Dynamic Parameters of Gaseous Detonations

7/28/2019 Dynamic Parameters of Gaseous Detonations

1/26

Ann. Rev Fluid Mech 98 : 33Copyrght 8 b a Rvws I rght rrvd

DYNAMIC PARAMETERS OF

GASUS DETNTNS

Jhn

Dprtmnt o Mchncl Engnrng McGll nrsty MontrlQubc nd H3 K6

INTRODUCTION

In ddton to gss mmb lquds nd solds n th form of ndroplts nd dust ptcls lso om plos mturs wth nplos mtur cn n gnrl support two mods o combuston hslow lmnr drton mod s t on trm; hr th mpropgts t typcl locts o th od 1 m s lt to t unburndgss nd th s nglgbl ovpssu dvlopmnt whn th plosons unconnd. t th othr trm s th dtonton mod n whch thdtonton w propts t bout 000 m s ccompnd by norprssur rs of bout 0 brs cross th w. h propgton olmnr dgrtons s gornd by th molculr duson of ht ndmss rom th rcton zon to th unburnd mtur. h propgton ofdtontons dpnds on th dbt shok compsson o th unbundmtus to ltd tmprturs to brng bout utognton Th ry

strong ponntl tmprtur dpndnc of chmcl rcton rts ngnrl mks possbl th rpd combuston n th dtonton mod. wophs lqud droplts or dustr mturs r smlr but thy rqur morphyscl procsss (g droplt brk-up phs chng mng tc) prorto ombuston Thus htst tm o lngth sls ssotd wthth ombuson ont usully much lg thn thos o homognoussous fur mturs h ssntl mchnsms of propton of thcombuston ws howr r smlr In btwn th two trms olmnr dgrton nd dtonton th s n lmost ontnuous

spctrum of burnng rts whr turbulnc plys th domnnt ol n thcombuston procss. Du to spc lmttons only homognous gsousul dtontons consdd n ths tl.

006648840115-01$000

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Annual Review of Fluid Mechanics Vol. 16 (1984): 311-336


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3

h pbm u-i pin h civ cnib nin incn y in cnncin wih h y pc -c npn qu pum nu h h Mi Inincin i h quin h pibiiy n cnqunc

hgni pin ini nucc cnnn wphiqui py n u pin cncn in ccin u in pchmic pn n in gin v n c min A u h cun wwi in in u-i pin, civch invving gc h bn c u in cn yIn hi pp, w in u h gu ui nin p u-ipin, png n h p m n h cun h

Accin u-i pin icu in h cn mnph Gugn (78) knch (178) n k (83) w in n

cn n viw ic by Shw (80). In iin, hpcing cn pcii ming n ui pin cninpg p cun civii viu bi un hw ( ui 18) h pn pp, h, vi upicin mi h cn b un wh m, hwv, kp h pp cnin

THE DYNAMIC PARAMETERS OF DETONATIONS

h cic hpmn-uu hy, in nc, h uniquuin h n-imnin cnvin quin c h nin n in which h w bhin h wv i nic I n qui knwg h ucu h wv n nvv ny nquiibium hmynmic ccuin h nin (i hnin vciy pu, mpu n niy i c hwv, n h quiibium cmpiin h puc g) hquiibium, ic, nin bin m h cic

hpmnuu hy upiiny w wih pimn bvin, vn in nimi cniin whn h w ucu n h ni hih himnin

h pm quiin knwg h ucu, n hnc hchmic cin , h nbiiy imi, h iniiin ngy, hciic ub im n h hickn h cin zn W hnch h pm h ynmic nin pm iinguih hm m h quiibium ic" nin binm h hpmn-uu hy A n-imnin m h

nin ucu w pp in h y 140 by Zvich,W Ding n vn Numnn (i h DN m) um pnhck w by cin n n inucin y pi hi

