UNCLASSIFIED

AD NUMBER

AD211313

NEW LIMITATION CHANGE

TOApproved for public release, distributionunlimited

FROMDistribution authorized to DoD only;Administrative/Operational Use; FEB 1959.Other requests shall be referred to AirForce Office of Scientific Research,Combustion Dynamics Division, Arlington,VA.

AUTHORITY

usafosr ltr, 3 aug 1983

THIS PAGE IS UNCLASSIFIED

I-) / -"-

I .* // /i: -- ,..d

'" " " I ,

mnI,

FRAYP.W C:XARLIN TIN IN CONECIO STNA D~aflc3 RLAE

GKMU-cURIUT 7Amt

NO RMS TZBLY, NOR ANY OBLIGTION WHATUOEVER AND TUN Y sT 'li r THE26 OVERNmEcNT MAY HAVE ftamuLATRD, Fumm w aR1 i ANY WAy s p.1 -t o THE

BAIL) DRAWDIS) 4Stff V, PWKS, OR OTVER DATA 33 NOT TO BE REW, i4)J Z InACATWOC ERW1J 2; ANY UANhEM !XZNW-1G THE HOLPLA 0)f! WY OTHER

VUttGO CS FaPATUt4, M* ICoewrM9o ANY ARMUTS OR PZRMUSO!" ;.) , UFACmTUR,XJ9 OR SLL ANY PATrWW)IVEFWOK TRAT WAY MN ANT WAY VC ES'. hi THERETO.

DISCLIMERl NOTICE

THIS DOCUMENT IS BESTQUALITY AVAILABLE. THE COPY

FURNISHED TO DTIC CONTAINED

A SIGNIFICANT NUMBER OF

PAGES WHICH DO NOT

REPRODUCE LEGIBLY.

I ~4

I FILE COPY

I ~~ASTIA (A1'ARLINGTON "AU. STATION AR:I

ARLIN.;TON 12. VIRGINIA

ATLM ITIC REJ-6AR W WIONALEXANDRIA, V1480W

ATLANTIC RlCrA-4C C--MP~rATION

ALV XAN OMIA, VIN IN IA

AFOSR -TN 59-173AID NO. 21-.313

III

THE MECHANISM OF DEFLAGRATION OF

IPURE AKMONIUM PUCHLORATE

IRaymond Friedman, Jwseph B. Levy,

and Keith E. Rumbel

IAtlantic Research CorporationAlexandria, Virginia

I

February 5, 1959

This work was supported by the Combustion Dynamics Division,Air Force Office of Scientific Research, ARDC, Washington. 25, D.C.under Contract Number AF 18(600)-1502. Qualified requsetere ,,may cb-tain crpiOs of this repc-_t from the ASTU Document Service Center,Dayton 2, Ohio. )Dapartment of Defense contractcrs muct be coa:blishedfor A=IA sorvices, or have their "need-to-knc' cert fted by thecognizant military agency of their project or contvact.

III!

ATLANTic PStARCH COR~PORATION

AL EKAN OfIA, VIRN NIA

TABLE (IF CONTENiTS

Page

1. SUHHARY1

11. * fIODUCTION 2

III. EXPEFTh1-ENTA4. RESUM~S 2

A. Prossure Limits and Catelyat Eficects 3B. &rfacm-Tomparatura Studios lIC. Efftct of Added Radiation on Bu~rning~ Rate 7

IV. D=S=T.O-" (W LOWER PRRS$I. L114IT 9

V.* DLX'WSSMNt CV flR.?AG"fON I4Ecvm.q1SM 1

VI. DISCUSSION OF CkL.4LYST EFFWUTS 14

VII. REFERLECr 17

APPENDIX~ A., Details of Swxfca-e'aratureMeav'irowzaents and Calculations

APPEbIDiI B. A Mthematical Ir4del foe a Defl.a-grating Hoionop3ua So. idjPT eJx ntIncluding an &xt ----tal Radiant Flux.

DLSTR!IUTION LIST

AT .ANTIC RCXC.AFP,H C RFPORATION

AL wXAN O # IA, VI ft I N IA

The Mechanium of Deflagration of Pure Ammon m Perchlorate

-aymcad Friedman, Joseph B. Levy, and X th E. Rumbel

Atlantic Research CorporationFairfax County, Virginia

L, SLM4ARY:

teemilts of new deflagration experimut, with ammonium per-chlorate, both pure and cataly.-e4, have ben presented. These inciude

studies of rates of deflaovatiot., rrecsure imaits of deflagration, sur-face teaperature, and effects of incident radiatien or. doflagration.

These and previous resulcs have been Interpreted fi tsrms of a Lcui-&Live

qualitativp, model of the d rlai-aiton prqess, suaario. belo4.

iTh crystalline amon=in perchlorata sublimes to rimnonia andperchlitic acid vapors by an enduthermic process. Reat is generated ina gain-phasg oxidation-reduction precess perhaps .L-L cm (30 mean free

paths) above the surface, at IOC tV.i. The final temp3ratuto is about930C and the surface temperature is one or two hndaed degrees cooler.Heat is conducted back through this thin layer to a-pply tA annrn

for pt !'..,ating and vaporit.S the crystal. The propagation Tate isgoverned primarily by the rate of heist generation in the gas phase and

the thermal 'onductivity of the gAaeous layar Just abov- rhe eurfrce.

The lou-pressure fla.wability limit is caused by radiativeheat loss to the surrowdinga, uhile the pruviortsly reported high-preseuie lmit is caused by coavecLvu beat loc -.d way t0o eliminated by

This research wau supported by the United States Air Force tlrcugh

the Air Force Office of Scientific Research of the Air Researtch

and Development Commands under Contract No. AF 13(6o)-150.,, Rc-oroduction in whole ox in part iv permitted f:,r any purporu of the

United States Goverament.

A..= XAN UIA VIPRO IN IA

-2-

suitable shielding of the sample. Catalysts accelerate the burning

rate by projecrini, from the surface into the thin gaseous reaction

zone and producing local acceleration of reaction rate. Very low

concentrations of catalyst, howfiver, act p'imarily to reduce flam-

mability by raiaing the lower rropes',re l!!mit, bar.Ause the cataly-t

increases the emissivity of this burning surface and hence the rato

of radiant heat loss.

The foreaoiug model, while pro!.a!=, is not rigorously es-

tablished, and is prestat.d at this tis pertly to stimulate further

research.

Ii. LTRODUCTION:

periments (i) have ahown that at certftia ambient conditions

a steady deflagration ',ave will propagate through pure ammonium per-

chlorate which has ;-eu pressed into aA essentially void-froes pellet.

Tbe rate of propagrtion cr- this process at typical rock-A pressurew

is, of the saoe orer of mcgtitude as the btrning rate of many ammonium

perchlrate-oxidlrcd solid propellauts, so the n " prchlorate do-

ccuposition flare may well exert a controlling influence on propellant

burning rates. Yvidence of the interrelation beteon the deeomposition

flame and the propellant flame may be adduced from data showing variation

of ecmposite propellant burning rate with piessure, ammrsn parchl.-oi.e

particle 91=9 8 an' catalyst; or Suhibitor effects. Such dis¢uesion will

be preLented ina another paper nnz in zreparation. The present paper

it cencerned with ds=ctions ir, rogard to tha machanim of the ammonium

perchlorate decomposition fla=, which at based largely oa new ex-

perimental findingfs reported belo,.

411. UPEIRETAL REsLV .S:

Certain experimental findings in regard to n 4eflagration

of pure and catalyzed ammonium perchlorate have been previously & -

potted (1). Further results are describni ,

ATL,!. T RESEARCH CIORPORATION

AL C XAN LIN I A, VI 0 IN -A

A. Pressure Limits and Catalyot Effects

Figure I is the curve of %Aflagration rate vs pressure

curve for pressed pellets of a,:=-±±um perchlorbte 4 m square and

38 mm long, burned at essentially constant pressure in a nitrogen

atmosphere. The propagation was downwvrd; no inhibitor was nsedsd

on the sidea of the swrples to prevent the formation LI u conical

burning surface.

The lower-pressure limit was previously reported as 4 5 acm.

In the present tests a much miore efficient ignit.on technique was

used, which consisted of an enorgetic propellant mixture instead of

a hot wire, and the lower limit wea accordingly extended to 22 atm.

The present lower-limit value is balieved to be independent of

nition energy, since specimens ignited at the limit pressure with

the present powerful ignitor wouid often burn partially before Ax-

tinction. Bxperimeui. have also ahown that the lower ilmit is in-

oensitive to sample size and to the substitution of helim for

nitrogen as the ambient atmosphere.

