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An Alternative Method for Estimation of Gurney Velocity Based on Assumed Detonation Products

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An Alternative Method for Estimation of Gurney Velocity Based on Assumed Detonation Products

    An Alternative Method for Estimation of

    Gurney Velocity Based on Assumed

    Detonation Products

    l4卷第6

    200612

    含能

    CHINESEJOURNALOF

    材料

    ENERGETICMATERIALS

    Vo1.14,No.6

    December,2006

    文章编号:1006-9941(2006)06-0449-04

    AnAlternativeMethodforEstimationofGurneyVzlocityBased

    onAssumedDetonationProducts

    MohammadHosseinKeshavarz

    (DepartmentofChemistry,Makk-ashtarUniversityTechnology,Shahin-shahrP.0.Box83145/115,/s/am/cRepublicof/ran)

    Abstract:AnewmethodforpredictionofGumeyvelocityofexplosivesisintroducedinwhichenergyoutputiseorl~la-

    tedwiththeheatofdetonation,thenumberofmolesofgaseousproductsofdetonationpergramofexplosiveandtheaverage

    molecularweightofgaseousproducts.ItisassumedthattheCHNOexplosivereactstoformproductscomposedofN2,CO,

    H20,CO2,H2,02andC(s)asdeterminedbytheoxygenbalanceoftheunreactedcompound.Goodagreementisob-

    tainedbetweenmeasuredandcalculatedvaluesofGurneyvelocityascomparedtopreviousc

orrelationswhichassumedthe

    reactionproductstoconsistofN2,H20,CO2andeitherC(8)or02. Keywords:explosionmechanics;detonationproducts;gurneyvelocity;correlation;explosi

    ve;metalacceleration

    CLCnumber:TJ55;0389Documentcode:A

    1Introduction

    Thedetonationproductsarelargelygases,whichin hightemperatureandhighpressureregime.arehighly non-idea1.Detonationparameterssuchaspressureand velocitycanbecalculatedbyacomputercode,e.g.TI- GER[,whichUSeSadatabaseofthermodynamiceharac

    teristicsofexplosionproductsandinitialcompositionof highexplosives.Moreover,empiricalcorrelationscanal- sobeusedtodetermineimportantpropertiesofenergetic compounds[.Somenewmethodshavealsobeenintro. ducedtodeterminedetonationparametersofidealand nonidealpureormixedexplosivesaswellastheother importantpropertiesofenergeticcompounds['.

    Sincespecificenergyvaluecanpermitcalculationof velocitiesandimpulseimpartedtodrivenmaterials,itis moreappropriatethandetonationpropertiesfortheballis- ticcharacterizationofanexplosive.Thepurposeofthis workistopresentanewmethodforestimationofGurney velocityinconjunctionwithasimpleenergypartitio

    ningmodeltosolveawiderangeofproblemsinvolving theaccelerationofmetalbydetonatingexplosivesofarbi- trarydensity.Inthispapertheeffectofchoosingnew suggesteddecompositionprocedures['1willbestudiedto estimatethereliableenergyoutputforC.H^N0dexplo- ReceivedDate:2006-07-24;RevisedDate:2006-08-30

?correspondingauthor.mail:mhkcshavmm@mut.ac.ir;mhkir~yahoo.tom

    sivesatanybulkdensityofinterestwithrespecttoprevi? OUSmeth0ds[26,27whichusethea88umeddet0nati0npmd. uctsofKamlet[28].Thenewmethodcanbeappliedto pureexplosivesaswellastosolidexplosivemixtures somewhatmorepracticalimportancetoexplosiveuserso thatitcalculatethevelocityofexplosively--drivenmetalo-? verarangeofgeometriesandloadingfactors.However, theresultswillbecomparedwithexperimentaldataof well-knownpuremixturesofexplosives,wheremeasured dataareavailable,andHardestyandKennedy(H&K)[261 aswellasKamletandFinger(K&F)methods+

    2GurneyVelocityBasedonKamletProcedure

    Detonationproductsareformedbythepossibilityofthe existenceofmorethanonephaseasdetonationwavepropa- gatesthroughtheexplosivemedium.Theequilibriumcorn- positionofgaseousproductscanbedeterminedfromexperi- mentalmeasurement,thermochemicalequilibriumcalcula- t.ion,orbyidentifyinganappropriatedecompositionreac- tion.KamletandJacobs[1suggesteddetonationpressures

    andvelocitiescorrelationsforCHNOexplosivesatinitial densitiesabove1g?cmonassumptionthatN2,H2O,C