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O TONTON

m prm h mpui f h mi prmr wh mfr h phic prc in i gin. wr ru frm uchcmpuin uing h ZN m fr h nin rucur r quifr frm h bin frm primn, min bu h ZN

rucur i unb n i nr br primn cp unrrin iin hi i in r wih primn brin h fui nin h hrimin ur ruur qunii hr fr h r cur nin rucur h bp hu, i m hr urpriing h cnur fr hnin phnmnn w r ini, n r igh r in hucfu hpmnugu hr fr h piin f h uiibriumprpri w prp, hr i i n qunii hr f imingh m ni prmr. h rmi prim

prmr, n hir murmn r n wihu m funmnifcui hr

i rrh up ui h r 970 w m furhrig ur urig f h ph hmi prin i h riu p f h nin phnmn i rniinfrm grin ni f i b iii hkinrcin pc ing h c muih r curucur, .). hu, nii miur f fu (g , ) wih purgn wr i gr h primn wr uu rri u ubmphi i prur f nni Murm f hmic prmr wr m m n fu-gn miur ubmphic inii prur inc h bjci f h murmnw u h pnnc f h nmic nin pmr nh hr primn rib. ru, hr fw primn n h mi prmr, priur n prim, prmi mpiri rrin b m.

n Vum 5 f hi ri ppnhim ukhi 197) g r

cmphi hric umr f nin rrch up h im w i bibgrph f h r wrk. f pricurinr i hir ric r h buifu hin cinmgrphicrr f h riu phi pr i wih h phm fr w h ur ruur f hi fr if h pi prim rr pri g quii unning f h nin phnmn, n rrr nurg fr hi ric fr phi bckgun n hubj. hr nwrh riw ri ummizing h i

ruur f u in r h f Ewr 1969) Srhw(1968). h n mngrph b Fk i 1979) gi gmphi riw f h bii ruur f ur i

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EE

r rcn rviws mhasiin h dirc iniiain and h ransinrm darain dnain hav bn ivn b (177) and n (18)

ma b cncudd ha b h ar 17s a ascs h dnain

hnmna wr ui w ndrsd, a as n a aav basishr is hwvr, a srn dcinc in riab rimna daa n hdnamic dnain arars aricuar in u-air miurs aamshric iniia rssurs ha ar racica inrs. Thr ar asvr w rsus n u-air dnains du h ac ha vr-hih-nrsrcs such as sid siv chars mus b sd r h iniiain as arsu hr raiv insnsiivi. As, h si h aaraus ruirdncssias ha h rimns b carrid u in h d. wvr as arsu h currn inrs in accidna u-air sins a numbr arsca rimns hav bn carrid in h as dcad n uairdnains W mhasi hr h discussin hs nw rsus andhir crrains and in h rgrss mad ward h rdicin h dnamic dnain aramrs.

HE DEONAION CELL IZE

Prhas h ms imran dnamic aramr is h avrag si a

c h dnain rn. Bcaus is undamna sinicanc i iswrhwhi rviw bri h ssnia aurs a car dnainrn ir shws h arn mad b h nrma rcin adnain n a ass a cad ih wih carbn s which ma brm ihr a wdn mach r a krsn am. Th cuar srucur h dnain rn is qui vidn. a simiar s-cad ishdma (r mar) i is insrd in a dnain ub h assa hdnain wav wi av a characrisic shsca" arn n hsmkd i iur is a squnc asr-schirn rcrds a dnain

wav raain in a rcanuar ub On h sid wndws has bncad wih smk and h sh sca arn rmd b h raaindnain n is vr w iusrad. Th daid shck cnrain h car dnain rn is is i srad b h inrrgram shwnin iur 3 h dircin ragain h dnain is ward hgh As can b sn in h skch a h crnr, hr ar w riins. A h rs ri in A, A and A rrsn h incidn shckand ach s h adin rn whi AB is h rcd shck. in Bis h scnd ri in anhr hrshck ach cnrain n h

rcd shck AB; h nir shck arn rrsns wha is nrarrrd as a db ach rcin Th hachd ins dn hracin rn whi h dash-d ins rrsn h shar discniniis