In previous tests an upper-pressure limit of about 250 Atm

was found. More recent tests with samples ignited on a deeply re-

cessed surface aad with standard-size asbestos-vr apped s, ples have

shotm that this effect was due to conveccive cooling, which becocees

9increasingly effective with increasing pressure. Figure 1, In con-

trast to previously reported data (1). shows that deflagration rate

increasee with increasing pressure at ieast to 340 atm, the limit ef

the apparatus. The hipi--pressure dal:a points on the curvo wcrc taken

with anbestos-wrapped s..: ans.

ci w Some of the un sual effects of the addition of copper

chroknte powdor (Harshaw Chemical Ccxpany, Cu-0202) cn the lower

pressure limit were previously described (1). all audittons raised

the limit, while large additions loraered it. Further systematic ex-

periments concerning the effect of additive concentration on pressure

limits have notr been made down to ;cry low cztalyet conccntratiuns,

.iLANrIC: RCSCANqCH C;QAYIt3N

the .zrra affiiainti.,gnitior efihn1iqun being used, with results as abown

in Figudre 2. 'flee copper c!-cmita pwider, the weight-average particle

ziz* of "hiicht was 8.5 micronis, was Mechanically mixed with ammnonium

perchiorate and the mixture was pressed into pellets at 50 tons persquare inch, Additions of as little as one part in 20,OG' aLc wo

ficient to raise the lorder-llmit prcasure four-f old,, 1he efevt is

maximited at: three parts pcr thoulsand of catalyst. Ab~ove thisB level,

both the upper ani1 the 1owdsr pressure limts widen. A cross-plot is

shown In Fiaure 3 of the deflagration. rate vs additive cov..intraclon

at 20J4 atm, a praaare ct which barnlimg wa obaAila at at4. concaqw'

trations (cf. 01gure 2). r~iflaraifxi z~t is edL.;utially 1ad.~penVt

of catalyst le*vel up, to orb part ptix thiousand and then rapidly increases

at higher concentreations. It ah1.lP(' " noted thaL iLhree effects -la~a'

of upp~r proseere lizait, tCmrtaos dof lower prossur.- limit, and incar-Sa

of deflagration rare - all oceci at about the same catalyst lavel.

At ht.gh catalyst levols (4 parta per 100 parts mixcure) t:z

deflagraO~on rate wiiaa a-rid ?.h--n decreases sharply with rurr~her

additiona. The catalyst perhapo =~y azt as a diluea! 4zt ,;k;ce-

trations. The lower pressure limit, surprisingly, continues to deere ,o

up to 40 parts of catalyst per 100 parts of mixture.

The data shown La Figure 2 were obtained with specimens of

4 = square cross-section and doiratxd propagation. The uppe- rrftassure

limit, at least, is knovio to be Atr.kSly affected by l he and

gecm-try, ao thai results in Figure 2 are mainly of iterest insofar as

Zhey indicate trend-- 4- cmuaic bch * .ic. = qimn:t.tativi conclusions

should cutC be drawn solely from these limits.

B3. Surface-Teumaratures Studies~

Photographs have been taken of the rerecting surface of defla-

grating "pcimne of amonim perchlorate b-y means of infra-rod Onsitive

film. This radlAtion is obviodsly the siu of thermal emisslim fyvxa the

~~r:~aand sl'emilumineacence (if any". Assigzuent of a value for thi

eurf-icc teupernuture from danfitcr&.vr1 measurmeonts of wach photcgrapha

ATLANTIC RIESIARCH CnO.POPATIOP4

j -5-

dep&ands on the asg :ttons made fort hq. ratio of chamiluminercence te

thermal radiation an's4 ti s dzzf1. .am ,saity. If the mainimum con-

ceivable values are assurkAid .".or thee:c ti'o unknown quantities, one then

may obtain an upper ft~ thG vlurftce tesperature. If 0-this ;:s

found to be eubatantuiti f., low the measeured final San temperature.

thert a significant corjglutanon may be drawn.

nh e~gc-~ were taken through the window Qf a tea.z ob

at 500 pai, the burnfr,- rjt;~fe-e making an angle of approximately 4.5

dagreoo with the i.daxis, with photographic conditions as follows:

% exposure, 1/2.00 sac; -?:ario of image distance to lens diameter, 4.2;

film, Kodak Uigh-S~iad Ioafra-Red; filter, Corning No. 7-69. Tho filter

cuts off below 71(y) atetrcin anita, wihile the film sensitivity curve

peaks at 8100 and hP3 dropped a factor of ten at 9100 Angstrom units.

The strands were I., s)m square, and the burning rate was such th'L he

surface regresed~ rou. 30 microns in 1/100 vacond. calibration was

cbtained by ph' ographixt5 an electrically heated rod c! L;aidter-

poriture and x,,ew emiaoivity through the acme window. Further details

ar6 piresented 'ia Appendix A.

By d4entometric measurements of photographs obtainad by this

I rocedure. an tppr limit for the vurfac2 temperaumrc was calculated.

The emissivity was taken to be 0.2, a reasonable low-limit estme-e,

z-,z1 a4"icd total emissiv ities oZ a lilst of 13 nonmetallic solidsat 8o0 C are all above thii value (2). The lower limit for chemilumi-nascence is obviously zero. On~ this basis, and with the use of Plan-..k's

j law, the upper-limit value for surface temperature was computed to be

I This result i.s basd on radiation in the spectral range 71-00-91.00 Angstrom units. 0thi--r c r.Lswith different film and filter@in the spectral range 6000-6750 -Augetram units r'ave an upper-limit

tevnrerature aboet 100 4ekreea higherL An even higher ap0parent tenm-

perature was obtained when thn cntlre vitlbe cp'ctriun was utilized.

* This may meau that there ic a ch~nd-l-rninescent component in the visible

,UTIC PruAfCMH CORPORATION

AL X AN IMA, ;Rn N IA

-6-

part of the spactrun. Visual oboervation in a darkened ram revealeda reddish glo;r frc. the spontaneously rtActing Lrface and a much

fainter ptnkioh Slov from the product ress. Gaydon (3) reports anammonia alpha-band due Co NH2 which emits prmnneLitly In the red for

H /M0 flames and which may be involved in thin ntuation.

Thase coneiderations notwithnaung, the sauface rowecature

must be below 616 ± 5C. unless the emissivity Is somehw below 04.

The product-gai twqeratura at 00 psi baa been easuraed with thermo-

couples as 932 ± 7C (1). It is clearly indicated, therefor&, that

the temperature rises at leaat by IfOW'C because =f exothermic gas-phase

reactLons.

This coeclusion would be invalidated if substactial absorption

of the emitted radiation by the ojau #&es oancurs. The absorptivLry

of water vapor, a pominent constituent, is wll known (4,5). A -.alcu-

lation shows that absorption. by water vapor In the spectral r'egion under

consideration is entirely negligible, for the prement gemetry. It does

not em Ilikely that any ot-a -pecias to be expected in high concentratoon

Y the product gases could absorb strongly enough to e-s dJIficulty.

Another possible objection Is that the effective surface

omissivity of the amoni= parchlorat. way be zbnormally low because of

the steep temperature gradln1w just below the surface. On the other

h -nd, the knon local roughnesi of the reacting surface should twai to

Increcet the effective emissivity.

L. su ,ry, the observationa reported herein stronS17 mawst

that the deflagration of amonin perchlorate involves a subotantial con-

trLbuton from the gas rhase.

A previously ranorted attempt to measure surface n-_srni-.

of deflagratIng msan/.num perchlorate (6) war unsuccessful because it was

zvot poss'lhle to fabrxate sufficiently small thermocouples.

ATLANTIC R %EAMCH C O.fJRF-'ATI N

AL EXAN D IA, VIM a GI4 1A

C. Effect of Added Radiation C" :. ral

Azxouium parchlorate will not normally deflagrate below 22

atmnospheres., However, a radiant-heating apparatus chesm in Figure 4

wcs found t,) produce conditions permittLng steady deflagration at

atmo-spheric prepsure.

Vie radiAit-heat source is a WO-watt projection lamp hav;ng

a coiled tungsten firtmen't. with an effective area of 1 cm aquare, operated

at a slight overvoltage. A pair of front-surface paraboloidal mirrora

U forms te- cptical avatam. Tha first iaicole has a dJ:au-oteo OLf1 U . i-t

and an f-umibei of G.,4, the second a diamter of 12.5 Inches and an

f-number of 0.48. The system has been calibrated with a radiant-flux

meter which consists of a blackened cavity in an externally insulated

copper block, the temperature rase of which ruy be followed. It has been

poesible to achieve an lrradiace up to 20 cal/sq cm-sec with this eystem.