    (s)andCO2(butnotCO)aretheimportantdetonation products.rI1leyusedtheparametertoobtainthefollowing correlationsforcalculationofdetonationvelocitiesandpres- suresatloadingdensities,P0,greaterthan1g?cm:

    P=Ktpp~

    o(1)

450含能材料第14

    D=A'P(1+Bpo)(2)

    where=NM'Q(3)

    andK.AandBareconstant.InEq.(3)Mistheaver- agemolecularweightofgaseousproducts,Nisthehum' berofmolesofgaseousdetonationproductspergramof explosiveandQd|Iistheheatofdetonationincaloriesper gram.Theheatofdetonationcanbedeterminedfromthe heatsofformationofreactantsanddecompositionproducts 0ftheexplosivethroughtherelation[28:

    Q一塑

    formulaweightofexplosive

    (4)

    Gurney[suggestedasimplemodelinwhichagiv

    enexplosivelibratesafixedamountofspecificenergy (E)ondetonationthatisconvenedtokineticenergypar' titionedbetweenthedrivenmetalandgaseousproducts. Sincetheprocessofmetalaccelerationmightbeaccoun

    tedbylimitingthedegreeofexpansionofproductsgases t0thatwhichisconsideredtooccurwithintheeffective interval.ithaslimitedduration.ThemeasuredGumey energyissignificantlylessthanchemicalenergyofunre actedexplosivebecauseanyinternalenergyremainingin thegaseousproductsdoesnotcontributetoitsvalue.The Gurneyvelocityorenergycanprovideamorerelevantab

    soluteindicatoroftheabilityofanexplosivetoaccelerate underawidevarietyofinitialdensitiesandgeometriesof C.HN.O—专Nz

    0''

d?"d告一

    .a+?岫d.z.+

    d2??

    interest.HardestyandKennedy(H&K)correlated Gumeyvelocities(^//2E)withandPoasfollows: =0.60.54(1.44.)(5)

    LaterKamletandFinger(K&F)introducedthefol- lowingcorrelationwiththesamevariables:

    =0.887~op.o(6)

    K&FcorrelationpredictsbetterresultsthanH&Kcorrela-

    tionwithrespecttothemeasuredGumeyvelocities. 3NewMethodforPredictingGurneyVelocities Themajorcomponentsofdetonationproductsof CHNOexplosivesmayincludeN2,CO,H2O,CO2and solidcarbonaswellasminoramountsofH2,NH3,02, NO8nd0therchemica1sDecies.CHEETAH[isaC

    versionoftheFORTRANequilibriumcodeTIGER,which canbeusedtoestimatedetonationproductsofexplosives. TheproductsconcentrationsforCHNOexplosivescalcu- latedbyCheetah2.0/JCZSindicatethatthegaseousspe- ciesH20,H2,N2,CO2andCOarepredominantdetona

    tionproducts.Toobtainagoodapproximationofma- jordetonationproducts,itcanbeassumedthatallnitro- gensgotoN2whileaportionoftheoxygensformH2Oand carbonspreferentiallywillbeoxidizedtoCOratherthan CO2sothatthefollowingpathwaysaresatisfied: dco+(.d)c(B)+H

    .CO(d.)H2o+(?一d.)H:

    (2口一d+-)cobH2

O(d一口一b)cO

    2

    o+.CO:+(o:

    Itisfoundthatpredicteddetonationpressuresandve- locitiesofexplosivesareclosetoexperimentalvaluesovera widerangeofloadingdensitiesgreaterthan1g.amas we11aslessthanlg.am-3[7-3.Moreoverpredictedheats ofdetonationbyusingabovedecompositionproductsaxe muchbetterthanthoseobtainedbasedonKamlet8meth

    0d[7,17.

    Itwasfoundthatpredictedheatsofdetonationfor H2O(g)usingthenewdecompositionprocedureandKam- letsmethodhaverootmeansquare(rms)deviationsof 0.954and1.006kJ?gfromexperiment.respectively.

    Moreover,Kamletsmethodshowslargerdeviationfromex- periment(rillsdeviation=1.365kJ?g)ascomparedto thenewmethod(rmsdeviation=1.048kJ?g)7jfor (78)

    (7b)

    (7c)

    (7d)

    H2O(1).However,theresultshaveindicatedthatEq.(7) cangivereliablepredictionofQdet,andtherefore,as comparedtodecompositionproductsofKamletsmethod.

