HYDROGEN RELEASE FROM A HIGH-PRESSURE GH2 RESERVOIR IN CASE OF A SMALL LEAK

Transcription

1 HYDROGEN RELEASE FROM A HIGH-PRESSURE GH RESERVOIR IN CASE OF A SMALL LEAK Xiao J. Tavis J.R. Bitung W. Rsach Cnt Kalsuh P.O. Box Kalsuh Gmany DuBois Pitz Tavis GmbH Offnbach Gmany ABSTRACT High-pssu GH systms a of intst fo stoag and distibution of hydogn. Th dynamic blow-down pocss of a high-pssu GH svoi in cas of a small lak is a complx pocss involving a chain of distinct flow gims and gas stats which nds to b undstood fo safty invstigations. This pap psnts modls to pdict th hydogn concntation and vlocity fild in th vicinity of a postulatd small lak. An isntopic xpansion modl with a al gas quation of stat fo nomal hydogn is usd to calculat th tim dpndnt gas stat in th svoi and at th lak position. Th subsqunt gas xpansion to. MPa is pdictd with a zo-dimnsional modl. Th gas conditions aft xpansion sv as input to a nwly dvlopd intgal modl fo a ound f tubulnt H -jt into ambint ai. Th modl chain was valuatd by jt xpimnts with sonic hydogn lass fom diffnt svoi pssus and tmpatus. Pdictions a mad fo th blow-down of hydogn svois with and MPa initial pssu. Th volution of th pssu in th svoi and of th H mass flux at th oific a psntd in dimnsionlss fom which allows scaling to oth systm dimnsions and initial gas conditions. Computd hydogn concntations and masss in th jt a givn fo th MPa cas. A nomalizd hydogn concntation fild in th f jt is psntd which allows fo a givn lak scnaio th pdiction of th axial and adial ang of bunabl H -ai mixtus.. INTRODUCTION In a futu hydogn conomy hydogn will b gnatd fom a vaity of pimay ngy soucs lik.g. sola wind wat and nucla fission. Hydogn will sv as th sconday ngy cai which nds to b stod and distibutd accoding to tim and spac dpndnt ngy dmands fom industy commc hous holds th tanspotation scto and oths. Fo all gasous stoag and distibution systms a high hydogn pssu is attactiv bcaus this incass th ngy dnsity and ngy tanspot capacity. Th isk assssmnt fo such high pssu GH systm must addss th consquncs of unintndd lak scnaios which qui an undstanding of th hydogn distibution and mixing pocsss with ai. This pap invstigats impotant safty paamts of unignitd jts fom a small lak namly axial and adial ang of bunabl H ai mixtus total bunabl volum bunabl mass and ang of mixtus with flam acclation potntial. Ths jt poptis can b usd to dfin safty distancs and appopiat isk duction masus.. DESCRIPTION OF NUMERICAL MODELS Th dynamic blow-down pocss of a high-pssu GH svoi in cas of a small lak involvs a squnc of distinct flow gims and gas stats as shown in Fig.. Phas : Rlas of high pssu hydogn fom a svoi though a postulatd small lak; Phas : Adiabatic xpansion to atmosphic pssu;

2 Phas : F tubulnt H -jt into ambint ai fom th vitual jt oigin. vitual jt oigin H isntops high pssu svoi lak position Gasxpanauf ba (-D) gas xpansion to ba f H /ai jt Intgalmodll fü Fistahl Fig. : Squnc of flow gims in th dynamic blow-down pocss of a high-pssu GH svoi in cas of a small lak.. Dischag fom a high pssu svoi Th analysis of th hydogn dischag fom a high pssu svoi quis a al gas quation of stat fo coct modling of th thmodynamics... Hydogn Ral Gas Equation of Stat Modn quations of stat [] a oftn fomulatd using th Hlmholtz ngy as th fundamntal popty with indpndnt vaiabls of tmpatu and dnsity ( T ) = ( T ) + ( T ) α ρ α ρ α ρ wh α(t ρ) is th Hlmholtz ngy α (T ρ) is th idal gas contibution to th Hlmholtz ngy and a (T ρ) is th sidual Hlmholtz ngy which cosponds to th influnc of intmolcula focs. Thmodynamics poptis can b calculatd as divativs of th Hlmholtz ngy. In pactical applications th functional fom is xplicit in th dimnsionlss Hlmholtz ngy a using indpndnt vaiabls of dimnsionlss dnsity and tmpatu. Th fom of this quation is α ( T ρ) ( ) ( ) ( ) = α τδ = α τδ + α τδ RT wh τ =T c /T is th invs ducd tmpatu T c is th citical tmpatu δ =ρ/ρ c is th ducd dnsity and ρ c is th citical dnsity. Th idal gas Hlmholtz ngy is psntd in th computational convnint paamtizd fom N α τδ δ τ τ k kτ k= ( ) = ln +.5 ln + a + a + a ln xp ( b ) () and th sidual contibution to th Hlmholtz f ngy taks th fom l m n α τ δ δ τ δ τ δ δ τ ϕ δ β τ γ i= i= l+ i= m+ d i ti di ti pi di ti ( ) = Ni + Ni xp( ) + Ni xp + i( Di) + i( i) (4) wh th paamts and cofficints fo paahydogn and nomal hydogn a givn by Lachman []. Th advantag of this nw xplicit fomulation of th Hlmholtz f ngy is that th vaious poptis such as th pssu compssibility facto (Fig. ) nthalpy ntopy spd of sound (Fig. ) intnal ngy Gibbs ngy and isochoic hat capacity can b calculatd fom patial divativs. () ()

