Explosive behavior of aluminized ammonium perchlorate

h Perchlorate DONNA PRICE, A. R. CLAIRMONT, Ucited

States

Naval

Ordnance

JR., and J. 0. ERKMAN

Laboratory, White Ouk. Silver Sprirtg, Mar,vfnrrd ,309lQ

Addition of aluminum to ammonium perchlorate (AP) increasesits infinite diameter detonation velocity and decreases its critical diameter. For 7-9~ AP and 7 & Al, the maximum of these effects occurred at about 10% Al. Regular detonation behavior could be observed only in the range 55-W: lower) behavior

(OF

theoretical maximum as does AP itself.

density

(TMD).

1. Introduction

A systematicstudy of modelsof composite propellantswasinitiated severalyearsago. Detonability, shock sensitivity, and detonation velccity ‘Mereinvestigatedasfunctions of loading density (pO)and chargediameter(d). Previouswork includedthe study of ammonium perchiorate(kP) [ 1,2] and that of AP/wax mixtures [3]. The presentwork is a continuation of the original study 2nd presentsresultsfor AP/AI mixtures in the range5-2076Al. Althor*& AP/Al is a familiar combination of oxidizer/fuel in compositepropellants,there is little quantitative information on the simple twocomponent

system. However, a recent paper [4]

doespresentburning ratesfor ?hissystemat l-1 00 atm. For both catalyzedand uncatalyzedmixtures,moderateatnountsof aluminum seemed to increasethe rate whereasexcessiveamounts depressit. The maximutn increaseobservedwas at 10%Al. There seetnsto be no available,comparablestudy on detonationratesof AP/Al. It is the purposeof this paperto presentsuchdata. To study the simple compositemodel, AP/wax, we usedAP of an averageparticle sizeof 25~. In the courseof the presentwork, we havelearned to handleand mix fine AP’s with fine Al. Conse. quently the datareportedherearefor mixtures in which the particle sizeis 10 L or lessand 71.1,re. spectively,for AP and Al. Despitethe finer state

All mixtures

tested

in this

range

cshibtted

Group

2

of thiecomponents,replacementof the v~~~t~~~ fuel (wax) with aluminum producedc~:~~~p~ic~t~~ We had found for pure AP that ~lthou~ Fk? de%onation velocity (D) vs reciprocaldiameter(tt)t datawere linear, their extrapolstion to u = 0 gavevaluesof n too high to lie on the ~~~~~t~ diameter-velocityiii vspo curvederivedfor i~%)m pactionsat or belotl.52% t~~eor~t~ca~ ~~~r~~~~ density (TMD) (21+ On the ~rtharhand,~~~~~~~ tent and reasonableresultsYV~F~ ~~bt~i~~at 55 and 6’7%TMD for waxedAP [3]. ~u~~~~~l extrapolation of datafrom the more greatly compacted charges of AP/wax was ~ttrih~ll~e~ tcr the higher reaction temperature and hence faster te-

action; theseare the resultsuf the ~dditj~~~~ens ergy produced by the fue~~ox~dant r~acr~~r~. Becausethe literature containsq~~~l~t~t~ve srarcmeritsindicating that Al and wax haves~~~~~ effects on the detonability of AP, we firrst Fried working at the same two cs~r~~~~t~~~~we for AP/wax. That procedureresultedin BEI parent Di vs $6 TMD curvefor APjAI, Sk3

sectmgthe pure AP curveat 45%~~~~~ES@, showingthai Al increatzdDi at a % TMB 2+ 45% and decreasedit otherwise. Check&XC~ min.ationsof D at 4@%TMD with 5i mm ~~~ eter chargescontradictedthis res&t; the tion veloc;ty exJ~b~t~~by APSAI.was~~e~~~~~~~~ -.--