    ThestudyonGumeyvelocityforvariousCH6N.0d explosiveshasshownthatitispossibletoobtainnewcor' relationbasedonfourdifferentmentioneddecomposition paths.Itisfoundthatthefollowingequationwithsome adjustableparametersaresuitableforfindingGumeyve' locitycorrelationofCHBN0dexplosiveasfunctionofthe

abovementionedbasicparameters:

    ~/j=z.z2pZ4(8)

    where,ismodificationofEq.(3)basedondecomposi'

6aromadHosseinarz:GvAnA1'e

    

    rna

    .

    tiveMethodfor

    451

    tionpaths(7a)to(7d)forallexplosiveofgeneralformula CH5NOdandZl-z5areadjustablecoefficientswhichcan beobtainedfromthebestfitofexperimentaldata.There

    portedexperimentalvaluesoftheGurneyvelocityhavebeen listedforsomeC.

    H^NOdexplosivesinTable1wheretheir

    measureddataareavailableinopenliterature.However, experimentaldataofTable1havebeenchosenasdata- baseforfindingadjustableparameterssothatR-squared valueorthecoecient0fdetermination0fthi8c0rrelati0n is0.991[32.Theoptimizedcorrelationcanbegivenas: =8.341+3.045po~'+4.2~

    

    0.

    0d

    3(9)

    Comparisonofthenewcorrelationwithmeasuredvaluesand estimatedvalue8fromthemetlIods0fH&KcandK&F[

    methodsareVeninTable1.ThecalculatedGurneyveloci? tiesbynewmethodshowsurprisinglygoodagreementwith

experimentalvaluesascomparedtoH&K[andK&F27

    methods.Averagedeviationsare0.02km?sforEq.(9),

    0.05km?8forEq.(5)and0.?km?sf0rEq,(6).

    Table1ComparisonofcalculatedGurneyvelocitiesbythenewcorrelation.H&K

    "1andK&F"1withmeasuredvalues

    Note:B)SeeAppendixfor#o~aryofcompoundnames;b)AllmeasuredviluesofGumeyvelo

    cityarereportedinRef[33]exceptwherenoted

    4Conclusions

    Anempiricalnewcorrelationisusedtocalculate

    Gurneyvelocityasanimportantparameterforthermo- chemicalestimationofexplosiveenergyoutputbyassum

    ingfourpathsfordeterminingdetonationproducts.The introducedcorrelationrepresentsasignificantadvancein aprioriestimationofexplosiveenergyoutputbyH&K[

    andK&FC'method8.Iti8foundthatnewdeeompositi0n procedurecangiveusanewcorrelationformorereliable predictingenergyoutputwithrespecttopreviouseorrela

    tionwhichuseKamletdecompositionproducts.Compari- sonofcalculatedresultswithexperimentaldatalistedin Table1maybetakenasappropriatevalidationofEq. (9)ascomparedtopreviousEqs.(5)and(6).The

    newcorrelationmaybeappliedtoanyCH5NOdexplo-

    sivesatanyloadingdensity.

    Acknowledgement:

    1wouldliketothanktheresearchcommitteeofMalek.ashtarUn1. Versit)rofTechnology(MUT)forsupportingthiswork.Thisresearch wsupportedinpartbyInstituteofChemica1.andScienceTeehnolo- gy?Tehran-IranResearchCouncilGrant(No.ICST-8103-2141). Appendix:Glossaryofcompoundnames

    I.HMX:Cyelotetramethylenetetranitramine(C4HlNl01)

2,NM:Nitromethane(CH3NO2)

    3.PETN:Pentaerythritoltetranitrate(C5HlN4OI2) 4.RDX:Cyelomethylenetrinitramine(C,}I'N606)

    5.TACOT:2,4,8,10Tetranitro-5H-benzotriazolo[2,1,a].

    benzotriazol-6?ium,hydroxide,innersalt(Cl2H|NlO1) 6.TETRYL:N-Methyl-N-nitro-2,4,6?trlnitmaniline(C7N5O8) 7.TNT:2,4,6-Trinitrotoluene(C7H5N3O6)

452含能材料第14

    8.COMPA3:91/9RDX/wax(C1.H3.7.N?,?02.46)

    9.COMPB:63/36/1RDX/TNT/wax(C..,H2."N2.ii02.67) 10.CYCLOTOL-77/23:77/23RD)TNT(C1.75H2.N2.s*02.69)

    11.CYCLOTOL_75/25:75/25RDX/TNT(C1.7lH2.58N202) 12.LX.14:95.5/4.5HMX/Estane5702-FI(C1.H2.92N2.,,O2.66)

    13.OCTOL?78/22:77.6/22.4HMX/rNT(CI.'/4H2.59N2.3902)

    14.OCTOL-75/25:75/25HMX/TNT(C?lH2.5,N202.69)

    References:

    [1]CowperthwaiteM,ZwislerWH.TIGERcomputerprogramdocumen

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