sciences l, oouP,Princeton, New Jersey 08540

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Micro-Rocket Impulsive Thrusters

4 0 1 1071 0199 r pi toputt and imelueive dowc)Scient ifi Final*U?'H" T niID. (Fl,.i name, middIe I.III.I, lasi name) '

Leonard H. Caveny and Martin Summerfield

4 0PO T .A . . 7,. TOTAL o. O, PAOCS . . NO , O ' , psNovember 1971 1.00 49S, CONNACI on OAN? NO to, ORIGINATOWC nPOnT NUM80ENIDDAHC 60-71-C-0034 AMS Report No. 1014

h, PROJECT NO

Ib. OTHER REPORV NO4St (Any othe numbela ht n t be eelfpadthis tapopt)

"l d,

1to OISTRImUTION SVTIMINT....

Distribution of this document is unlimited

ll. SUPPI.IMCNTDP. NOTES. (IA. SPON50MINO MILITANY ACTIVITV

U. S. Army Advanced BallisticMissile Defense Agency

Light weight aolid propellant motors which supply high t1rusts(>500 lbf) for durations on the order 0.010 sec. (referred to asimpulsive thrusters) require special analysis of items such aGinternal ballistics, propellant combustion, ignition stimuli, exhaustplume envelope, and inert hardware. An almost explosive ignitionand pressurization coupled with the requirements for reproduciblethrust versus time programs are analyzed by a mathematical model thatemphasizes gas flow and propellant combustion dynamics. Studies weredirected at analyzing a center-vented motor approximately 7 incheslong and 0.3 inches in diameter with a total impulse of 3.6 lbf-secand a web time of 0.006 sec. A survey of the rocket motor conceptsrevealed that tho desired thrust versus time program can be achievedby internal burning grains and existing high burning rate compositepropellants. Limitations were placed on volumetric loading densityas a result of uncertainties of how the center-vented flow affectsthrust vector alignment and nozzle flow losses. The mathema::icalmodel for transient internal ballistics developed during the ,tudycan be applied to a wide range of high performance rocket motorswhich experience rapid ignition and pressurization transients.

I D 1 1 mncI iIedD,.00OV1 173 Ucassified

BestAvailable

Copy

Unclassified 11

ISoulty Massification

AtVy Welke$

Solid propellantIHigh pressure rocket motorsPropellant combustionInternal ballistics

* Rocket motor ignition

Very small rocket motors

Unclassified

MICRO-ROCK ET IMPULSIVE THRUSTERS

by

Leonard H. Caveny and Martin Summerfield

AMS Report No. 1014

November 1971

Performed under Contract No. DAHC 60-71-C-0034 issued by theU. S. Army Advanced Ballistic Missile Defense Agency.

Qualified requestors may obtain additional copies from theDefense Documentation Center.

Guggenheim Laboratories fox the Aerospace Propulsion SciencesDepartment of Aerospace and Mechanical Sciences

PRINCETON UNIVERSITYPrinceton, New Jersey

-iA--------- - e- e

IFOF;WARD

This is the final report issued under Contract No. DAHC60-71-C-0034. Reported herein is work performed over aneleven month period starting 15 November 1970, by theAerospace and Mechanical Sciences Department of PrincetonUniversity.

The work was monitored by Dr. David C. Sayles of theHuntsville Office of the U. S. Array Advanced BallisticMissile Defense Agency.

I

ABSTRACT

Light weight solid propellant motors which supply highthrusts (>500 ibf) for durations on the order 0.010 sec.(referred to as impulsive thrusters) require special analysisof items such as internal ballistics, propellant combustion,ignition stimuli, exhaust plume envelope, and inert hardware.An almost explosive ignition and pressurization coupled withthe requirements for reproducible thrust versus time programsare analyzed by a mathematical model that emphasizes gas flowand propellant combustion dynamics. Studies were directedat analyzing a center-vented motor approximately 7 incheslong and 0.3 inches in diameter with a total impulse of 3.6lbf-aec and a web time of 0.006 sec. A survey of the rocketmotor concepts revealed that the desired thrust versus timeprogram can be achieved by internal burning grains and existinghigh burning rate composite propellants. Limitations wereplaced on volumetric loading density as a result of uncertain-ties of how the center-vented flow affects thrust vectoralignment and nozzle flow losses. The mathematical modelfor transient internal ballistics developed during the studycan be applied to a wide range of high performance rocketmotors which experience rapid ignition and pressurizationtransients.

I

iv

TABLE OF CONTENTS

Title Page

Forward

Abstract iii

Table of Contents iv

List of Figures v

List of Tables ix

NomenclatureSubscripts

xiii

Introduction 1

Summary of Requirements 2

Survey of Approaches 6

Dynamics of Impulsive Thruster Performance 14Analysis of Chamber Flow and Burning

Rate Dynamics 16Functional Relationships for the Chamber 19Functional Relationships for Propellant

Combustion Transients 21Example of Measured Dynamic Burning Rates 27Rocket Motor Performance Parameters 31Total Impulse of Moior Rotating in Plane

of Desired Thrust Vector 34

High Burning Rate Propeli;nts 18General Consilerations 38Survey of High Burning Rate Propellants 40Propellant T',' jies 40

Motor Design and Trade-Off Considerations 43Baseline Motor Design 43Calcula-. -d Pressure Responses 57

Exhaust Plume C-,nsiderations 68Exhai:st Emissions 68Back Flow of Exhaust Gases 70

Performance Analyzed in Terms of F vs t 76

Conclusions and Recommendations 89

References 92

Appendix i, Bibliography of Modern High Rate Propellants 97

DD Form 1473 100

vLIST OF FIGURES

Paaz

Fig. 1 Events that occur during the operation of 4an impulsive thruster (representat.ive ofHit type of applicatin).

Fig. 2 Photograph of inert motor showing overallHit impulsive thruster configuration (Inthe foreground is a cross-section throughthe propellant grain).

Fig. 3 Influence of motor diameter and operating 7tirme on propellant web fraction.

Fig. 4 Rocket motor configurations that use 9porous propellants.

Fig. 5 Example of impulsive thruster that uses iipellets to achieve high mass generationrates.

Fig. 6 Components of center vented impulsive 12thruster that uses internal burning pro-pellant grain.

Fig. 7 Propellant grain configuration suitable 13for low burning rate propellants (e.g.,%4 in/sec).

Fig. 8 Chamber and propellant control volumes 15considered in analysis.

Fig. 9 Schematic drawing of motor that defines 22various regions considered in analysis,

Fig. 10 Schematic drawing showing relationship 24between experimental data and the re-quired heat feed-back function for thedynamic burning rate model.

Fig. 11 Corparison of calculated and experimental 28pressure-time traces for two A values(example dvnamic burning and ptessuriza-tion effects).

Fig. 12 Dynamic burning rate and chamber tempera- 29ture overshoot deduced from test I.

Fig. 13 Experimentally determined burnin rate 30correlated with a dimensionless p.

Fig. 14 Schematic drawing defining nomenclature 35used in analysis of ignition delay errorson total impulse vector.

I

vi

Fig. 15 Typical thrust versus time program used to 37demonstrate interaction between F and •

x

Fig. 16 Influence of error in centroid of F versus 37t program on thrust vectors and totalimpulse.

Fig. 17 Motor case configuration and dimensions 45considered by program (Dimensions are notin proportion for micromotor configuration).

Fig. 18 Submerged nozzle configuration ane dimen- 46sions considered by program (Dimensionsare not in proportion for micromotorconfiguration).

Fig. 19 Effect of burning rate and chamber pressure 50on burning surface area and web fractionof baseline motor.

Fig. 20 Relative web spectrum and attributes of 51neutral burning grain designs (afterBiliheimer).

Fig. 21 Configuration efficiency as a function of 52volumetric loading factor for graindesigns of various typical web thicknesses(after Billheimer).

Fig. 22 Effect of burning rate and chamber 54pressure on burning perimeter of grainconfiguration in baseline motor.

Fig. 23 Effect ;f case diameter and volumetric 53loading density ol total motor length(Baseline motor conditions exceptD E=0.5).

Fig. 24 Surface temperature of nozzle throat: 56uninsulated steel and a refractorycoating on a steel shell.

Fig. 25 Surface temperature of nozzle exit, uninsu- 58lated steel and 0.002 inches of a refrac-tory coating on a steel shell.

Fig. 26 Parametric map of effect of loading 59density, case diameter, and nozzle exitdiameter on motor specific impulse.

Fig. 27 Effect of varying nozzle exit diameter on 60performance of baseline motor.

Fig. 28 Chamber temperature and burning rate 64dynamics during motor operation.

vii

Eate

Fig. 29 Head-end and nozzle-end pressures. 65

Fia. 30 Effect of decreasing throat diameter 66on pressure versus time history.

Fiq. 31 Schematic drawing showing limitiiig stream 71lines of contoured and conical nozzlesexhausting into a vacuum.

Fia. 32 Effect of ratio of specific heats and 72nozzle geometry on back-flow of exhaustgases (showing domain of no spillage).

Fig. 33 Motor parameters as a function of nozzle 74exit diameter (For motor described byTable 5).

Fig. 34 Nozzle exit diameters and propellant 75formulations where spillage is notencountered (Datum case motor withdivergence angle, a0=0)

Fig. 35 Calculated thrust versus time programs 77s. owing how a baseline configuration isaltered by core misalignment whichincreases sliver fraction 5%.

Fig. 36 Calculated thrust versus time programs 78showing how a baseline configuration is

altered by decreasing pressure of nozzleclosure removal.

Fig. 37 Effect of F vs t program on total impulse 79vector.

Fig. 38 Calculated thrust versus time programs 81showing how a baseline configuration isaltered by reducing nominal operatingpressure.

Fig. 39 Calculated thrust versus time programs 82showing how a baseline configuration isaltered by cross-sectional area of port(i.e., volumetric loading density).

Fig. 40 Calculated thrust versus time programs 83showing how a baseline configuration isaltered by combined effects of reducingpressure of nozzle closure removal andreducing port area.

Fig. 41 Calculated thrust versus time program 85showing off design condition produced byincomplete ignition of burniing surfaceprior to nozzle closure removal.

IIviii

Page£

Fig. 42 Calculated thrust versus t ime programs 86showing how a baseline configuration isaltered by replacing composite propel-lant with a double base propellant.

Fig. 43 Calculated thrust versus time programs 87showing how a baseline configuration isaltered by a double base propellantoperating in an off-design condition.

Iiix

LIST OF TABLES

Page

Table J. Summary of Requirements for Hit System. 3

Table 2 Typical Properties of Candidate 39Propellants,_

Table 3 Example Specification for Micro-Rocket 44

Table 4 Configuration to Demonstrate Interactions 47Among Propellart Parameters(Baseline Motor),

Table 5 Micro-Motor Performance Parameters 61(Design No. 2 for Outer Motor).,

Table 6 Comments on Developmental Test Conditions 69That Relate to Metal Oxides in the,Exhaust

Table 7 Hit Propulsion Design Considerations and 91Their Possible Effects on the Program.

ENOMENCLATURE

a coefficient of apn burning rate law

Ab propellant burning surface cm 2, in2

A p cross-sectional area of port cm 2 ,in 2

A s pre-exponential factor in pyrolysiso law ci/sec, in/sec

A t throat area cm2 , in2

c specific heat cal/g K, Btu/lbp R

C P specific heat of combustion gasesat constant pressure cal/g K, Btu/lbm R

c'k characteristic velocity of combustionproducts cm/sec, ft/sec

CFXm thrust coefficient corrected for losses

D diameter cm, in

Es activation energy in pyrolysis law cal/g-mole

f some unprescribed function

F thrust kgf, lbf

g gravitational constant

Ahf net heat release during propellantcombustion cal/gm, Btu/ib

Ah s heat required to volatilize Prouellantsurface prior to establishing flame cal/gm, Btu/lb

r rotational total impulse (see Eq. 43) kgf sec, lbf sec

Isp d delivered specific impulse lbf sec/lbm

Lu standard deliverable specific impulse sec lbf /lbmspsIT total impulse kgf sec, lbf sec

L length cm, in

L* ratio of motor free volume to throatarea, Vch/At cm, in

R! xl

Nomenclature (continued)I m mass flow rate g/sec, ibm/sec

M Mach number

MW average molecular weight ibm/lb-mole, g/g-mole

n exponent of apn burning rate law

p pressure atm, psia

qign heat flux from ignition stimulus cal/cm2sec

r, R radius cm, in

R universal gas constant 1.98 cal/g-mole K

r burning rate, regression rate cm/sec, in/sec

s material strength kg/cm 2, lbf/in

t time sec

At time required for nozzle closure to

araseparate from the nozzle sec, msec

tZeld time at which stable flame occursaccording to Zeldovich criteria sec

T temperature K, R

Tif effective temperature at the interfacebetween the thin quasi-steadysurface reaction zone and the non-reacting condensed phase K, R

T0 initial temperature of propellant K.R

T temperature of propellant surface K, Rs

mean velocity of gas in chamber cm/sec3 .3

Vch chamber volume of motor cm ,in

x distance cm, in

thermal diffusivity, nozzle 2divergence angle cm /sec, inL/sec; deg

y ratio of specific heats

xMOW-

Ixi

Nomenclature (continued)

y+lr a function 2 2(y')

C expansion ratio of nozzle

Cpropellant configuration efficiency(fraction of propellant converted toimpulse under rated pressure of thechamber and nozzle)

A thermal conductivity cal/cm K sec

Svolumetric loading density of case

7Kn temperature sensitivity of burningrate at constant Ab/At

density g/cMn3

temperature gradient at interfacebetween surface reaction zone andnonreacting condensed phase K/cm, R/in

a angle centerline of nozzle makeswith desired direction of totalimpulse vector rad, deg

8 angle of limiting streamline ofplume rad, deg

a standard deviation

a temperature sensitivity of burningP rate at constant pressure (3inr/T 0)p K !

T characteristic time SecT thickness

cm, inTb thickness of propellant burned cm, in

0 design factor

W angular velocity of vehicle rad/sec

the value is on the order of

~xiii

Sub:Sczpt

am art ent conditions

act theoretical values corrected to actual condition

app apparant value based on back calculation

b burning propellant

blow nozzle closure blowout

bo burn out

c condensed phase, motor case

ch chamber

cen centroid of F vs t program

E nozzle exit

eq steady state condition which corresponds to instan-taneous pressure

ero throat erosion

err error in time of F vs t centroid

f flame condition, flame zone

fin final

h head end of motor chamber

i,init initial; condition of a controlled environment

if interface between the very thin surface reactionzone =nd the nonreactioning condensed phase

ig igniter

in insulatiop

1 liner

mean conditions of mean flow in chamber

n nozzle, nozzle end of motor chamber

meas measured

MO .totor

xiv

o outside diameter

port port

prop propellant

ref reference conditions, p=1000 psi, T0=70F, aE=0.0

S surface reaction zone, smeared thrust due to rotation

t nozzle throat

v volatiliza-;ion

w,web web of propellant configuration

x in x direction

Y in y direction

o stagnation conditions, ambient condition of unburnedpropellant

Superscript

o steady state

--- 1---

INTRODUCTION

In some solid propellant applications it is desirable toproduce a controlled high thrust for a very short time, thatis, to make the burn-out time no longer than a few milli-seconds. All of this must be accomplished in high perfor-mance systems, i.e., maximum total impulse per motor weight.We will refer to such systems as impulsive thrusters or micro-rockets. Typically, these syscems use less than one-tenthpound of propellant and are less than one inch in diameter.Broadly speaking, two internal ballistics approaches are pos-sible. The first approach is to desion the propellant grainso that the effective web thickness of the propellant grainis very small and to take advantage of increased burning ratesat high combustion pressures (circa 15,000 psi). However,very thin webs are practical only if the unsupported web thick-ness, T , is an appreciable fraction of the propellantdiametee (e.g., 2T /D > 0.1) and if accelerationand gas drR 0°orces are Allr°Because of the difficult prob-lems in grain design in pursuing this route, a second approachmay be more attractive. The second approach is to utilizehigh burning rate propellants, which may be faster by five ormore times than the standard propellants. An additionalconsideration to the development of impulsive type microrocketsis establishing the most efficient case, nozzle and igniterdesigns.