3 Compssibility Facto Z K isothm 5 K isothm K isothm K isothm K isothm Sound Spd c (m/s) K isothm 5 K isothm K isothm K isothm K isothm P (MPa) P (MPa) Fig. : Calculatd compssibility facto with Lachman s NIST hydogn quation of stat. Fig. : Calculatd sound spd with Lachman s NIST hydogn quation of stat... Dischag Analysis of a High Pssu Rsvoi W can wit th macoscopic mchanical ngy balanc fo a fictionlss vsibl adiabatic systm (an isntopic pocss) as th Bnoulli quation [] dv dp. + ρ = (5) Th upstam svoi vaiabls wh th vlocity is oftn assumd zo at location at any instant a considd in a quasi-stady-stat and as such th vlocity at a downstam xit location can b xpssd in tms of th intgal along a stamlin in Eq. (5) outsid th bounday lay flow to yild p p p ρ p v = d. ρ ρ p At this xit location th dischag mass flux is thn (6) G = ρ v. Th task is to find th maximum of this function that is to find th pssu P so that th mass flux is maximum which is th dfinition of th classical citical flow o chokd condition. Should th maximum occu at th lowst pssu in th systm th flow is considd subcitical. In ith cas th coct flow condition must b dtmind bfo th dischag dynamics can b computd by (7) dρ Vol = CD A MAX[ G] dt wh Vol is th svoi volum A is th bak aa and C D is th dischag cofficint. (8) Using th quation of stat fom th pvious sction a tabl of dnsitis and pssus can b computd along an isntopic lin fom th stagnation conditions to th ambint pssu. With this tabl Eq. 6 can b numically intgatd fo ach paid pssu and dnsity in th tabl fo succssivly dcasing pssus. Th maximum mass fluxs fom Eq. 6 a thn dtmind fo ach of th paid tabula pssu and dnsitis. With th compltd tabl Eq.8 is solvd with any odinay diffntial quation solv wh th pssu dnsity mass flux tabl is intpolatd fo

4 intmdiat valus. Th numical intgation of Eq. 8 continus until th svoi pssu quals th ambint valu.. Adiabatic xpansion Th a sval invstigations addssing th xpansion fom th actual nozzl to th vitual nozzl wh th pssu bcoms qual to th ambint pssu. Bich [45] studid undxpandd natual gas jts fom a convgnt nozzl and dvlopd a modl to calculat th paamts at th psudodiamt. Schf s appoach [6] to study th high pssu undxpandd hydogn jt is ntily analogous to that of Bich in which only th consvation of mass and momntum a usd to dvlop an xpssion fo th notional nozzl diamt. In this appoach th ngy quation is not solvd and th tmpatu at th vitual nozzl T v is takn as th stagnant tmpatu T. Yucil [7] conductd an analysis simila to Bich to stablish th xit paamts of th vitual nozzl. In od to dtmin th tmpatu T v and dnsity ρ v at th vitual nozzl th ngy quation was solvd. In Yucil s modl th dischag cofficint of th nozzl was assumd to b unity and th idal gas quation of stat was usd at th actual and th vitual nozzl. In ou notional xpansion modl th compssibility facto at th actual and th vitual nozzl was considd and th ngy quation was solvd to obtain th tmpatu at th vitual nozzl. It is assumd that th is no mass flux though th bounday of th jt in th xpansion pocss and that th notional xpansion pocss is adiabatic. Thn a st of quations conncting th gas stat at th actual xit nozzl to th vitual jt oigin v can b fomulatd fom th basic consvation laws: ρ( πd /4) v = ρv( πdv /4) vv P( πd /4) + ρ( πd /4) v = Pv( πd /4) + ρv( πdv /4) vv (9) CPT + v = CPvTv + vv ZρT ZvρvTv = P Pv wh Z is th compssibility facto at th actual oific. P v T v ρ v v v D v C Pv and Z v a th pssu tmpatu dnsity vlocity diamt spcific hat capacity and compssibility facto at th vitual nozzl spctivly. Th Mach numb at th actual nozzl xit M is dfind as: v M = c wh c is th local sound spd: c = P γ. ρ Solving th consvation quations (9) yilds: () () w vv = v + γ M w ( γ w ) ( γ ) w + Tv T = γw γmw Zρ γ Mw ρv = Zv γmw( γ + w ) ( γ )( w ) Zv γmw( γ + w ) ( γ )( w ) Dv = D Z γ M w + γ( w ) () 4