DONNAPRICE,A. R. CLAIRMONT,JR.,and J.0. ERKMAN ~o~seque~~~~, a more studjl ofDCpa, d) had to bf: imadefor the ~~~~~i~~zed AP”sthan for the waxrd .Ws, It ~~3wedthat restriction of extrapoIati,snproceretitu x G 55%producedac:aptableDi uesof A mixtures. AP exhibits Croup 2 e.+plosivebevior IS] asdo waxedand pure AP In other its d~~~)~~~jo~ failure (or crit I,:SaI) diameter (c&I ~~~~eas~s wWr increasingpo, andits LJ ~~~~~~ pa curvesat variousd exhibit a resultant r~cte~sticpattern, This explosivebehavror trastawith that of TNT-tike or Gioup 1 materials;they show decreasingd, wW increasingp. Al addedto AP increasesdetonabillty (decrease, ter t&j and incredscs11‘to its maxiabout 10%Al. The mximurr: in.. ly about half that attain4 with wax asthe fuel. The effect of Al on the D(p,, d) pat. tern of AP is the oppositeof its effi,:cton organic is to be expected‘from the an that of AP.

wed waspr~~~lant gradleurrti contained 2% t~~~aI~~urn phosphatesIt wasgroundat the aval~rd~a~~eStation (Indian Head,Md), and und underthe sameschedule. a weight meanpart!& sizeby ~~~~r~~~~e~~~~aPh of 7.2-923~;the d~fff~re~tlots WQM~~~~r~d to be ~qu~~lent in the presentwork. T5ltre aI~rnj~urn usedwasdi~hr~matedspherical

powder suppliedby Valley MetallurgicalProcessing Company. It wasdesignatedH-5 and had an averageparticle sizeof 7~ by Fishersubsieve sizer. Preparation and Experimental Procedure Mixtures of fine AP and fine Al were preparedin batchesof one kilogram. The mixing wascarried out in a paint canshakerwhich also contained0.5 kg of 12 mm diam ceramicballs. Although the AP is, of course,storedunderdesiccant,the weighingand mixing can be carriedout under ambient conditions. The loosepowdershould appear uniforn after mixing; if it doesnot, it must be discarded,for only grossagglomerationof the AP causesdetectablenonuniformity at this stage. Our usualtest of adequatedispersalis preparation, by isostaticpressing,of a compactedplug which is then machinedinto a cylindrical charge. Only if the machinedsurfaceseemsuniformly gray can the original mixture be consideredcompletely satisfactory. If aggregates of AP appearaswhite speckson the surface,their sizeand number determine whether the chargeis fired or rejected. For example,a 3.5 cm diam X 22.9 cm long charge showing6 specksof an averagesizeof 125p (largest200~) is considereda good one. A good mixing operationis of basicimportance to the quantitative study; Appendix A of Ref. 6 goesinto detail about the developmentof the one we haveusedhere. All nun &al data will also be found tabulatedin that reference. All chargeswere either unconfinedor supported Charge

@.re&ettic7ord. ?&at893oFM/AI, 95/Sat pe1:1.087g/cc. Timeincreases from

left

to right.

ALUMINIZED

AMMONIUM PERCHLORATE

in 0.08-mm-thick celluloseacetate. They were compactedby hand(h), by hydraulic press(IQ, or by isostaticpress(i). All chargeswere conditioned at 25°C before firing. Chargeswereof variousdiametersup to 7.62 cm and were 22.8 cm long. Boosterswere of SO/50pentolite (1.56 g/cc), of the samediameter as the charge,and 2.54 cm long. A pentolite witnesswasfrequently placedat the end of the charge. The shock-induceddisturbancewasrecordedby a 70 mm streakcameraat writing speedsof 1 to 4 mm/csec. Streak camerarecords were similar to thoseof previouswork [ I]; a typical record is shownin Fig. 1. Record reductionwascarriedout asin previous work [ 1,3]. The averageprecisionof the replicatesin the 95/5 serieswas0.3%with a rangeO.l0.7%;in the 90/l 0 series,0.7% with a range0.11.5%. Theseresultsreflect the better charge preparationachievedin the former seriesas well asan improvement overthe waxedAP mixtures I31. Irig. 2. Effect of charge density and diamerer WV~e~~~ tion velocity of APIAI, 95/S. ICTt‘harge diarraetr?rr jk’pp~): * 1.91, ‘1 2.54, [: 3.47,. 5.08, and x 7.62.)

