Numerical Simulation of Explosive Combustion Following Ignition of a Fuel Vapor Cloud

Transcription

1 Numercal Smulaton of Explosve Combuston Followng Ignton of a Fuel Vapor Cloud ZHIXIN HU and ARNAUD TROUVE Department of Fre Protecton Engneerng Unversty of Maryland College Park, Maryland 074, USA ABSTRACT The objectve of the present study s to examne the feasblty of a Large Eddy Smulaton (LES) approach combned wth a partally-premxed combuston (PPC) model for smulatons of transent combuston events occurrng n fuel vapor clouds. The PPC formulaton uses: a premxed combuston sub-model based on the fltered reacton progress varable approach; a non-premxed combuston sub-model based on the Eddy Dsspaton Concept; and a premxed/non-premxed combuston couplng nterface based on the concept of a flame ndex. The PPC model s mplemented nto the Fre Dynamcs Smulator (FDS) developed by the Natonal Insttute of Standards and Technology, USA. Because FDS uses an ncompressble flow solver, the present study s restrcted to combuston scenaros featurng low Mach numbers (e.g., scenaros wth no blast wave). The enhanced FDS modelng capablty s evaluated by detaled comparsons wth an expermental database prevously developed by FM Global Research, USA. The test confguraton corresponds to controlled gnton followed by explosve combuston n an enclosure flled wth vertcally-stratfed mxtures of propane n ar, both wth and wthout ventng, and wth and wthout obstacles. All studed cases develop sgnfcant compartment over-pressures; these pressurzed combuston cases present a partcular challenge to the bulk pressure algorthm n FDS whch has robustness and accuracy ssues, n partcular n vented confguratons. The FDS bulk pressure algorthm s modfed n the present study n order to allow detaled comparsons between measured and smulated pressure tme hstores. Overall, the comparson between numercal results and expermental data ranges from far to good, and confrms the feasblty of a LES treatment of explosve combuston. KEYWORDS: fre modelng, CFD, exploson, deflagraton, partally premxed combuston. INTRODUCTION The present study s motvated by fre and exploson safety questons followng the accdental release and possble subsequent gnton of vaporzed fuel n ambent ar [1-5]. Such questons are asked when examnng a number of real-world fre hazards, for nstance spllng/leakng fuel tank or fuel ppe scenaros, mnng accdents, and backdraft scenaros. We assume n the followng that the fuel release takes place n ambent ar, and that there s a sgnfcant delay between the start of the fuel buld-up and the gnton event, thereby allowng the formaton of a szeable fuel vapor cloud pror to combuston. Dependng on the velocty of the fuel-ar mxng process, the composton of the bulk of the fuel vapor cloud wll be ultralean (.e., below the lower fuel-ar flammablty lmt) n the case of fast mxng, ultra-rch (.e., above the upper flammablty lmt) n the case of slow mxng (Fg. 1), or flammable (.e., wthn the flammablty lmts) n the ntermedate case (Fg. ). The fast mxng case corresponds to a desrable safe dsperson scenaro n whch there s no fre or exploson hazard; we focus n the present study on the slow mxng and ntermedate cases that correspond to a hazard (Fgs. 1a-a). We further assume that gnton takes place at some flammable locaton n the fuel vapor cloud (Fgs. 1b- b). Followng gnton, the combuston wll proceed ntally as a thn deflagraton or detonaton wave that propagates across the flammable portons of the fuel vapor cloud. We focus n the followng on the deflagraton scenaro, n whch the premxed flame propagates at subsonc speeds and pressure remans quas-unform across the combuston zone (pressure may change wth tme but not wth spatal locaton). Even wth ths lmted scope, the combuston dynamcs reman qute complex snce they depend strongly on the state of the fuel-ar mxng feld found at gnton tme. In the case of an ultra-rch fuel vapor cloud, combuston corresponds predomnantly to a dffuson burnng mode (Fg. 1c); n the case of a flammable fuel vapor cloud, combuston ncludes an ntense premxed burnng mode (Fg. c). In cases wth FIRE SAFETY SCIENCE PROCEEDINGS OF THE NINTH INTERNATIONAL SYMPOSIUM, pp COPYRIGHT 008 INTERNATIONAL ASSOCIATION FOR FIRE SAFETY SCIENCE / DOI: /IAFSS.FSS