This report summarizes the investigations (conducted atPrinceton University) to determine and evaluate approaches tothe development of solid propellant, impulsive type micro-rockets. The applications of these investigations were di-rected at satisfying the Hit propulsion requirements. Theetudy at Princeton University consisted of the following items:

I. Analysis of approaches to achieve controlled thrustfor very short times and the development of a com-prehensive mathematical model for predicting theperformance of micro-rocket, impulsive thrusters.

II. Analysis of methods of achieving ultra-hiqh burn-ing rate propellants.

III. Study of operating characteristics and methods ofmaximizing performance of the most promising im-pulsive thruster concepts.

The major objective of this study is to establish a soundtechnical basis for evaluating the various competitiveapproaches to the impulsive thrusters for Hit.

-2-

SUMMARY OF REQUIREmENTS

Before beginning the discussions of the approaches to im-pulsive thrusters, a discussion of the operating conditionswill help to focus more clearly on the requirements that apractical motor design and .repellant must meet. Rapid ignitionand pressurization (all within a few milliseconds or less) arecharacteristic requirements. Thus, the propellant should becapable of withstanding an almost explosive ignition impulse.As in most solid rocket motors, it will be necessary to pro-vide pressure level control by means of a prescribed burningsurface area versus web thickness; thus the high burning ratepropellants should lend themselves to being molded or castinto various geometries. Unfortunately: some of the mechanicalapproaches to achieving high burning rates are better suited,or end-burning grains rather than internal-burning grains.Of major importance is that the process which is used to in-crease burning rate must be reproducible and repeatable inpractical rocket motor configurations.

Table 1 shows in summary form the basic requirements ofthe Hit propulsion system (a complete specification is givenin Table 3). A pressure versus tire program cozresponding tothe Hit requirements is shown in Fig. l. Note the very shortburning time and the high pressure of the system. The massfraction requirement becomes very restrictive when it is re-viewed in terms of the center-vented requirement and miniaturesize of the components. The photograph of a model of the Hitimpulsive thruster shown in Fig. 2 gives an impression ofthe size and general configuration. Note the cross-sectionof the propellant grain showing the very small star pointsand port passage. Small errors in aligning the internal portof grain can greatly alter the burn-out characteristics ofthe motor.

I

-3-

SUP-NARY OF UIREMENTS FOR HIT SYSTEM*

I T~eb' l1k-f sec 3.6

tb' sec <0.008

Mass fraction, W pro /-qM 0.49

Minimum lezigth, NO4 , in 6.0

Safety factor 1.4

Peak thrust F lbf 700

Ignition delay to first thrust, sec <0.0015

Variation of centroid of pulse,3a, sec <0.00125

Chamber is center vented (i.e., side vented)

Thruster is rotated on the outercircuirference of a cylinder andits nozzle is aligned perpendicularto the cylinder centerline.

An example specification is given in Table 3

PRESSURE AT WHICH

rNOZZLE CLOSUREBLOWS OUT WEB BURN OUT

r- IGN1TER BURN OUT HED END0~WEB BURN OUT0 r NOZZLE END

/ SLIVERBURNOUT

IGNITER

ca~ CONTRIBUTION OFw ~ RPELN GRAIN /

z

0

PROPE LLANTSURFACE !GNITED

TIME, msec

rig. 1 Events that occur during the operation of animpulsive thruster (representative of Hittype of application),

...... ..... ................... ..... .............

NOT REPRODUCIBLE

'0

0

00

00

0 0o

0 c

0-1-

(N

-6--

SURVEY OF APPROACHES

Over the last two decades, many attempts to develop moder-ate size propulsion systems (between 2 and 4 inches in diamet6r)with high mass discharge rates have been reported. The iargepart of this work has been directed at increasing the effectiveburning rate of the propellant. To a lesser extent, the feasi-bility of various methods of employing very thin webs has beenexamined. Because of the requirement for high total impulseper motor weight (IT/WMo) systems such as the cap pistol motorwere not considered. The high thrust requirement eliminatesfrom consideration systems such as the subliming solids andmonopropellant vernier control motors.

The various methods of extending burning rates includethe use of mechanical modifiersl1 2 (metal fibers and tubes),very small oxidizer sizes, burning rate catalysts 3, and speciallyformulated propellant ingredients4. These methods have notachieved the full range of increases in buring rate that arebeing sought. However, some of the requirements for moderatelyhigh mass discharge systems can be zmet by high rate propellantsin conjunction with high surface area (i.e., thin propellantwebs) reasonably structurally sound propellant grains. As thedesired operating time decreases and the motor case diameterincreasesthere are limitations in following the approach ofusing high burning rate propellants in conjunction with verythin web, internal burning propellant configurations, (e.g.,a wagon wheel type of configuration). Configurations withsmall Tweb/Dprop ratios will not withstand the loads producedby high velocity gas flow and acccleration of the system.When the fragile propellant star points are broken off andejected through the nozzle, erratic pressure traces and in-efficient motor operation will result. Figure 3 shows theextent to which decreasing operating time affects the thick-ness of unsupported portions of propellant configurations.For the particular burning rate (10 in/sec) which was con-sidered in Fig. 3, reasonable web fractions are obtainablefor the H.t operating time and case diameter. However, suchhigh burning rates are available only in recently developedpropellants many of which can not be considered state-of-the-art with respect to the Hit requirements.

Vario ; mechanical methods of modifying propellant burn-ing rates Lave achieved limited success. Vecy thin metallicfibers (e.g., aluminum, titanium and zirconium) embedded inconventional propellants will produce significant burningrate increases 5 . However, these increases are less than thedesired high burning rate. The overruling objection to usingmetallic fibers is that no practical method has been developedto incorporate them into thin propellant webs. When effortsare made to manufacture thin web, internal burning perforations,the casting processes aligns the fibers parallel to the burn-ing surface so that they are not effective burning rate

-7

OPERATING REGION FOR HIT PROPELLANT

GRAIN TYPE:

SLOTTEDDch: = TUBE00. 5, 1.0 2.0 .-

ESTAR

WAGONWHEEL

BURNING RATE SCROLLS;XS 10 in/sec PELLETS

_____-_ _ __ __ POROUS0 0.010 0.030

MOTOR OPERATING TIME, t, sec

Fig. 3 Influence of motor diameter and operating timeon propellant web fraction.

J

I

|I

-- 8 -- -

enhancers.* Also since the fibers accelerate the burning ratelocally at a relatively widely spaced points, uniform burnoutof the propellant is not obtained.

To obtain high loading densities, reasonably high portarea to throat area ratios, and high performance in impulsivethrusters, it is necessary to operate at high chamber pressures(e.g., greater than 5,000 psi). At these pressures severalpropellants demonstrate abrupt changes in their burning char-acteristics, for example the burning rate of some ammoniumperchlorate (AP) composite propellants is known to rapidlyincrease with pressures above 7,000 psi 6 ,7 ,8 . These rapidchanges in exponent are associated with the thermal stressfailure of oxidizer particles and are reasonably reproducible.However, the burning rate exponent greater than unity (i.e.,dlnr/dlnp > 1) has disccuraged the use of such propellants.

Another approach which has received attention9- 17 is theuse of porous propellants. Figure 4 shows two methods forinstalling porous propellant grains. The important rate con-trolling process in porous propellants is convective heatingof the walls of the pores rather than conduction from theflame to the planar burning surface, as in the case of con-ventional propellants. Under a favorable pressure gradient,hot combustion gases flow intothe pores in the porous pro-pellant grain. The primary impetus for studying porous pro-pellants was the requirements of a rapidly burning charge atthe base of proiectiIes in traveling charge gunsl-1 16. Severalinvestigators9'1 6 demonstrated high burning rates using porouspropellants under the conditions of dynamic pressurization.But when these propellants were used in traveling charge guns,they proved unsatisfactory from a structural standpointll, 14.There are several important differences in the requirementsfor traveling charge guns and for impulsive Thrusters. Thetwo most important differences are: the web thicirness of animpulsive thruster is generally much less than the web thick-ness required for the traveling charge guns and the acceler-ation field of impulsive thruster is generally less severethan the axial and centrifugal accelerations experienced inthe traveling charge gun. Several methods foi making porouspropellants have been demonstrated9 ,16,17 . These methodsinclude pressing the propellant ingredients to the desireddensity, cementing balls of propellant together and thenpressing to the desired density, and making a high densityfelt out of thin propellant filaments. The last two methodscan be used to produce propellants with a wide range ofporosity. Propellants have been pressed to within less than2% of their theoretical density. More details on the com-bustion and use of porous propellants will be given in areport which is now being prepared.

One approach to achieving improved structural integrityis to mechanically reinforce the propellant grain. SchultzY8

reported the results of a series of motor tests in which thin

* Perpendicular alignment of magnetic staples can be effectedin a strong electromagnetic field.

9

a) CASE BONDED GRAIN OF POROUS PROPELLANT(REQUIRES ELASTIC PROPELLANT WITH GOODPHYSICAL PROPERTIES)

CONVENTIONALPROPELLANT

POROUS PROPELLANT

b) PRIMARY PROPELJANr IS ROD OF POROUS PROPELLANTAND SECONDARY PROPELLANT IS CONVENTIONALPROPELLANT BONDED TO CASE WALL

Fig. 4 Rocket motor configurations that use porouspropellants.

-10

layers of propellant were supported by a thin screen wire mesh.

The sheets of reinforced propellant were rolled into scrollL.Tests demonstrated that the motors could be rapidly ignitedand operated at high pressures. However, structural integrityof the reinforced grains continued to be a problem. Also, thewire mesh that supports the propellant was largely unburned,and thus its presence greatly decreases the performance of theoverall propulsion system.

Another approach which has been atteumpted 19,20 is to usepropellants with conventional burning rates and to obtain thenecessary increase in burning surface area by means of smallperforated pellets of propellant. The concept of using pro-pellant pellets to achieve reproducible impulsive thrusts iswell established in guns. Since high gas velocities in thechamber and high accelerations tend to eject the burning pel-lets, in some exploratory designs the pellets are retained inthe motor by means of metal cages. The primary shortcomingof this approach is the necessity for the cage since the cageabsorbs heat and its weight detracts from the overall perfor-mance. The previously described difficulties of retainingpellets may be overcome in some applications by taking ad-vantage of high acceleration fields. A schematic drawing ofsuch a rocket motor is shown in Fig. 5. The propellant is intwo forms, a thin layer of conventional propellant bonded tothe case wall and the remainder of the propellant is in theform of pellets. After the rocket motor is ignited, thecharge bonded to the case wall burns as a conventional internalburning charge and thus insulates the motor case. The pelletsare consumed in the usual manner. The acceleration forcescounter the cendency for the pellets to be entrained in theflow of combustion gases and ejected through the nozzle. Onepossible disadvantage of this approach is that the center ofgravity of the motor depends upon how the pellets orientthemselves.

Through out this discussion we have alluded to a lessnovel approach of applying, in a scaled down fashion, thesame techniques as would bE used to design conventional sizeboosters (see Figs. 6 and 7). This is the approach on whichwe have concentrated czr efforts during this study. In thesections that follow, we will describe this approach. Inpursuing this approach, it quickly becomes apparent that con-ventiona] internal ballistics design techniques are inaccuratefor predicting and analyzing pressure and thrust versus timeprograms since over 40% of the operating time is dominatedby pressurization and tail-off transients. While we concludeas a result of this study that scaled down booster type designsare the proper approach for the Hit imDulsive thruster, wepoint out that the very short operating fime makes it man-datory for the designer to analyze the impulsive thruster byproperly accountinq for the gas dynamics and burning ratetransients. These analytical techniques are developed inthe next section erd then applied in the subsequent sections.

CASE WALL DIRECTION OF

CONVENTIONAL HIGH RATE PROPELLANT ACCELERATION

PROPELTLANT PELLETS HELD AGAINST

~~E~Lll' ........ ....*****

NOZZLE, SUBMERGED

SIDE VIEW GAS FLOWNOTE: MOTOR CASE IS CYLINDRICAL DIRECTION

WITH HEMISPHERICAL ENt SECTIONS

Fig. 5 Example cf impulsive thruster that uses pelletsto achieve high mass gen~eration rates.

E -12-

E-44u z G4

04 u 0

4-I(a)

I-

0-41

z Ix

P4-

4jI

Q)

--4

WEB THICKNESS =0.030 IN. (FOR 0.310 OD CASE)VOLUMETRIC LOADING DENSITY =0.627

CAS0 WALL

PROPELLANTR

DENUDRITE COMPOSED OF

WAGONWHEEL AND STAR POINTS

Fig. 7 Propellant grain configuration suitable forlow burning rate propellants (e.g., '-4 in/sec)o

-14 -

DYNAM4ICS OF IMPULSIVE THRUSTER PERFORMANCE

A major portion of the study was devoted to developingmathematical models and computer solutions to evaluate selectedimpulsive thruster configurations and propellants. The dynamicchamber interactions that must be accounted for are indicatedon Figs. 1 and 8. Figure 1 shows the four major phases ofmotor operation: 1) the ignition phase where the igniter heatsthe propellant to ignition, 2) the chamber filling phase wherethe gases from the igniter and the burning propellant pressur-ize the chamber to operating conditions, 3) the operating (orsustain) phase dominated by the mass generated from the pro-pellant grain, and 4) the blow-down and tail-off phase afterthe propellant web burns out. The nozzle is fitted with ablow-out disk which will sea! the nozzle until a predeterminedpressure is achieved.

The measured performance of solid rocket motors duringrapid pressure excursions (such as occur during rapid ignitionand variable throat area operation) differs greatly from pre-dictions made using steady state burning rate data and simpletransient mass balance solutions2 1 - 2 5 . The very nature of theimpulsive thruster dictates careful consideration of the theor-etical and experimental aspects of the dynamic response ofburning rate, chamber pressure, flame temperature, and chambertemperature during both the rapid pressurization period (aslarge as 107 psi/sec) and the high pressure operation period.Also, the influence of these dynamic effects is very dependenton the type solid propellant being considered. For example,the rapid pressure rise following a "hard" ignition can pro-duce burning rate overshoots in excess of fifty percent aboveequilibrium conditions. In related studies 24 ,25 , we haveshown that the seriousness of these overshoots increases rapidlywhen propellants with high temperature sensitivity of burningrate are used.

Studies of dynamic effects have been limited by combustionand gas dynamics models that are incomplete and by difficult-to-interpret data. Two opposing combustion effects cause theinstantaneous buzning rate to differ greatly from the steadystate burnin rate at the corresponding instantaneous pressure.These are: I) the nonsteady thermal prcfile in the ccndensedphase of the propellant and 2) the out-of-phase blowing effectof the reactive gases leaving the burning surface. At thelower burning rate during the ignition and pressurization phase,the thermal wave penetrates further into the propellant thanat the operating pressure. As the burning rate increases, thetransition to a thinner thermal wave occurs. Since the pro-pellant is in effect preheated, the burning rate is enhancedwhile the overheated surface layer is being burned out. Thepreheating effect is only partially countered by the excessblowing effect in the flame zone, which tends to decrease theheat feedback from the flame when the burning rate exceeds

-15 -

FIAH FLAM ZO

T -SURFACE REACTION LAYERs L-/ INTERFACE\T CONDENSED PHASE

ENLARGED SECTIONITHROUGH PROPELLANT

Fig. 8 Chamber and nropel1ant control volumes consideredin analysiz

16

the equilibrium burning rate. The interactions resulting fromthe rapid changes in pressure will also affect the flame temper-ature and chamber gas temperature, which will affect in turnthe mass discharge rate through the nozzle.