3, Resultsand Discussion Detonation

Velocity

Relationships

The data obtainedon the AP/Al, 95/5, mixtures are plotted D vs% TMD in Fig. 2. [The ratio of chargedensity to its voidlessdensity is defined as A. The percenttheoreticaldensity (% TMDJ is 100 A,] The curvesof Fig. 2 showa typical expkJSiVe Group 2 behavior,fanningout from some point at low A and exhibiting a maximum in D prior to reachingthe failure or critical A. They alsodemonstratevery clearly why extrapolations of D vs u at 67% TMD gaveunacceptableresults for Di; the D vs% TMD curvesarelinear only in the range40~55%TMD andd > 2.54 cm. Extrapolationsof D vs u datawere carriedout at 40.3%and 55.0%TMD, The resultingstraight lines, which area leastsquaresfit to the data,are D = 3.454- 13.4Ou,

A = 0,405,

(1)

D =4.286 - 17.85u,

A = 0.550.

(2)

Here and :hrau$c-,tt the &-per, the units of D and u (tre,respectively,mm/psec and 1/mm.

Neither set of D-f4data show any s&n of a ~~~~r~ changein slt:pesucha that fourrdin the L) vs M curvesof mixtures of AP with the volariie fuelis, wax and HMX 131. With the assurnpt~~~ ahatthe infinite diameterdetonationvelncity (Q) is a lin. ear function of A, the two intercept v&uesfrom Eqs.(I ) and (2) give

for 9515,AP/Al. In Ref. 5, it wasremarkedthat the 3 *vsd CUT\I for the Group 1 explosives(TNT and NBX* I ) fannedout from a common Q ~~~~ at A * 1.O with slopesincreasinglinearly with ~1,~set analogousGroup 2 curvesseemedTVh;rrve mon point at somelow A andto fan out from it with slopeswhich decreasedwith U, OsrrWW~

DONNA PRICE, A. R. CLAIRMOPJT, JR., and 1.0. ERKMAW

‘$-

I 1

I

I

I

2

3

4

RECIPROCALDIAM?Eft, Id”

Imn-‘1

Fig, 3. Variation of coefficients of D vs A curves for AP/Al, 95/5 with reciprocal diameter. (Solid line derived from D vsu curves, o from D vs A curves.)

(a D/au),

= a’+b’A,

(10)

wherethe prime indicatesa derivativewith respect to u. By definition, /3(A)= @D/au), ; henceEq. (10) can be written &A) = a’ t b’A.

(11)

Sincefor any givenA, , we find D(A, , u) vs u linear,@(A,) must be a constant. Hencea’ and li’ must be constants;in other words,a(u) and b(u) are linear functions of u, and, asEq. ( 1I) shows,/3(A)is a linear function of A. Moreover, equatingthe right handside of Eq. (8) at two specificvaluesof u showsintersectionof the D vsA curvesat a valueof As = -a’/b’.

(12)

If the requiredlinear relationshipsare known (or assumed)to exisi, Eq. (11) is particularly useful. Two Q vs u curves(Eq. 9) definea0 , bo, and two valuesof P(A); the latter in Eq. (11) definea’ and b’ and hencethe generalequation D(A, u) = a0 + a’u + (bo + b’u)A,

(13)

applicableto the specificexplosiveused. The sameprocesscanbe followed with two D vs A curves, but, aswith AP/Al,95/5, smoothingthe D-Ucurvesseemsto producebetter results. Tbis

ALWMINIZED

AMMONIUM

PERCHLORATE

393

stems,in part, from the greateramount of data availablefrom detonability determinationsand, in part, from the more reliablelinearity of the D-u curves;they are frequently linear when the D-A curvesare not. It shouldbe noted, however, that the aboverelationsapply only when there is linearity in both planes,the D-A aswell asthe D-u; this colnbination constitutesregulardetonation behavior. The coefficientsa0 and b. are characteristicof the specific chemicalexplosive, but the parametersa’ and b’ dependvery strongly on physical propertiessuchasinitial particle sizedistribution and shape. APiIAI, 90/l 0

Becauseof differencesin preparingthe mixtures, resultsfor AP/Al, 90/ 10, aremore scatteredand somewhatlessprecisethan thosefor the 9F/5 mixture. They are quite adequate,however,to demonstratethe samebehaviorpattern for both mixtures, Figure4 showsplots for AP/Al, 90/10, of D vs A for variousdiameters As ir. the caseof the 95/5 mixture, it is a typical Group 2 behaviorwith D-A curvesfanningout from somesmall A value and a slopewhich increaseswith increasingd. The curvesof Fig. 4 weregraphicallysmoothed andvaluesfrom the smoothedcurveswere used to constructD-u curves. The intercepts(u = 0) of thesecurveswere then usedto obtain Di = 1.130+ 6.1078,

