Numerical simulation investigation on propagation of the detonation wave for small-charge

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1 34 Numrical simulation invstigation on propagation of th dtonation wav for small-charg Haixia Zhao 1,Shuangqi Hu 1, Shaoming Zhang 1, Qingji Jiao, Xinchun Xu 1 School of Chmical Enginring and Environmnt, North Univrsity of China, Taiyuan , PRC Stat Ky Laboratory of Explosion Scinc and Tchnology, Bijing Institut of Tchnology, Bijing , PRC Abstract In ordr to study th ffct of charg diamtr and confinmnt on small-diamtr dtonation prssur, which th dtonation prssur in diffrnt condition is studid by mans of numrical simulation and xprimntal invstigation. Th rsults indicat that is nlargd with charg diamtr nlarg undr th sam charg. And dtonation prssur of 45# stl is biggr than PMMA. Th ffct of constraint condition ar biggr whn th charg diamtr is littl 3mm. Th charg of 45# stl is suprior in th axial dtonation propagation. Th conclusion indicatd that th numrical simulation rsults ar in accordanc with xprimnts. And th dtonation prssurs of smallr charg wr simulatd. Kywords: charg diamtr, confinmnt, dtonation prssur, numrical simulation. 1. Introduction Thory rsarch, xprimntal rsarch and numrical simulation ar thr basic mthods on xplosion mchanics in modrn tims. Th xprimntal mthod is dangrous in opration and its quipmnt is long pric. Th xprimntal collctd data is vry poor bcaus of som tchnical problm. Only using simplifid xprimntal rsarch has mor biggr limitation. Utilizing numrical simulation basic on xprimnt is a vry usful mthod. A larg numbr of financial rsourcs, matrial rsourcs and human rsourcs can b savd. Th numrical simulation rsults is mor and ovrall than xprimntal data that is bnfit to profound undrstand of propagating to th dtonation wav in small charg. Th intrcoupling of hydromchanics and chmical raction kintics nonlinar partial diffrntial quation can b rsolvd in suitabl mthod of dtonation numrical simulation of. t is basic on thory and xprimnt. In crtain filds dtonation bhavior can b mor dply and finnss udrstandd444 than in thory and xprimnt. In 198, shock snsitivity xprimnts was simulatd on DE program by Huang and Arbuckl[1] in US Army arms rsarch offic. In 1994, shock initiation xprimnts on B xplosivs was simulatd on DYNAD program by Murply and L[] in Los Alamos National Laboratory. In 198, Lvl St was usd to DSD by Aslam and Bdzil[3]. A numrical calculatd mthod of using arbitrary complx D boundary condition was dvlopd on propagation of dtonation wav. In 003, dtonation procss of shapd high xplosiv charg was simulatd and analyzd in SPH program by M.B. Liu tal[4]. In 004, PBXN-111 boostr dtonation procss of cornr ffct was simulatd in LS- DYNA by J.P.Lu and F.C.Christo1[5], pictur and data of cornr procss wr gaind. In 1999, th propagation on non-idal dtonation of IHE was simulatd by Xu Zhang [6]. In 1999, shock initiation and dtonation propagation wr simulatd in on dimnsion by Zhnyu Zhang [7]. In 198, th nonlinar finit lmnt cod was usd to calculat and analysis th dimnsional ffct of shock to dtonation of JO-9159 by Changgn Fng [8]. In 198, th blast ffct was rsarchd on numrical simulation and xprimntal invstigation by Bin Liang [9]. Th small charg dtonation propagation was numrical simulatd by LS-DYNA program. Th conclusion indicatd that th numrical simulation rsults was compar with xprimnts.. Numrical Simulation Modl.1 Crating and Simplifid Modl In this papr, th small charg of 1.0~5mm dtonation propagation charactristic was simulatd. Th 5mm charg of 45# stl as a xampl was dtaild dscription. Th Fig 1 is xprimnt instrumnt of dtonation prssur.