In previously published studies, either the interactionsbetween the chamber and propellant combustion were not consideredor the burning model was not realistic for composite propellants.In our development, the dynamic burning rate law will be basedon the Zeldovich-Novozhilov (Z-N) method. The Z-N method hasbeen extensively developed in the USSR but has only recentlybeen investigated in th3 U.S. 2 4 . We could use a properly for-mulated flame model for solid propellant combustion, but webe.lieve the Z-N method is most suitable for +-his applicationsince it provides a more direct method of considering complexpropellants in which the flame zone parameters are not known.The chamber pressure and mass discharge responses are calcu-feted from a mathematical model whose primary components arecoupled through numeri cEl solutions to the energy equation forthe propellant, the Z-N equations, and the energy and continuityequations for the chamber, which include the effects of throatablation and chamber volume charges.

We have emphasized the dynamic burning and pressurizationof the impulsive thruster because we believe that these are thekey elements in evaluating and predicting the performance ofHit motor designs that use high energy smokeless prooellants.*

Analysis of Chamber Flow and Burning Rate Dynamics

The analysis and assumptions are discussed as they applyto impulsive thrusters with internal burning, perforated grains,e.g., pressures up to 20,000 psi, burning rates in the rangeof 2 to 20 in/sec (over the range of pressures), and dp/dt upto 5 x 107 psi/sec. Because of the wide range of events andspecial purpose propellants that may be considered, the assump-tions used in the analysis should be reviewed for each situationconsidered. As indicated in Fig. 8, we are considerinq twointeracting sets of dynamic processes: 1) the flow of gases inthe chamber and 2) the propellant combustion. The assumptionsand equation development for these processes are treatedseparately.

The assumptions for the propellant are:

1) The rate processes in the gas phase and in the surfacereaction zone can be considered quasi-steady in thesense that their characteristic times are short comparedto the transition time of the pressure change. No suchlimitation is necessary for the thermal wave in the con-densed phase.

2) No kinetic heat release occurs in the condensed phase

below the surface reaction zone. Although the surface

As will be pointed out in subsequent sections, a properly de-

signed motor will operate in a domair. where these effects arenot detrimental. Thus, one of the objectives is to greatlyreduce the very effects we are cmpnasiing.

m~ 1.7 -

reactions occur in a zone of finite thickness, the zoneis suffioiently thin that it can be considered as quasi-steady.

3) The condensed phase of the propellant is accurately repre-sented as being homogeneous and isotropic.

4) Propellant combustion zones are not influenced by axialposition and external forces such as shear forces fromthe flowing chamber gases and acceleration.

The assumptions for the chamber are:

5) Effects of axial variations of chamber temperature andpressure can be accounted for by defining a mean burningrate point between the head end and the nozzle end ofthe chamber.

6) The chamber gases can be treated as perfect gases.

7) Heat losses to the inert parts are negligible.

8) The specific heats and average molecular weights for thechamber gases, flame and igniter gases are equal.

For the conditions considered in this study, the justifi-cations for assumption 1 closely follow the arguments pre-sented in Ref. 24. Thus following Ref. 24, the characteristictimes for the condensed phase, surface zone, and gas phase are:

Tc = ac/r 2 10 - 4 sec for r = 2.0 in/sec (1)

10- 6 sec for r = 20.0 in/sec

Ts = R Ts/E Tc - 0.1 Tc < 10- 5 sec (2)

Tg = [Xg ccPg/(Xr, CgPc)] Tc ~ 0.01 ,c < 10-6 sec (3)

:34nce the times of the monotonic portion of the pressure excur-sion considered in this paper are approximately 0.001 sec.,the conditions of assumption 1 are satisfied.

The arguments for assumptions 2, 3 and 4 are the same as

presented in Ref. 24.

The condition of negligible axial temperature variations

of assumption 5 is more nearly justified for an internal-

burning propellant grair with a low L* than for an end-burningpropellant grain wit.' a large L*. In the former case whichis the situation in this study, the combustion gases leavingthe burning propellant surface are distributed along the lengthof the rocket motor And have radial velocity components (normal1to the axis) which promote rapid mixingt of these gases withthe gases flowing from the head end of the motor. Also, inlow L* combustors the stay times of the combustion gases in thechamber are considerably less than the transition time forthe pressure change, and as a result large axial thermal gra-dients can not develop. For example, the characteristic staytime of the datum case chamber,

T ch = Vc/At c* r2 (4)

is 0.0003 sec while the monotonic portion of the pressure transi-tion is approximately 0.001 sec. Also, axial temperature vari-ations are reduced by the mixing produced by tcrbulence,free convection currents, and vortices. It should be noted

that the stipulation that L* be small is not a restriction tothe analysis since dynamic effects are prominent motors withrelatively low L* values. The limitation imposed by assump-tion 5 is that the propellant can not be susceptible to erosiveburning. Because we are considering veg high burning Kqtepropellants, the analyses of Willoughby' and Saderholm" indicatethat erosive burning will not occur. Saderholm's criterion,which has been successfully applied to a number of high burningrate composite propellants, indicates that for lach numbers lessthan 0.3 and chamber pressures above 10,000 ps erosive burningwill not occur if the basic burning rate is in excess of 3.0in/sec.

Assumption 6 is widely employed in the combustion litera-ture for the conditions considered in this study.

Assumption 7 is consistent with the small amount of exposedmotor hardware in properly designed high performance, internalburning systems. Also, the small amountsof refractory insula-tions that are used absorb very little heat. This is demon-strated by the delivered specific impulses of well designed,high operating pressure motors having delivered specific im-pllses that are within 5% of the theoretical specific impulses.

t These flow patterns have recently been photographed in -.high L/D, low L* window burner which is being developed atPrinceton to study ignition transients. The rapid mixing ofthe gas is evident.

19-

The conditions of Assumption 8 were tested for the datumcase usina the calculated equilibrium thermochemical resultsof Ref. 28. The values of specific heat and molecular weightvaried less than 5% over the 500 F range of temperature.

Functional Relationships for the Chamber

The previously discussed pressurization sequence is shownin Fig. 1 and chamber interactions are indicated in Fig. 8.The initial conditions are

r= 0

Pch = Pinit (5)

Tch T init

At = 0 i.e., nozzle closure in place

The nozzle is blocked by a nozzle closure which completelyseals the throat until a predetermined chamber pressure, Pblowlis attained. Then the throat area is allowed to increaselinearly in a prescribed time interval for the nozzle closureto clear the throat, Ata.ea* During motor operation the throatdiameter is permitted to increase due to erosion,

It

ADt = 2 ( peroPt) dt (6)10

then in turn

At = w/4 (Dtiit + ADt) 2 (7)

The mass continuity equation for the free volume in themotor chamber (see chamber control volume in Fig. 8) is

d(PchVch)/dt + mn = mb + mig (8)

where for a perfect gas

mn = PchAt g/c* (9)

and

-20-

= PAb(t) r(t) (10)

During the ignition phase, the burning surface area increasesas the flame spreads along the propellant surface; followingfull ignition the burning surface area is a prescribed func-tion of the grain geometry in terms of distance burning. Thus,

t.for r Vfs dt / < 10 Lprop

Ab = Ab'i v dt/Lprp (11)

and for | Vfs dt > Lprop

Ab = f dtj (12)0

By expressing PchVch in terms of the perfect gas law,the following relation for dPch/dt is obtained from Eq. 8

dpch/dt = - (Pch/Vch)dvch/dt

+(yR/Vch) (--mnTch + mbTf + mign'i'g) (3)

The energy equation for the free volume in the motorchamber is

d(pchVchTch)/dt + mnTch - mr'bTf - miTig

- (1/c p)d(pchVch)/dt 0 (14)

-21

Multiplying the mass continuity equation, Eq. 8, by Tvh andsubtracting it from the energy equation, Eq. 14, multipliedby y yields

dTch/dt = -(mn/PchVch)Tch(y-l)

+ (mn/PchVch) (YTf - Tch + YTigmig/mb)

(15)

The chamber volume increases as the propellant is burned:

dVch/dt = rAb (16)

The several regions in the motor which were coupledthrough one dimensional compressible flow solutions are shownin Fig. 9. The solution for Pcg and Tc applies to themean flow condition for Ihe chamber and satisfies A , Vc, andA mean From these mean conditions, the stagna ion con-dlois at the head end Ph, Aport h' Tbh and rh and thenozzle end conditions p p , Mand Apor n' Tb nani rare calculatoned using the i-Bdiinension coiiressibte flown

(with mass addition) equations. The thrust calculationsare based on the stagnation pressure at the nozzle, Pn-

Functional Relationships for Propellant Combustion Transients

In this development, the dynamic burning rate law isbased on the Zeldovich-Novozhilov (Z-N) method. The Z-Nmethod offers important advantages when considering the burn-ing rate transients of propellants whose burning rate mec-hanisms are not understood (e.g., highly catalyzed propellants,propellants with complex r vs p relationships, and propel-lants with high percentages of metal fuels). It is importantto note that the validity of applying the Z-N method to aparticular combustion situation (an only be established byflame zone studies that determine the applicability of theassumptions. Flame zone studies revealed that the Z-N methodis valid for the range of conditions being considered for Hit.

We emphasized in Ref. 24 that the usefulness of the Z-Nmethod was limited because of the lack of T (p,T ) data. Aswe planned experiments to develop this data, it Became appar-ent that the concept of a surface temperature in the sensethat Zeidovich meant it is misleading. The steadv-state datawhich is used in this development of the dynamic burning rela-tionship is correlated by the pyrolysis law

B -22-

TYPICAL BTRNING SURFACEDURING MOTOR OPERATION

HIEAD MEAN NOZZLEEND END

I I I-ZINTIAL- h

bmeab b,r

:,ig. 9 Schematic drawing of moror that definesvarious regions considered in analysis.

1 23-

r = As exp(-Es/RTif) (16)

which is based on the temperature at the interface betweenthe very thin, quasi-steaCy surface reaction zone (seeassumption 2 and Fig. 8) and the nonreacting condensed phase.(It is important to note that under dynamic conditions T.is not a single valued function of pressuze but is dependenton the pressure and burning rate history. This is a departurefrom previous applications of the Zeldovich method (and laterthe Z-N method) in which a surface temperature, T, (i.e.,the temperature at the gas/burning surface interface) wasused in the pyrolysis law. Once it is realized that thesurface theLmal zone is not a well defined zone, it is moremeaningful (and less arbitrary) to base the pyrolysis lawon Tic rather than T

The energy equation for the condensed phase (-C < xc S 0)showin in Fig. 8 has the following eigenvalue dependence onT (0,t) = T. (t)c if

Pccc[Tc/at + r(Tif) Tc/3X] = Ac 2 Tc/ X2 (17)

where under conditions of full ignition the burning rate ris related to the interface temperature through Eq. 16.

The initial condition for Eq. 17 is,

T(x) = T0 at t =0 (18)

The first boundary condition is

aT/Dx = 0 as x -0 (19)

The second boundary condition is a series of conditions:

1) heatup to gasification

c (aT/3r )c 0if = qin for 0+ < t _ tv (20)

2) gasification prior to establishment of flame

- rpAhs for t < t <qign r v )Zeld~(21)

U -9 -

ENERGY BALANCE AT SURFACE:

rpc cc ( T if - TO ) =c, = r c Qs +kf 0 f if

STEADY STATE EXPERIMENTAL RESULTS:

/1P3n r 1r/ P21,,

i/Ti TO

r =A s exp(-E s/RT)if r r(po TO )

TRANSFORMATION TO r- COORDINATES:

= (k/pc) (Tif -TO) MEASUREDc iDDL POINTS

P P2 P3T 0. 2

0 =dT/dx) if

Fig. 10 Schematic drawing showing relationship betweenexperimental data and the required heat feed-

back function for the dynamic burning rate model.

_____ ___ - - j5 -- L.

3) combined heating from ignition stimulus and from gasDhase and surface reactions

qign + c (r,p(t)) for

t < t. (22),,,eld < Ign,off

4) burning during conlitions of full ignition

= Xc(r,p(t)) for t > tignfoff

(23)

where is the Z-N heat feedback function developed in Ref.24 except that it is based on Tif rather thar Ts -

Figure 10 contains a concise outline of how the heatfeedback function € is developed.

The following relationships are available in principlefrom laboratory experiments

ro = r ° (T 0 ,P) (24)

and

T* = T0 (p,r) (25)if if "

The information of Eq. 24 can be obtained by routine burningrate experiments (for a limited temperaure range). Experi-mental measurements of the dependence of T4 f an p and rare much more difficult and have yet to be accomplished withgood accuracy over the desired ranges of r and p. TheZ-N method uses steady-state burning rate data in conjunctionwith the following expression for the steady-state energybalance in the -ondensed phase

-6 = r*occ(Tf -- T0 ) (26)

As indicated in Fig. 10, r(T =) and r(p,T ) data can be combinedith Eq. 26 to obtain the fotiowing functional form, which re-places the corresponding function which is normally derivedfrom flame model,

0,pO) = (t),p(t)]. (27)

f

I

El - 26

This relation, which is obtainable from steady-state experi-ments, is the key element of the Z-N method, since it expressesthe heat feedback to the condensed phase in terms of two para-meters, pressure (p) which is externally imposed, and burningrate tr) which is the important explicit result desired fromthe solution. Assumption 1 is the justification for applyingthe steady-state result of Eq. 28 to transient conditions.

At a given pressure, there can be a wide range of burningrates, r: 1) during steady-state conditions, r is variedby changing T0 2) for dynamic conditions, the value of r iscontrolled by the heat balance at the propellant surface.Based on the arguments in Ref. 24, it is maintained that for agiven r and p (regardless of how the value of r is ob-tained) the value of (r,p) is the same for both the steady-state and transient conditions. It is important to realizethat even though Eq. 27 is obtainable from 3teady-sLate data,transient burning rate calculations can be performed only ifthe transients in the cnndensed Phase are calculated, (i.e.,(t)) by solving the transient heat condition equation (Ea. 16)

with its boundary conditions. Thus, the chamber pressure, p(t),is one of the dependent variables to be obtained from thesimultaneous solution of the energy and continuity equationsfor the chanber.

At expression for the dynamic flame temperature may be

obtained under the following conditions: 1) the adiabaticproduct compositicn in the flame zone and the heats of re-

action in the surface reaction zone and in the flame zone arenot affected by the dynamic condizions, and 2) the specificheats in the surface reaction zone and the flame are equal.It follows from € (r/c) (Tic-T ) that the energy balancefor both steady and unsteady sta~es is:

Archf = . + rocCf(Tf-Tif). (28)

Therefore by considering a reference condition,

) F 1, F ~ licIc 7 /l0 - T l .c 'C _ i i fTr f(9i - -- i T. -i, iLH= + T (29)

-cCf Liref r! --= "f,re-

The result of the foregoing analysis of the chamber andpropellant burning conditions iz a coupled set of three non-linear, first order ordinary differential equations (Eq. 13,15 and 16) for D -, TcD. and Vch and one nonlinear, secondorder oart-ial drCerenial ecuation, jEc. 17) for T(x).

itRo,:E.17Io x

27 -

Equation 17 with its boundary conditicns was solved using themethods of explicit finite differences. Equations 13, 15 and16 were integrated by the fourth order Runge-Kutta techniqueusing a variable time step. For special limiting cases, thenumerical results agreed with closed form solutions for cham-ber venting, adiabatic compression, etc.

Example of Measured Dynamic Burning Rates

In a related study, transient pressure data (from whichthe dynamic burning rates can be determined) were obtainedby suddenly reducing the nozle throat area of a motor witha rcd-and-tube propellant charge designed to have a very smallfree volume in order to have a rapid pressure rise . (Thisis referred to as the Low L* Combustor.) After ignition, themotor is allowed to reach equilibrium at low pressure, andthen the throat area is rapidly reduced by insertion of apintle driven by a pneumatic cylinder. The chamber pressurerises sharply to a new equilibriwm level. This method of ob-taining rapid pressure changes and dynamic burning rate datagives a more direct result than previously attempted methods.For example, Wcoldridge and Marxman2 2 used propellant powders(as a secondary charge) to pulse their combustor, as well asa rapid decrease of the throat area. Establishing the dynamicburning rate from such an experiment is complicated by theimpulsive changes brought on by the secondary charge. Similar-ly, obtainini dynamic burning rate information from T-burnerexperiments q complicated by approximations of the losses inthe T-burner 9 . Also, it is not feasible to deduce dynamicburning rate information from the rapid pressure rise follow-ing ignition since the complexities of ignition processespreclude isolating the desired dynamic burning effects.