Ammcnium perchlorat.- pellets of im t square cross section , ad38 ma" long are fad horizontally inuto Via focal point of the rs 4ation

apparatus from a tube water-jacketed to pgevent radiant heatia.g of the

sides of the specimen. Pure amonium perchlorete ignitas in &. few

seconds and continues to deflagrato aa 'on as an adequate radianL U ,

is mairtaiued. !slcw about 10 cal/sq cm-sec, deflagration can neither

i, pi.%Zuced nor maiuiained, although very slow sublimation occurs.

Figure 5 shows the variation of the iaJiLation-induced deflagration rate

with radiant intensity. The deflaqration rate was taken as the feeding

rate necessary to yield ate-dy.,state deflagration at the tube opening.

For pure ammonium perchlorate there is a critical radiation

level (10 cal/sq cm-sac, as shown in Figure 5) below which caly slow

oublimation occurs and abrve which deflagrat:!,m occurs. The deflagratior.

rate is essentially liner with radiation flux, and extrapole.-s to a

finite rate at zero radiant fluct

Addition of catalyst profoundly increesses the deflagration

rate and reduces the threshold flux required f o ignition. The inter-

cepts at zero radiant flux for the throe curves with 0, 0.5 and 3.0

ILANTIC Ri dMARCH CORPORtATION

At L XAMURIA, ViRC|Nt^

per cent Cu-0202 catalyst increase in the ratio 1:1.9:3.1, whiln the

slope. increase in the ratio 1:4:13. ho -4 ncrease I. the interceptvalues may be a measure of the chemical augmetatlon of deflagra onrate by the catalyst, while the greater knnrei-itrr .a slope with In-

creAsing catalyst. ,;oncentratjton may inclula this effect and also the

azeater ab t.':vity of the svrface for radiation when catalyst ispresent. No method has been devised for measuring the surface re-

3d flectivitLs uader actual deflegration conditions, but scme crudenasurements of reflectivities az room temperature have vialdod rA-suits ac follows.

Specimen Reflectivity

Pure NH 4C104 0.63

NH1 cl04 + 0.5% Cu-o02 0.32

NH l04 + 3.0% Cu-0202 0.21

Presumably the same trend of decrease in reflectivity with increasing

catalyst level exists at defLagration conditions, so the higher dfpendence

of the slopea of Figure 5 on the catalyst level may be in part attributable

to this Affect. It is also possible that a 'Iorm.-holing' effect !a in-volved as the radiant energy penetrates the translucent perchlorate and

is absorbed by the catalyst particles. A similar effect has been dis-

cussed for dcebla-basA n'-,llents (7).

A number of radiation-inductd defla.ation experiments with

oth r additives have been carried out, the reults being generally cisilar

to, but not as striking as, those with copp-ar chromite. An experiment

with a three per cent addition of magnesium oxide was noteworthy, as the

radiation-inluced combustion was associated with a fusion oi the specimen.

Some of the material burned and the reist ran down the side of the ap-

paratus and resolidified. Addition of either calcium oxide or magoesium

perchlorate to ammonium perchlorate led to a similar effect. It is

postulated that under pre-defiagration conditien the magnesium oxideor calcium oxide is converted to the corresponding parchlarate, whichforms a meltabie eutectic with anmonium perchlarata.

ATL-NTIC Rr-(;-CH COMPORATOPJ

ALI XANI IA, Vl nli IA

~-9-

DISCUSSION OF LWEP PRESSURF LD4MT:

Spalding (8) arn! mayer (9) have independently shown that

nonadiabatic easeous flave muet possess a eArp flammability limit

which is reachod by progressive change of any independent variable

which reduces the flziw, temperature, as long as the rate of heat l0s

dues act vy-y as rapidly wih a chano of flae temperature as doer

the rate o2 heat genecatimn. Their mor hanism involves the follmrin"

sequence: flame temperature is dropped slightly; reactiou rate d.-

creas; Aqflagratit- -_czaa an aahat1

from reaction zone becomes a larger fraction of heat generation, and

this furthcr louers flame temperature; the reaction rate decreases

further, etc. The situation wv.coually eithar stabilizes at a recuced

combustion intensity or the flame goes out, depending on the rumerical

parametert. It is proposed that this mechanism is broadly applicable

to the lower pressure limit of ammonium parchlorate.

Pot deflagrating ammonium perchorate, the rate of radiant

heat loss from the hot solid-g.s interface is essentially press, e-

independent while the deflagrat on rate, and henco the over-all

of heat generatton decreases with decreasing preosure. Hence, reduction

of pressure must produce t lowa.:Iag of flame temperature, and at sea

critical point the :lame is weak enough that extincticu car " rrj by a

Spalding-Mayer instability of the gas-phase flcre.

SupportLih evidence of three kinds may be citee to.. As view:

I. It this theory is ccrrect, precooling of the sample below room

temperature should reduce the flame temperature as effectively as the

* low-pressure radiant heat-loss mechanism, and -precoold strands should

be nonflammable even at high pressures. On cooling to minus I8C, it

was indeed found that ignition could not be obtained at any pressure up

to 270 atm (1).

Ii. The theory implee that addition of external radient energy

should promote flammability. It haz bewn found that stable atmeopherif:

.4i'nic ReCUCAICH LC3RFOAIA,I JN

ALC XAN IRA,V1YIN N A

-10-

flaunablity is obtainable when a radiant fluwL of c~t least 10 ca4/.*q

am-sac is introdxsed. A portion of this fluw. is reflcti~d and a portion

is transmitted Into the interior of the sample, subsequently B 1n

lost by conduction to the sides. The remainder, which is effective In

haatlag, Cho surface, Le. clear..y coparable in cre.r of magm1itude with

1.6e(T e/1tJ0)4 ~1d cm-sac. the rate of radiant loss from the our-

race, if T: the surface temperature (*K), iz --' -he r'rder of W,,D-..100*K

(c in the surface esusivity.)

* ::"I Addtioni c very sma~ll prsp6rtione oi copper ch -itesa a Llack

powder, very grftctly affects the low-pressure limit (Figure 2), reducing

flammability, while larger proportions promote flammability. Other dark*0-

mdbafthadditives Lehave similatly * This is readily n,darstane l i h

primary effect of a small proportion of the black additive Le to imz,rease

tie eissivity of the surfact, prctnoting heat loss, and **,=a lite zlicaible

on any other basis.

In vim,- of this evideonee, a heat-loss mechanism for this limit

aeous to be established. That insensitivity of the limit to sampla size

a~nd to nature of ambient gas tnItrogen vs helium) is further evidence

that radiAtive heat ioss is more Important than convective lose.

DSCUSN F EgAXIO CIANW:

The reactiomn

NH4~Cl04 (c) --- Hl (g) + 1.5 H12 (g) + 0.5 N ~

is exothermic by- 39.3 :wul at 25 !n Ti. corresponds io an adiabatic

flame temperature (at constant ptessare) of 1136%. Thia conclusion is

modified all.,htly by the pressure-dependsM esquilibrum

2liC1 (a) +0-50 2 2 H0 (2) + l2

which is exothermic by 13.7 Vtal at 25'C upon shifting to the right.

At 100 atm the equilibrium ratio of C1l to HCl is 0.11. and the corrapondixg

calculated adiabatic flame temperature in 1167*C.

.Addtion of 0.25 per cent platinum black raised the lower limit from 22

atm to above IM atm. Cf. also (21).

ATLANTIC RrE~rARCH CO %ttF4-'I.

ALKXANDM1AV14Ggt 4

that tht zde "::1Ar::j.j-'cttioaLthe 4avP-1ntii*'Atf(sA euergy Ir. j z, z

.100fl atm. The f ' problema i'.: ~lti b trsf 'Ar'4 i" tC a: AbIik,

v -t ithc 4j-i xOf at vh~ch t t -*tf Lu 1L.ratuO.