(14)

for 90110,AP/Al. Like the 95/S mixture, AP/AI, 90/10, hascoefficients for the linear portion of the D-A curves (Fig. 4) which arelinear functions of u. Those relations,illustrated in Fig. 5, leadto the general expressionfor D of the SC:/10 mix: D(A, U) = 1.13+ 7.76u t (6.107 - 43.7u)A. (IS) APiAI, 80/20

Very few shotswere madewith the 80120mix and thesewereon chargesat 55% TMD (H) and thoseat 40% TMD (h). From the two points obtainedby extrapolatingthe D-u curves,

for this 80120mix. If we assumethat this rni3c showsa similar set of linear refationsto thy found for the 5 and 10%ALmixtures. its genes equationwould be

The 90/10, AP/Al, mixttre ~c~wedthe hr effect of ALon detonationveisciry; this mix be usedto iilustrate the D(A, u) beh aluminizedAP. Equation ( II5) de~~~b~~ diameterand compactioneffectsoo trated in Fig. 6. In this casethe D-A ~~~~~ r from a common point of A& - 0..i 6 wi demwing linearly M u i~l~~~~s (or creases).The solid Inca ~~~j~~~~ the ex

DONNA PRICE, A. R. CLAIRMQNT, JR., and J. 0. ERKMAN

Fig, 5. Vnrtition of cwfficien:s cI‘D vs .L curves fol APEAt.90110, with reciprwaf diameter. Fig. 6, Explosive group 2 behavior cf APIAI, 90110. (Numbers on curves art value of u in mm-‘.) ifi Fig. 8. This is a q~ar~tit~t~~le :xantple

of the

ttcrrt.describedqualitatively lip Ref. 5 herearevery few diametereffect studieson ~~~~~ir~~~ed ~)r~anj~fi.E. The Tao of which the ~~t~~~~r~ know areHBX-I [S-8 1 andTritonal ~~~~32.2 [S] . The Group I pattern shownby the Tritonrt up~ars in Fig. 7. ln contrastto BP/Al, the curvescoincideat hiighA, (ca. 1.I2 in this CJWZ) and haveslopesirycmzsirtgwith in~r~~~~~U. The diametereffect is appreciably ~1~~~~~~ than that found in alurnhrizedAP, asmight expected* The presentdata show that the mixture of the ?~~~~ex~l~$ive fuel Al with an exploeiveexhibits the groupbet~~vi~~r of the explos~vc: ccmpt~ent , as~3r~~ina)~y proposedin Ref. 5;

theL+ curvesfor AP/wax paralleledthe Di curve for pure AP; their maximum increaseoccurredat about 20%wax and amountedto about 24% at 55%TMD, To the authors’knowledge,there areno exactly comparabledata for ahtminizedorganicexplosivesexcept for a singlepoint comparisonbetween TNT andTN’TIAI, 67.8/32.2. However, Coleburnet al. [8] havestudiedthe effect of Al on the detonationvelocity at a fixed diam (SO.8 mm) of TNT, RDX, and TNETB. Their results for TNT/AI are il!ustratedin Fig. 9. The trend

110

The ~~~~~t~ diameter detcmtiun

3

velocity of

pm AP is given 131by

Fig.7. Explosiveproup1 behavior of TNT/Al, 67.8/X.2. (Numbers on curves am value ofrc in mm-* .)

ALUMINIZEDAMMONIUMPERCHLORATE

J PERCENT T)(EOREflCAL MAXlMUM

OENSITY WOAI

(b)

0

10

20

ALUMINUM

Fig. 8. Effect of Al on Di of APiAI. (a) D vs A curves. (Numbers on curves are percentage of AI in mixture.) (b) Di and relative rates vs percentage of Al. (Numbers on curves are compaction as % TMD.)