Figure 11 shows a rapid pressurization and overshoot (inthe case of test 2) resulting from the dynamic super-rate ef-fects for a sudden throat area decrease (in 0.001 sec). Al-thcugh test I also exhibits a strong super-rate effect, theovershoot of pressure effect is muffled by the somewhat largerL* associated with the smaller final A,. The propellant was70% AP, 29% PBAA, 1% CuO & Cr20 3 . Other motors have beentested over a range of chamber conditions. The instantaneousburning rates and chamber tenperatures were deduced fx-om themeasured p vs t by ineans of a solution to the energy and con-tinuity equations for the chamber. This solution is for amuch simplier situation than the one previously described inthis section since flame temperature (not the chamber temper-ature) is assumed to be constant and the partial differentialequation governing heat flow to the condensed phase is notsolved. Figure 12 shows the dynamic burning rate, rdetermatined from test 1. In Fig. 13, r/r is displayed-interms cf3 the dimensionless p parameter which was used byVon Eibe . The dynamic burning rates of Fig. 13 demionstratea iysteresis-like character rather than a simple straight-line relationship between the dimensionless * and dynamic

28

ILI00

- __ ____ ____ ____ ___

C40C14 N1

0'4

04 04J

E-L

4J

00 z

w t wt

~4

P-11

50

0 -4

-4

I4U-0

-29-

X $/req% CHAMBER

TEMPE=TUTRE

C44ra

,.~ 0 2 46T'IME, t, MSEC

Fig- 12 Dynamic burning rate and :hamber tem-perature overshoot deduced frbm test 1

-30 -

TEST 1

3.4

4 0P AND READ OFF-MEASU RED PRESSURE TRACE

0 12 3 4ac dlpch

r17 -dteq

U0

0 2TIME, t, MSEC

Fig. 13 Experimentally determined burninV ratecorrelated with a dimensionless p,

~1

- 3r1 -

burning rate, as given by some of the previoasiy developeddynamic burning rate equations.

Rocket Motor Performance Parameters

The basic inputs to the analysis are desired averagethrust, total impulse, propellant properties, and nozzlecharacteristics. These inputs were selected since they arefrequently specified as requirements to achieve a particularmission. The motor performance equations are presented toavoid confusion concerning how the motor parameters wereapplied.

The steady-state burning rate along the grain is ex-pressed as a function of static pressure, P, and graintemperature, To ,

r = a pn exp[ap(Tref-T0)] (30)

The values a, n and ap are measured properties of the pro-pellant. The factor

exp [Tp (Tref-T0)]

accounts for the changes in steady-state burning rate causedby the departure of :he grain temperature, TO, from the ref-erence temperature Tref -

A compatible set o combustion gas properties is estab-lished by starting with calculated combustion gas properties(obtained from thermochemistry computer programs such asRef. 28) and then adjusting the calculated properties to ob-tain agreement with measured mass flow rates and thrusts.The measured value of c* that is normally used to calculatethe mass discharge is established from motor firing data bythe following equation

g At pdt= CI = (31)

meas3)Wprop

The quantity c* is used to relate instantaneous mass flow rate,mn , to throat area At and chamber pr, ssure pn

mn = At Pun g/c* (32)

1 - 32-

From isentropic one-dimensional compressible flow theory,mass discharge rate can be expressed in terms of the gasproperties as follows.

y+l2(y-l)

Y lm =PnAtg (33)

g R Tch/

Ideally, c* is defined in terms of the chamber gas propertiesas

/g R Tch/i.,C* =(34)

y+l

Y 12 [1-2 y -T

Ta have a compatible set of relationships, the interrelationbetween c* and T . that is established by Eq. 34 ismaintaieReroughou htitanalysis. The measured value ofc* is input and Tchact is calculated from Eq.35

2

r ~Y+lTch,act = gR I meas (35)_+

It is interesting to note that the measured c* values correctedto ideal standard conditions are within 94 to 97 percent of thetheoretical c* calculated from thermochemical programs such asRef. 28.

The ratio of specific heats, y, is an average effectivevalue for the motor and nozzle. When possible this ,alue was

meow-33-

determined from experimental data. Because of shifting equi-librium in the actual gas, this vplue is little more than em-pirical correlation constant. When satisfactory experimentaldata is not available, an effective value based on thermo-chemical calculations can be deduced from the relationshipbetween theoretical gas properties at chamber arid exit con-ditions,

Y-1

[1= n1 (36)

TE

Thrust is expressed in terms of a thrust coefficient as

F = CF p 0O n At (37)

The thrust coefficient is

+ X am (38)CF m Cm FV N + (1-AN) T- Pj E

where

CF= 312 y-jIV 2 ) -7::1 1 - ( E - (39)_+ - L P0,n

+ E E (PE)

P0 ,1

I

-34 -

and XN=(I+cos a )/2 (40)

The value of motor coefficient, C.,? used in the equation isfor nozzle-end stagnaticn pressure and should not be confusedwith values that were determined from the relationship betweenhead-end pressure and measured thrust.

Total Impulse of Motor Rotating in Plane of DesiredI Th-rus-t Vector

With the specification of a thrust time trace directedradially from the axis of rotation of the vehicle, it isdesirable to specify the time at which ignition should occur,such that maximum thrust is delivered in a given direction(See Fig. 14). In this discussion the vehicle rotates withconstant angular velocity w, clockvise, and thrust is to bemaximized in the +y direction. The given thrust time tracehas total impulse (when stationary) of

IT=t Fdt (41)blow

The radial position of the vehicle is described by:8=wt+O. (42)

1

where 8 is the angle formed by the thrust vector and the +yaxis. It is assumed that w is such that motor burn-out takesplace in a fraction of one revolution.

A rotational total impulse is defined Dy:

I =(FxFy)=Lti F sin Odt 1,tf F Cos edt ]43)

blow blow

and Fy is to be maximized, while Px should be small.yA

Substituting for e in Ir, and solving for the magnitutdeC'f Ir ,

tIr= [[Itfin F sin ([t+6t)dtl2+jjfin cos (wt+Oidt2]Stblow E/ tblow

[rfft finF sin wtdt)2 + [Kin . cos wd 211/2 (4411blow Lblow

Since II! is constant for a given w and always lessthan I., it may be regarded as the maximum effective thrustattainable with a given w.

- 35 -

t=tcen

Fv

t o

IFII +,ItF-

F \ A r .- cen + err -F F

f i terr

t-4-

t AND 0 =C COINCIDEcen

---. t enOCCURS WHEN 0=A~t err

-cos

h MhUST

Otow cen tfIj

TIME

Fig. 14 Schematic drawing defining nomenclature used inanalysis of ignition delay errors on total impulsevector,

IIZ'

-36-

Define the centroid time of the thrust versus timeprogram , tce n , such that:

[cen 'I finjt Fdt = t Fdt (45)blow tcen

A series of calculations were performed to demon-strate the influence ignition delay errors on the magni-tude and direction of the thrust vector. The ignitiondelay error is defined as the time interval between theinstant the nozzle centerline is aligned with the de-sired direction of the total impulse and the centroidtime, t en , defined by Eq. 45. Figure 15 is the thrustversus ime program used in t'he calculations. Figure 16shows the influence of the ignition delay error on thethrust vector. Note that an ignition delay error of0.00125 sec. (the 3a value in Table 1) results in thethrust vector being misaligned by 11 degrees. The thrustsmear factor, defined as

F =/I '46)

s r T

has a maximum value of 0.95 when ignition delay is zeroand falls off slightly to 0.93 when the ignition error is0.00125 sec.

In the section entitled "Performance Analyzed in Termsof F vs t", the effects of motor and propellant variables onFs and Ir will be considered for a particular design.

ir

I

-37-

4

C~CD

S-:11xE

44-

4i CV J)n

00'lou u

0 T

CV 00vr-4 U) .40

0 ~ :1 0 4

W~ Uo

-,I

1 0) (a 4

CT~4- 0 0k ~ E

4jC4j 0

X ) - 0

CO 4-'

E-4 4-i

4 01-4

009 00t, -44-0

4-' .*-a Dwl U

10

HIGH BURNING RATE PROPELIANTS

General Co-side&at a -,s

A wide range of high burning r-te propel! ... --ereinvestigated. The most explicit cor:§ - pro-pellant is that it have a burninq .rate -)f .-tv least 6 in/secat 10,000 psia. As indicated lf " 2 se oral propellantsystems can meet this _rquire.ent- T other items whichinfluence the propellann selctto)r. ar.= -,'re subtle andmust be evaluated - tcrm, of system r %,o:,Irements and motortrade-offs.

As with most volume limited systems, we are seekinga propellant with a maximum i o product. This maximummus- be obtained without us. p elemenal metal fuel addi-

tives such as aluminum. Independent of exhaust plumeconsiderations, elemental metal additives are excluded be-cause they form metal/netal-oxide agglomerates that arelikely to restrict the throat and to present serious twophase flow problems in the very small, center vented cham-ber. Generally the dual requirements of high I., andburning rate are compatible since high oxidizer-loadingsincrease both burning rate and specific impulse. However,the upper limit of propellants I and 2 in Table 2 may de-pend on processing and casting limitations resulting fromthe high specific surface of fine armnonium perchlorate (AP).Greater flexibility in burning rate and more nearly opti-mum ammonium perchlorate packing fractions can be obtainedby using an iron compound burning rate catalysts (e.g.,propellant No. 2).

A primary consideration in! the propellant selectionwill be the reproducibility and predictability of the cent-roid of the thrust versus time trace. Reproducibility prob-lems can originate during the flame spreading phase. Basedon our present understanding, a propellant with a very rapidflame spreading rate is necessary since the rapid flamespreading characteristic will dominate the ignition processand tend to overcome effects of nonuniform heating by theigniter. Also if the flame spread period is small (i.e.,less than 0.0002 sec.) relatively large percentage deviationsin the flame spread rate will not produce large deviations inthe ignition time interval. Another advantage of an easilyignited propellant is that the igniter weight will be small.Indeed, it is expected that by proper propellant selectionthe Hit impulsive thruster can be ignited by a squib with acharge on the order of 0.1 gm. Propellant No. 2 is known tohave rapid flame spread characteristic and to require a rela-tively low ignition energy.

The exha-st plume considerationson propellant selectioninvolve several overlaping objectives and will be discussed

- 39 -TABLE 2

TYPICAL PROPERTIES OF CANDIDATE PROPELLANTS

i2 3 4 5JFAP

Composite NC/NG jCompcsite HighUFAP with Fe Double mod. dou- energy

-_ _ Composite catalysts base Ible base smokeless

I D Isoj Is';z hdard theoretica! 241 239 247.8 250 254isn d 0.T95 x241 0.95 x239 Tstanrdard delivered = 229 = 227 234.2 _ 244 244

r,' 10,000 psiain/sec 5.5 > 8 14.0 to 5.1 > 13.0 > 12

n, exponent 0.55 0.6-0.7 0.81 0.75 0.7

Pc' densityg/cm3 1.65 1.66 I 1.60 i1.72 1.73

P= r/BT0 )p 0.25 0.25 0.45 0.45 > 0.30

ch , g/g-mole 24.04 26.0 28.36 22.60

Vh 1.2 1.21 1.2 1.26

Tf,chTheoretical, K 2746 2700 3194 3091 3010

Tf,ch IActual, K 2470 2430 2880 2773 2710

c*, ActualFt/sec 4670 4874 4826 5240

cal/g K 0.53 0.4052 0.42 0.42

cc cal/q K 0.3 0.30 - 0.39 0.3

cal/sec K cm 0.0009 0.00075 0.00098 .0009

-Jr_ ___ ____ _ _________ I__________ __________I -

- II_ _ I _ _ j _ _

____ ___ ____ I _ _ _ _ _ _ _ I. _ _ _ _ I___________ I _______ _______ ______ ______

-J

in a separate section of the report.

Survey of High Burning Rate Propellants

A wide range of solid propellants have been examined interms of the Hit requirements. On 17 May 1971, M. Summerfieldand L. H. Caveny of Princeton visited the Feltman Laboratoriesof Picatinny -.rsenal and discussed the propellant selectionwith J. P. Picard, C. Lenchit , R. Wetton and R. P. Baumann.On 11 May 1971, L. H. Caveny visited the Naval Ordnance Stationat Indian Head, Maryland and discussed the Hit propellantselection and internal ballistics with A. Camp and J. H.Wiegand. Since both the Feltman Laboratories and the NavalOrdnance Station are primarily concerned with double-basepropellants, the discussions centered on what can be done toincrease the burning rate and performance of double-basepropellants. It was generally agreed that the standard M-7propellant represents an upper limit of burning rate combinedwith good specific impulse. As a result of these discussionsa series of M-7 strands was burned at the Feltman Laboratories.At 10,000 psi, the strand burning is 4.0 in/sec. This isprobably the upper limit of burning rate since M-7 and M-9burning rates in motors are lower than strand burning rates.Thus the Hit requirements can be achieved only by using verythin web propellant configurations,such as a double webinternal burning, case-bonded propellant grain with a sin-leweb thickness of 0.030 inches.

On 31 March 1971, L. H. Caveny visited the HuntsvilleDivision of the Thiokol Chemical Corporation and discussedhigh burning rate AP composite propellants with W. E. Hunter.D. A. Flanagan and J. 0. Hightower. Much of the Thiokol inform-ation is included in Ref.2 In response to letters requestingspecific propellant information the Atlantic ResearchCorporation 3 and Alleghany Ballistics Laboratory of HerculesIncorporated 3 3 provided information on several propellanttypes.

Because of the many considerations, in our opinion it wasnot advisable to eliminate at this stage of the evaluationseveral of the propellants that have qucstionable character-istics. The five propellants (which we believed to becandidates) are listed in Table 3 which also contains a listof properties which are needed to make a preliminary evalua-tion of each propellant. All of the propeXties in Table 3are input properties to our Transient Gas Dynamics andBurning Rate Model and Motor Components Model.

Propellant Types

The propellant to meet the requirements of Table I shouldhave a burning rate of at least six inches per second at10,000 psi and have a high specific

a

- 41.

impulse without the use of metal fuels, since there is no

ideal system in terms of availability, high specific impulse,high density, and low temperature sensitivity, it is necessaryto consider various trade-offs among these parameters todetermine the most suitable propellant. A bibliography ofmodern high burning rate propellants is given in Appendix I.

Some propellants based on boron compounds have highburning rates, high specific impulses, and excellent tempera-ture sensitivity characteristics. Tests of these propel-lants have demonstrated that the castinq properties, thebonding capability, and the pl-ysical strength are adequatefor use in thc Hit system. It should be noted that thesepropellants w;.l! have a high percentage of boron oxides intheir exhaust. A potential advantage of the boron compoundpropellants is that the boron oxides in the chamber willassist in dissipating some types of combustion instability.It is expected that these oxides are in the sub-micron sizerange. However, these oxides will increase the cool downtime of the exhaust plume.

NF propellants have been actively considered in studiesto obtain a low smoke propellant. These propellants containno metal oxides in the exhaust and have high specific impulsesover a satisfactory range of burning rates. A difficulty withthe NF propellants is the high temperature sensitivity ofthe burning rate , as great as 0.40%/h. Based on our recentstudies of pressure overshoots resulting from dynamic burningrate" - we expect that propellants with temperature sensitiv-ity values in this range will have serious ignition problems.One of the problems experienced in obtaining a truly smokelessNF propellant was the condensation of exhaust products at sealevel conditions. Under the vacuum conditions of Hit, exhaustcondensation is unlikely. Thus, the NF propellants may pro-duce a 100% gaseous exhaust. In the considetation of the NPpropellants, we must balance the potentially poor temperaturesensitivity against the highly desirable exhaust which is freeof solid particles.