5 wh w =P /P v =P /P a is th atio of pssus at th actual nozzl and th vitual nozzl and γ is th spcific hat atio of th gas. Whn th compssibility factos Z Z v a qual to on Eq. is idntical to Yucil s modl. Howv fo th high gas pssus of intst h al gas ffcts nd to b takn into account (Fig. ). Th gas xpands to th ambint pssu at th vitual nozzl. It should b notd that th notional xpansion dos not xist in th physical sns. Expimnts and numical simulations [4] hav shown that a vy complicatd flow stuctu xists in th xpansion gion clos to th nozzl. Th aim of th psnt study is not th solution of this xpansion gion but ath th ngining modl fo th fa-fild downstam of th xit nozzl. Eq. povids a consistnt link btwn th dischag modl (Sction.) and th intgal jt modl (Sction.) in th sns that all th sub-modls only ly on mass ngy and momntum consvation. Th gas stat of th vitual oigin divd by Eq. is not ncssaily qual to that of Bich s psudo-diamt [45] wh th tmpatu stos to th stagnation tmpatu in th svoi. Low tmpatu and high spd will b obtaind at th jt vitual oigin with Eq. and th location of this vitual oigin is clos to th actual oific than Bich s psudo-diamt. In th intgal modl s calculation vy apid vlocity dcay and tmpatu covy will b sn in th na fild (sn in Sction ) which is consistnt with Bich s obsvations. Th sults of this adiabatic xpansion modl sv as input to an intgal modl fo a ound f tubulnt H -jt into ambint ai.. Intgal modl fo ound tubulnt jt An intgal modl has bn dvlopd fo th dsciption of hoizontal buoyant jts with abitay dnsity diffncs btwn th jt and th ambint. This non-boussinsq modl can also b usd fo momntum dominatd flows. This sction outlins th modl assumptions and govning quations. Th jt fomd fom a ound oific dischags into th unboundd stagnant unifom ambint as shown in Fig. 4. Th dnsity of th ambint atmosph is ρ a. Th axis of th jt is takn as a paamtical coodinat s and th coodinat n is takn to b nomal to th axis s. θ is th angl of th s-axis with th hoizontal diction. Th initial dnsity vlocity and adius in th oific a ρ v u v v. Th dnsity and vlocity along th s-axis a ρ s u s. Th gnal assumptions mad fo th intgal modl a as follows: ) Th flow is fully tubulnt which mans th is no Rynolds numb dpndnc. ) Th pssu acoss th flow is assumd to b unifom and qual to th ambint pssu outsid of th flow bounday. ) Th longitudinal tubulnt tanspot is small compad with latitudinal convctiv tanspot. 4) Th adial vlocity concntation and tmpatu dficincy pofils a assumd to hav Gaussian distibution: ss Fig. 4: Hoizontal buoyant jt dischag fom a ound oific into th unstatifid ambint. 5