found with 5 1 mm diam chargesshouldbe the sameasthat which would be found with Di althoughthe velocitiesin the former casewill be lessthank)i values. The pattern of Fig. 9(a) is very like that of Fig. 7, i.e. increasingu (decreasingd) or increasing% Al decreases D; the D-A curvesfan out from a point at high A (here A6 N 1). For TNT/Al,ao and b. arelinear functions of % Al; a0 increasesand b. decreases with increasing% Al. Aluminized RJJXand TNETB showthe sametrendsalthough theil coefficients arenot quite linear functions of % Al. For AP/A.l, a0 staysnearly constantand b. exhibits a maximum at, or a bit beyorrd,10%Al. Aluminum in organicN.E. decreases D; the greaterthe % Al and the bwer the A value,the grsaterthe percentagedecreases, asshown in Fig. 9(b). As remarkedabove,Al increasesD of AP (up to a limiting eonti‘nt) and the percentageincreaseis greaterat the h&M A value.

Fig. 9. Effect of aluminum on detonation ~~~~~~ M TNT. (a) D vsA curves for d = curvesiire percentage of alumin D(d = 5 1 mm) and reiative rate hum. (Numbers on curves are c I TMD.) Detonabiiity

A detonability curve(critical diam d, for AP/Al, 95/S, is shownin Fig. IO ~~~~~ includesthe analogouscurvesof 13~ AY [ 1 ol’25p AP/wax, 90/10, [3f for corn~~~~ otle point wasdeterminedfor the RI/It andthat is alsoshown in Fig. IO, Sfa fcr 95/S iollows the form af that for closely,it seemsreasonableta mournst for 90110would follow that for W/S closely. It is evidentthat ad~jt~~~erf greatesteffect on lowland & at lo the reverseof its effect an 8). Fir&y, AI geemsfar fessaff~ti in decreasingde of AP. chmid

tlhwidrr~ns

Thereareavailabletwa t gramsthat canbs us4 for the prcstlnt syst.tem.The fi

,319

DONNA PRICE, A. 8. CLAIRMONT, JR.,

are desl~~~d to make ~h~~r~~~~yn~t~lj~calculations --of ~~~~~~~~~frekmct here, the l~lqu~!~~~i~~~

rat~l~eandthe composition .rf productsobrainedwhen propellantsburn at a selectedchamber ~fessufe (say 1000 psi). Many such codes exist; they areall basicallyequivaient and produce recuts ~~~~~~~~11~~ entirely by fh? ctmnistry of the ~~~i~~~i ~~~~~~j~~. The secondtype of computer ram is that designs for detonation pherza.Not only must the the~~od~na~licrelatj~~s~~~~s be ~t~s~ed~but also thr hydrodynamic ~~~a~~~~s~~ps of det~~at~o~tkeor~~.Thus,equihbrium product compositioncan ordy be obtained by ~t~r~t~~~betweenthe two setsof conditions ~~~c~must be sjmultan~~usiysatisfied, Moreover,the P~~~r~~n requiresa valid constitutive ~ati(~~for the productsat pressuresof the order tmder!f 100kbar. The equationof state 1$1the initial density of the material both e effects on the calculatedvalues. AIt~~~~~~severalsuchprogyamshavebeenconstructed,only one hashadfairly generaldistribttaim. That one is caalledthe pTu& C&e. Na ~qu~~b~iu~~ c~lnput~tio~shaveyet been ca~~~~~ tlut with the R&y C&e for detonationof a& s~sten~APtAl, but a numberhavebeenmade cm ~~~t~ds~stes~saiadwith prop&ant codes. For ro~e~~rltis APIAljca. (CHs&, , psi snd essentiallyvoidless

andJ. 0. ERKMAN

of completereaction of the Al; the detonation temperature(Tj) computed was3 19g”K and 97.5%of the Al appearedasAlrOs [lo]. Hence for complete reactionof Al m a void&s solid, rr seemsto be a good approximation of q and the major aluminum product is AlzC,, The prope?lantcodeshowsHCI asa major product; at approximat:ly the sameT, but at detonationpressure,the Ruby Cc&eshowsCl as a major product for the voidless charge. For AP/wax, 90110,nearlya stoichiometric mixture, it was found that Tf approximatedthe R&y valueof q better at 50%than at 80%TMD ]3] ; for pure AP, the approximation wasacceptableonly in the vicinity of 50%TMD. SinceAP and its mixttires with Al show regulardetol\ation behavior(i.e. linear D vsA) only at 40-55%TMD, we will confine ourselvesto low compaction. Moreover,at 50%TMD, the major Cl product shownby Ruby wasHCI aswasalsothe casefor deflagrationin the propellantcode. From this generalinformation, it seemslikely that T’ computed on a propellant codewill furnish a good estimateof Ti computed on the Ruby Gtie at A - 0.5, and that the atomic ratio All0 for the mixture might.be a good index of composition and performanceof the /#/Al mixtures. Both of theseassumptionsaremadefor a complete reactionof*the aluminum. The itoichiometric mixture would be 27.7%AI(Al/O of 0.4125) and the equationfor the assumed reaction 2.00 NH4C104+ 3.33 Al + 2.00 HCI + Nz t 3.0r,H20 t 1.67 Ai203.