The marked difference in the 'emperature sensitivitybetween the NF and the boron compound propellants can be tracedto the different mechanisms of their burning. The NF's havea high heat release since they burn as energetic binders. Thebinder in boron compound propellants is pyrolyzed as a conven-tional hydrocarbon binder and therefore reacts in the gasphase. It is expected that the boron compound propellantshave surface temperature similar to the hydrocarbon bindersand that the HF propellants would have a lower burning surfacetemperature corresponding to that of double-base propellants.These trenqj are consistent with the trends predicted by theKTSS model , which showed that increasing the heat releaseon the surface (e.g., using an energetic binder! and loweringthe surface temperature tend to increase the temperaturesensitivity of burning rate.

Since the NF propellants have been found to be particle .:ree inthe flit operating pressure range, it mry be necessary to ;.ncludean additive such as carbon black as a suppressant for combus-tion instability.

-42-

Another well characterized famidly of propellants, thecomposite modified double-base propellants, can also meet theHit burning rate requirements by using moderately small AP.

The conventional ammonium perchlorate composite propel-lants can meet the burning rate requirements only if they arecatalyzed with metal oxide producing burning rate catalyst.However, their high specific impulses depend on high percent-ages of ammonium perchlorate which result in very viscouspropellants that are difficult to cast. There is an interest-ing trade-off be. qen the viscosity of high AP percentagepropellants and the easier to cast propellant grains that takeadvantage of the higher burning rate propellants. WIen ironcompounds are added as burning rate catalyst, metal oxideswill form in the exhaust. For example, to relate the percent-age of ferrocene added to a propellant to the percentage ofmetal oxides in the exhaust, an approximate calculationindicates that 2% ferrocene will produce 0.4% Fe 0 in theexhaust. 23

Examining the various propellant systems in terms ofstorability, a large amount of data exists on the primarypropellant ingredients such as ammonium perchloiate andbinders. However, several of the ingredients such asnitroglycerine and ferrocene plasticizers must be carefullyexamined 1-fore tnev can be considered for either vacuumstorage or storage in fiber glass type motor cases.

i

I

MOTR ESGN NLLRDEOFFCONSIERT ONS

Baseline Motor fStIgn

Thedesgn f abase"lnertriakesep;ndfig

theprolem tas equrefurther std.The prolanreqireent canotbeestablished until trade-of fs between

items such as burning rate, chamber Pressure T I~ soecificimpulse, and case diamoeter are -valuated and uflcerstood, Theinformation for Table 3 was extracted from. Ref." -and fromconversations with ABMDA and LTrV p ersonnel. Tabl-e 3 is a use-ful starting point for these stu.dies, 'kowev-tr, the relativeimportance of the various items in the spec-,fication must beestablished before a thorough trad1e-off alaysis can becompleted. For example, it may b-: possible to r-educe actiontime by reducing the mass fraction. Also, the mass fractionca-n be increased by using a nozzle with an eliptical exit butonly at an added fabrication expensr to the end-itema assembly.

F'igure 17 is a schematic drawing which shows the case andnozzle configuration which was con~sidered. The equations f or

the dixr~nenslons, weights, aad volumes of the case and nozzlecomponents have been progra.-red for computer solutions. Thesolutivns are formulated so that the primrary constraints arecase diameter, port to throat area, and total impulse. Licht-weight nozzles are considered. For example, Figure 18 showsasubmezyed type of nozzle that has a throat insert and

refractory insulation on the exit cone. No attempt is madeto include all of the details of items such as flanges andwelds.

4The range of designs which can be considered is constrainedby three Zspecial features of the Hit impulsive thruster: theIvery short action time, the high length to diameter r~-tio, andthe center 'ented chamber. A range of workable motor desiganswere arrived at by an iterative procedure. We will discuss

j the calculations and results that were used to make ourdecisions by making co-mparisons ito +,'-e baseline motor describedin Table 4. The results of Fig.19 relate the r-arqe of burzingrates required to meet the action time requirement to theavailable web fractions shown on Fig.20 The summa_-y on Fig.20indicates that star type of propellant configuration can beused with a case diameter of 0.30 inches and a burning rateof 10.0 in/sec. (The bases for selecting a Case diameter of0.30 inches will be discussed when Fig.23 is discussed.) if ahigherv burn-Ing rate pr-opellant is selected, e.g.. 15 in/sec.Ia wagowhael type of propellant config-uration will be required.As indicated on FiC,.2l1 wagonwheel configurations generally

EXAAXPLE. SPEC IFICATION' FOR MICRO-ROCKET

Units are inches, seconds, pounds mass, pounds force, andI-arees F.

Baseline

Total impDulse, -lbf sec 3.6

Action time, t-a .0-08

Peak thrust, Ib-F 700.0

Thrust misaliqn-ment, 3 i, deg 0.25

Outside diameter of cs, D co' n 0.25-0.45

Minimum desian factor, -- 1.3

Maximum tCernperature or. outsideof case, F 200.0

Mass fraction of c~oplate motor Z0. 49

Overall ienqth.,, in 2:6.0

Ionitiox delay to first thrtst, see <0.0015

Variation on above ;qnitiondelay, 3a, t <+20

'Variation of centroid ofoulse, 10r, sec <0.00i25

Metal oxides and other solids inexhaust, % <0.1

Operating condinions vacut=

Motor temperature, F 50-70

Axial acceieration g's 120

Spin r-ate about central axis rps 25

4-

ItI

fzI

14

-- 4

S41

~ 4 --

00

A6A

-

r. Ix- w

U: z

0 E-x

a 0

-34z-4

4:-

Io I

1 1 CaI

'Baseline Desian lio. 1)

Units are inches, seconds. c counds ma s, noundsI force, oon

per square inch, and degree P.

Overall Per fornance Par azetzs

*Total imnm-uise diurinq . 3.59

Ti--, wceb burning, -- 0. 0069

'total br.-r

* Pressiure, average during, t V 10, Ow.

, a'i.U instanm.arnwns -~12, 000.

SThrust, avexzag,!' during "Lb ib 522.

O'ierall ceesign .p

Fuael -gt/ctrwigt1%0.345

?ype Nwr-netzllized, A? co=-posite with energetic

Specific lips~efrnc 248.1

,~ ~ deiee, 1 STFD 5S6

Characteristic velo.city, ft/sec '0

Burnirng r-ate -34t 10,000 vsi,2fL.1/sec 10,0

Burnixng rate e-D--1et 0.5

ta~ezature sensiiti-,-tvw of bux-r= rate 0 .00i5at constant pressure,-1

tepeau~esensitivi;ty of burning rate 0. W 34at constant V

Aprescribed value

Case lerth 5.798

Case ocne x etr030

Length of" exit cot-e beyond case 0.58

19.3.1

Overall Weicttbts

Case 0.0207

Case liner and- insulation c 0. 001

?iozzle 0.0-378

Ignie

Mo-tor 003

Propellant Geometrical aantr

star

Outside diam-eter- of propellant 0.276Chauracteristic lengzth, initial, L'307

Cr-ss-seczional ioa-kdiw den-sity 0.7106

Web ~kes0.069

Max~- achnbe _anpot after =-A..e

ope-.<0.6

Liner t-h.c:kraess C- 02

Z f e-' .. a - r area-' t th roat are 5

atr10% Of vwe-4 has buarned 1.283

InSt~1 rrtarea tothoa area 10

- ye r&Xchwt tu& v- 1 t:-

flte' si)t~g'nzr-el. Gade250

strenth i2el Si40,030I X

insulation C-ase- wall and: end- can.s

Case n~thicknmess (t)-010 IS

So=nle

Sxmnsion- Ratio 8.74

Thrat ia~-mr0. 203

tShell Pyateria1 rgrltellrd 250

, stev-rgt level24.0'

Shell u--" tbicmess a-,nsr 0.010

.A ~at ent0 04

-50-

a0 - Pch,web 10,000 psia

0 .25

H. 0.30

-4

64 10 12

BUR~NING R~ATE, r, in/sec

Fig. 1.9 Effect of burning rate and chamber pressureon burning surface area and'web-fraction-.of baseline motor.

I -5!-I

DENDRITE WAG0kr-iAZEL STAR SLOTTED(FORKED TUBEWAGONWHEEL)

@ $N

CONFIGURATION WAGONWHEEL FORKED STAR, I STAR, SLOTTELWAG ONWHEEL IDEAL jTHICK TUBERELATIVE WEB 0.12-0.17 0.20-0.25 0.3-0.4 D.6-0.8 0.8-0.S

WEB/RADIUS

GROSS VOLUME LOADIX 60% 70% 75% 85% 95%

SLIVER (IDEAL) 2% 3% 5% 4% 0%CONFIGURATION 90% 92% 93% 95% 98%EFFICIENCYS I

MAXIMUM L/D FOR UNLIMITED 5:1-8:1 4:1-5:1 :1-4:1 :1-3:1NEUTRALITY*'

SE EXPOSURE NONE TO WEE NONE TO WEE NONE TO NONE TO PRIORWEB WEB TO WE

COMMENTS PERTAINING LOW VOLUME GOOD GOOD LOW LOWTO HIT LOADING L/D L/D

*L/D IS BASED ON /2 OF MOTOJ LENGTH

Fig. 20 Relative eb spectrum and attributes of neutral burninggrain designs (after Bilheimer)

-52-

1.0 OPERATING RANGEOF BASE LINE DESIGN

S STAR0 WAGONWHEEL SLOT AND CONOCYL

0 DENDRITE j -- GRAINS (WEB TYP.GROUP CENTER / . 0,8 OF RADIUS)

I 0.9 /U . i.. LA ,

rz4 - ASTAR TYPE GRAINS

0 / (WEB TYP 1/4 TO0oH a e 0 1/2 RADIUS)

0.92"0 j WAGONWBEEL TYPE GRAINS

-(WEB TYP 1/4 TO 1/3

Z RADIUS)

a___ LDENDRITEE TYPE GRAINS

SE LINE (WEB TYP 1/6 TO 1/40A8port/ IBAt N OF RADIUS)

TOO SMAL0..U 0'.8 1.o

VOLUMETRIC LOADING FACTOR,p

Fig. 21 Configuration efficienty as a function of volumetricloading factor for grain designs of various typicalweb thicknesses (after Billheimer)

- 53-

have lower volumetric loadinq densities and configurationefficiencies than starpoint configurations." Thus usingthe lower burning rate of 10.0 in/sec does not penalize thesystem and gives us more latitude in selecting the propellantformulation. Another consideration for a neutral burningpropellant configuration is the burning surface perimeter.Figure 22 shows the range of the ratio of burning perimeterto the circumference of the grain. The baseline design isin the proper range to achieve a neutral burning propellantconfiguration. However, as the buring rate increases, itbecomes progressively more difficult to achieve a neutralburning propellant configuration. (Neutral burning meansthat the burning surface area stays reasonably constant asthe propellant burns.)

One of the constraints on the system is that the motormust exceed a minimum length. Figure 23 shows how a rangeof lengths affects volumetric loading density. If the casediameter is too small, e.g., 0.25 in.. the loading densityis very small since the cross-sectional area of the port mustbe larger than the nozzle throat area (e.g., Aort/A >1.0).The rapidly increasing Mach numbers of the intErnal flows asA /A approaches unity produce serious performance lossesscn as pressure drops in the direction of flow, nonuniformburnout of the propellant web, and thrust misalignment. Thelarger diameter motors are more inefficient since volumetricloading densities are too low.

Even if a relatively small initial port area to throatarea ratio is used, the high degree of surface blowing pro-duced by the very high burning rate propellants eliminateserious erosive burning effects. This o ervation is supportedby the recent calculations of.12 illoughby and was reviewed interms of Saderholm's criterion

Even though the action time is short, the very high opera-ting pressures being considered complicate the nozzle design.Several series of heat transfer calculations were conductedto evaluate the nozzle insulation requirements. Two designsituations were considered:

1) an uninsulated steel throat section and exit cone

2) a 0.010 in of A1203 type of refractory coating ona steel throat section.

The convective heat transfer coefficients were estimatedusing the equations of Ref. 36, and the baseline propellantgas properties Figure 24 shows that situation 1 is marginalfor chamber pressures 10,000 psi and unsatisfactory for 15,000psi. Situation 2 appears to be generally satisfactory sincethe surface temperature is well below the melting point ofthe refractory coating and since there is only a slight increase

P 10,00pi- ch, web ,0-- 15.000

'~BASELINE MOTOR

D =o 0.35

E- N-

IN,

.2

~ I10 12BURNflM RATE, rin/sec

Fig. 2 2 Effect of burning rate and chamberpressure on burning perimreter of-grain configuration in baselinemotor.

5-

0~ I

0~~ 35

_.RG. WHR POR AREA-ISTOO SMALL

Pig, 23 Effect Of case diameter and Volumetricloading den~sity on total motor length(Batelin. motor c-,nditio"e except D E C55)

-56-

M TEMPERATURE OFSEVERE EROSION

0- , =15,000 psiao= 10, 000 Sc .. " -

REFRACTORY

COATEDSURFACE

;e "EXPOSED1/ STEEL

SURFACE

C

0.002 0.004 0.006

EXPOSURE TIME, t, sec

Fig. 24 Surface temperature of nozzle throat:• minsulated steel and a refractorycoating on a steel shell.

-57-

in temperature at the refrdctory coating/steel interface.Calculations were also carried out for the exit cone (Fig. 25'.

The ratio i /W is a good performance indicatorfor the motors wl-1 sNdyinc. The ratio W /Ww(used in Ref. 34) is not as revealing since H° oes not fullyaccount for the importance of specific impulse. Figure 26shows that the baseline case diameter does not produce themost efficient motor. However, the L/D requirement limits usto a diameter of approximately 0.30 inches. As shown in Fig. 26,the nozzle weight is a larue fraction of the overall motorweight. Because the chamber pressure is high and the ambientconditions are vacuum, large increases (e.g., 30 sec.) in 1scdcan be achieved by increasing the exit diameter. To limitthe vibrations in the system, it is necessary to use a rather 34stiff nozzle ring and to firmly secure the exit cones in placeFor these reasons the exit cone shell thickness (&n4 on Fig. 18)was maintained at a minimum value of 0.005 inches. The netresult is that any performance increase obtained by a largerexit cone is nullified by the increased weight of the exitcone. This trend is shown in Fig. 26 when the exit diameteris decreased from 1.5 to 1.0 inches. Figure 27 shows that agood value of DE is approximately 0.6. Another importantresult shown on Fig. 27 is the effect of increasing chamberpressure. The increased Is-- and loading density correspond-ing to the higher chamber pkessure are nullified by theincrease in case weight.

The interpretation of results of Figs. 19 through 27is a first step in defining the opexatin? range and propel-lants. However, interpeting the results has to be evaluatedin terms of items such as: the basis for selectin7 a particularmotor length, the relative importance of IT/WMO in terms ofmaterial :csts and ease of handling, the penalty for increas-ing action time, and conditions under which increasing actiontime while increasing IT/Wwo is a net cain.

Calculate-I Pressure Pesponses

The analysis section emphasized the necessity of accuratelytreating the transient burnina rate and the interactions betweencombustion and gas dynamics. The results*in Figs. 28 and 29are typical of the results which are obtained from the tran-lent gas dynamics and burning rate model. The uniform p vs tduring the first two milliseconds (shown on Fig. 29) wasobtained after condvcting several computer experiments whereigniter mass flux, igniter heat flux, nozzle closure blow-outpressurre, and propellants were varied. Figure 28 shows someof the aetails considered in selecting propellants, operatingranges, and igniters. Note that at approximately 0.5 milii-seconds, the propellant becomes fully ignited and any addi-tional contribution from the igniter is not required. Oneitem that is necessary to achieve precision of the thrustversus time trace is to find the domain where the propellant* These results are for the design described in Table 5 whichwill be discussed in the section entitled "Perfo:jaance AnalVzedin Terms of F vs t."

