Appendix A. Expressions for equation of state parameters of TNT explosion products
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1 Appedix A Expessios fo eqaio of sae paamees of TNT explosio podcs May aemps ee made i he pas o esimae he volme expasio ae of explosive clods. Glassoe 96 obaied empiical elaios/expessios fo he volme expasio ae fo hih eeeic explosios by fii he meased vales fo vaios device yields applicable fo hih yield devices i he ae of kilo- ad mea-os. Tco ad Y 997 sed vaios fcioal foms of volme expasio ae fo he aicaf ad volcaic plmes i hei model. Hoeve he volme expasio aes meioed above ae eihe vey eeal i ae o specific o a paicla physical pocess ad hey ae o applicable o he lo yield explosive sysems ivolvi maeials like TNT i he pese ok. Alhoh siifica amo of lieae is available abo he eqaio of sae paamees i.e. pff volme pesse ad empeae hei ime depedece has o bee fod paiclaly fo lo yield TNT explosios. I he pese sdy hese sae paamees as a fcio of ime ae obaied by combii he heoies of Taylo 963 ad Joes ad Mille 948 fo he eqaio of sae vaiables Seekah. Coside a spheical as clod of adis R mass M empeae T ad pesse P expads adiabaically. Le dr be he icease i adis of he clod he he ok doe dw by he as i expasio ca be ie as. 4 A. A. hee a is he acceleaio. The pesse p is obaied fom he JWL Joes-Wilkis-Lee eqaio as A.3 73
2 hee A = 37. GPa; B = 3.3 GPa; C =.45 GPa; = 4.5; =.95; =.3 ae all cosas ad hei vales ae ive fo T.N.T of desiy.5 /cm 3 Zkas& Wales 997. Wii he acceleaio a i ems of adial disace R as ad sbsii he Eq.A.3 i Eq.A.he volme of expadi spheical pff is ive by A.4 hee R he adis of he expadi pff is obaied by meically solvi he Eq.A.5ive belo: A.5 hee. By sbsii he Eq.A.4 i Eq.A.3 oe ca obai he pesse i he expadi pff as A.6 Similaly a expessio fo he empoal evolio of he empeae i he expadi pff ca be obaied by si he folloi elaio fo he eqaio of sae vaiables Joes ad Mille 948 ive by A.7 heev is he volme ad N he mbe of moles a empeae T ad pesse p of he aseos podcs of he deoaio of mole of explosive. The vales of he coefficies fo.5 /cm 3 loadi desiy of TNT ae = 5.4 = -.4 =.33x -4. By eaai he Eq.A.7 ad ii he eqaio of sae vaiables as a fcio of ime e e A.8 74
3 Eq.A.8 ca be applied o ay amo of TNT explosive maeial ih loadi desiy.5 /cm 3. Eqs. A.4 A.6 ad A.8 povides he expessios fo empoal evolio of he sae paamees of he TNT explosive maeial. Noe: The iiial empeae ad pesse of he clod a = is esimaed o be 34 ad.5 x 5 am especively obaied fom he eqaio of sae pescibed i he lieae fo a loadi desiy of.5 /cm 3. The chemical eacios amo he TNT deoaio podcs C CH 4 N CO CO ec. coie ill he empeae of his clod eaches o 6. Sice i is easie o calclae he asies fo a fixed composiio of deoaio podcs ad also he fac ha he volme chae o his sae also he ime o each 6 is eliible Joes & Mille 948 he simlaios ae caied o by assmi he iiial empeae as 6. The iiial clod volme is cosideed o be eqal o he exploded device volme. 75
4 Appedix B olme expasio ae of a diffsi pff Tco ad Y s fomla fo he svival facio is ive by Tco & Y 997 F N a N T A. hee NT d ad N a is he oal mbe of paicles i he iiial volme is he cosa coalaio keel ad is he volme of he aeosol pff a ime. Sice he expasio of he pff is pely oveed by he diffsio of aeosol paicles coaied i i he volme expasio ae of his pff may be descibed as b 3 4D A. hee is a ko cosa o be deemied b is he iiial pff idh ad D is he diffsio coefficie of he paicles. Sbsii Eq.A. i Eq.A. ad eaai F A.3 N a 8Db 4D hee b ad d 3 The svival facio fomla deived si he diffsio appoximaio model is ive by F A.4 4 N a 3 Db By compai eqaios A.3 ad A.4 e e 76