The twc or'rad possibi!~..1 .t .idftundo-pin'5e 6,11da-~ajexothrmic react, up, Three tyy col a ddico,

below, strongly x : &,Ast that th, cursi in.iV-Z~~'~

the Skaa WW'e:

1. It has b -i r ~ . ~-s~ting of amov" ;In horr

produces sublimatit .v vI h substa ~ e- wary of recondensed a&*";.,-

PlrhOL S The igirh-il decov*x: ytl dvaeps a porous br--ere

which may be assocJ ii,-id vith a t !.v s ublimatic-n rate of i Lhe iat-

mosaic mat- w zll I ~'~. s heated at 2Wi-4300C iuidei an,

inert gas iastead o' under %c roh' .4mation is redpved ad pascru&'

Ioxidation-reduction jir,,4=uts ma, I.iru,.overed. Thet rate of sublixet..

increases more rapi Ily with inc :. temperature than the raite '-i f-'-

jcomposition. Thaee'st may i Lavnably be latarerpraec' by aisu'-ngE

competition between '~proces ! (,k) tha# crystal sublimes to W.-

I II~~~Rl% vapors which 4n use swa- id ro':ondseca et t nt'i i.:-and (B) an oxidation .. ,ueton~-w ozeiret. At the hifshtk t(W'-

peratureis character,-. :,%- of de :L- ':( (above 9004C) direct tsi

I reaction of H, and R~.1 on ',t;ca.ibly be qu.itrj-apiO.

above facts imply the: ts~io. mtc-~ut~ 'to. / . --*

at deflagration tempei tures.

d I~T. The rskte ot izfloij~r :t.'-c pr-:e es-tx.h' ar ' nf~

with icreasing_ pressu (1, -:43 o% a~n Toir e~ "# Y(I

sure, as well so the s* 4acet. co '. '- ar:u mic rt rvO±,

I ~is evidence that gas-i. ae r, it-u4 L;e V~~-,i~Tic ~f~rA/' s.

is of the or&,,r of one tihw '~ !I t' 'a~ war, ic;. r. th dii-

cussion of the lower pr,, sxwr I~A: ~ '1 -- : ~burnr

1?-LA~ ~ ~ ~ 1ig --L rwa.d)~

Surfrne-r. I thu\ "r'.e purely a ourleca a~ not a eas-phane

,etC~owoa, w oo.0d expect I.he defle~raclux r ntt aL £a4Q-

>:'-~i.,ti Co such 0." 'za~r; ,i:.~'' ~

ta. L 1/40 oif thi5 1,t dar acx ,c2-

'' ~ art iswclved. rinai.y, cko ~ :..)in

-. ' ~ot w4., or &~ Jx'-eA.zrto1) :*lbUP.'

Q6' is. janoAly shio'n that ,hisj beavicz c-ss to

t~,.. .i~~ a~~-~C~rO8dadtw;d frcam nteO.*lt y of su'41aca-

:*.dtte ~ ~ ~ ~ -1 *'A~>c. '~~ Juxfocc tr.~rature Is kbalcv

nrLcm2.6 a hu~ ?'I.~or i'. -heer. ,wi7,.ici. b V

phaes. The posrt..'., -; a~ 7,3 b.'Li~a eamn .~~i

Appeildix B

*Thi naxt pro),,e ~. " '-c :i<:,* '- thep MCInan.'M u Of

oa therLuodynamIc m,: a k5-,tcq ui~. 1lbr:U=

exlata boIwaan solie. ;,tnd v '-;'c lvia '-.- the

x ate of cndewatkri;\ hin8 w r,~' . 'sg - .h.

rapvly of hieat. T'- flnetle ,CA~~ LO bai04; Ur~ ~'.1U .

as fact . :%,; .& .boP~: v;evta 3 ~dI .'r~~~ m3

fcotepirature wo41rh in -vn r''be b"-,7L 4

In b oth casa , than, tlA oadc;.4nn~ , 41 % r , I C

limited by the rate oi heat Tf V '~~m . ~ C.c

anrlod to ift&ri. :, - * p.~~.-& zcv'~z

* .in k."

xJ xnsideor tkM 6con~&ry ail' -'zkib, t' e adca4d Imeat raleas che f lamke~awn&raurep heui'e the s X~u~ev-t X-,r . , Un4 ultatl Lie Ste-PU64

u~ tii~ r~oIperaturo eradientw dr t-r '. t I heat flux to the uf/

Another quead~m e, .41- riv u5e of the hypotta8aZd1 -rGA~~~''CtiVA A-i g, ve m.~ say be made ax follows

'it '(W ntm, whark the -a4~i ft/:rr. -!-t Is. readily

c'-.. ,aa tb-: a t f.li'. --r vi ft ~:q e is requk ild to suipplyI i Y *cLh.qA hwead A x%: :41 rlai) and a ho ': of sub-xA 9vr" 56 k.;i>!,, * ~ ~ :&e. ii the theLA4,. '

A,~ oute~ Qitabov~e '~t!r t. ').(MI6 cal/sq cm-9 "K

pvcz this heat :*. - X Wril the total temperatureIx ths gac pha canokt be Lao.:,vx t.. Xy & ~greee, the

EL'C"' tl,kedZ LS1UC be of tiLa order of 341' ..o FW or radiotf.cti-amvK'teO, &tie rc~tioa at iv c tzeus'lire, !; d afLar-g " '.or rati 1.;

DIE' ":',.;I'Z4 OF C41ALLY? i-7,

-~The irr~arJU of a cat*Lytv L4; tqP*.,tao~r chrosnIte is

to.~ be the e~ aiiof the ga-itcv, ':cL~ in the zoneuaboo the surface. _tii ":,,loct :!A utvfrt ~~ .t sure 3. and

is± Lao mi\7ident Mx isotheema-1 decampositt-vtto ; p~arln ;i ot 200-300*CUjr

&oaer h ca!.alyst' aens tc so a~ ;,=N. f. :tion as--. -ad 111"";h Its ability t,-. absorb ad ew-Ur.r.d~ vr ~,~ which Is

pa. WuP'~y1wovn w hen hij r.i~alydjt ci~m- iti , ,v a r w

a :r .- T; e , Taal radiant f u,,. i.R preent. th.t-%i - li igurea2 c.j el"3 have a~rrvady been from teiron v1We,(i' r-

Ths apparent axtrevs ihinnea cf :N. Srk, /it, 'ction zone.m- :Al ready been di cus',oi hais i. bcarkij cm : r,.'.. atni= by w.hich

rc r.ztic1.,s are effectiv'e to qugmeutjm~ :h f'.11 Yy ai rate,

ATLANTIt: RRICARCH COWPanAyIMN

ALCXAND PMIA, VI N IA

J - 15 -

?.TeI i- .ease'le that the primary effect of the catalyst particlesmust be tz increasa the rate of the rate-controlling gaseous reaction.

FTf the rnftiOn gone veAe F-b-t*it.vl).y thcker than the raliAt

, & Aa diameter, the crtalytic effect voild occur as the gas-borne

catalyst particles are carried through the Hoever, the catalyst

particles, of t. order of o- 3 cm diameter, are roughly I00 times as

0 htck as the reaa.±oo sotre at 1,) atm, and hence wou.d be effective while

still partiaily embedded in - .d 4mnowuin porchlorate. This would

-v.:, two consequences. In the first pLace," the catalyst would mn e

throue. rocti-a none at the solid velocity cather than the -1-c"h

higher %- 'welocity, and ths the cataly@Z wouLd have a longcr 1.4ms to

Q.t. _ ""l tec'Lfd place, the au&akUed heac-rclease rate around each

catalyst parLLlo would cause loca l p~ka tco W burned into the per-

chlorati. vhich later flatten out, the cer-el! hiher d-flag-rotion rate

being associated with this process. This deduction sugpest that needle-

l ke catalyat particles c=-Linted norml tz. the burning surface should be

highly eff.ective.

The "worm-ho' ing" mochaniji by which catalysts may act when a

sufficient radiant flwz is pr-eent should also be discussed. In th s

mchaulaw, & atalyst particle below the surface is heated by radiant

ocurgy. It is certainly possible that such effects may be Impcrtant for

propellants with very axih fI'me n!-peraturas and correspondng intense

radiation emission. However, several arguvauts may be put forch which

suggest that ;hera is no need to invoke this effect In explaining

presently desciibed experizzents:

1. hen catalyzed amonium perchlo-caie deflagrates at elevated

pressure ..ithout externally added radiation, tC products are not very

hot (9306C), so the radiant flux emitted would be relatively low. Yet

the deflagration rate, of the order of five cm/:ec, is cmparable to

that of energettQ propellontq in which amoium parchlorate Is the

oxidizer, and which have f3r bigher flama torperatursn and norres-

poningly more intense radiation fluec. Henco, radiation ca'not be

too i portant as a rate-cmntrolling procesa in alevatod-preus'ire

doflagratioa.