1 -58-

0

Pch = 15,000 psia

I i 10,000

10 4a REFRACTORY

COATED SURFACEI =4

EXPOSED STEELrz~ SURFACE,e =4

Q

REFRACTORYU) COATED SURFACE

E =25

- - ~EXPOSED STEEL____ ____ ____ ____ ___ SURFACE, E =25

0 0.002 0°004 0.006

EXPOSURE TIME t, sec

Fig.25 Surface temperature of nozzle exit,-uninsulated steel andO.002 inches ofa refractory coating on a steel sheel

-59 -

UPPER MAP DE 1.O0

L47uER MAP 1.5

010

7 1REGION WHERE PO.FR AREAisTOSMALL

*BASELINE MOTOR EXCEPT FOR DEPiq.26 Parametric map of effect of loading

density, case diameter, and nozzleexit dihmreter on motor spec-ific impulse

-c=-AHI~E MOTOR

r ?ch~vwb - i.oo pI - -15.000

I141?

16 ~o-

~r c c~f /

OLJ C;010 . 0.

onz~ maDA-MUDE

Fi-2 'Efc fIari

4ofr-rc Ofbaelnu=ooI

Un its are izm-ches, se-v~s, n a ss, pcr2nds force, n.-d

ver sm-r iracb, a-.-- deegree .

OverallI Per forzuian,-e Pazaz e ,ers

Dirte-ted total immpulse/total impulse 3,.a2. /~i4 10

. . -

Z'tt~ buin-C 3=2 tal-Of.F too = 5 pLz

' Pressure, -. =inal dur ing, t Olr

. *ax== in.Is t a xt ane -%.s z 0=00.

*Thimst' * vexrace du ~~t .lb..

Overalll de-sign fac tor~,

70tal inmulseAmotor- weigbts., /

Proell-ant eu-

Typer (So. 1 in 'Table 3) S-nneta-lized, AP cc p-

z!SPLecific in-oulse. referenxce dslivered 2-,

- .' lere 4

C -a-rzcterist ic v~elcc itv. ift/se_ 0

esi t Yj. C-. O&

3urrnLnq rate at 10007 Psi- i/sec

.In ng rat e xpon-ant Z

~~r~zzese-sitiv,_tv of urmi= -,ateat ccv-s4tan -r-ss''re. -

mez. P- a ture s an.s -I t vI yof b - -gat-

zd-esiribked va Iu

Perif-cr-mwce int degraded for losses resg -ng f r c-r cenza2rvented =-=z le

-62-

TABLE 5 (Cont.)

Overall Dimensions

Case length 7.91

* Case outside diameter 0.31

Length of exit cone beyond case 0.53

Length to diameter ratio 25.5:1

Overall Weights

Propellant, W 0.0160pr op

Case 0.0217

Case liner and insulation None

Nozzle 0.0038

Igniter

Motor, WMO 0.0415

Propellant Geometrical Parameters

Configuration Internal burningdouble web

Outside diameter of propellant 0.300

Characteristic length, initial, L* 11.22

Crcss-sectioncl loading density 0.53

Sliver fraction 0.05

Web thickness 0,073

Maximum Mach number in port after nozzleopens 0.21

Effective port area to thvnat area after10% of web has burned 1.5

Initial port area to throat area 1.4

i~- 63-TABLE 5 (Cont.)

Chamber

Type Hollow cubing withbonded end cap

Material Maraging steel

strength level, psia 300,000

Nominal thickness 0.010Insulation

Case wall not insulated;end zaps lined

Case wall thickness (0.005 isminimum value from manu-facturing consideration) 0.0]0

Nozzle

Type Submerged: conical exitcone; refractory coating

Expansion Ratio 12.5Divergence angle 15.0Effective exit diameter of eliptical 0.60exit plane

Throat diameter 0.168

Shell Material Maraging steel, Grade 250" " strength level, psi 240,000

Insert material Refractory coatingShell wall thickness at insert 0.014

exit 0.005Igniter

Type Squib at one end

Propellant weight 0.10 gDuration

0.001 sec

Heat flux to surface 200 cal/cm 2secPropellant type No. 1 in Table 2

I - 64-

RESULTS ARE FOR MOTOR SIMILAR TO MOTORDESCRIBED IN TABLE 5 EXCEPT NOMINALOPERATING PRESSURE IS 10,000 PSi RATHERTHAN 15,000.

I I

" ' /TfrfTchTf ref

K j7 rreq$4

Kk

I ""- ... /---

P/P2k

Ko

0.0 0.002 0.004 0.006 0.008

TIME FROM ONSET OF IGNITION STIMULUS, sec

Fig. 28 Chamber temperature and burning ratedynamics during motor operation

0

%0to

4

0 E41 1Ut

TIME, -C, secFig. 29 Head-end and nozzle-end pressures

-66 -

RESULTS ARE FOR MOTOR SIMILAR TO MOTOR DESCRIBED INTABLE 5 EXCEPT NOMINAL OPPERATING PRESSURE IS 10,000PSI RATHER THAN 15,000.

HEDEND

NOZZLE END)

P 1ESS 00EIAS EL

EnE t e

Fi.30EftofecesgthotdaeeonreseW4ss iehitr

-67-

becomes fully ignited in a uniform manner. For example, ifthe igniter heat flux is too great the mass contributionfrom the propellant will depend on the rate at which theigniter volatilizes tihe propellant surface rather than onthe inherently moze stable process of self sustaining pro-pellant combustion. Felatively small igniters produceextremely rapid flane spreading rates along the propellantsurface since the conditions of high burning rate propellants,high pressure, and low AJ/A combine to increase the heattransfer to the propeilaft .

The decrease between the head-end and the nozzle-endpressure is a result of the acceleration of the gases alongthe port. It may be desirable to reduce the pressure dropin order to achieve a more efficient motor case design.Figure 30 shows that decreasing the nozzle throat diameterso that the motor operates at 15,000 psi rather than 10,000psi increases Anort/At and thus decreases the pressure dropalong the port. In the 15,000 psi casethe nozzle closure wasset to open at 95% of the operating pressure and i:z the 10,000psi case the nozzle closure was set for 75% of the operatingpressure.

While it was not possihle in this study to evaluate allof the trade-offs in the motor selection process, several ofthe design parameters used to achieve the W /iw in thespecification (Table 3) indicate clearly

thkTbC 3 is

presently unrealistic. Table 5 describes a motor that satis-fies many of the requirements in the specification. However,the basis for several of the parameters is questionable. Toachieve the low inert hardware weight miniature seals andflanges were assumed and very high strength steel was used.A higher propellant loading density could be obtained by using avery low port area to throat area ratio which results inhigh Mach numbers (0.3) in the port. This is a particularlyserious situation since the two opposing high Mach numberstreams must be turned 90 degrees. The decrease in specificimpulse resulting from turning the two opposing flows andthe short flow path after the turn has nct been established-To proceed into the next phase of a motor development programwithout more information on the effects of opposing flowscould result in the selection of motors that are light weightbut with inherently unsatisfactory thrust alignment and non-repeatabie thrust versus time traces. in other words,adequate information must be obtained for establishing atwhat point decreases in motor weight actually degrade theoverall s:stem performance.

j-p

| - 68 .

EXHAUST PLUME CONSIDERATIONS

The exhaust plume considerations are complex and involveseveral overlapping objectives and requirements which willoccur during the development, demonstration, and operationalphases. The literature on contamination from exhaust impinge-ment-' ° and flow fields ,S-9 is only partially applicable.Our interpretation of a reasonable course of action is to useas a goal the requirements as set down in the specification(Table 3) but not to penalize the performance of prototypeilIulsive thrusters by items that are not important to theprototype tests. In this manner, the system can be developednd tested while allowing for improvements and changes that

will zccur during the development and demonstration phrses.For example, during the development and demonstration phaseslong term storage is not required; however, reproducibilityof the centroid of thrust versus time tzaces is very important.

Similarly, many of the tests can be conducted using propellantsthat produce submicron size, small amounts of xv.tal oxidepa:ticles (< 2%) in the exhaust. Since the 'dtrimental effectsof metal oxides have not been established, studies to evaluate

-! metal oxide effects can be conducted concurrently with testprograms that use prototype versions of the iLpulse thruster.For example, one of the items to be evaluated is the size ofthe metal oxide particles (in the exhaust plume) produced byiron compound, burning rate catalysts. If the iron oxide doesnot agglomerate into large particles, then the thermal responseof the iron oxide may closely follow the thermal response ofthe expanding exhaust gases. It appears likely that the presentHit impulsive thruster requirements can be met with a propel-lant that does not produce metal oxides. However, improvedmotor performance can be achieved if the present limitationon iron compoundburning rate catalysts can be relaxed.

Table 6 lists some of the developmental test conditionsthat apply to metal oxides in the exhaust. It is importantto note that the three test conditions are very different fromeach other. (We realize that Table 6 deals with only oneaspect of the exhaust plume considerations.) In all Fitua-tions, it is unlikely that appreciable quantities of therelatively heavy metal oxide particles will come into contactwith the system. A potential source for concern is the accu-mulation of gaseous exhaust products during the tests undervacuum conditions. In that case, the lighter molecules maybe the most likely to come into contact with system.

Exhaust Emissions

The reasons for eliminating metal oxides from the exhaustcan stem from several requirements. One requirement is thatas the hot metal oxides are exhausted, they are slow to cooldcwn under vacuum ccndition3 and therefore can be detected byvarious heat sensors. Internal balliftic studies indicate thatthe exhaust pressure will be greater than 50 psi and thus the

-69-

TABLE 6

COiMENTS ON. DEVELOPMENTAL TEST CZONDITIONS THAT RSLATE TOMETAL OXIDES IN ThI EXHAUST

Tests at normal Tests under Plightambient conditions vacuum conditions tests

Environment !g ig1 atmosphere .- 0.05 atmosphere <0.05 atmo-60 to 80 F sphere

Gaseous exhaust Smoke -ay be removed Exhaust gases c3n , System isconsiderations by low velocity air accumulate in accelerated

flowing past motor. vicinity of away fromsysten. exhaust

gases.

Metal oxide For a motor fired For a motor fired The in-ivid-considerations downward gravity and downward gravity ual metal

momentum of exhaust and mementum of oxide parti-products act so as exhaust products cles in theto prevent metal act so as to pre- exhaust have

* oxides from acctmu- vent metal oxides much greaterlating in the vicin- from accumulating memeointumity of the system. in the vicinity than the

of the system. molecules ofHowever, some of the gaseousthe lighter gases products andmay diffuse to- thus are no-ward the system. i likely to be

entrainee bythe svstem.

Storage period :1 yr. -1 yr. yr.

Operating 60 to bC F Not established Nottemperature established

plume will be relatively deinse. An all1 gaseous exiiaust vwillrapidly. dissipate and leave t -.er-y low thermal signature.

Radar return can 1 greatly influenced by the fgeeelectrons in the exhaust. NF propellants produce C). jtoattract the free electrons. The CIO in the exhaust is notdisturbed byv the radar because of its r-elatively high mass.However, the low mass free electrons in the exhaust areexcited by the radar and will reflect; radar waves and dinminishthe transmission through the exhaust products. The serious-ness .)f this depends on whether the radar is corcnunicatincwith the vehicle or whether the radar is trying to locate thevehicle. Propellants containin- aluminum will hazve a higherflame temperature which v'ill p....Lce more ionization, andth,.us more free electroniz and hnigher thermal em-issions.

The wavie lengths of radar transmissions are largecom-,ared to the micron size of the exhan~st products. Accord-ingly, the scattering cross sections of the particles are muchsmaller than the actual cross sections. Thus, the Hit systenmoperates in a good recime as far as radar c'etection is concerned.However, it is not in a good regime as -:ar as near inf'ra-red isconcerned because the particle d' iameter -is an appreciablefraction of for larger than) the wave length of the radiation.

Thne benefit of reolacinc Ar with HMX in smokeless pro-pellants at sea level conditions is that the concentration ofECI is reduced. 1hCI provnotes the condensation of water byreducin= the vapor pressure of small droplets. Again, becauseof vacuum conditions, the likelihood of condensation of watervapor is remote even with the oresence of a high concerntrationof MU-..

Back Flow of Exhaust Gzses

As tbe under-expanded gases flow past the exit plane ofthe nozzle, they undergo fur-ther exoa.nsion and turn away fromthe centerline of the nozzle. This will bin referredi to as thzPitm-e interferance zroblem. Under the conrditilons of sufrficientlylow back pressure a-nd high exit Pressure, it is possibhle finprinciple) for Part of' the exhauist gases to turn 100 degreesand impDirge on the -motor c.ase. This im-incemnent (also referredto as spilllage) can have complicating effects and should beavoided.-

Vie tuarning azgle of t-ne exhaust gases flowing past thenozzle exi 14-Plane (i.e., showndf in Fig. 3]) can, be approxi-mated in terms of" the Prandtl-Meyer anale. This turninu analeis a first approximation &M~ the limiting strea.~ Line of theexhaust Plume. n.s a general r-ecuir-ement, -~, should be lessthan 90". Figrure 32 illustrates those items which tend toreduce E-,- incryeasi;nq the diameter of' theei lae(-.the exvansion ratio) and the ratio of s'cfcheats of the

1 -71-

tDt

MO\\ CASEa)~~~ N=-MI OIMEALEMNZR

br OZMMl LO ~txa~w PoC_/1_L

F-9.31 ScI,%-e9t~ r~n hoig iiigsralre

490, ~k- Cotuedadcnia ozlsa1aut'a vacu=

____ 'sam -r~z zzracz ;

39 - O-~~S Z E D V W I E A i Z0

.4

~~L 2

:- -z~

g

Z. u

naoi Is.

ISI ~

32 2 ~ N..1E f

e; m t -y ocz Zackof neh-ust

I - 71' -

exhaust gases decrease the turning angle. The effective cross-sectiona1 area of the exit plane can be increased (within thepresent envelope constraints) by using an exit cone with aneliptical crosc-section. Indeed, losses resulting from thecomplex flow patterns in the nozzle resulting from the center-vented configuration, may be reduced by using a throat sectionwith an eliptical cross-section. Such a nozzle should have amore uniform pressure distribution at the exit plane. Also, asindicated on Fig. 31, reducing the nozzle exit divergence anglehas the effect of straightening the flow. It is important tonote that under hard vacuum conditions vehicle movement duringmotor operation has no appreciable effect on the shape of theexhaust plume.

A series of calculations was performed to investigatethose items which tend to reduce the likelihood of 0. beinggreater than 900. As shown in Fig. 33a increasing the nozzleexit diameter decreases IT ./WM, ince the increase indelivered specific impulse'(rfig. ,3b) does not off-set theincrease in nozzle weight Fig. 33c. As indicated in Fig. 32,the exhaust gas composition has a large influence on 6.. Forvery short nozzles, the question naturally arises as towhether there is sufficient time for shifting composition tobe valid. Figure 33d indicates that the extent to which thecomposition does not shift as the gas flows through the nozzlehas an appreciable effect on the conditions at the exit plane.

Figure 34 shows the combined effects of tailoring thepropellant so that it has a higher ratio of specific heatsand increasing the expansion ratio, c. Any change that shiftsthe opecating point toward the upper right hand corner of thefigure decreases the likelihood of spillage. (The theoreticalboundary of no spillage is shown by the row of arrows). Sincethere are envelope constraints on DE,, can be increused bydecreasing At and thereby increasing the operating pressure.Previous discussions pointed out that if an AP composite pro-pellant is used, the tradeoffs between I__ , burning rate,processability, and metal oxides in thei ekaust will influencethe AP percentage. These tkadeoffs are further complicatedsince lcwering AP percentage significantly reduces the like-lihood of spillage.