(19)

The heat of reaction is then 2280 cal/g; the gas products, 18.43;moles/kg. The Ruby Code(v&h its current library and equationof state)hasbeennotorro:rslyunsuccessft?l in computing the detonationpropertiesof AP. However,if the Ruby resultsareusedin a relative fashione.g.(computed parameterof mix)/(compured parameterof basematerial), they seemto give reasonablerelativevalues. Thus in the caseof APfwax (25~ AP, 125~ wax), they indicated that only about half of the wax was reactingin the detonation [3]. Fingeret al. [ 111haveusedthe

ALUMlNlZED

AMMONIUM

PERCHLQRATE:

Ruby Code for computing relative energies(avail-

able for moving the metal wall in the cykindertest) of HMX/perchtorate/hydrocarbon3 /Al systems relative to HMX. For the nonaluminizedsystem, their resultsindicated complete reactionof 61 AP in the two-inch-diamtest, the expectedparticle sizeeffect on reactiontime of perchlorate(3~ KC10490% and 44~ KClO,, 30% reactedin 0.5 psec),and the fact that reactionof the Al is postdetonation,e.g. 95% of the aluminum present had reactedafter 4 psec. It seemsevident from theseresultsthat sufficiently fine AP/HMX mixtures canexhibit detonation velocitiesenhanced by the APlfuel reactiondespitethe fact that that reactiondependson diffusion. It alsoseemsevident that evenfine Al, say 5~ , ti;.-zot be expected to react rapidly enoughto contribute to the detonation front of organicexplosives. The presentresultsindicate,however,that some reactionmust occurbetweenthe A9and the AP in time to contribute to the detorrationfront. Although the effectsof Al on decreasingd, of AP could be explainedqualitatively on the basisof physicalphenomenaalone,it is hard to seehow the observedincreasein D could be obtained without a chemicalreaction. For the purposeof studying the resultsat relatively high porosity (40-50% TMD), the arbitrary product distribution of Eq. (19) will be used. This convertsall Al to Al203 (solid or liquid), all Cl to HCI and the remainingH to HzO, As Table 1 shows,the productsof deflagration areaswell approximatedin this fashion aswere thoseof AP/wax, 90/10, at 50%TMD [3]. Moreover,the flame temperatureof the aluminized APis nearlythe sameasthat of the waxed; the production of gasis, of course,lower. Prediction

of D

Kamlet [ 121hasdeviseda simple calculation which closely approximatesthe valuescomputed in the Ruby Codefor most organic(C-H-N-O) high explosivesat SO-100%TMD. His expression for detonation velocity canbe written

or

Di z PZ”~M”~Q”~

(1.01 f 1.31PO),

Di =~I~‘~M”~Q”~

(1.01 + I .31 pv A),

3FIuorinated

in some CBSI,S.

(20)

Hz0 A120310 HCI Cl C!L

02 0 HO HOz Hz H AICIJ /WI* AlOCI N2 NO tl(moles/kg) Q(rallg) T/P K)

f I .506 I .X48 6,441 1175 ___d

0.039 5.991 0.146 0.927 0.004 0.1 f 3 0.029 0.002 0.002 0.00s 3,570 0.520 30.4 I 798 2933

L t A89 1 .iwJ 7.661b 0

0 6 !!~H1 0 0 0 0 0 0 0 0 3.830 0 .v29,7% 950 ...

