unclassified ad number - dtic · limit, at least, is knovio to be atr.ksly affected by l he and...
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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
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