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GAOU TONATON

r s ns asscad wh he r-shck ach cnurans Thnr rn ADE s nra rrrd as h ransvrs wav and raas nrma h drcn h dnan mn (dwn n hrsn a a au he ud ed h rdu a ha

een shwn ncusv ha s he re-n rens a A and hawre n he sked . h eac chancs hw he re-nrn ds h wrn s n car. has bn suad ha h hhshar a he dscnnuy causs h s arcs e erased. ur 4shws a scheac he n he denan rn he sh-scaeaern s a ecrd he rajecrs he re ns. s mran ne he ccc mn he denan rn. Sarn a h ae he ca A, he dnan hck rn s hh vrdrvn, raan a au

Figure ar om h orma ro of a ua oaon o a mokga a

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316 EE

o

o

m

igure Laser-schlieren inematography of a propagatig detoation in lowpressureH202 mixturs, with hal pattr shown on a sootoatd widow (ortsy o

A K Oppeem).

16 ms h uibrum ChmJuu di vcy. wrdh d h c h shc s dcyd bu 6 ms hChpmJuu vy br s mpusvy r bk shhy vrriv s wh h rsvrs wvs cd sr h

y i r h rs h h r rm A BC, h wvsrvs s h ch sm h cd shcks h djc cs urih scd h rm BC h wv h bcms h icd shck h ch sms h hbr cs s h vrii hshck srh d chmc rcs s c c b u rcr by bu . (8). AD s usuy s h h hc, d BC ds h c dimr (s rrrd s h c wdh rh rsvrs-wv sc) Th vr vcy h wv s cs h ubrum Chm-Juu vcy

W hus s h h m r d r s r rm hsdy d -dms m gv by h DN md sd, rcds yc mr whh h shk vy ucus wh

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ASOUS DTOATIOS 7

c abu h uiibum hamaJuu au. hmica racis assiay m wihi a cyc r a c nh. wr asdyamc w srucur s hh hdnsn ad u qubrai h rasrs shcks, s ha h w bcms ssiay

dmsia w rbaby ak a adda dsac h rdr a wmr c hs.

Ieeom o the deted obe Mheeo oto o te tteofa celar detonatin fn (utesy ofD H Edwad).

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Forpersonaluseonly.


8/26

3 LEE

A

Shemt o e popgto o ell eonto ot howg te tjetoeo te tpe pont

F h h cua ndn h aa shsca s h

aag c sz can asud Th ndn cd gs h cuapan a n pcs nsan Th aa cd h ps hdnan sd as as ang h ngh h s uchas y a pc u h chaacsc c sz h aa cdhus h ndn pan is n usd in gna csz asuns

Eay asuns h c sz ha n cad u sy n pssu uygn ius diud h n gass such as H andN (Sh Eng 969) Th pups hs nsgans s p h das h dnan sucu and nd u h acsha cn as n un y cny ha Bu a (1) ads c-s asuns n schic u-a ius a asphc pssu Du h undana panc h c siz n hcan h h h dynac paas a sysac pga hasn caid u y nysauas asu h c siz asphic ua dnans n a h cn us (g z z Z s l and h dng u M) h n ang ucpsin n h is (nysauas a 93) Schc

us hs us h pu yn and wh ayn dgs N dun a asphc pssus as sudd (nysauas a9) T nsga h pssu dndnc nysauas a () ha

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AOU TONATON 3

a maurd h c z n a vary chmrc u-xynmur a na rur rr ur 5 v h yca-had crv h varan h c z r m h cmmnhydrcarbn uar mxur wh h quvanc ra ( = r

chmrc cmn) h mxur. Th mnmum c z uuayccur a abu h m dnab cmn ( ). The c z rrnav h nvy h mxur Thu n dcnn rdr

W'W

FUE

we ee tat te aboe teo e R L o te ta tubeamete d 2L tke, of a etoato wae eote by wa et a 6 to bebetwee 2 to e et, o to 8 e amete. Tey bae t eut omeauemet of e eay of te taee eue bato eeubato of e taee ok oxyoe a oxyaetye

mxtue Te eut ae ao wt ee eeet meauemet by Vae et a 2 ak a aeae aue of fomwa et a' obeato .e. L 6. we ee tat te ooeteo ea to te eut 2 3, w efetaeemet wt exemet. Fom te aboe uo, te ta-tubeamete obem tu eue to te eouto of te yoyam oeete tke of te eua etoato fot. owee of L emt to be eteme