'U

,'LAWTIC RESCAMCH COPPOAATION

ALCXANORtA,VINtINIA

II. The burning rates of ammm.um parchlorato-based ?ropellants

Are at liaat roughly the same in 1i.1jo rockets and In small strand

burners, although zie radiation envlronmst in grossly dieferent.

j

J

,-A-ANTIC RestARCH COkI, ':A-J,.

ALEXAN CPR A, Vi f 4 0 . A

-17-

REFElENCES:

(1) Frlecian, R., Nugant, R. G., Qumbel, K. E., and Scurlock, A. C.

1957., -.1 61Z2-61.,

2) MeAdams, V. H.,Heat Trani ission, McGraw-Hill, !4*w York, 1954,pp 72-279,

(3) Gaydon, A. G.., The Spectroecopy of Flarrua, John Wiley and Sons,New York, 1957, v. 90.

(4) Hlardy, A. C., and Pevrxia F. ti., TMh Pri-cViis of C Me 'cGraw-. iil, New York, I9 'e, p. 1)1.

(5) Forzvythe, If. E., Smith~onian Phyc kal Table6, Ninth ReviseJ Ed:tion,

(6) Nugont, R. G., Friedman, R., and Rumbel, K. E., Air Force Ofi cf of

Scientific Research Technical Notb 57-21.2, A:TIA AD No. 126509,March 1957.

(7) Avexy, W. H., Journ. Phys. and Coll. Chem. 4, 917-928 (1950).

(8) Spalding, D. B.,, Proc. Royal Soc. (London), A240, 83 (1957).

(9) Mayer, B~., CaWou-.ion and i'lame,i, 438-452 (1957).

(10) Bircmuahaw, L. L.,and Newman, B. H., Proc. Royal Soc. (London),

AM 115 (195h4); Mg. 228 (1955).

(u) Sct-i.c, a.. D., and DMl ker, it. O., 3,rth S';osi'xn (Interns - ona l_

on Cr bueac.i, Rei.nhold, New York, '957, . 6iZg".

(12) Spiugler, H., Z,. Physik. chems.,j2, 90-.106 (1942).

I

w L

4 4"

z

/ 9 UNSHIELDED SAMPLES

(D 2

/ OSr$IELDE'D SAMPLES

u .O~-/

wJ 0.03 A

/-Extrapolated value5 // horn fig. 5

1 3 10 30 100 300 100

PRESSUF (ATM)

FiG. I VARIATION OF DEFLAGRATION RATE OF PUREAMMONIUM PERCHLORATE WITH PRESSURE, AT250C INITIAL TEMPERATURE

I

KUENCH! NG J(.0N~IT!VE

LJi

CL o

'QUENCHINGV(BELIEVED DUEi iTO RADIAIK4

:O-6 10- 5 10-4 10-3 10-2 -

I WT. FRACTION OF CATALYST INAMMONIUM PERCHLORATE

IFIG.2 EFF~cb.To OF COPPER CHR OMITE CONCENTRATIONON PRESSURE L!MITS OF DEFLAGRAT'ON OF AMMONIUMPERCHLORATE INITIALLY AT 25* C.

5

4c

K VV1~e

WT. FRACTION OF CATALYST 1*4 AMMONIUMPERCHLORATE

F! G. 3 EFFECT OF COPPER CHROM!TE CCNRACON AMMONIUM PERCHLORATE DEFLAGRATION RATE AT204 ATM AND 250C AMBIENT CONDITIONS

f O36 4 r1f/.48I MIRROR MIRROR

J, I P/U

7 SAMPLINGFIOOO-WATTL- PROBE

/(AHR -COOLED)'

~-MANIUALLYOPE:RATED

LEV/ER

IFIG. 4 APPARATUS FOR STUDYING EFFECT OFIRRADIATIO~N ON DEFLAGRATION

10

I

! ~~0,18" ,",' "'. ..

3.0% COPPER CHROMITE

0.16

0 .

0-5 COP ERCHLORATEI

o' o PURE AMONU

0.02 1co GI0

0 5 I0 15 20 25I INCIDENT RADIANT FLUX (CAL/SQ CM-SEC)

!l iG.5 EFFECT OF ,!M,,!Du' RADIANT FLUX iNTENSITY ONS DEFLAGRATION RATE OF PURE AND~ C;ATALYZEDO AMMONIUMUU.

~. UEAMNU PERCHLORATE TOEAMSER

0.00 0 1 0 2

INIETRDIN LX(AmS MSC

ATrLANTIC kEUKAPKCH CORPORNAT1IN

A LtXAN flft A, V1 M0INI A

APP1'DTI

Dtta11.e of Surface-Teumpotature Hesasuremento and Calculations

T. Fi.lm Nusituaaetry

Ou, September 13, 1957o a serizaa cf *a-tn snapshots of a ref-

erence body at various tuperaturea and two snapshots of b)urning strands

were taken and developed together. Deniowstric measurements of the

reference body are tabulcated:

( (U- , Dens:.i;," (arbitrary units)

650 o.62700 i.4o

750n 2.1,r

850 2.47

900 2.5595d0 2.70

(The reference body is a statiless steel tube heated by electrical re-

si~.tance, the outer surface 'eing coated with Bureau of Standards Cerr-mic

Glaze A-418. The ternp'ratur3 was measured with a chromol-eluuiel couple

uithin the tube. A ch<-. k rr -he validity of tki - mear1irpnrent wae obtdined

by applying a mia:erial of knoiin melt-ti prn (JZ*c) Lo r-ba outstde of

the tube.)

The two strand photographs taken together with the ohmvq cali.-

bration vere found t~o huave densities of 1:65 and 1.80, corre~poading to

apparent temperatures of 7156"C and 725*C. (These would be true teiinpera-

ttares oply if the emissivities were th-e ars for the reference body andthe strand surface.) All phntographic conditi.na we:ze the amne for the

in asecnd erin o phtogaph onSoptembex. .1.7, 1,957, con-

ILAINTIC IRIECARCH C ORPORATION

AL= KAN 'RIA, VIRGINIA

- -29 -

calibratict valuoi; ware:

T ( OC) !).-=A!Y (erbirttry tm~~

700 i.20

750 1.50

8o 1.90

(These valuee are seen to differ alightl.y frc the e.z-&1r calibration.)

The two strand dnasitias were each 1.60, corracpand n to apparent

tomPeratures Of 730 and 730*C.

11. FILI.ter end, Pilm MahractotrltiAc

Kodak z!pp)J e the following data for spectxiil seasitivity of

their high-ped infi-.red filn:

Wavalcngth (micrm!) Log zaxaitivLty

0.65 . o.Mn

0.75 + o.8o0.80 + 0.95

0.85 + 0.90

0.90 + 0.100.93 - 1.00

0.97 - 2.00

TMus the sensitivity is roughly a thousand times *a great at

0.80 microa as at 0.97 microns.

=-, T-64 filtcg wick vas uaced transmit~ted as f~ollows,

acco.dJan to Corning:

Wavelength (microns) Transmittance ()

0.20 - 0.70 00 71 0 +

0.72 60.73 25

ATLANTIC RESCARCH CORPCONRA*TION

AL C XAN MR IA VI01'NI A

0.74 45

o. T5 65

0.80

0.85 800.90 710 0.95 572.00 35

I' ,* .L.V 15

1.10 5

III. Calculation of !kgar-Llat." Temora are fros r Aparent Tuperatur

I Since the emissivity of iwhe strand surface is unknown, one

can try to est'mate upper and lower limits of emiseaivit.y cIrVuMarieon

with other materials. Only the loqrer 14-4t of c=Lwalvity may bea 6aa -

mated, however, since the upper lizxit ir. the spectral retgio of interest

nay he affected by chewlluminsenie in an unpredictable way.

McAda s (') 1ts the following total emissivkt3..es for nonmetala

at 8ooc (i4To*F):

Nickel oxide o.66

Aluminum trioxide 0.2T

Cuprous oxide o.66

Magnesium oxide 0.22Iron oxide 0.87

Thorium dioxide 0.22

I ~Silica 04

Zirconium 8ilicate 0.55I taesita brick 0.38 (1832*F)

Carboz.aau 0.92 (1,350F)

I Building brick 0.45 (O32'F)

Firebrick 0.75 (1832"V)

Carbon O.rj (1900 F)

I

MiLANTIC R2ZARtCH CORPORATIONS ALI )AN A, V! RUIt i

-21

No ,/1UWA is below 0.2, no this te taken as the low" limit. It is

aserad that these valums feo. totAl eiseivity on a"licable to

spectral emissivity in the vicin.rty of 0.8 u5.rn.