2 dtontor boostr 3 confinmnt 4 PMMA pad 5 manganin snsor 6 PMMA block 7 small xplosiv Fig.1 Exprimnt instrumnt of dtonation prssur Th PMMA pad and block, manganin snsor, small xplosiv pot all can b abbrviatd in tsting dtonation prssur. Th Fig 1 was simplifid to Fig. Fig is calculatd modl. x boostr initiation point confinmnt th diamtr is 30mm in physical modl. Th fixd-lngth hxahdral mapping msh was adoptd in physical modl. Eulr grid was adoptd in modling of xplosiv and air, th grid is 0.05mm. Algorithm of Arbitrary Lagrangian Eulrian was usd in lmnt. Point initiation was usd in boostr charg. Th quartr of ovrall systm was accssd on computational modl and symmtrical rstraint was addd in ordr to conomiz computing tim and improv th calculation prcision. Th initial strss of all matrial is zro. Th rst boundary all is fr intrfac only confinmnt charg. Basd on Fig th finit solid modl of 45# stl confinmnt on 5mm charg was stablishd as Fig 3. Fig 4 is finit msh modl. Fig 5 is rsult on simulation prssur-tim for x boostr of 45# stl confinmnt. Th rst of prssur-tim of diffrnt charg is gnrally similar. Calculatd modl Fig. Th A=0mm is not changd, but a=5mm 3mm 1mm can changd. Charg diamtr is changd with a. Th rlation of charg diamtr and dtonation prssur can b dfind by numrical simulation.. Msh Explanation High xplosiv burn modl and JWL stat quation wr slctd on dtonation products of x boostr. Slcting paramtr is in Tabl 1. Johnson-Cook modl and Grunisn quation wr slctd on 45# stl confinmnt. Its slcting paramtr is in Tabl. PMMA confinmnt slcting paramtr is in Tabl 3. No shar forc flow modl and linar polynomial quation wr slctd on air. Slcting paramtr is in Tabl 4. Th mm-kg-ms systm of unit was adoptd to modl. Th altitud of confinmnt is 38mm and th xtrnal diamtr is 0mm. Th altitud of boostr charg is 38mm and th diamtr is 5mm. Th altitud of air is 60mm and Fig.3 Finit solid modl Fig.4 Finit msh modl 3 Slcting Matrial and Corrsponding Dscriptiv Equation 3.1Constitutiv Rlationship of Condnsd Explosiv and Dtonation Product Th form of condnsd xplosiv JWL stat quation is: ω ω ω P = A 1 R 1 + B 1 R V R1 V R V + E V In quation V=V / V 0 is rlativ volum, V is unractd spcific volum, V 0 is initial spcific volum. P and E is rspctivly prssur and nrgy dnsity, A,R 1,R, ω is constant. B is ngativ valu that can b prmittd tnsion. ω is paramtr. Ths constants ar dfinitd by fitting xprimnt hugoniot data and initial sonic vlocity. whn V=1,T=98k, P =0. (1)

3 36 Tabl 1: Paramtrs for x boostr and dtonation product paramtrs unractd dtonation product A/Mbars B/Mbars R R ω Cv(Mbars/k) T0/k 98 E0/Mbars 0.10 CJ dtonation paramtrs ρ0(g/cm3) D(mm/μs) 8.08 Pcj/Mbars Matrial Modl and Stat Equation of 45# Stl Confinmnt Dynamics rspons bhavior of 45# stl was dscribd by Johnson-Cook modl and Grunisn stat quation[11]. Th form of Grunisn stat quation is: p 1- γ a ρ C μ μ = 0 3 μ S μ + 1 μ + ( γ + aμ)e ( S1 1) μ S 3 ( μ + 1) () Whn matrial was xpandd, P = ρ 0C μ + ( γ 0 + aμ)e (3) μ = ρ In quation 0 ρ 1, C is static sonic vlocity, γ S1,S, S3 is hugoniot rlatd paramtr, 0 is Grunisn γ cofficint, a is th first-ordr volum corrction of 0. 