‘Also considered and present in c~~~l~~tia~~~% c I@“” mole/kg: NH, AlHO2, A120, AK?, NH2. AIS A@& On* AIO, AlH, N2H4, N, NH3, ;Ind AlzOl.

whereDi is in mm/gsec,~1is numberof raoh~of gasproduct/g explosive,M is average~~~~~e~~l~~ weight of the gasproducts,fj is heat of reacti calfg explosive,andpU is the voidltessdensity of the explosive. Sincenhf = (mass gas ~~~~~~~~~~ (massexplosive),

wherex is the massfraction of ~~r~d~~~e~ pr ucts. Hence Eq (20) can be written

Equation (2 1) displaysd bir more ~~v~~~~ Fh Eq. (20) the effect of d~~re~~~~n wh ing Q andx, as reactionwith Al. ~4

DONNA PRICE, A. R. CLAIRMONT, JR., anti J. 0. ERKMAN

It

i .‘1W

34.M

405

1.o

li

s f0

I .977 2.006

32.97 29.78

678 1032

0.906 0.811

I.11 l.i7

1 1.11 1.18

t.5 20

2.035 2,065

263% 23.38

1388 I 740

1.20

1.21

1.19

23 27.7

E.083 2.113

21.46

1955

0.717 8.622 0.566 0.478

1.20 1.19 1.15

18,42

)_e2280

1.19 1.14

I “0 1 .OR

1.o 1.09

1.13

1.14

1 *OS

1.06

ableoxygen. Even for the smd’est amount of Al (S%), dl of the Al wasnot availableto reactin time to contribute to the detonationvelocity. This qualitative information and similar trendsof the curvesof Fig. 11 suggestthat Eq. (21) and the arbitrary reactionmechanismchosendo give guidancein the relativeeffects to be expected from aluminized A.Pfor reactionof all Al present.5 In particular, 2ndin contrastto AP/wax, the computations of Fig. 11 show the maximum increase in D at about 15%Al (Al/O of 0.192) insteadof at the stoichiometric concentration. In other words, the effect on D of decreasingthe volume of gasproducts is more than offset by the increase in chemicalenergyreleasedup to 15%Al. Ht no point, however,will APlN be aseffective as APjwax althoughthe temperatureof the products (for complete reaction)iscolnewhathigher for AP/Al. i[n a 3-componentmixture wax could be -- --.‘Use of this method nf prediction must be restricted to A - 0.5 and mixtures of finery cip+ed components for severalreasons. This is the region in which &z results show regular detonation behavior and, therefore, !rhe one most favorable for good comparisons. Then the detonation pressure, temperature, and hence reaction products will probably differ at different csmpactions. Thu5, AP alone saemsto form cl2 at all practical dens&is6for detonation [ 23 but AP/wax seamsto Porm Xl at low A, Cl2 (or Cl) at high A [ 31. S6con& it is difficult to obtain an acceptable comparison of predictions

madewith totalconsumption of thefuelto resultsobtainedwith only partial consumption. Finally, the

present method seemsto check out at A u 0.J but does not reproduce the relative trends over any ran@ of A.

ALUMINIZED AMMONIUM PERCHLORATE

I 0

I

I

10

20

I

30

PERCQT ~LUMlNUft4

Fig. 11. E&ct of aluminum on detonation velocity of ammonium perchlorate (* calculated, CJexperimental).

usedto maintain the volume of the gaseousproducts and Al to increasetheir temperature. It is possiblethat with the volatile fuel to raisethe temperaturemore rapidly, a greaterportion of the aluminum could reactin time to contribute to ‘he detonationfront. Eyring Reaction

Zone Length and Reaction

The state of subatvisionhasa largeeffect an t (e.g.AP [l] ); it folloa~ from Eq. (23) that the stateof subdivisionhasa largeeffect on 8’ and6’. As in the caseof IZuby Co& results,rch~tivr valuesof z arepreferredbecaua t~~,~ ~~~~#t~ valueshaveLrc~tbeenshown to havephysk significanceand alsob~~~~~~the refativev shouldbe the samefor e&herthe Eyrirq c front treatment or tite Woodand ~~r~w modification of it. Like wax, ~~~~~~~ AP haslittle effect err the reaction20~ Reactiontimes (7) areof more ~nte~ reactionzonelengths. How doesthe reactlora time of AP, presumablya ur~irnolec~~~ sition at relatively low te~~per~t~~~ (ca comparewith the reactiontime of AP/ sumablyinvolving dec~rnp~si~i~nof AP fo&c by diffusion andsome~xid~zer~f~~l~~~et~~~~~ somewhathigher te~lpeeatnr~‘~If the r~~~&;~ reactiontimes arecomputed,asin the earlier work 131by

Time

The Eyring reactionzonelength z is defined [3], in our presentnotation, as Zi = -~/Of,

(W

Henceover the rangeof regularbehavior(i.e. A Q OSS), Eqs.(22) and(11) give ti = -(a’ + b’A)/(Uo t bo A).