The total leMisivity of the ceramic coating on the referencebody ban bhon -asured by D Corso and CiLt (LaIN Trans. 77, 1389 (1955) )aas 0.89 at 125*C. The asswyto vil be: wad that this is a grcy body.

7_%Pt following esression, whic.h foLlows at one frma Plack,'claw, was used to ccakulati the taeperatu:o -of the perchlaroa m-rfec

-(1.439/T) 1. (1,.-9)Z.) -

C),e ' is a...etral =iiIvity; X. is im".4.mnoth T~~ Isttemperature (OK) and subscrIpt. x .ad R refer to unknown and refrisce

bodies. As dic~useod, . a taken as 0.2 anda )- as 0.89. TR ist* kxas 998*K (725*c), thes average %! the rcboVe-asecribod four data poilrte.The wave-length X, is taken as a x io" 5 cm (0.8 micron) on the bei:. ofthe filtr a=d flIxM cut-o~ff eb ta.hw.-hm. 1A CMIC1ttien

shows that a ton per cent ertror I- chi'e ef wavele.th would cause

only a one per cent error in tev9eraturer.)

With the above values, TZ caAes out to be 816*c.

Maasuremeants and calculatio.s for other films and filters wrehandled similarly cad will mat ta "A=-ti.led bre, zncc no quantitative

conclusions vere based on th"m.

ATLANTIC P: Z A CN-2-

A Iathwatical M~odel for a Def lagparing Hoav.nszae

_S421±-A Propellant, in.,iuding en Xxternal Radiant Flux

Th Mkk1 It Is. sowed that a one-dimansiongal homogneous soltA (whichfligh- be inommiun Perchlorate, as discussed in this raport) sublimes at a

surface, the vapor reacting exothermkealy above the surface with a ra-sultia& feedback of heat to the *,'mfaeA~, Steady-Wte nara~t's of tha

surface results.

This modal would also be applicable to a liquid uc~rcoC1*?ntI vtwhich veaoTis and reacts e~totharleally in the vapor phase just abovci

* Ithe sutic-a.

j ~~~Whan the seanjphase exothermic reoc !cl ir n ~not be doimritoe4 quan Ltativftly from,# 2&I ~roj~ledgk, its :.ate may bedeacrTibed formally in ace fauhion lAith adjustable pczircmters. Wie chooseto do thin. In the slupleat cOncei',ble way so as to per---t etraight-forvard

anayt~aa soutinsto t~ke resajtlng differential e#:uatlons 6fcrbn

Twhich Isgreater ta a*I pca aeeult)tosrs..

temperature Too Above T ' the ratoisassumed to proceed at A COCA-stet ateq c~lcuex-ec unilthe ratnsare consi.med.

Wiitbh this model, recetton rate ip, Independent of reectant em~-centrat ion, so that 10oleCuler diffusion In the reaction son* need not be

I considered. Weat is cocducted from the reaction some, th:-vtgh thegaezkt preheating xcne, and to the surface. The heat flux across the

I interfaca -2. AQ, where Ai is the bum.ningirate (pjsq cm-sec) and Q Is theViu Of Lhe hoat necessary to raive the solid frow ambient tscq;*anrcz T.

*to surface Unperat~mz T 0and the heat cGf sublIzmatiw.. As an optional*feazwu A %Xternal radtant flux q. (cal sq ca-sec) may be asasmd to

* pass without absorption through ths gases and be absorbed at tho inter-

face; a negative value ~Ov would correspond to radiant heat loss trcmthe, surface to the Ruroundins, the W~ iinmediat1~y above the surface*piain beina trananarent. The sketch in Figure BI suawarizea the rno2~o.

4 ANTIC PZZCARC' CORPORNATION

ALCXAN OI, VPi! IN i^

-23-

The zPtheattcaL behavior~ of the MOdAl will first bi d~VeSOPed

hat &It~~& (No 1adiattm; z asume that the Site theiluaal

conductivity I and4 isobaric heat capacity Cp are ladpon4ant of temera"r..

The co6rdinata sys*.m is a%;omm to move with the ualid-gas interface, so

thAt .601- is tigug-a47*&jAat, ^ .dqmw va 'At1onGG

pressing~ Consrvation of theTmal anergy in the rekdtioa acme to

The bouadary conditions on tha dolrmftream side of the reection zone are

Td us T and-, 0 ibeax U x(B2)

Since I is conhtant, equattev. (Bi) is readily integrated witha boundary

codiditLon (B2) to Yi~ld

T T - ~ a+ (Y- .X)-1 (03)

iand -()

x . _-L 1 1- a Afi(B4)

ILn the Rasecus preheat &Care (between T3 ard T1 ) the equAtion for con-~Att ~~nof emergy is

d~l p dx

The boundary cnadtione on the upstrcsm cida of thie Iton are

T T and X w aQ t I is (B6)

ATLANTIC P'UEAPICM CORPORATION

ALWXANI3RtIA,VI1%GIN IA

24 -

Integration2 of (B5) with boundary Li.IAtio!Ie (B6) yields

.1T

+ T- T ;I

At the igmiltion place x - xwhere the gaseous preheat zone

deacribed by equation (B7) and the reacticn zopi described by equation

(OA.) meets dT/di muist be ceintiuou9 if a crriady state -PIACt. Hence,

(M4) and (B7) may bs. equated at this pl.ane, y1i33.eing

It is poasiblo to 8l~plify this qustion by aliminatitig the

quantity xf - x as follows. The ov.er-all enev balance oi thne Elin"m~

ma~y be 'write&

The reaction~-zone thiskn-tse - X, maiy be elfm~nated between equations

(B8) and (fl9). 'his irtroduf-eu a ac-,z pa-_irmeter TV fc,~utiis readily evalunted it, any ii case3 ftom thr-.wot;ynamik cmnideratio'is,

The result1ng equaition can be expre,-ised most co.actly in dlmensionlass

a(l 4) 1 (n~o)

whcre

- (T,. T.)/

P

Equation (B20) permits calculat~ion of the burning rate j; when the other

parameter' are known. SiruL. equation (RIO) is tr~uiaccwdental, it is not

possible to w~crees Ia explicitly as a function of the othor quantities.

Hlowevier, an inspa~ction of the dimensionless groups shows at once% that

(-&q)'- /2

j'Tic RINKAtCH COPWPmnnTjoN

A11XANCOtt, VI N1N IA

Au exact quantitative deacription of the r-latioa between a, a and r is

given in the fol1owing table, which might readily be =tnded by £,u.ther

cmputAtions:

1.00 0

1.05 0.1

1.11 0.2

1.19 0.3

1.39 0.5

1.72 0.72.01 0.8

2.56 0.9

1.0

For the special case where y is small co.pared with unity, equat ---.ion (Bl o)umy he expanded in good approximation according to

2•e l-x+ 2

This yields the asympototic expr~esio-i

; - )/(1 + r) 2 fuoz yZ<l (B12)

Ithamstical Relat o.mLh (Radi tion Iicladed): An 4zte a. radiant fluxqR (cal/sq cm-sec) is asommed to be incident ou the solid-gai interfo-e

and to a .italy ab,;= .d, without reflection or re-radiation. An.aftive value for qp corresponds to radiant heat loss from the .4nerface

to infinity. Equation8 to describe the foreoLng model with thi. additional

feature will be developed.

Equation. (Bl). (02), (3). (A4). and (35) are still valid.Hlowever, Tf vill obvioualy he a function of a , according to the relation

C(Tf,-r) - p(1f T 0 + %A (u/3)

• - .. . . . . . " 1

ArLA':T;iL HtNKANIH CORPORATION

A MAN OlIA, lQ* V I N IA

-26-

This is based on the assumption that Q is independent of qR.

Instead of equation (B6), the boundary conditions at x becoet

T = T and dT + (B14)

Integretion of (B5) with bouudry coaditions (B14) gives

* -.