5 A.5 The he volme expasio ae of he pff fom Eq.A. is ive by b D 3 A.6 4 A = he acal pff volme 3 b A.7 77
6 78 Appedix C Similaiy fomlaio of diffsio-coalaio eqaio The coalaio-diffsio eqaio fo a oe-dimesioal sysem is ive by d d D A3. Assme a scali solios of self-pesevi fom A3. saisfyi he cosais d d. Sbsii he Eq.A3. i Eq.A d d D A3.3 Le ad he d d ad d d. Sbsii his i Eq.A3.3 e e 3 3 d d D A3.4 Fo keels of homoeeos ype A3.5 Usi his elaio Eq.A3.4 is eie as
7 d d D A3.6 Mliply by hoho he Eq.A3.6 ad ieai he eie eqaio fom o ifiiy ih espec o dd dd C D C A3.7 hee d C The doble ieal i he secod em of he RHS of he Eq.A3.7 is sho belo schemaically: The fis ieal iemos ih espec o is ieaed fom o ad he he secod ieal oe oe is ieaed ih espec fom he limis o ifiiy. This ieaio is eqivale o ieai fis..o fom o ifiiy ad he..o fom o ifiiy. This is schemaically sho belo: f
8 8 The ieals may be iechaed as d d d d Le - = X he d = dx he he above ieal becomes X dx X X X d Replaci X by d d No his ieal is chaed o he fom ha appeas i he hid em of he RHS by asfomaio of vaiables. The he Eq.A3.7 becomes dd dd C D C A3.8 Taki he zeoh mome..o i.e. sbsii = i Eq.A3.8 e e R D A3.9 f
9 hee C d ad R Sice N he Eq.3.9 becomes dd N N D R N A3. Taki he fis mome..o i.e. he = Eq.A3.8 becomes D dd dd A3. The secod ad hid ems o he RHS of he Eq. A3. ae eqal oce i ieaed ad hece D A3. 8
10 Appedix D Eqaio fo oal mbe coceaio i he case of v v keel The ae of chae of aeosol coceaio i a chambe ih coios soce ijecio is ive by S { } v d d d A4. Le s coside he addiive keel of he folloi ype v v A4. hee is a cosa. Sbsii Eq.A4. i Eq.A4. ad ieai he Eq.A4. hoho ih espec o he paicle volme e e N S d d d d N v A4.3 hee N d S S d ad he size depede emoval ae is eleced i his case. By oi fom Appedix-C asfomaio of Eq.A3.7 o Eq.A3.8 Eq.A4.3 ca be asfomed o N S Sice N S d d v N d Eq.A4.4 ca be eie as N N v A4.4 A4.5 The esla eqaio afe sbsii he dimesioless vaiables defied i Eq.5.7 i Eq.A4.5 ca be sho eqivale o ha of Eq.5.8 deived si o-op model. 8
11 Appedix - E Lis of Pblicaios Pblicaios i Refeeed Joals. S. Aad Y.S.Mayya Coalaio i a diffsi Gassia aeosol pff: Compaiso of aalyical appoximaios ih meical solios Joal of Aeosol Sciece S. Aad Y.S.Mayya A simplified appoach fo solvi coalaio-diffsio eqaio o esimae amospheic backod paicle mbe loadi facos coibed by emissios fom localized soces Amospheic Eviome S. Aad Y.S. Mayya M. Y M. Seipebsch G. aspe A meical sdy of coalaio of aopaicle aeosols ijeced coiosly io a lae ell sied chambe Joal of Aeosol Sciece * Peseaios i Cofeeces ad Wokshops aeded. S. Aad Y.S.Mayya A sdy o simlaeos coalaio ad dispesio i a coceaed aeosol clod Idia Aeosol Sciece ad Techoloy Associaio IASTA-7 Cofeece o Emei Teds i Aeosol Techoloy ad Applicaios Nov a NPL Ne Delhi.. S. Aad Y.S.Mayya Modeli soce seh modificaio de o coalaio i a diffsi aeosol pff Eopea Aeosol Cofeece EAC-9 Sep 6-9 a Uivesiy of alshe alshe Gemay. * Coibios S.A. ad Y.S.M. desied he sdy ad developed he models. M.Y. M.S. ad G.. povided he expeimeal paamees fo model compaisos. 83
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