Te eet exemeta wk of u et a. 83 a ao oue ome

teet eut tat e fute t o te ta-tue-ameteobem. I tuy te tamo tou a oe ate tea offom a tat tube, t fou tat te ta oe amete etia

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GASEOUS DETONATIONS 3

t te ctc tbe mete s te stem esse enncementfm te eecte etntn te ce te es nt nence tetnstn cess m n t sec we. Te eecteetntn genetes y cnegng sck we wc ke te

efctn wes gtes tw te tbe xs t bt te snsee f te oct gses s est of te g temetes n encewek sck) Te ct tt tee s n eence between te cesnngctc ce n te ctc tbe metes sggests t te nttente ce ne te tbe xs te tn te ets te exctgsynmc w stcte ben te cte we mntes teeement f te sec etntn.

Exements n te tnsmssn tog eent-se oce tes. se ectng tng n etc) ncte tt te

cetn st s f eecte mete deff wc s te me e te gest n smest mesons tt cctee te oce enng sse e. deff ). qe ce se engt he smestcctestc mensn w be W, we te gest w be tegon w s te eecte mete o te se oce wo bedeff j2(W J) .2 ence def ges /.2) 08 n cse geement wt te ee bsetns f 0 bytofno & Skn ) n ws et ) Te eectemete s s te men e f te mete te ccmscbe n

nscbe cces of te ce oenng. It w e tt te smestmensn s be me mtnt snce t cnts te tme teefctn t enette te we. wee wen te tw cctestcmensns e not t een te exnsn s tee-menson nts te men e w be moe ote to cctee tegsynmc cess.

In geneng te ests ne c so ntce te cncet o wecte. Te ctc cntn tnsmssn c ten be stte ntems of mnmm s o cte of he ce e. f eefctn wes ge se t cte te cte etntneceeng cetn ctc e ten fe of te we ests. Temxmm cte mnmm s cte R w be tee of bt te yynmc tckness H .e. R H .) f tetee-mensn cse f te tnsmtn m bty sen t sec gemety

ectng ces sts) wee te sect t /ge eg

Liu et . 98) n tt te sme engt nw cnts tetnsmssn cess te tn te men e te tw cctestcmensns n W se n te we-cte cncet te c-

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6

rspodg radus o curatur o a twodsoal cyldrcal wawould be oe halthat o the sphercal wae or th sae curature. Thus R or th thrdsoal cas R /dsoa cas Ths s aget wth the eetal esult o u

that 32.Sc u's prets ar basd o rectagular slot orcs oL/W: 7 so largscal epres o wo-dsoal rcaguarchals wh /983) to ry the 3 lt. Ther perts usd -ar ad ar ures a atospherc pressures stead ohe HO-N ad CHO-N turs usd by u. Th results hower cord the twodsoal lt o 3 oud by u. urtheror a halchalprt was also prord that dostratd sytry about th

cetrl that a alu o /These ry recet eperetal dgs are etrely testg. t s

clar that the crtcaltubedaetr probl prodes uch sght tothe couplg chass btwe gasdyacs ad checal tcs. hsudd rgc ro cod to ucod spac ssc subctsth dtoato to a t prturbato Whether t sures ad readjusts tothe ew gotry or als wll dee the u requrets or the selsusad propagao o h wa udr ts w rot. Th rcstudy o Murray & ee (983) o detoato alure whe the dtoato

trasts ro a rgd stel tub to th plastc tub s o partcular tersti this rspct. By usg pastc tubs o drt wal thckss th styo th gasdyac epaso ca b cotrolled ad th alure crtero ths cas ca th b rlatd to th wa curatur It should b otd thate rgd tubes the egate dsplaceet thcss o the boudarylayer causes ow drgce uch le th yeldg plastc wall prto Murray e (1983. Thus raracto was ar geratd at th wallswhch the propagat toward the tube as ad cause the wa to b cured.Drct asurts o th radus o curatur o a dtoato wa hab carrd ou rcy by Dsbords t a (98) Thy rpord a raduso curature o about or a plaar detoato a -c-daetr tubeThe correspodg curatur o the wa s uch saller tha the crtcalau or h aure o a spherca ae .. R .). Thus apparsthat th u radus o curatur o a sphrcal wa would b aboutth hydrodyac thcss 3.curatur uch largr tha th crtcal alu a locty dct rsults Thusalure rgd ad plastc tubs as well as sudde epaso to

ucoed pac ar all slar procsses ad dr oly y t dgree oth tasrs paso tsl c th latral paso rsuts acurd rot th propagato crtro udr drt boudary codtos ca b ued udr the wa-curatur cocept.