The foregoing discussion was included to illustrate thespillage consideration in the overall motor design process.There appears to be reasonable latitude available to designaround the occurrence of spillage.

a -74 -

NOTE: CROSS SECTION OF NOZZLE EXIT PLANE MAY BE ELIPTICAL

0

N

0

LIGWIWEIGaT >

'ON

EXIT CN

0W4

H>

~ I DATUM0

0.4 0.6 0.8 0.4 0.6 0.8NOZZLE EXIT DIA.,D E IN. NOZZLE &XIT DIA., D sIN.

a) ~b)o E4 0

0 0:1;4E-)00

4±f;-i)~: URN .

c) EXT DI~g 0 ' IWasafntono ozeextdaeedecEedb-4be5

- 75 -

REASONABLE OPERTING RANGEFROZEN COMPOSITION DURINGEXPANSIONSHIFTING COMPOSITION

PROBABLE| NO SPILLAGE I! DESIGNe POINT

.Q E-0 SPILLAGE " --r,- .... AP z

__:84% AP

o4 -88% AP

DATUMCASES

100 1NOZZLE EXIT AREA/T OAT AZEA

0.4 0.6 0.8 1.0EQUIVALENT CIRCULjR DIAMTER OFELIPTICAL EXIT PLANE, DE, IN

Fig,34 Nozzle eztit diameter& and propellantformulations where $pillage is notencountered (Datum ease motor withdivergence angle, a0 M0)

U -76-

PERFORMANCE ANALYZED IN TERMS OF F vs t

The transient ballistic pe;:formance model was used tostudy how various motor and propellant variables influencedthe performance of the motor described in Table 5, referredto in this section as the Baseline Design. The results arepresented by comparing thrust versus time programs (F vs t).Since the Hit impulsive thrust rotates about an axis parallelto its axial center line, it is important to understand howthe shape of F vs t affects the directed thrust vector (tr)and smear factor (Tr/IT). These terms are defined and dis-cussed on Page 34. It should be noted that the calculatedF vs t results are idealized compared to measured F vs t forsystems as complex as the Hit impulsive thruster. The re-sults are idealized primarily because there is no practicalway of fully accounting for the nonuniform burning of thepropellant. We expect that the sharply defined on-set oftail-off in our calculations will not be observed even inthe most carefully manufactured Hit impulsive thrusters.However, we expect that the extent to which changes in motorand propellant variables influence both measured and calcu-lated F vs t will be comparable.

An important manufacturing consideration is the dimen-sional tolerances to be held on the propellant grain. Thesetolerances will strongly influence the final selection ofthe type of grain design and manufacturing technique to beapplied (e.g., extrusion of an internal star or casting ofa longitudinal slot). As an example, calculations were madeto simulate the effect of off-setting a star-point mandrelby 0.0035 in. (about 5% of the web thickness). The F vs tresults of Fig. 35 show that the effect is slight. Eventhough the dimensions of the grains are small, it is reason-able to expect dimensional consistency to within * 0.003 in.

All of the performance predictions discussed thusfar were for motors with nozzle closures designed to openvery near to the motor operating pressure. The success ofnozzle closures (that open after the motor is near its oper-ating pressure) in obtaining reproducible p vs t historieshas been conclusively demonstrated (e.g., the micro-motorballistic test device developed by Rchm and Haas). Sincethe Hit impulsive thruster is to be stored and ignited undervacuum conditions, some type of nozzle closure is essential.The primary questicns that remain are: what is the mostdesirable opening pressure and what mechanical design ismost suitable from overall system considerations. Figure36 shows calculated F vs t for nozzle closures with removal

-77-

DATELINE DESIGN, TABLE 5SAME AS BASELINE EXCEPT SLIVER IS INCREASED 5%

BY OFF SETTING STAR-POINT MANDREL 0.0035 INCHES

0

~0

0

0 4

0 _00

N\

0 _ . . .

0 0.002 0.004 0.006 0.008 0.010 0.012

TIME AFTER ON SET OF IGNITION STIMULUS, t, SEC

Fig. 35 Calculated thrust versus time programs showing howa baseline configuration is altered by core misalignmentwhich Lncreases sliver fraction 5%.

Iw

SL -78-i BASELINEP- DESIGN."TABLE 5

SAME AS BASELINE EXCEPT PRESSURE OF NOZZLS CLOSURE

REMOVAL IS nECREASED FROM 14.000 TO 5,000 PSI

SAME AS BASELINE EXCEPT PRESSURE OF NOZZLE CLOSUREr REMOVAL IS DECREASED FROM 14,000 PSI TO 1.000 PSI

NOZZLECLOSURE I,/I,

gf .PRESS.

14,000 0.9485,000 0.951

It1 1 0 0' 9 5 1

I I

- aV

I ,IIz IU

........ I -

0 0.002 0.004 0.006 0.008 0.010 0.012

TIME AFTER ON SET Op IG=T4ON STIMULUS, t, S=

Fig. 36 Calculated t-1r=st versus time programs showirg howa baseline confguration is altera by decreasingpressure of nozzle closur removal,

I,

-79-

r,mnax LBF-SECA-ELINE DESIGN, TABLE 5 3.82

:SEE FIG. 35)

-- SAME AS BASELINE EXCE2PT NOZZLE CLOSURE 3.81REMOVAL PRESSURE IS DCREASED FROM14,0o0 PSI TO 5,000pSI (SEE FIG. 36). SA-E AS BASELINE EXCEPT NOMINAL OPERATING - .74PRESSURE IS REDUCED FROM 15,000 PSI TO10,000 PSI (SEE FIG. 38)

-TASLIM " 4.01 LBF-SEC

>4

-zVIT0 ;Ok /

SoL ,

SPECIFICATION j0 +0,1 +0.002

ERROR IN ten At er.sEc

EARLY LATE

Fig.37 Effect Of F vs t, Program o.n total impu.1sevector,

-80-

pressure of 14,000 5,000, and 1,000 psi. As the nozzleclosure pressure decreases,the action Lime uf t.e votcorincreases and the P vs t shape becomes progressively morerounded. On first appearances one might expect that themore rounded F vs t would have a much smaller smear factor(Ir/IT) and smaller IT. However since the motor is oper-ating under vacuum conditions with a prescribed nozzle,Isp d to a good approximation is independent of pressure.Figure 37 shows that approximately 2% additional losses in'r coupled with thrust misalignment of 12 degrees occurs atthe specified 3K limit on tcen. Rounding of F -s t as inFig. 36 results in only slight additional losses: an addi-tional 0.5% loss in directed total impulse (Tr) and no apprec-iable change in the degree of thrust misalignment.

Throughtiut this series of calculations, it was notedconsistently that small departures in F ve t had insignifi-cant effects on Tr . This observation is strong evidencethat the operating point of the Baseline Design has beenproperly selected. As an example of the effects producedby large departures in the Baseline Deisng F vs t, F ws twas calculated for a nominal pressure of 10,000 psi ratherthan 15,000 (see Fig. 38). This change increases the actiontime by 0.0013 seconds and decreases the directed totalimPulse Ir by about 2%.*

The effect of decreasing Aport/At has been discussedpreviously in terms of the adverse effects that the higherinternal Mach number would have on thrust misalignment andlosses produced by turning the port flow 90 degrees. Fig-ure 39 shows a F vs t prediction for a 50% reduction in theport area. Figure 40 shows the combined effect ot decreasingAport and the nozzle closure removol pressure. The high pres-sure drop along the grain has the effect of rounding off F vs tand the increased mass addition losses decreased the total im-pulse by 30A. The turning losses were not accounted for. How-ever, one should anticipate that turning two opposing Mach0.46 streams will produce serious mixing losses at the con-verging section of the nozzle. Contoured vanes may reducethe total pressure losses and likelihood of the flow fromone end interferring with the flow from the other. Untilthere is m-re experimental information (either cold flow modelstudies or motor firings), there is no basis for expectingthat increasing the loading density of the Baseline Design bydecreasing Aport will produce an overall increase in perfor-mance.

A series of F vs t predictions were made in which theBaseline Design ignition conditions were perturbed. Forexample, the igniter mass flow rate was varied ± 50% andthe igniter heat flux was varied * 25% while holding the netmass and heat generated by the igniter constant. The net

The lighter mot-r case resulting from operating at a nominal

pressure of 10,000 psi increases I iWHo by 14%. However, themaximu, Mach number in the port is increased from 0.21 to 0.30,which greatly increases the uncertainties associated withturning the port flow 90 degrees.

- ASELIN DESIGN, TABLE 5

I ~~SAXE ;LS wfts=LIr- 2 P?PRESSURE IS RE1UCEn FROM 15.000 TOI 10, 000PSI (SEE FIG- 36)

gi !IG.0 .0 .0 .0 .1 .1

1 4T 5SZZ 71m.rmS-L.Mj.t -L

LI9 3 acltdt.zt-0 s, iszo-ssolgha ati caiu~t~ salII y eu~

n~~i-..a- SL1V33in prossur

PORT DECREASEDBY 50% (PROPELLANT WEIGHT IS HELD

BASEINEMODIFIEDMOTOR MOTOR

0.21 0.46

1hp)mx 10 1.26T 10.5 0.958

(1.0 3.94

M twe 0.100.15

Ul fSLIVER BURNOUT

ra1C:I

00.002 0.004 0.006 0.008 0.010 0.01.2

TIME AFTER ON SET OF IGNITION STIMULUS, t, SEC

Fig. 3 CalcLiated ttirust versus time programs shiowing howa baseline configuration is altered by cross-sectionalarea of port (i.e., volumetric loading density)

BASELINE DESIGN, -TAULE 5-sua As BAbELINE EXCEPT PRESSUREOFhC,7P

CLOSURE REMOVAL !S DECREASED FROM 14,*000 PS TOI5,000 PSI AND CRO0SS-SECTIONALARAOPRTI

EQ I ISLIVER BVR=N0I7'

E-4 ad

0 0.002 0.004 0.006 0.008 0.016 0.01

TIME AFTER ON SET OF IGNITION STI1(LUS, t, SB:Z

Fig. 40 Calculated thrust versus time program-s sn1tg~owa baseline configiaxation is altered by c--nbi nedeffects if reducing pressure of nozzie elosureremoval and reducing port area,.

res-utt vas a vAar-ion lin the centrojI- of -7 vs t of lessthan !5.415,13 seod.These rec-Sults aolai dem-nstz -atle thatthe -D-esicrr esicn ooeratinqi in a rei: where ;;:t a

relt:~~j- ise~itveto Of f-desic n condi t-io-as and . n, :fact::~tvar~tion. Th strona jn--C2itlof se-auenece wn-d

1-1h nozzle closure tozessure (> 10GA psi) are 3kev e~ame-ts-SIrnce -,e Ahic1h ne-ss and h-ea-t fnLuxes frithe zx~qm-'e- d-cdnate the transients~ of notor ic5:rit-iv Drace-Sses. ,AISO-wnder iiir.can zmreduce overpressures followimnz rozzle

C.T. ure renzova. -Such a sittiati-on will b des-cib -we?ic . 43 i-c cisc-;ssed,.)

Wie could~ -. esent a series of' re1-StIs for undericmition S~tuxatioftS A-t eCmxe a qco d iesign a'-'veat such results are I-argely uninteres-t-ing One exa-Ie',fa mo4-ssilble d-fiz-ul to diaxv.sm-se experim~ental coGnditizcm Issnocnm s c.41 reue 141 showis tbe resul 'ts of us 4nc an

zai~: o: hatdoe ne co1et L=A-~ie the rpI ts-face or i or to rserinxc t:h. -nzoz.'e clos-,-e. Sie fle '1svreadi nc -4- =ot cczlet- when the closure :loIcws ot-*e

C6--r S--resuxe can noct be sius' ~ed ---2 rapidly dcreasesbunn s---A is -cntd ril o-

cition of -74&c. 1*9 I.s scaeu-t em ar- Iit 4a5 Lnmemd toi'1ustrate vda -- ha .-ppen if a sizngle 7weak i'-'~e Un ehead-end! I-sue zn a -cNter? -qent-d chanb-er - Am- 1-rc -Zdesimmed sincle ;iO7.iter cam. have mafcin ~as ge: eratcn

jcapacitv L.-t :1isht not have a plrooer 4heat flx itrtztc-or ran-.c flai-e spreadinc.

base provellamts t* deteMM Le the _MIse-c ! as c-coparedto thec~s .e or=;e11-w- in the Baseline Desicqn) of.h.gIcer "~-mr rt exponment (--% -and t-eprtr sensitvit

or ourn-= r-ate icQ cc.-ed with icwar X-'i ate is'eTable 2,; These --- e ---e- =romzel-nt chances that =Ost st r,g-aqcravalte d-vnawdc 3urranc rate overshoots. ?icrure 42 scr-that the lhigher bunicrate oversncots 2save a Snailefec

cm~~ F st Een t~~c th ________ cbrri~qra-effect of the double base zroceilen -- Ae run~daryz

~2res~zs ~ ~d ahe. cccpared to the c ste relan-the o t:-- ~ect ! .s esetia1- over rb2:cre the

n0,ze closur-e is rerov-ed isee -7-c. 28) and4 thas there i=lite --t on 4= - t C istr-uctizc an o:csocenit ~-that acoelarat~s the chazrber 7:re-s-rizZt~I= Or-

cess am~ oves the nszzle be*o- tn!e psr cd OF dvn.ic ornin s -N ver, ve can -c-ere the very Zet .. neta

diiio i Fc. 43. St shou-16 be =Ite tht__ el

Desicm th-a F' -s t of the 327;c- 43Z t yns iU lin u-nby o w3a3. cha± es i4= - raze~tes SwchLn as _=c _ni e~r

mass 1911x, Zc Zi % .I = -.

reVal nressuze. Dcri~'~nI h relssure SD;;,.e

An _q~vae- of the .. ese of the peressure

Z9.5noe tht ne mericd Of heeti:.=, o:)or t ,Iic-t~on?- too - m. As. a. reut a rli--e

2v th;*.

prehea ted orooeilazt reginc is burzned at an acceleratedrate.

~-85-

It

33% OF SURFACESIGNITED~/

L i

__i=z

I' °

| 33%Y OF SURFACE ,/IGIGNITE/

I0A /

I' /

01 jISURFACE

0 0 / FULLYT A IGNITED

\ /\ /

I /

I -\I 60% OF SURIFACE

0 I

0 0. 002 0. 004 0. 006 0. 008 0.010 0. 012

TIME AFTER ON SET OF IGNITION STIMULUS. t, SEC

Fig. 41 Calculated thr-ust versus time program. showing offdesign condition produced by incomplete ignitionof burning surface prior to nozzle closure removal.

Ir

SAME AS BASELINE EXCEPT COMPOSITE PROPELLANTIS REPLACED BY DOUBLE BASE PROPELLANT (PROPELLANtZ'VOLUME IS HELD CONSTANT)

F

f - - -- -~COMPOSITE DOUBLE- -1

N. I -, -BASEF /0. 0014 0. 0025S1 n 0.55 0.8Sr a 10.0 4.o

1 10,000

I I

IItI

TIME IGNITION STIMULUS8 t, SSC

,-g. 42 Calculated thrust vers~us time programs showin~g howa baseline configuration is altered by replacingcomposite propellant with a double base propellant.

- BASELINE DESGZGN: TATE 5SAME AS BASELINE EXCEPT: 1) COMPOSITE PROPELLANTIS REPLACED BY DOUBLE BASE ROPELIANT, 2) NOMINALOPERATING PRESSURE IS REDUCED FROM 15,000 TO10,000 PSI, AND 3) PRESSURE OF NOZZLE CLOSUREREMOVAL DECREASED FROM 14,000 TO 9,250 PSI

00

to

c '

ra

01 0.01.0 .0 008 000 00-

- i SLIVER BURNOUT

.

TIME AFTER ON SET OF IGNITION STIMULUS, t, SEC

-Fig. 43 Calculated thrust versus time programs showing howa baseline configuration is altered by a double basepropellant operating in an 'off-design condition.