U Thne owe-all enrgy balance now isx- U& +Cp(T - T (n1)

One can eliminate T1 between (113) and (Bl7), and then eliminate (If - ibetween the resulting equation and (n6), finally to obtain

. ( 1 )-i- eg(1 + ) (aiR)

f nri q;' 2

wher Q" + CpT "- s26)O

!; EIqatton (BiBl) is seen to be identical to equation (110) when in (Bi0)

• is replaced by -o, and the pre:'iousl' tab,. ated soiutions are 'alid on

P. !

~this basis. It should be noted that Cx contains q, which one weiuld ez-

pect 1:0 bie a function of (T1 + Tf)/2, vhile Tf in *' . is a function of

qkt:'~ giLven by, equati ,c (Bi3). It is not: i,.pro,,u.'8: - ..-. to .-p~c.laie on,

the functional relation betwee~i actc rate q end ten~rtuc1 bhtt

obvl. usly a&ny desired function may be introdiced,

To ov ea. are eoeattaliy taking Tf an q to vary

, +r Csm ina~ (T ft This(17

with an while T1 , T 3 Q, )., Iand Cpare a end te.n ent (x i

choice is purely erbirnw" the other quantities could obviously be e-

a' ' + - a) "" 1 -( +-)38

pressed se " s and the ure wiused, at thu cost of incresli

'czompe'ty.

thsbss tsol entdta acnan ,wihoaw]l xpett eafnto f(.+T)2 wieT - -c safnto f

AsXXAN.,MV.1NA

A qualitative understanding of the affect of the radiation

parameter a sty be obtained from Figure W., which Is a plot of 9 vs

(!- a), f,= paraztr-c va.iUuc; of - ft-ca zro to iafiiity. It ia a--Chat t a buraing-velocity parmatar a lacrosses with Inreasing a and

decreases to zero for suffi antly Lregp negatiVe a corresponding to

axtittautAhmnt. TW" =t atical coai.ton for e.tngulaiament Is

?vsi.yid.l ii... *,At ti* raiiant he.st lose (nzcgauvQ Ca) in suf-ficient to reduce T f below Ti.

3)Approxi~mta YrJ'titon (B12) * valid for sani rz. mv bec 9e

ac - (c + r -( s)/(I + r) And K<2 (DM)

It follows that

( )2 z2 V<<3.cand v<1ba ,r, (1.+-r) =

ip.roximte relation (D21) is interestinig in that it might bet Ated eVpertmetally if o variation of q with . wer known.

Nomemclature

Sburning rate (m/sq cm- c)C - spctflic beat of gas at constant pressure (cal/am-.C)P

Q beat of sublimation plus sensible beat needed to raise

solid from ambient to surface tempeta ta (cal/em)q* radiant flt to or from surface (cal/sq ,.a-.gc)

q = rate of gaseous exothermic reaction (ca!.f-cm cm-6ec)

1 - rab l conductivity of gas (cal/co-kiec-1c)

T Tr surface temperature ('C)5T£ ignition templature ('c)

T~ fin.*! am* tuqparatur4t (11)

, U. T diMWniQUlesI grGUPs

Figure B!, Model of Solid-prupellant Flame.

ISfi-sqL-

q

Xs Xi Xf

+x

II

!

Figure B2. Nunicrical solutions of equati

.6

C0

. 810

S0.4

0* 0

0.4-

-0.3 -0.2 -I 0 0.1 0.2 0.3j3-. (dimensionless)

I2f

,j

ui6rlibution List

Chief, Document Service Center i Commander

.A-med Services Tschnical Wright Air Development Csnterinformation Agency Attn. WCLOT (1)

Arlugton Hall WCLJC (1)Arlingtnn 12, Virginia CLPF-3 (1)

Wright-Pattere. Air Forcc Bane. JhioCommander1Ballistic Missiles Division Cou nder

Air Force Unit Post Off ce Air Materiel CuamandLos Angeles 45, California !.right-Patterson Air Force Base, Ohio

Comanacer 2 Office of the Chief of OrdnanceAF Office of Scientific Research Department of ArmyAttn: SRDC Attn: ORDTBWashingtc. 25, D.C. Washington 25, D.C.

Commander 1 Director, Balits .a Research LabAir Force Armiment Center Aberdeen 1roving GroundEglin Air Force Base, Florida Aberdeen, MarylandCormnder 2 Cae'-anding Officer

Arnold Engineering Dev.Jopment Center Office of Ordnance ResearchAttn: Library, P.O. Box 1 .2 s l.iuiiahoma, Tennesaee Durham. North Carolina

Cc mander 1 CommanderAF Cambridge Research Center Army Rocket & Guided Missile AgencyL.G. Haiscom rield Redstone ArsenalAttn: CRQST-2 Attn: Technical LibraryBedford, Massachusetts Alabama

Commarder I Communanding OfficerAF Flight Test Center WhIt3 Sands Proving GroundEdwards Air Force Base Las CrucesMuroc, Calif otula New Mexico

Commander 1 Naval Supersonic LaboratoryAF Special Weapons Center Attn; LibraryKirtland Air Force Base Masaachuisetts Institute of TechnologyNew Mexico Cambri.dge 39, Massachusetts

Crander . Chief of Naval ReseerchHoll-n Der Development Center Department of the NavyHolloman Air Force Base Attn: LibraryAlamogordo, New Mexico Washington 25, D.C.

I C cai td= 1 Direc torAir Force Hicsile Test Center U. S. Naval Reeearch LaboratoryPatrick Air Force Base Attn: LibraryCocoa, Florida Washington 25, D.C.

I

Distilaution List, page 2

Chief, Bureau of Aeronautics Commander 2Department of tbha N,;'Ivy AirT Research and Development Cou-en,Attn: Library Attn: RIR!ashington 25, D.C. Andrews Air Force Baso

Washi'ngton 25, D.C.Chief, Bureau of OrdnanceW

Depa ?tent of the Navy CommandantAttn; Library USAF Institute of TechnologyWashington 2;, D.C. Attn: Technical Library, =!CL1

Vrl ht-Patteraoo Air Foce Bas,Ccumandea. Dayto., CoNaval Ordnance LaboratoryAttn: LiUrary Aaerojit-Geeer,- CuporationWhite Oak Attn: R. Cha.kenSilver Spring, Maryla.4a Azusa, California

Communder Atlantii -esearch Corpiratua 1Naval Ordnance Test Statiua Attn- LibraryAttn: Library AlcandrtL, i';-aiaInyokernChina Lake, California Utah Uiv,.xicv

Attn: Dr. A. CookDirect r, NASA 5 Salt Lake City, UtahAt::n: Library1512 H Street, N.W. Princei:on UkAversltyWashington 25, D.C. Attn: Dr. Sumrfield

Prlae:on, New JerseyNational Bureau of StandardsM': Library Cbustion and Explosives Research

1.0: 7Aivwr auualngOffice of Technical Serviae Pf. Pitzt .h 19, PennsylvaniaDepartment of CommerceAttn: Library Lockheed Missile System 2Washington 25, D.C. Attn: Dr. Nachbar

Sunnyval,, CaliforniaU. S. Atomic Energy Comission 1Technical Infrmation Service Stanford Research Institute 11901 Constltution Avenue Attn: Dr. 4oetonWashington 25, D.C. Menlo Park, Cal .fornIABureau of Mines I -ein ilpiane omupanyAt=; L -bw:-y Pilotless Aircraft DivIsion

Department of the Interior Attn: R. BarberPittsburgh, Pennsylvania P. 0. Dex 3925

Seattle 24, WashingtonCommander 3A7 Office of Scientific Research CounanderAir Research and Development Command right Air Development CenterAttn: Library Attn: VCLPFWashingtor, 25, D.C. Wi..tgt-Patterson Afr Force Hese, Ohio

oI

Distribution~ LiUZ, Page 3

U. S. Buremu of M~ines 1 Coczmaading GeneralAttcn: Libra!.y Frtakftr AracnalBartlesville, Oklahoma Bridge and 7Tacruy Streets

Philadelphia, FlennsylvanxiaSolid 11rc.cll.1ant infcrmation Agency 3 Attn: Pitma.Duan LaboratoryJohns Hopkins UniversitylApplied Physics Laboratory (Cotwnding Off lezAttn: K. G. Britton Ficatiany Arional

fl Silver Spring, Maryland Dov: 'ct New JerseyAttn: loilrary

ArJaL-General C'rporaclon1IAttn~: Dr. D., L. A,,strong Commanding GeneralAzusa, Calif oraiia Ordnuance Ammunition CommnandJoliet, Illinois

Dertment of the Air Force 2 Attw* OLYDLY-AREL, En . AbraryHk. UWAF, DC.S/DWashington j aC. Ce~nanwd&b OffilcerAttn: APDRD-& Diamond Ordnance Fuzz 1-1zrarorleeI ~ 25, D.C.Cosutder .1 .';.itu: C~iRM' (012)Wright Air Development CevterWright-PattersOn Air Force Base, Ohio .4partmtnt of the NavyAttn: AFMIRKr-1, 1, Poretz Bur. iu of Ordoacac

Wahington 25, D.C.Commander 1 Attn: R.56I Air Research and Development CxmmaixdAndrews Air Force Base of the NavyWashington 25, D.C. Bureau of OrdnanceAttu: RDTA.PR Washington 25, D.C.