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ASEOUS EOATIOS 32

CCL NG O D NON

perenlly s ound h or gen ure gen nlcondons dene quny o energy us be used o ne deonon nsnneoul. B nsnneousl s en h henl ong bl we genered by he poweul gne upon he pddeposon o s energy decy sypoclly o ChpnJouguedeonon. I he gner energy s less hn cern crcl lue herecon zone progressely decouples ro he bls s decys nd degron resuls nce he rnson ro degron o deononunder unconned condons ereely dcul een posblesphecl deonons e los lws ned n pcce he deco blsnon ode. Snce he ubec o drec non hs been

horoughl reewed preously ee 9 suces o consder only herecen deelopens nd resulsThe ners n unconned uelr deonons n recen yer hs led o

nuber o eperenl sudes on he eureen o he crclnon energ The os eense o hese esureens or uelrue e hoe b Bull e l. 98 The dependence o he cclenergy or equlenly he wegh o he old eplose chrge used onhe equlence ro s lke ll dync preers n he or o Ushped cures wh he nu round sochoerc copoon e. 4

= I. he nu enegy 4 = h been ued ele eure ohe sensy o he ous uel o deonon Mu & ee 98 lsoby specyng soewh rbrrly n upper l o he crcl energyboe whch he ure s rendered nondeonble he U shped cure cnbe used o dene he deonbl ls o unconned deononsAhough here re uber o eperen preer h ynuence he non energ eg. he pe o gner s geoer energye chrcescs ec. cn be concluded h s long he e o heenergy deposon s shor copred wh he chrcersc e o he bls

we [e. RoC where R EP s he eploson lengh nd C s hesound speed] he bls we cn be condered s n del pon spherclbl chcered by he ol energ onl hu eeenlesueens o he crcl energy n uelr ures usng concenedsold eploe chrges ss h condon nd we ned no consderoher del o he source sel.

The ous heores or he crcl energy he lredy been reewedee 9 They ll how cubc dependence o he crcl energy E on henducon e or sphercl deonons e E ) oweer he lcko n oerll checl lengh o e h chrcee he el hreedenon cellul ucure o he deonon we pee ll heeheorecl eors ro beng copleely qune. The use o n

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28

expeel d po s usully ecessy o elue ce coso popooly bewee Eo d s exple cosde he splesheoy bsed o el'dochs ceo see ee 977) h whe heg bls hs decyed o he hp-ougue segh he decy

e us be o he ode o he duco e. s so-bls heoyee (977) deed he ollow expesso o he ccl eegy Eo:

Eo=kjPoW+3[()/2]+1T+1, )

whee k n, 4n o = 0,1 coespodg o he pl cyldcld sphecl eoey especey I s uec cos h s uco o he specc he oy oy 1.4 I 04,066,11 oj 1 especely) Po s he l desy D s he hp-Jouueeocy d s chcesc chec e he dco e

eued he shoc epeue coespodg o hp-ouguedeoo s used o , Equo 1) es lues o Eo bou hee odeso ude slle h he expeel lues oe ppopeoell checl e c be deed o he cell leh whch sppoxely wce he cell dee becuse checl ecos eesselly cplee wh oe cell legh. hus we y dee

" A/D,d Equ 1 he becoes

Eo= kjpoI(3)j+1D2A+1,

Eo 500poID3 o

2)

(b)

owledge o he cell dee o expee pes he eluoo he ccl eegy Eo The hp-Jougue elocy D d he lue ohe cos I c be deeed esy whe he l se d hexue coposo e speced.

ohe sple eloshp l he cell dee o he ccleegy c be obed he ccl be dee Bsed o he wok

doe coce ee & Msu 977) deed sple exesso o d s

E P o4c '