45# stl slcting paramtr is in tabl, σ s is yild strss. constitutiv Tabl : Paramtrs for 45# stl constraint modl ρ (g/cm3) G/G pa Pr Tm A B N C M σ s /Gpa Matrial Modl and Stat Equation of PMMA Confinmnt constitutiv stat Tabl 3: Paramtrs for PMMA constraint modl ρ(g/cm3) G/Gpa σ s /Gpa C(km/s) S1 S S Fluid Modl and Stat Equation of Air For ALE mthod, air grid of ovrlaying all dtonation scop was stablishd, and prssur flow was applid to boundary of nodal point in ordr to avoiding rflction. No shar forc flow modl and linar polynomial quation wr slctd on air. Slcting paramtr is in Tabl 4. constitutiv stat γ 0 a E0/Gpa V E Tabl 4: Paramtrs for air fluid modl ρ(g/cm3) Pr Mu C0 C1 C C C4 C5 C6 E0/Gpa V Numrical Simulation Rsults 4.1 Numrical Simulation Rsults of 45# Stl Constraint Numrical simulation on charg diamtr ffcting on dtonation prssur solid modl is agr with msh modl. Fig 5 is rsults of simulation prssur-tim for x boostr charg 5mm of 45# stl constraint. stat C(km/s) S1 S S3 γ a E0 V

4 37 T= 0μs T= μs T= μs T=1.498μs T=1.9974μs T=.496μs T=.9999μs T=3.4963μs P=0GPa P=.0157GPa P=4.657GPa P=5.7174GPa P=5.507GPa P=5.685GPa P=6.3636GPa P=5.1781GPa T=1.998μs T=.498μs T=.9968μs T=3.4997μs T=3.9963μs T=4.498μs T=4.9999μs T=5.4976μs P=5.919GPa P=6.7731GPa P=6.8559GPa P=6.8769GPa P=5.351Gpa P= GP P= GPa P=.686GPa Fig.6 Simulation prssur-tim for x boostr charg 5mm of PMMA constraint T=3.999μs T=4.4984μs T=4.9977μs T=5.4978μs P=7.3491GPa P=15.351GPa P=5.5993GPa P=.73583GPa Fig.5 Simulation prssur-tim for x boostr charg 5mm of 45# stl constraint Dtonation prssur gradually incras with nlarging tim, and whn T qual to 3.999μs, P is th biggst valu qual to GPa, thn P gradually rduc until xtinguish what can b sn from Fig 5. Numrical simulation on charg diamtr ffcting on dtonation prssur of 5mm charg is dclard as a xampl undr sam PMMA constraint. Fig.6 is rsults of simulation prssur-tim for x boostr charg 5mm of PMMA constraint. Dtonation prssur gradually incras with nlarging tim, and whn T qual to.9999μs, P is th biggst valu qual to GPa, thn P gradually rduc until xtinguish what can b sn from Fig Matching Rsults of Simulation and Exprimnt Th corrsponding dtonation prssur is simulatd by changing charg diamtr. Th rsults ar displayd in Tabl 5. Tabl 5: Simulation and tsting of dtonation prssur for small charg x boostr diamtr 45# stl/gpa PMMA/GPa /mm simulation xprimnt simulation xprimnt Not: Th xprimnt valu that is invrs valu aftr attnuating PMMA pad is dtonation prssur valu of PMMA intrfac. Fig 7 and Fig 8 ar obtaind by using Origin8.0 fitting curv from Tabl 5. T=0μs T= μs T=0.9993μs T=1.4971μs P=0GPa P=.5403GPa P=4.6684GPa P=6.1039Gpa

5 Conclusion Fig.7 Th 45# stl constraint fitting curv of xprimnts and numrical simulation rsults Fig.8 Th PMMA constraint fitting curv of xprimnts and numrical simulation rsults Dtonation prssur is nlargd with charg diamtr nlarg undr th sam constraint can b sn from Fig 7 and Fig 8. Undr th sam charg, dtonation prssur of 45# stl is biggr than PMMA. Th charg of 45# stl is suprior in th axial dtonation propagation. Th rsistanc of 45# stl is biggr than PMMA, and dformation of PMMA is clarly biggr than 45# stl, this is agrd with xprimnt and thory. But th rsult of simulation is clarly biggr than xprimnt. Th small varianc is xistd from thm. Th rsults of xprimnt is dviatd of simulation bcaus of losing radial nrgy. Simulation is ntirly dpnding on mathmatical modl. Som simplifid trating was invitabl procdd in stablishing modl. Th rsults of simulation is