Attn: ReW3&Comm& A-*drArmed Services Tech. Information Commander 2

Agency U. Se Naval Air Missile Test CenterN~,. all Static= Po-- * %&.U&I

Axlin;tou 12, Virginia Attn: Technical LibraryAttn: TIPDR

Coimmanding officer1Commander 1 U. S. Naval Air Rocket Test StationWright Air Development Center Lake DemnmarkWright-Patterson okir force &Ass. Ohio Dover, Few JerseyAttn: WCLP?'P Attn: Technical Library

Commander 1 Cowmanding Officer 2Wright Air Developmeut Cvanter LT. S.. Nvel Procllat PijiatWight-Patcerson Air For,.' Base, Ohio Indian Head, MarylitndAttn: WCLTRP A~t-Pn? izza.rch and 1Develcjm'int Dept.

Cotmarding Ceneral 2 CcsuanflerIAL-rdr'.9. F-rving Groind U. S. Naval Froving Grouznd/ berdo en, YKrryland Lvahlgren, VIrginia..ttn: Eallistic Research Laboratories At".- Technical Library

ORDBC.-BLI

* Dii. Acn L'.stt page 4

f1ipstment of the Navy 1 Zat Propulsion Laboratory 2Office oi Nsval Research Z48 01," GrOVO DriveWashington 25, D.C. asadena 3, C&LIforniaAttn: Code 429 Attn: L go Newlan

p.... tsnt f te Nay 1Chisf, Reports Group

Bureau of Ordnance Arthur Do Little, Inc.Washington 25, D.C. 15 Anarn Park

* Attn: SP-27 Ccibridge AeO, MlassachusettsDenarientof th Va~'y 1 Attna: W. A. Saryar andDepabsen of he Fvy IMiss V. R. Valeri

}>urcau of Or+%anceUaahington 2-5, D.C. The Htrtin CompanyAttn: trcUlb Baltis~ore 3, MarylandI Attn-: I*."S TuhyC cAmadin Off Icerviale ?4odical Raearcb Institute Midwesst Resesarch InstituteNaticeAl Naval 24oedkal Center 425 Volker BoulevardBethoesda 14; .)"-land Kansas City .10, Missouri

Attn: Lt. Nl. D. Baidridge Attn.- LibrarianHrues Powder Couvany 2 Phillips Petroleum Comipany

AlZ 3n allistics Laboratory Room 145 Chemical Laboratories Dldg.

^ uinberlaid., Maryland Bartleeville, OkclahomaAttn: Library Attn: Logan it. Taylor

Armour R~esearch Foundation of Forrestal Raesarch Center1Illinois Institute o ehooyPictnUiest

Techoloy CeterPtincetoii, Sw JerseyChiceso A., Illinois Attn: LibrarL4'z'Attn: P-r.pulsion and Structural

Research; Department H4 Purdue UniversityIDepteacn of ChcAmistry

Mxperizaent, 7ncorporated 1 Lafayette, IndianaP. 0,, Box 1-TtnD.Rlp ,Mre/Richmsond 2, Virginia At:D.RlhA ognHAttn.: Librarian Rohu and Heas Company1

Redstone Arsenal Research Divielon.The F'ranklin Institute 1. Huntsville, Alabama,Zth and Parkway Attn: Librarian

Philadelphia 3, PennsylvaniaAttn: Chemical Kinetics Branch S&dV UCVU

W. R, Scott R**zaroh DepartmentFe.0. sox 431

FExplosivQw Departurant 1 whtLaS, Indiana

Hercules Powder Company Attn: B. H. Shocrtker

Wilmington 99, Delaware Thickol Chamlcl Corporation 2Attn: A. M. Ball 780 ff- rlinton Avenue

T?:enton 7, New. Jersey

Attn: H. R. Ferguson

I Dis* -.ution Lint, page 5

Thiokol Chemical Corporation 1 yandotte Chemicals Corporation 1Elkton Division Wyandotte, MitchIganElkton, Marylaad A.tn: R. A. GrahamAttn: Librarian Department of CoAtract Research

] tasearch and Developmt D

Olin Mathieson Chemical Corporation 1

'_-rion, Illinois Vitro Laboratories 1Attn: Research Library, Box 508 200 Pleasant Valley Way

West Orangs, New JerseyReaction Motors, Incorporated 1 Attn: LibraryDenville, New Jersey

At#-: Librarian AeroJet-General Corporation 3Box 168

Minnesota Mining and Manufacturing Co. I Sacramento, Calikornia900 Bush Avenue Attn: Mirtam S. Nylin, LibrarianSt. Paut 6, MinnesotaAttn: Dr. W. 11. Pearlson Thiokol C-samical Corporation 1

VTA: Dr. We McElroy, Utah DiVIblai!SSecurity Administrator Brigham City, Utah

Attn: Technical Diretor

Astrodyne, Incorporated rSP.O0. Box 54 3 The Martin Company 1

McCregor, Texas Orlaado, FloridaAttn: A. P. Anderson Attn; Library

B. F. Goodrich Aviation Products 1 Olin Mathieson Chemical Corporation 1P. 0. Box 395 Niagara Falls, New YorkRialto, California Attn: Miss Eleanor F. SmrinaraAttn: Mr. A. U. ,a, Manager P. 0. Box 43&

Rocket Motor DevelopmentShell Development Company 1

American Machine and Foundry Co. 1 4560 Horto. Z~iaeLMechanics Research Department Rtcryville 8, California1104 South Wabash Avenue

j Chicago 5, Illinois lu'han, Trroo t -enyAttn: A. D. Kafadar Aircraft Division

Culver City, CaliforniaSouthwest Rjsearch Institute 1Department of Chemistry and U.S. Borax Research CorpurationChemical Engineering 412 Creacent Way

8500 Culebra Road Anaheim, CaliforniaSan Antonio 6, TexasAct: F. A. Warren -thyl Corporation, Research Labs.

Box 3411 aocketdyns; __O of . h Eaton Rouge 1, Louisiana

American Aviation663 Canoga Aven,:e Pen1sular Chemical Research, Inc.Canoga Park, CWl 4 rornia 1103-5 N. W- 5th AvenueAtn: Library, Dept. 596-6 F. 0. Box 3597, Uliversity Station

Gainesville, Flori&Grand Central Rocket Company 1P. O. Box 111Redland , CaliforniaAttn: Helen Asmbn. Librarian

I

Distribution List, page 6

1Hthyl Corporation, Research Labs. 1 British Joint ZArvicos Mission1)500 West Eight Mile Road The BUS/HS Scientific and TchncalFfirndale, Michigan Information SectIonAtt: 9. B. Rifkin, Asistant Director, V, 0. l

Chemical Research Beniamin Frank.in StaticaVashinvton, D.C.

The D w Chemical Company 1 Attn: Technical Information Offica,Midlani, MichiganAttn: M. A. Auro, Technical Services -VIA- 4

and Development Dept.Abbott Road BuLiding Departb-nt of the Navy

Bureau of OrdnanceMinnesota Mining and Manufacturing Co. 1 Washington 25, D.C.900 Bush A'enue Attn: Ad8St. Paul 6. Minnesota

VIA: R. W. McElroySecurity Administrator Defence Research Member 4

Canadian Joint Saff (W)Esso Research and Engineering Co. 1 2450 MassachusetCs Avenue, N.WChemicals Research Division Vaehiugton 86 D.C4P. 0. Box 51Linden, New Jersey -VIA-Attn: Dr Charler E. MorrellVIA: Chief, New York Ordnance Dictrict Department of the Navy

Bureau of OrdnmnceAmerican Cyanimid Company 1 Washington 25, D.C.1937 W. Main Street Att-. Ad8Stamfe'Z. C rICUtAtt: Dr. A. Lo Peiker

Aeronutronic System, Incorporated '.

1234 Air WayGlendale, CaliforniaAttn: Dr. IN . Aliwp

T Jj: i : J,,),*

ervies c Rca Ur

ARLINGTONj HAL SA4'O

lk.

Amed MQO=hfM RQ= ServiJes Technical IOfRr M~o b:f R'IcAmOWTMAYPRLING0"MTN HAL SORZTNM WOTE-'ZATNo v~~u~RLq f IGTON 12TBZ1 VIRGIN- ACTT.o

I X4