()

whee P U d e he pessue pcle elocy d soud speed he hp-Jouue ple s he e-Hugoo codoscoss hp-Jougue deoo Equo ) y lso be we s

p D 297p DJE - (4)o - 4yy +1) c 4y(y + 1)

we he 1 coelo s used o

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19/26

GASOS EONAONS 329

ecenly ee e al (198) ae popose a more rec ln beween heao rgy a cll s a crcal ub ameer. Te ea sbase o e rquremen o a mmum surace nrgy beore a planarwa ca eol o a spercal wae wou alure Ts mmumsurac rgy soul corrspo o ara o crcal ub nd/4us n blas naon he blas energy Eo mus be suc ha when hewae has ecaye o he Chapmanougue sreng e surace energy ohe blas spere mus be a leas proporonal o nd/4. Equang reclye suace area o e blas spere o e area o ccal ube we wre

4nR nd/4,

an hence

Rc d/4

wr Rc s blas raus w s srng as cay o CapmaJougue alue (.e Rs - Re Ms - Ml were Ms s e soc Macumber) Usng srongblas heory one can easly eermn blasenergy as a uncon o blas raus an he resulan epresson s genby

E 4nYPMlI(13A/4)

(197 /16)npIDp (5)

wc s qu smla o Equaons (b) an (4) Usng e cellsze aa oysauas al (198 1983) crcal rgs a b cmpu ore common uelar mures where epermenal aa are aalable J. EElswor pae communcaon) The resuls ncae a Equaon ()base o suracergy cocp ges e bs corrspoc. gure7 sows a comparson oe pec resuls usng Equaon () w osoba by Elswor rom rc prmnal masurmns o ecrcal weg. Te crcal nrgy gure 7 as bee epresse as an

equalen carge wegh oeryl 1 g eryl s equalen o470 ) or easycomparso w Elswors epermenal aa e agreemen n genrals reasonably goo n ew o e smplcy o e moel. No epermenalaa o crcal rges a bee rpore or Car murs o prma comparso w prs prco rom Equao (5) or mosraccal suaos Equao (5) can be us o prc crcal naoenergs (or charge wegs) w que accepable accuracy

DEONABILIY LIMIS

Composo lms reer o mmum an mamu ul concnraonn wc a selsusane eonaon ca propagae rom e preous

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0

w(!U

z0j

1

.I

5

HC4CSHeC4O

0

H2

02' -EQVALN RT

Fgur 7 Comparison of crtcal-eegy data fo fuea ixtes wth the sufaeeegytheory.

dsusson s cy nngss o spcy h oposon whougn h ds o h boundry condons or h nronn n whchthe wave propagates. Thus for a planar detonation propagatig in a igid

ub o ccul coss scon h ub d us spcdsunousy wh h coposonmts Scy spkng h nu oh w so nunces h donon popgon. hus h rnd s suc oughnss us so b spcd. In gn dn ubso drn ds or o drn orc cross-scon r wroughness, etc w a have ther respectve ean and rch ts Cyndrcand sphc donons ccodngy w so h h pcutng concentratons It pps tha to be rd o h boundy pobcopy ony cyndrc or sphrc donon s cn b consdd s u s chcsc o h u. W sh un o oudscusson o h s or unconnd donons r

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GASOUS DTONATONS

Conser he case of sooh crcular ubes where only he ubemeer nee e spece n reln e lmng cmpsn ereess he prblem f an epermenlly erve peranl enn fhe lms nce very sron naors mus be use fr he near-lm

ures he rs queson o be reslve s how lon us he ube bebefore he nuence of he naor can be cnsere nelble an hewave s ruy self-susane. Eermens ncae ha he eec of henar aes n eremely lng me ecay (e.g. unres f uemeers). here re srn ncns h n cnne ues he snlehea snnn me can be nae n mures use he lms fr aven ube se f a owerful ner s use Once nae, he snleheaspnnn enan oes no apear ecay a all as prpaaes owne ue. I s nlgus an unsble rce m resnng a e