6 u = u s / b wh b is a chaactistic adial distanc fom th s-axis. () Th dnsity pofil with spct to th ambint dnsity ρ a is assumd to b of Gaussian shap: ρ ρ ρ ρ = a a s ρa ρa /( λb) wh λb is th chaactistic lngth of th pofils; λ is th tubulnt Schmidt numb. In this study λ is takn as.. Th tmpatu pofil is also assumd to hav a Gaussian distibution: (4) T a T Ta Ts /( λb) =. Ta Ta 5) Th ntainmnt lation fo th ound jt is givn by th quation: (5) Em = π bρau = πβ j pbρaus. (6) wh E m is th local mass ntainmnt at u is th local ntainmnt vlocity u s is th chaactistic vlocity along th s-axis ρ s is th local dnsity along th s-axis ρ a is th ambint dnsity and β j-p is th local mass ntainmnt cofficint. Th local ntainmnt cofficint fo th ound jt is assumd as [89] : Ri j p ρ s β j p= β j+ ( βp β j) sin θ (7) Ri p ρa wh β j =.55 fo th pu jts and β p =.85 fo th pu plum. W should not that th valu of β j was obtaind fom low vlocity flows. Fo flows with high vlocity β j may vay. Ri j-p is th local Richadson numb dfind as [8]: / mφ Ri j p= 5/4 mo wh th mass flux m is m = udd = u b + th momntum flux mo is π ρ πλ ρ s ϕ π s ρa λ ρa π ρ π πλ ρ s ϕ s ρa λ ρa mo = u dd = u b. + and th local buoyancy flux φ is (8) (9) () π ( ρa ρ) πλ ρ s φ = guddϕ = gu sb () ρa + λ ρa wh Ri p is th Richadson numb in th pu plum gion dfind as: Ri p = ( + λ ) 5 π β p. () 6

7 Th basic govning quations nglcting th dissipation and tubulnt tanspot in compaison with th man flow consist of mass momntum ngy and concntation consvation quations: i( ρu) = ( ρuui ) = x ( ρuu j ) =Δρg () y i( ρuh) = i( ρuφm ) = wh h is th snsibl nthalpy Ф m is th mass concntation and Δρ is th dnsity diffnc of th ambint and th vitual jt oific. Whn th divgnc thom is applid th basic govning quations bcom: d π ( udd ) j pb aus Em ds ρ ϕ = πβ ρ = d π ( ρuu cos θ) ddϕ = ds d π π ( ρuu sin θ ) ddϕ = ( ρ ) a ρ gddϕ ds d π ρu( C ) PT CPaTa ddϕ ds = (4) d π ( ρφ u m) ddϕ= ds dx = cosθ ds dy =sin θ ds A systm of fist od odinay diffntial quations is thus obtaind aft th intgation of Eq. 4 wh th svn unknowns a th dnsity ρ s vlocity u s tmpatu T s along th tajctoy th chaactistic jt width b th local angl of th jt with spct to th hoizontal axis θ and th local coodinats of th jt tajctoy x y. With initial conditions th systm of odinay diffntial quations was solvd with a 4 th od Runga-Kutta mthod to obtain th buoyant jt tajctoy th vlocity th dnsity th tmpatu and th concntation.. MODEL VALIDATIONS Th chain of modls includs th isntopic dischag modl th adiabatic xpansion modl to. MPa and th non-boussinsq intgal modl. Rsults of ths modls w compad to jt xpimnts caid out in a spcial FZK facility. Hydogn was lasd with th stady mass flux of. g/s fom oifics with diamts of mm and mm. Fou xpimnts with vaious initial pssus and tmpatus w analyzd (Tabl ). Th gas stat in th svoi is givn in columns to 4. Th pssu P is th thotical pssu which is calculatd by th modl in Sction. to obtain a mass flow at of. g/s. Th sults of th dischag and th adiabatic xpansion modl a shown in Tabl fo th actual oific and th vitual jt oigin. Th paamts at th vitual jt oigin svd as input fo th intgal modl. Th xpimnts w pfomd und stady stat conditions with sonic flow vlocity at th nozzl. Fig. 5 compas masud and calculatd hydogn concntation dcays fo th fou tst cass using th oific diamt D as scaling paamt fo th distanc S fom th oific. All xpimntal data 7