(23)

the valuesof Table 3 areobtamed, The nto& nificant changeoccursfor 90110APJAI rt d a 0.4. Herethe reactiontime ia definitely kn &an that of 14P;hencethe increaseof te~?~~ result of the oxidizer/fuel reactionmust creasedthe rate considerab’lymore than

TABLE 3 Effect of Aluminum on Relative Reaction Times lbscd on Relative Values of Eyring Reaction Zone Lengths

-

Relative Rcactiun Time Material Ak APIA1 9515 AP/Al go/10 J-/AI

a0 bo mm/r set 1.15 1.13

5.05 5.73

1.13

6.11

1.10 80 ‘?O -s @Derivedfrom &A

5.57

a’

b’

mm2/jbsec -9.140 -6.090 -0.99 -30.61 7.ib

-10.3

-43.7

-4.6

?&Tf(AP

Tit A = 0.4)

A J 0.4

A = ass

1AM 1.00

0.42 CUM

0.67

Q.64

OM

0.67!

relations for d = 50.8 I-WI and far d = -,

DONNA PRICE, A. R. CLAIRMONT, JR., and J. 0. ERKMAN

usedin conjunction with Kamlet’s method of calculation in lieu of the Ruby Code. The relative results,~~~~Al)/~~.A~), differed from L>eexperimentalresultsin the mannerto be expected for partial reactionof the AI. The maximum increasein Q observedwasat 10%Al; that predicted wasat ~a. 15%Al. References 1. Price, D., Clairmont, .Jr., A. R, and Jaffe, Il., Cumbusrion andFlame 11,415 (1967). 2. Price, D., Clairmont, Jr., A. R, E&man, 11.O., and Edwards, R. J., Combustion und Fdame 13,104 (1969). 3. Price, D., Clairmont, Jr., A. R, and Erkman, J. 0.. Combustion nndRame I?, 323 (1971). Seealso Naval Ordnance Lab. Tech. Rept. 69-16, 1969. 4. Cohen Nir, E., in Thirteenth Symposium (Enternationa!} on Combustion, The Combustion Institute, Pittsburgh, Pa. (1971), p. 1019. 5. Price, D., in Eleventh Symposium (Internationalj on Combustion, ‘lhe Combustion Institute, Pittsburgh, Pa. (1967), p. 963. 6. Price, D., Clairmont, Jr., A. R, and Erkman, J. O., Naval Ordnance Lab. Tech. Rept. 72-15 (2 May 1972). 7. Rosiund, L. A., and Colebum, N. L., in Fifth Symposium (International) on LktonaHon, ONR Report ACR-184 (1972), p. 523. 8. Colebum, N. L., NOL, private communication. 9. Gordon, L. J., and Boerlin, H. EL,in Kinetics Equilibria wd Performance of High Temperature Systems (C. S. Bahn and E. E. Zukosk$ Ed.:, Burterwortbs, Washington, UC. (1960), p. 152. 10. Chaiksn, R. F , Comments on the Ruby Code, App. II of Vol. II of project Sophy-Solid Propellant Hazards Program, AFRPL-TR 67-2 11, Aug. 1967. il. Finger, M,, Horn&, N. C., Lea, E. L., and Kury, J. W., in Fifth Symposium (International) on Detonation, ONR Report XR-184 (1972), pS137. 12. Hamlet, M. J., and Jacobs, S. J.,J. Chem. fhys 48, 23 (1968). 13. Eyring, H., Powell, R E., Duffy, G. H., and Pa&n, R B., Chem Rev. 45,69 (1969). 54. Wood, W. W,, and Kirkwood, J. G.,J. c%em. Phys. 12,1920 (1954).

(Receivedi%wember,I9 72;revisit received February, I9 7.3)