funamenal ransverse oe of nsably as ravels own he ube a hehpmn-Jugue velcy The epermens f Wlns e l (198) nmehanear enan are n emple f hs, sne he 5mameerube use s uch saller han ha requre for he roaaon ofmeanear eonaons Ye no noceabe aenuaon has been observen ver we rnge f mehne cncenrn, he enan prpges he unamenal spnnng me. he esence f such phenmenamaes eremely cul esablsh he lms epermenally. Perhapshere crrespn ceran ls where rrespecve of he srenh f he

gner, a suersnc wave a he funamenal snnn me raana abou he Chapman-ouue velocy s no ssble wever, hereess rnge f cmpsn eween he rs nse f e funmenlspnnn m n ven ue an he cmsn when s mpssle nae a suersnc combuson wave he uesn hen arses as owheher he suersonc combuson waves n hs range are ruly selfsusane eonans. ha he snglehea spnnng eonaon s helowes pssble sble me n a ven ube (hus he lm) was prose

lng g by Dve & Wagner (1960) mng hers wever he recensuy y Dna (98) perhps shes sme lgh n hs uesn f wh scnsere as ruly self-susane snleheae sn In suyn hesably f he nearl eonaons, Dnao foun ha by an a neerurbaon (such as a few uns f a wre spral nse e ue) esryhe spnnng wve, he enn wll recver n cnnue prpage s spnnng wve nly when he cmpsn f he mure crrespns he rs nse f snle-heae spnnng enan n ha parcular ubeIn her wrs lhuh he use f a srner ner can nae a snle

hea spnnn enan wave belw he cmsn when spnnngeonaon s rs bserve he wave s no sable o he ne erurbaonby he wre srals Once esrye he wve wll rns c he

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332 LEE

donaion od. h o cn sudis by a. (1983) of ubuna accaions in ubs and ansiion o donaion con h susof Donao. I as found ha ansiion o donaion is ony possib inixus boundd by h coposiion iis ha cospond o h s

ons of sing-had spin n oh ods, ansiion o donaion is nopossib in ius h h oposiion s poo han ha osponding o h ons of sing-hadd sucu. Fo h ons of a sing-hadspin, h ub cicunc cosponds o on cop c hus, hav rD hich fo a givn ub dia s h ciica vau of .Hnc h cosponding ixu coposiion can b dind Foxap fo soichioic H-ai ixus = 1. c. hus, hiniu ub dia ha coud susain a sab spinning donaionoud b D 0 c. Fo h akans h iniu dia oud b of

h od ofD 1.7 c fo soichioic coposiion. I is of ins ono ha accodng o h c siz pod by Mon a. (1983) fohan i.. c) a iniu ub dia fo ab donaionpopagaion in soichioic hanai ixus oud b of h odofa as c. hus, h sus pod by Woanski a. 981) in a -c ub shoud cospond o ovdivn ansn avs ony. hs issuppo y h ac ha hy osv sngha spnnng avs ovh ho ang of fu concnaons sud. Basd on sayconsidaions h coposiion ii can no a as b dnd

xpinayWh h c siz knon as a funcion of coposiion, h iis fo any

gvn ccua ub can no b spcd by h con rD Fo odnsona ana channs Vasiv 198) cny found ha h ccacondiion fo a sab av cosponds o a chann idh qua o .hus W = psns h ciion fo o-dinsiona canguachanns of ag aspc aios. Wha ains o b don is an xpinasudy of h condiions fo sab popagaion in ubs of abiaygois. I appas ha a unid ciion fo iis in ubs can bdivd on h bass of h iniu avcuvau concp dscussdai.

h qusion of h iis fo unconnd cyindica and sphicadonaions is uch o dicu. H h a no boundais o bconsdd, and h ans us i ihin h daid pocsss of hcua sucu In pacua, h is us b dind fo hcondions hy h cs can uipy in an unconnd av abpopagaion qus ha h avagd c sz b consan fo a gvn

ixu nc, h donaion cs us uipy in a divging avfon in accodanc ih h a a hich h sufac aa incass. hchanis o h uipicaion of h cs is in h ansin pocsss of