8 and th calculatd sults of th intgal modl collaps whn th scaling of th distanc includs th atio of th dnsity in th svoi ρ and th ambint atmosph ρ a accoding to Dq = D ρ / ρa (5) wh D q is th scald oific diamt (Fig. 6). Not that this scaling also covs th significant tmpatu vaiation in th initial jt conditions (8 K and 98 K). Fig. 7 compas masud and pdictd vlocity along th jt tajctoy U s. Th vlocity dclats apidly in th na fild du to th ai ntainmnt into th jt. At th distanc S/D = th vlocity has dcasd to about % of th initial vlocity and th volum faction of hydogn in th jt cnt is about.5%. This indicats that th jt is wll mixd and buoyancy has littl ffct on th flow in th low vlocity gion. Fig. 8 compas PIV masud adial vlocity pofils with pdictions of th intgal modl fo cas in Tabl. Th pofils cospond to axial distancs S/D = and 5 (top to bottom in th lgnd). Th vy good agmnt suppots th assumption of Gaussian distibutions in th intgal modl. Fig. 9 and Fig. dmonstat th apid dnsity and tmpatu covy to th ambint conditions du to th ai ntainmnt fo th fou cass spcifid in Tabl.. It should b notd that in ths cass th ntainmnt cofficint β j was slightly incasd fom.55 to.7 in th intgal modl to achiv th bst agmnt with th xpimntal data. Th valu of β j =.55 was obtaind fom xpimnts with low vlocitis and small dnsity atios [89]. It sms asonabl that high vlocity and tubulnt intnsity will induc a stong mass ntainmnt. Th non-boussinsq intgal modl was also compad to litatu data fo slow pu jts (ai into ai) and fo slow wakly buoyant jts (N into ai). Excllnt agmnt was found with β j =.7 which confims th pdictiv capabilitis of th dvlopd non-boussinsq intgal modl. Tabl. Rsvoi conditions of th und-xpandd hydogn jt xpimnts and computd gas stats fo th actual oific and th vitual jt oigin aft xpansion to. MPa. Cass P (MPa) Rsvoi Actual oific Vitual jt oigin T (K) ρ (kg/m ) D (mm) P (MPa) T (K) ρ (kg/m ) v (m/s) D v (mm) ρ v (kg/m ) T v (K) v v (m/s) BLOW-DOWN OF A HIGH-PRESSURE H GAS RESERVOIR In this sction th abov dscibd modls fo th flow conditions at th bak location th notional jt xpansion to. MPa and th ound f jt into ambint atmosph a applid to th simulation of a small lak in a high-pssu GH systm. Th slctd systm dimnsions a a pip lngth of m a pip diamt of cm and a lak diamt of cm. Th total systm volum is 7.8 m. Th initial tmpatu is K and th diffnt initial pssus a analyzd: and MPa. Fig. shows th assumd isntopic xpansion path fo ths cass basd on th abov dscibd al-gas quation of stat. Two-phas conditions a not ncountd. Th mthodology dscibd in Sction. lads to th mass fluxs shown in Fig.. Th dimnsionlss tim t + mass flux G + and pssu P + a dfind as 8

9 4 cas (data FzK 7) cas (data FzK 7) cas (data FzK 7) cas4 (data FzK 7) cas (Intgal modl) cas (Intgal modl) cas (Intgal modl) cas4 (Intgal modl) 4% cas (data FzK 7) cas (data FzK 7) cas (data FzK 7) cas4 (data FzK 7) cas (Intgal modl) cas (Intgal modl) cas (Intgal modl) cas4 (Intgal modl) /C H /C H (S+S )/D (S+S )/D q Fig. 5: Masud and calculatd H concntation dcay along th jt axis. Fig. 6: H concntation dcay along th jt tajctoy (scald by D q ). data FZK 7 intgal modl 5 data FzK 7 Intgal modl 5 U s (m/s) R/D S/D Vlocity (m/s) Fig. 7: Vlocity dcay along th jt tajctoy (cas in Tabl ). Fig. 8: Compaison of masud and calculatd adial vlocity pofils (cas in Tabl ) T (K) 5 Dnsity (kg/m ).6.4 cas (intgal modl) 5 cas (intgal modl) cas (intgal modl) cas4 (intgal modl) 5 5. cas (intgal modl) cas (intgal modl) cas (intgal modl) cas4 (intgal modl) S/D S/D Fig. 9: Tmpatu covy along th jt tajctoy. Fig. : Dnsity covy along th jt tajctoy. 9

10 t + = t t cha G G + = Gcha and P P + = P wh th chaactistic quantitis a: (6) (7) (8) Vol tcha = (9) A c and () Gcha = ρ c. H Vol is th svoi volum A is th bak aa and c is th initial sound spd in th svoi. This scaling povids a clos agmnt of th th analyzd initial pssus. Fig. allows scaling of th computd dischag mass fluxs to high-pssu systms with oth volums bak aas initial pssus and initial tmpatus fo t + up to about 5. Fig. dmonstats that th usd scaling is not appopiat fo t + >5. Th stas in Fig. psnt th tims wh th pssu atio falls blow.9 and th flow bcoms sub-citical. Fig. 4 shows th dimnsionlss pssu dcay in th tank duing th dischag. Using Eq. 6 this plot allows th stimation of th pssu dcay in oth high pssu GH systms. Not that th valu t + =5 mntiond abov cosponds to a vy low maining pssu. Tabl summaizs th initial conditions and sulting dischag tims fo th psnt svoi poblm. Tabl psnts dtaild sults fo th MPa cas. Th gas conditions in th svoi and at th lak position a givn fo fiv tim points ( s 5 s s s 4 s) aft bgin of th dischag. Tim (s) Initial pssu (MPa) Tabl : Initial conditions and sulting calculatd dischag tims fo th th diffnt initial pssus in th GH svoi. Initial dnsity (kg/m ) Initial sound spd (m/s) Dischag tim (s) P (MPa) Tabl : Computd gas stats fo th MPa hydogn blowdown fo fiv diffnt tims aft bgin of th dischag. Rsvoi Actual oific Vitual jt oigin T (K) ρ (kg/m) D (mm) P (MPa T (K) ρ (kg/m) v (m/s) D v (mm) T v (K) ρ v (kg/m) v v (m/s) Th thid pat of Tabl shows th sults of th notional adiabatic xpansion modl dscibd in Sction.. Ths gas stats sv as input to th intgal f jt modl dscibd in Sction..