appard dviation bcaus of ignoring som influncing factor. Propagation of th dtonation wav for small-charg is no stady and polytrophic complx procss. Input paramtr in mathmatical modl is usually rlativ constant or variabl in limitd rang. Tru cas was not rally rflctd by modl paramtr what causing distortion of simulation rsult. (1) Dtonation prssur is nlargd with charg diamtr nlarg undr th sam constraint. () Undr th sam charg, dtonation prssur of 45# stl is biggr than PMMA. Th charg of 45# stl is suprior in th axial dtonation propagation. (3)Nonlinar dynamic 3D-finit programming of LS- DYNA, ALE algorithm and constraind Lagrang in solid mthod wr usd to simulat th non-idal dtonation procss for x boostr in small charg. Th rsult of simulation is agr with xprimnt. Th constitutiv modl and paramtrs ar suitabl in th papr. Rfrncs [1] Huang,Y.K.,Arbuckl,A.L. Numrical xprimnts on th shock snsitivity of munitions.tchnical rport ARBRL-TR- 0387,198, pp.56 [] Murply,M.J.,L,E.L.Composition-B shock initiation rport,de ,1994, pp.06 [3] Aslam,T. D., Bdzil, J.B., Stwart, D.S. Lvl st mthods applid to modling dtonation shock dynamics. J. Comput. Phys.,Vol. 16,1996, pp [4] Liu, M.B.,Liu, G.R.,Lam, K.Y.tal. Msh fr particl simulation of th dtonation procss for high xplosivs in shapd charg unlind cavity configurations. Shock Wavs, Vol. 1, 003, pp [5] Lu, J.P., Christo, F.C., Knndy, D.L. Dtonation Modling of Cornr-Turning Shocks in PBXN th Australasian Fluid Mchanics Confrnc.Th Univrsity of Sydny, Sydny, Australia. Vol. 11,004, pp [6] Xu Zhang. Th Ls Mthod Applid to Thr Dimnsional Dtonation Wav Propagation. Mianyang: China Acadmy of Enginring Physics(in Chins) [7] Zhnyu Zhang.A Msomchanic Modl of Shock Initiation in Solid Htrogonous Explosivs. China Dfns Scinc and Tchnology Rport(in Chins) [8] Changgn Fng,Jiashan K,Lang Chn. Numrical simulation on th Dimnsional Effct of Shock to Dtonation Transition of Solid Explosivs. Chins Journal of Explosivs & Propllants,00,4:16-18 (in Chins) [9] Bin Liang, Zhongfu Chn, Yonggang Lu. Invstigation of blast ffct of xplosiv charg with diffrnt shll matrial. Chins Journal of Explosivs & Propllants.007:8(5):49-433(in Chins) [10] Zhang guan-rn, Chn Da-nian. Dynamics of Initiation in condnsd xplosivs. Bijing: National Dfns Industry Prss,1991 (in Chins) [11] LSTC.LS-DYNA Usr Manual. Vrsion 940.Non Linar Dynamic Analysis of Structurs in Thr Dimnsions. Livrmor Softwar Tchnology Corporation, LSTC, Livrmor, Jun, 1997 [1] Stinbrg D J.An Equation of Stat for Polythyln mtharcylat[r].lawrnc Livrmor Laboratory rport UCID-1698, 1975

6 39 [13]Dangyong Shi, Yuchun Li, Shngmin Zhang. Study on xplicit dynamics analyz on ANSYS/LS-DYNA 8.1. Bijing: Tsinghua Univrsity Prss,005(in Chins) Mr. Haixia Zhao rcivd th Doctor Dgr in scinc from North Univrsity Of China, in 008. Currntly, sh is an associat Profssor at North Univrsity Of China, China. Hr rsarch intrsts includ numrical simulation of dtonation. Mr. Shuangqi Hu rcivd th Doctor dgr in scinc from Bijing Institut of Tchnology, in Currntly, h is a Profssor at North Univrsity Of China, China. His rsarch intrsts includ dsign of xplosiv charg. Mr. Shaoming Zhang rcivd th Doctor Dgr in scinc from North Univrsity Of China, in 009. Currntly, h is an associat Profssor at North Univrsity Of China. Hr rsarch intrsts includ xplosiv aptitud tst.