-88-

Ifollowing nozzle closure removal is eliminated by smalladjustments to the motor and igniter parameters, the re-sult would be a motor that is very sensitive to smallmanufacturing variations.

The results shown in Figs. 35 through 43 illustratethat the design (as it applies to internal ballistics)presented in Table 5 represents a good set of operatingpoints which are relatively insensitive to motor-te-motorvariations. It is interesting to note that we have usedanalytical techinques that can predict pressure and burningrate overshoots to isolate operating domains where thoseparticular transient effects are not detrimental. Thuswe end up with the ironic situation of describing a motorwhose performauce can be approximately predicted withoutconsidering dynamic burning rate effects.

I

CONCLUSIONS AND RECOMMENDATIONS

Attention was focused on developing analytical techinques forpredicting! the performance of impulsive thrusters and on analyzingseveral o the design considerations. Since specifications forthe Itit sy'sten are still undergoing modification, it was not mean-ingful to study in depth designs to meet a particular specifica-tion. Tnstead, typical designs were evaluated to indicate theqeneral trends and the important system considerations. One ofthe n aj '-r accomnlishmentsof the study is the development of ana-lytical techniques which can be readily applied to analyzeparticular motors.

The mathematical model for analyzing impulsive thruster in-ternal ballistics and performance contains several features thatwere previously unavailable. In particular, the model considersinteractions between chamber gas dynamics and burning rate dynamicsover the entire duty cycle of the motor. Through the use of theZeldovich-Novozhilov method transient burning rates can be calcu-lated from input values that are more readily obtainable than theinput values required by previously reported models.

One of the explicit results of this study is the impulsivethruster design of Table 5. The overall quality and practicalityof the design can be evaluated from two aspects: i) the motorhardware and 2) the internal ballistics. From the aspect ofmotor hard--are the design may be idealistic since it calls for thefabrication of high strength case joints. nozzle to case flangesand ioniter bosses that use difficult to work with steels. Accord-inqlv, W /wT, requirement in the specification (Table 3) willbe diffi ? to meet. From the aspect of internal ballistics,the design looks very good. The design was placed in an operatingdomain where generous manufacturing tolerances and off-designconditions car be permitted without serious performance losses.The use of a strong igniter and nozzle closure designed to openabove 1000 psi are key items in obtaining control over the ignitioninterval and a reproducible centroid of the thrust versus timeprogralm.

As a result of this study, we have formed several opinionscon erinc nhow the propulsion system development should proceed. Webelieve that cnter-vented impulsive thrusters :an be built withaood nerformance. However, proceeding with the design of a rotorto meet th:e requirements of Table 3 without concurrent experimentalevaluat:ons av delay obtaining information needed to size the motorcomponents, (e.g., thrust vector alignment of center-vented motors,effect . lo A /A. on repeatability, and plume interference).The danaer is tR th propulsion problems (and subsequent fixesusinaeier motors to achieve the desired AV) will be discoveredsecent;talvy during future development programs. We would like tofocus attention on items that may require a quantitative determina-tio -to U: ra4e the propulsion systems that are being developed.Thes- ie s are:

--hat is a realistic upper limit of propellant loadingin center-vented motors without destroying the

90

desir-ed 1 W, charact~riSticzS by ine-tfsinu q rtMSIaltanment4Cang 'tail-off.2) What is the effect of out-gassinc from plastic zcases

(if used.) and case insulation.

3) To what extent do impoinging internal flo-f.s -.ause inter-actions that produce nonrepeatable and :iisa~i;,edthrusts.

4) To what extent can back flow of' the plume !,e allevi-atedby desiqn ch-Anges involving such itemm an propellants,pressure level, nozzle contouring tcross-sectional andaxial contours), and exit cone surface coatinnis.

The effects, chardcterization: and alternatives resultinq fromthe above iteis zire included in swnmary in Table 7.

Th mgntu--f he effects associated with Items 1through 4 can b-e evaluated only by direct testing. .'ote t0hat thetests do not require that the teL:, moto-s use e!laborate frabrica-tion, techniques, high safety factor hairdware will do. Analyticaltreatments associated with each item would be 'alual-Ae in findingthe best oper;-tinq points and desi-gn Fixes Uif required). Inparticular, we strongly recommnend studies be conductc~d on t-hefollowing internal ballistics and gas dynamics items:

1) Diagnostic 'Casts under vacuum conditions to evaluatethose designs and pr-opellants th-at alleviate b3ack-f lcwOf the plume (and not merely measure the plume spillagefor a few ccnfigurations)

2)1 Systematic tests in a high precision m'ulti-comoonentthrust stand (or *I-ie equivalent ballistics device)to quantitatively establish the influence ot' internalflows on the 'thrust vector alicinent.

3) Conduct a test series to establish the rr~peaiabilityv ofthp thrust versus time trace.

Finally, we recomsmend thas the analytical techniq~uesdeveloped during this study be subi-ected to the test of predict-ing the perfor-mance off nart-ictvlar develo-,nental. m.otors for theHit systems.

?AKA8 7

I)e" It I'. .s .- if Is~ fss Wlort ra liest Detection Design rim or tcinentor 1i- tram and Chracterigation Alternative

*IIsIts I,. M. , :,I f.. I.-O.,. .I It) nnvz. Toot of heavy walled motors Increase case 10t doereas Thr ue 'If very hIIIh burn-tss I .' Ar.'jss vause propellant lsaan density I n isle1. ps'cpe Iants jfrext -

s. J's. *;wIllanl ly *edue&* theIssoibil sty:11"' j. of "M:',5%00 rosive burnit' PwinqpisI sIts i isAlt an Importantt c',nssdorstion

it. j-sif.I11jy IWt9 I1i hoa s.,-end

2. ()Ws 1.1s.411 1 ': 1- p s.s..tsftr-vacuum tests of duration of aI 2Ilimnatv requirement.-it,. t - ,' 1's. ... , , .I.' , I igint 0.010 to 0.050 See alter for internal insulatison

.9,5I",55 M)i' .I. - -!" !.r Ms'~a motor burnout: teot in thin by usinq grain cant if-al7n trsi,.s .. I s., r- s l, tat.'t eA5 l- wall motori; to establish uratiots that do not

7ts : nr"* insulation requiromerts epose case prior to.7 ~ t,*,'* sto tai-ort? use nonsbla-<I Als'.........' ,. ive insulation

,st Iron It .a . Is bp UseP metal cases, X ,I i t "I 1, 1, fs~ I" I) Obtain direct propel-

lant to case bond

V .......... r. Nt. nrjs'.itat-.us* anrd Iss. a) Photographs of plowes dur- a) Lower internal Mach flum ror some situations C"ffis l*Iii '-.. I *isr'ss.t voc- ing vacufn tests, multi- bert baffles at nosxlo potitsve flows 'ram theii n~'...-n*..t ~ t .1 9.0 P, IVrop-Aritblep component thrust measure- and dual igniters ito right and left .jrain seti-

isA~,. 9 .. siI t . 75 99r595991d ments of heavy walled reduce unbalance in ments cuild produ.u pori-.1.59' I,;.t "Iffl ff motors grain regression) odic oscillations whieh

pr.*.s-oft it, s i 5 in turn would produce Pell-and, 1i'V staii.s.. I. dically varying thrust

vectors normal to the can,-9,5 lrssr.A f! pr ter line

Man-- I It' -,$I.

r I fr sR. if I, k I. I'f i. ip...

4. i'luin'i"t tsI . t"9w!~ inlsitint Systemaitic tests of motors Increase expansion ratti Psa her than accept ther-' f tnt r."e with candidate chanes. for elliptical nasale, con- plume spillage of present

alleviating plum intorferons, tour nouslof exit con# configurations, deasqnsurface coating, propel- changes that alleviate thelent formulation spillage problem should he

cons idered and evaluatedconcurrently with proqrams.to evaluate the effect ofplume interference rinsonsir performance

'~. le.'~i.'...Iis.,s.V .1'. ,'s.'.. andss n-mroproduri. Test of heavy walled motor Abandon use of circuss-5g-.irris'r..rs ti i . iles %isit in '-)(propel- seories for reproducibility forential slots

lwii.rs iii sto producesI v.,595.ttm9445 r *,a t

h. Hs.;rst is n fPrl..--t s f -wer pe.rf~rMnC111 non- Ageinig tests of flight type Changee propellants, slims-stiir.-.ivess ir,1 -;'hvsf Y.54., vs t motors note case materials thatplaosw i is. 'r ,.il-absorb propellant inqredi.t s~n onto

Best Available COPY

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94

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=1 2-i

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3 4. Pi.rr~ E. . an~d Freemza.-, H. E.. , Szate=-nt of Workr S o_ ia P ro I lan I Ro ck et M 4oor Arrav and Feasibility

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-95-

35.Bi~him:,J. S. , amd Xarshall, . A., 'Feasibilitv ofAlcor;ithmic Definition of Solid Propellant for FwnctionalDesign", AIAA Paper No. 69-432, presented at AIAAN 5thProvulsion JointL SpeciLalist Conference, U. S. Air -ForceAcadeiy, Colorado, June, 1969.

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-96

46. Brock. Aipoxa Lio -o = 2oz

ZIX. - l~_Fa IM -una r- ncca n

, a -- V- J - e- -L_

Rocets, Val. 65, Rock*t S,~as 16"i- , 4-

17 i.4- '4 i. * _ & ~ k!

S. Greecvtanda, ~ -. kas VAol.~At 7,r-- . ebrury lo7

Desclrlpton or -a Nozzle -x-haui~t-i- :-t-- a Viacun'.;k ~ ~ o f S-pacecr a ft aznd R.-ock e ts, voL, o

Exhaust Fl__.ow Fiecbarnics Toea-~av~a echBref- CPIA Rublicaztior. izt; 207, The Johas Z-ziook'

Phyic La197=YSil--

97

APPENDIX 1

BIBLIOG;RAPHY OF MODER1Y HIGH BURNING RATE PROPELLANTS

Andeson S.E..Beaon, . R, Both D.W.,Chaille,J. L., and Hill, W. E., "High Burning Rate Propellants,"CPIA Publication No. 188, Proceedings of 4th ICRPGSolid Propulsion Meeting, May 1969, Vol. II, pp. 2191.

Beason, L., "Fast Burning Double-Base Propellants,"3rd ICRPG/AIAA Solid Propulsion Conference, June 1968

Beason, Lew W., "Fast-Burning Composite Propellants (U),"Technical Report No. S-223, September, 1969, Rohm andHaas Company, Huntsville, Alpbama.

Bossermxn, E. D., Essick, M. L., and Lo';inger, J. A.,"Ainmo.um Perchlorate: Particle Size Measurement andBurninel-Rate Correlation (U)," Technical Report No. S-197,Jaruary, 1969, Rchm and .Iaas Company, Huntsvi11l-- Alabama.

Brandon, W. W., "Suppression of Combustion Irista&-ilityin Solid Rocket Motors with Propellant Additives andPhysical Methods (U)," Technical Report S-289, November1970, Robinm and Haas %Company, Huntsville, Alabama.

Chai'lle, J. L., "Handbook of Propellant Formulations (U),"Tpechnical Report No. S-290, November, 1970, Rohmn and HaasC inpany, Huntsville, Alabama.

Cole, R. B., "High Pressure Solid Propellant CombustionUsn Ui losed Bomb," Rohmn and Haas Company, Special

Rep ;rt S-68, 1965.

Cole, r . B., "Combustion of Solid PropellantE at Highi-ressures - A Survey," Special Report No. S-71, May 20,196'-., bc.hm and Haas Company, Huntsville, Alabama.

Cole, P. P., "Burning Rates of Solid Composite Propellantsat Pressures up to 20,000 psig (U)," Report No. S-80.

Scr~:r: r5, 1966, Rohmn and Haas, Huntsville, Alabama.

- 98 -

Derr, R. L., Beckstpad M. 1., dud Cohen, N. S..!-Combustion Tailoring Criteria for Solid Propellants,"Technical Report AFRPL-TR-69-190, June 1969, LockheedPropulsion Company, Redlands, California.

Gehlhaus, P. H., "Compatibility of CB Propellant andPropellant Ingredients with Glass-Fiber--Resin Material(U)," Technical Report S-276, October 1970, Rohm andHaas Company, Huntsville, Alabama.

George, R. L., "Development of a Specific Impulse ScalingTechnique for Smokeless Propellants (U)," TechnicalReport S-286, November, 1970, Rohm and Haas Company,Huntsville, Alabama.

Groetzinger, W. H. III, "In-Tube-Burning Rockets forAdvanced Light Assault Weapons (U),' Technical ReportS-208, April, 1969, Rohm and Haas Company, Huntsville,Alabama.

Groetzinger, W. H. III, "Evaluation of In-Tube-burningRockets for Advanced Law (U)," Technical Report S-244,December, 1969, Rohm and Haas Company, Huntsville,Alabama.

Jones, M. L. and Wood, W. A., "High-Burning Rate Pro-pellants," Proceedings of 6th ICRPG Combustion Conference,December 1969, pp. 147-157.

Jones, M. L. and Wood, W. A., "An Investigation of High-Burning-Rate 'B and NF Propellants (U)," Technical ReportS-257. April 1970, Rohr, and 11aas Company, Huntsville,Alabama.

Jones, M. L. and Booth, David W., "Reproducibility ofStrand Burning Pates for RH-H-120i Solid Propellant (U),"Technical Report No. S-273, October, 1970, Rohm and HaasCompany, Huntsville, Alabama.

Jones, Marvin L.. "An Investigation of NBF Propellantsand a Comparison of NBF and NHC Burning Rate Modifiers(U)," Technical Report Nc. S-274, October, 1970, Rohmand Haas Company, Huntsville, Alabama.

Jones, Marvin L., "Characterization of NF Propellantsfor Variable-Thrust, Extinguishable Rocket Motors (U),"Technical Report S-281, November 1970, Rohm and HaasCompany, Huntsville, Alabama.

Lovinger, J. A., "Fine-Grind-Ammonium-Perchlorate Tech-nology (U)," Technical Report S-283, October 1970, Rohmand Haas Company, Huntsville, Alabama.

I

- 91 -

Manfned, R. K., O'Neill, P. L., Pearley, E. R., andLista, E. L., "Fast Burning Propellants with Sub-MicronNI.CIO " CPIA Publication No. 188, Proceedings of ICRPGSoh4d tropulsion Meeting, May 1969, Vol. II, p. 311, 323.

Matthews, Richard L., "NF Smokeless Propellants (U),'Technical Report No. S-247, February, 1970, Rohm and HaasCompany, Huntsville, Alabama.

McSpadden, B. D., Brandon, W. W., Ignatowski, A. J.,Martia, Ke.:neth J., and Viles, J. M., "A Survey of theState-of-the-Art of High-Energy Smokeless Propellants(U)," Technical Report No. S-171, July, 1968, Rohm andHaas Company, Huntsville, Alabama.

Placzek, D. W.,' "Effect of Interior Ballistic Parameterson Rocket Exhaust Smoke, Part II (U)," Technical ReportS-282, November, 1970, Rohm and Haas Company, Huntsville,Alabama.

Placzek, D. W., "Effect of Burning-Rate Addi ives onRocket-Exhaust Smoke (U)," Technical Report S-287, November1970, Rohm and Haas Company, Huntsville, Alabama.

Reed, S. 2., Jr., "Silicon-Containing Modifiers for High-Rate Propellants (U),' Technical Report S-279, October1970, Rohm and Haas C3mpany, Huntsville, Alabama.

Viles, Joe M., "An Investigation of Dragon Side-ThrusterMalfunctions (U)," Technical Report No. S-278, October1970, Rohm and Haas Company, Huntsville, Alabama.

Willoughby, D. A., "Experimental Technology for AdvancedAntitank-Weapon Propulsion (U)," Technical Report S-285,November, 1970, Rohm and Haas Company, Huntsville, Alabama.