11 .6 Tmpatu (K) Satuation. MPa MPa MPa MPa MPa MPa xpansion MPa xpansion MPa xpansion Entopy (kj/(kg*k)) Dimnsionlss Mass Flux G + = G/G cha Dimnsionlss Tim t + = t/t cha MPa dischag MPa dischag MPa dischag Fig. : Isntopic xpansion pocsss fo high-pssu hydogn dischag cass. Fig. : Calculatd dimnsionlss hydogn mass flux fo th th invstigatd dischag cass. Dimnsionlss Mass Flux G + = G/G cha. MPa dischag MPa dischag MPa dischag sonic-subsonic tansition. E- Dimnsionlss Pssu P + = P/P MPa dischag MPa dischag MPa dischag E Dimnsionlss Tim t + = t/t cha Dimnsionlss Tim t + = t/t cha Fig. : Calculatd dimnsionlss hydogn mass flux and th sonic-subsonic tansition. Fig. 4: Calculatd dimnsionlss pssu in th tank fo th th invstigatd dischag cass. Th intgal modl fo a ound f jt pdicts th vlocity tmpatu and hydogn concntation fild downstam fom th vitual jt oigin. Fo safty invstigations th hydogn distibution in th jt is of main intst. Fig. 5 displays th computd hydogn contous (4 to 75 vol % H in ai). A hoizontal las diction was assumd in th calculation. Th maximum axial distanc of bunabl H -ai mixtus (> 4 vol % H ) falls fom about 64 m at s to about 7 m at 4 s and th cosponding maximum jt adius dcass fom 7. to m. All concntation contous in Fig. 5 a slf-simila with a atio of maximum adial to maximum axial distanc of.. Th bunabl volums of H -ai mixtu at th fiv tims a 65 m 59 m m 8 m and m spctivly. Th cosponding hydogn masss in th bunabl pat of th jt a and. kg. Th hoizontally ointd jt is puly momntum dominatd which mans th is no visibl ffct of buoyancy on th hoizontal jt tajctoy. Th dpictd hydogn concntation fild is thfo indpndnt of th las diction. Fig. 5 dmonstats that in ound unignitd jts fom high pssu systms with sonic outflow into a f nvionmnt th ai ntainmnt is sufficint to dilut th lasd hydogn down to unbunabl mixtus within th jt flow fild. No plum with bunabl mixtus will main futh downstam; an additional combustion isk in th fa fild is xcludd. Th spac gion with hydogn concntations abov vol % is of spcial intst bcaus ignition in this gion lads to a stabl

12 tubulnt diffusion flam which popagats back towads to th hydogn lak. Ignitions at low concntations only lad to a tansint local bun which is convctd downstam and qunchs in gions with lss than 4 vol% H [5]. It is wll known that fo th momntum dominatd subsonic incompssibl tubulnt f jts th concntation dcay along th jt cntlin complis with a hypbolic law [] : C.5 KD ρ a s = S S ρ + wh C s is th cntlin concntation K is th slop which givs th dcay constant and S is th vitual oigin displacmnt. Bich s study [45] has shown that this concntation dcay law can b applid to undxpandd jts with chokd-flow lass. In Houf and Schf s wok [] Eq. was also usd to calculat th concntation dcay of high pssu supcitical chokd-flow lass of hydogn. Th intgal jt modl dscibd in Sction. and th FZK xpimntal data giv th following lation fo th nomalizd cntlin concntation dcay of th hydogn jt as shown in Fig. 6: () Dq CsH 7.6. S + S Th nomalizd diamt D q is dfind as: ().5 Dq D ρ =. ρ a Th vitual oigin displacmnt S will b futh discussd in Sction 5. If w tak S = D th following non-dimnsional axial distancs S fom th nozzl a obtaind fo - th low flammability limit: () ( ) S = D q 4%H th gion of stabl ignition: ( ) S = D q %H 78 - th upp flammability limit: (4) (5) ( ) S D q 75%H = 4. (6) Th axial distancs in Fig. 5 fo th 4% % and 75% H contous ag wll with ths colations. Eqs. (-6) can b applid to oth f ound high-pssu jts to stimat th axial ang of bunabl mixtus. Th cosponding maximum adial xtnsions of bunabl mixtus R ad a appoximatly Rad.S (7) Fo any givn tim in Fig. 5 th axial distancs S a popotional to ( ρ ).5 ρ and th bunabl a volums a popotional to ( ρ ).5 ρ du to th slf-simila stuctu of th jt. Fig. 6 shows th a nomalizd hydogn concntation contous. Whn scald by D q all th contous in Fig. 5 collaps closly to th contous in Fig. 6 which is usful to stimat th maximum bunabl adius and lngth of an undxpandd hydogn jt.