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GASOUS DTONAIONS

oube Mach reectons (n partcuar how the secon Mach stem sorme an eveops to orm a new ce). ven n nonreactng mea theprobem o escrbng varous tpes o trpe-shock nteractons has notbeen u resove For the ceuar-etonaton case urther competes

are ntrouce b the aton of ame fronts nto the area compexshock pattern he nteracton process s aso hgh transent an smartpes o appromatons ma not app. part rom the unamenta mtmechansm o ce reproucton for unconne etonatons t s asocut to ormuate the necessar operatona enton or the epermenta meaurements o mts or vergng waves It appears that thecurrent meto of arbtrar specfng an upper ntaton energ abovewhch the mture s renere nonetonabe s reasonabe at east rom apractca pont o vew. s such the ce sze aso enters through the

ntaton energ pecng an upper vaue or the ntaton energ s theneuvaent to specng a mamum vaue o the ce sze beon whch themxture s too nsenstve to be etonabe Athough there are other meansof specfng reasonabe mts for unconne etonaton rom the practcapont o vew such as the use o the sze o the etonaton kerne as themnmum eonabe voume the mt probem remans unamentanke to the nature o the ceuar structure

CONCUON

he ce sze has been emonstrate to be the most funamenta parametercharacterzng the namc etonaton propertes It has aso beenemonstrate that a knowege o the etoaton ce sze permts thenam arameters to be etermne reasonab we. owever there smuch room for renng the exstn reatonshps that nk to thesenamc parameters. he correaton between the ce sze an thecrtca tube ameter s present a pure emprca reatonshp Itsvat s ase on experments on the common hrocarbon ues.though the ranges o nta contons an mxture compostons stueare ar we, a the ues stue have smar knetcs o hrocarbonoaton. hus t seems worthwhe to test the correaton nother etonabe sstems such as or - mxtures where otherue moecues are nvove. so the correaton s reate to theconcept o an eectve or hronamc thcness o the etonaton wavethen the use of varous nert uents to mo the soun spee n theprouct gases shou nuence the eubratons o the transverse wave

an hence the hronamc thckness hs ma have an eect on thecorreaton trehow (98) has area emonstrate that theuse o heav argon uton has sgncant nuence on the reguart" o

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334

he euar ruure o H eonaon. urher uy o he ranon ro eren eoere a we a he ranon ro r oexe wa ue ou roe aona nh no he h ehnhe 3 orreaon. A orre heorea oe o exan h e

orreaon w ae he way o he eeoen o quanae heoreor he oher yna araeer.earn he reon o A ro he en kne an hya

roere o he xure he onon o he auhor ha rue ore"nuera ouaon w no ea o he ouon o he roe. Theeay o nuera uaon an he roaaon o woenona euar eonaon hae areay een eonrae. Theexenon o he uaon o hree-enona euar eonaon nrne oe. I howeer no ear wha aona hy an e

earne ro hee oex ouaon erany he ue o hee oeo oue he eze aa ro he a kne o he ye noeae ro he eno anon. I wou e uh er o oane-ze aa exerenay. There however an uren nee o roveoh he ehnque an auray or eze eaureen an oenae h exerene aor" n he enaon o he onan ee n an reuar aern. I a reaonh eween he e e ananoher ore eay eaure yna araeer an e ry eahe hen erha he e ze an e eerne nrey ro heeaureen o h araeer.

Thu ee ha an e reae a a unaena araeerharaerzn he eonaon oe o ouon hen we are we on heway o eeon reve heore or he oran yna araeer o raa nere. he e ze A, ke he unaena kneraeonan o he eeenary reaon an e onere a a unaenaroery o he xure. Aon uh a on o ew he heory oaeou eonaon an e a o e ery oe o oeon aer a

enuy ne he na ovee.

CKNOWGMNT

Ahouh nuerou oeaue an uen a an reen haveonrue rey or nrey o h are . nyaua Gurao Moen Y u P Thau M. Donao an Murray hou e neou or her nauae nu h Proo reone or urnn yee re no a anur I ao wh o hank Manon, D H

war Waner an worh or her oen on a ra ohe anur. I unorunae ha e oe no er her vauaeueon o e nororae no he na ra.

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Dynamic Parameters of Gaseous Detonations