13 4 R ad (m) s - -4 S (m) 4 R ad (m) R ad (m) R ad (m) S (m) S (m) s s s H Conc. vol% 4% 5% 6% % 5% % % 5% 75% S (m) 4 R ad (m) s - -4 S (m) Fig. 5: Computd hydogn concntation fild of f ound jts fom a MPa hydogn svoi fo diffnt tims aft dischag (svoi conditions in Tabl ). R ad /D q S/D q H Conc. vol% 4% 5% 6% % 5% % % 5% 75% Fig. 6: Nomalizd hydogn concntation contous of a f hydogn jt with sonic dischag (scald by D q ). 5. MODELING UNCERTAINTIES Most of th publishd intgal modls basd on Gaussian distibutions and th Boussinsq appoximation w validatd by xpimnts with low jt xit vlocitis and small dnsity vaiations. In ou intgal modl th Boussinsq appoximation was not usd so that th modl is valid fo cass with lag dnsity vaiations []. This modl can b usd fo buoyant jts which a influncd by both th momntum and th buoyancy as wll as undxpandd jts which a dominatd by th momntum. Howv th mass ntainmnt cofficint β j usd in th intgal modl was obtaind und th xpimntal conditions with low vlocity and dnsity vaiation. In th simulation of th und-xpandd hydogn jt xpimnt in Sction.4 it was found that th ntainmnt cofficint β j fo th pu jt incass fom.55 to.7 to obtain th bst agmnt with th xpimntal data. Although it sms asonabl that high vlocity and tubulnt intnsity will intoduc a stong

14 mass ntainmnt th ffct of th high vlocity and lag dnsity vaiation on th ntainmnt cofficint nds futh study. Bfo th Gaussian pofils a stablishd th initial unshad pofils undgo changs in fom of piphally gowing axis symmtic mixing lays. This initial gion is calld th zon of flow stablishmnt (ZOFE) which lacks slf-similaity. Th tansition in this gion is complx and apid. Fo th low spd flow th distanc xtnds up to 5~ D fom th oific [9]. In Xu s numical simulation of und-xpandd hydogn jt [4] D fom th al oific is found to b a citical location which maks th nd of th shock stuctu and th na fild xpansion of th jt and th location of th Mach disk is oughly at D with a diamt at 5.6 D. In ou study th intgal modl s vitual oigin displacmnt S is 5D fo th subsonic flow. Fo sonic o supsonic flow S is about 5~D dpnding on th pssu atio btwn th svoi and th ambint. Futh study of th vitual oigin displacmnt fo undxpandd jts is dsiabl. Howv th fa fild pdictions mad in this study will not b affctd significantly bcaus th bunabl hydogn jt xtnds to a long distanc away fom th oific. A futh issu in th non-boussinsq intgal modl is to vify th hydogn volum faction at th location wh th slf-simila flow is stablishd which svs as input to th modl. In th Boussinsq-basd intgal modl sinc th dnsity diffnc btwn th jt and th ambint can b nglctd th volum faction at this location can b assumd as %. Howv lag dnsity vaiation btwn th jt and th ambint might lad to a mass faction blow % du to th mass ntainmnt in this tansition gion. Xu s numical simulation [4] fo an und-xpandd hydogn jt into ai indicats that th is no ai ntainmnt pio to th Mach disk and at th location D th H volum faction is naly unity. In th psnt intgal modl analysis th initial volum faction of hydogn at th vitual oigin is assumd unity. Anoth unctainty is th dischag cofficint which is cas snsitiv. It dpnds on th systm pssu tmpatu and bak paamts lik shap siz and wall thicknss. It psnts an impotant unctainty fo any accidnt simulation and som spaat stimation of dischag cofficint should b attmptd. W compad th masud and th thotical mass flow ats in ou cass and th is only % dviation btwn th masud and thotical. In th study w assum that th dischag cofficint is. which is consvativ fo th safty analysis. 6. CONCLUDING REMARKS A chain of ngining modls fo hydogn jt fom a small lak of a high pssu piplin has bn dvlopd and vifid by th FZK masud concntation and vlocity dcay along th cntlin of undxpandd hydogn jt. Th nwst al gas quation of stat was applid to calculat th dischag of high pssu hydogn though a postulatd small lak. An adiabatic xpansion modl considing th ngy quation and th compssibility facto was usd to obtain th paamts at th vitual oigin as th input fo th intgal modl. A non-boussinsq intgal modl with an ntainmnt cofficint adjustd to sonic H -jt xpimnts was dvlopd to calculat th concntation vlocity and tmpatu vaiation along th cntlin th bunabl lngth width and volum fo th safty analysis. Th divd non-dimnsional sults can b scald to oth high-pssu systms using th givn lations. ACKNOWLEDGEMENT Pat of this wok was pfomd within th ICEFUEL pojct ( which is fundd by th Gman BMBF ministy. Th authos a indbtd to Jacob Lachman fo his xtaodinay hlp and suppot with th al gas quation of stat. REFERENCES. J. Lachman Fundamntal Equations of Stat fo Paahydogn Nomal Hydogn and Othohydogn Mast of Scinc Thsis Univsity of Idaho 4

15 . J.W. Lachman R.T. Jacobson E.W. Lmmon Fundamntal Equations of Stat of Paahydogn Nomal Hydogn and Othohydogn to b publishd in J. Phys. Chm. Rf. Data 9.. R.B. Bid W.E. Stwat E.N. Lightfoot Tanspot Phnomna nd Ed. pp A.D. Bich D.R. Bown M.G. Dodson F. Swaffild Th Stuctu and Concntation Dcay of High Pssu Jts of Natual Gas Combustion Scinc and Tchnology Vol. 6 pp A.D. Bich D.J. Hughs F. Waffild Vlocity Dcay of High Pssu Jts Combustion Scinc and Tchnology Vol. 5 pp Schf R. W. Houf W. G. Williams T. C. Boun B. & Colton J. (7). Chaactization of high-pssu und-xpandd hydogn-jt flams. Intnational Jounal of Hydogn Engy () K. Bülnt Yücil M. Volkan Ötügn Scaling Paamts fo Undxpandd Supsonic Jts Physics of Fluids Vol. 4 No. pp Dcmb 8. W. Rodi Tubulnt buoyant jts and plums vol. 6HMT Th Scinc & Applications of Hat and Mass Tansf Pgamon Pss G.H. Jika Intgal Modl fo Tubulnt Buoyant Jts in Unboundd Statifid Flows. Pat I Singl Round Jt Envionmntal Fluid Mchanics 4: G.H. Jika Intgal Modl fo Tubulnt Buoyant Jts in Unboundd Statifid Flows Pat Plan Jt Dynamics Rsulting fom Multipot Diffus Jts Envionmntal Fluid Mchanics 6: 4-6. C. Chn W. Rodi Vtical Tubulnt Buoyant Jts A Rviw of Expimntal Data Pgamon Pss 98. W.G. Houf and R.W. Schf Pdicting Radiativ Hat Fluxs and Flammability Envlops fom Unintndd Rlass of Hydogn Intnational Jounal of Hydogn Engy Vol. pp. 6-5 Januay 7.. J. Xiao J. Tavis W. Bitung Non-Boussinsq Intgal Modl fo Hoizontal Tubulnt Stongly Buoyant Plan Jts Pocdings of th 6th Intnational Confnc on Nucla Engining Olando Floida USA May B. Xu J. Zhang J. Wn S. Dmbl J. Kawatzki Numical study of a highly und-xpandd hydogn jt Intnational Confnc on hydogn Safty Sp. 8-5 Pisa Italy 5. A. Vs G. Stn M. Schwall N. Kotchouko M. Rottnck G. Fast M. Kuzntsov W. Bitung Stuctu and Flam Popagation Rgims in Tubulnt Hydogn Jts. Pocdings of 7th Intnational Symposium on Hazads Pvntion and Mitigation of Industial Explosions Saint-Ptsbug Russia July 7-8 Vol. pp