2 Ultra -lean Ignton Dffuson Flame Ultra-rch (a) Fuel Ar (b) Fuel (c) Fuel Fg. 1. Problem confguraton correspondng to (a) the formaton of a large ultra-rch fuel vapor cloud, followed by (b) gnton and (c) dffuson burnng. Ultra -lean Ignton Premxed Flame Flammable Ultra -rch (a) Fuel Ar (b) Fuel (c) Fuel Fg.. Problem confguraton correspondng to (a) the formaton of a large flammable fuel vapor cloud, followed by (b) gnton and (c) deflagraton. sgnfcant premxed burnng, one may also dfferentate between pure premxed and partally-premxed burnng modes. Pure premxed burnng modes are observed when the bulk of the fuel vapor cloud s flammable fuel-lean, whle partally-premxed burnng modes are observed when some portons of the fuel vapor cloud are flammable fuel-rch (n that case, the combuston starts as a fuel-rch deflagraton wave and propagates across the flammable regon whle leavng excess fuel n the post-deflagraton gases; the resdual fuel may then subsequently mx wth ambent ar and burn n a dffuson flame mode). Our objectve n the present study s to examne the feasblty of a Computatonal Flud Dynamcs (CFD) approach to smulate the range of scenaros llustrated n Fgs. 1-. The subject of accdental combuston n fuel vapor clouds has receved sgnfcant nterest n the scentfc lterature. Prevous CFD modelng studes typcally belong to one of the followng two categores: studes n whch flammable condtons are assumed across the bulk of the fuel vapor cloud, and combuston s descrbed as premxed [6-11]; and studes n whch ultra-rch condtons are assumed and combuston s descrbed as non-premxed [1-16]. Clearly the gnton/deflagraton/dffuson-flame scenaros presented n Fgs. 1 and requre a more general formulaton n whch combuston can be descrbed as both, smultaneously or sequentally, premxed and non-premxed. The present study consders such a formulaton and focuses on specfc ssues resultng from the couplng of premxed and non-premxed turbulent flame models. Ths couplng has receved growng nterest n recent years, prmarly drven by the need to adapt combuston formulatons for a CFD treatment of lfted turbulent dffuson flames [17-19]. The burnng regme n the stablzaton regon of lfted dffuson flames s usually referred to as partally-premxed combuston (PPC). The present study may be vewed as a contnuaton of the PPC modelng work n Refs. [18-19]. The developments and tests presented heren are made n the context of a CFD solver called the Fre Dynamcs Smulator (FDS). FDS s developed by the Natonal Insttute of Standards and Technology (NIST), USA, and s orented towards fre applcatons; t uses a Large Eddy Smulaton (LES) approach for turbulence (based on the classcal Smagornsky model) and a fast chemstry model for non-premxed combuston (based on the Eddy Dsspaton Concept) [0-1]. A premxed combuston modelng capablty has also been recently ncorporated nto FDS [-5]. The present study s a contnuaton of the work presented n Refs. [-5], an extenson to FDS Verson 5 (earler developments had been made n the context of FDS Verson 4), as well as a new valdaton study that uses an expermental database prevously developed by FM Global Research, USA. 1056

3 MODELING OF PARTIALLY-PREMIXED COMBUSTION Deflagraton Modelng We start from the classcal descrpton of premxed combuston based on the concept of a reacton progress varable c: c = 0 n the fresh reactants, c = 1 n the burnt products, and the flame s the regon where c goes from 0 to 1 (see Refs. [-5] for addtonal detals and entres to the deflagraton modelng lterature). The c-framework s general and flexble, and t has been prevously adapted to a LES treatment of propagatng turbulent flames. The treatment s based on a transport equaton for the LES-fltered reacton progress varable c. We adopt n the followng the closure models of Refs. [6-7] and wrte: ν t ρuslδc c 6 c (1 c ( ρc ) + ( ρu c ) = (( ρ + ) ) + 4ρusLΞ ) + ωgn (1) t Sc 16 6 / π π Δ t c where ρ s the mass densty, u the x -component of the flow velocty vector, ν t the turbulent eddydffusvty, Sc t a turbulent Schmdt number, ρ u the unburnt gas mass densty, s L the lamnar flame speed, Δ c the LES c-flter sze, Ξ the subgrd-scale flame wrnklng factor, ω gn an extra source term, and where the over-bar (tlde) symbol denotes straght (Favre-weghted) LES-fltered quanttes. The frst term on the rght-hand-sde of Eq. (1) represents subgrd-scale convectve transport and molecular dffuson transport of c; the second term represents producton of c due to chemcal reacton; the last term represents gnton. The subgrd-scale convectve transport term has been expressed assumng gradent-transport and usng the classcal turbulent eddy vscosty concept. The molecular dffuson term has been expressed accordng to the realzablty requrement that under lamnar flow condtons, the flame propagates at the lamnar flame speed s L [,6-7]. The chemcal reacton term ω c has been expressed usng a classcal flamelet closure expresson. Whle elaborate closure model expressons are avalable n the scentfc lterature to descrbe the subgrd-scale flame wrnklng factor, we choose n the present study to treat Ξ as a model coeffcent (see the results Secton). The correspondng expresson for the LES-fltered fuel mass reacton rate (n unts of kg/s/m 3 ) s: 6 c (1 c ) m eq ω p = (4ρu slξ + ωgn ) ( YF YF ) () π Δ c m eq m where Y F s the value of the fuel mass fracton n the unburnt gas, and Y F ts value n the burnt gas. Y F s an nput quantty to the combuston problem that characterzes the pre-combuston state of the reactve eq mxture; Y F s a quantty that characterzes the post-premxed-flame state. Upstream of the deflagraton front, c = 0 and the mxture composton corresponds to the pure mxng soluton, m YF = YF (Z ), wth Z the LES-fltered mxture fracton, whereas downstream of the deflagraton front, c = 1 and the mxture eq composton may be approxmated by the classcal Burke-Schumann equlbrum soluton, YF = YF (Z ). m eq m eq We have: ( YF Y ) = Z f Z Z st ; and ( YF Y ) = (1 Z ) Z st /(1 Z st ), f Z Z st. F F The fltered-c model n Eqs. (1)-() has prevously been mplemented nto FDS and tested n confguratons correspondng to homogeneous, lamnar or turbulent deflagratons []. Ref. [] presents a detaled dscusson of the grd resoluton requrement of the model formulaton n Eqs. (1)-(), and of the relatonshp between the LES c-flter sze Δ c and the computatonal grd cell sze Δ. It can be shown that the 1/ thckness δ f of the LES-fltered flame s δ = Δ π 6(1 + (16 6/ π ν ) /( Sc s Δ )) (.e. s of order Δ c ), f c / t t L c and the flame s correctly resolved on the computatonal grd for values of (Δ c /Δ) much larger than one []. The numercal tests performed n Ref. [] suggest that the fltered-c model n FDS requres a flterto-grd length scale rato equal to or greater than 4, (Δ c /Δ)

4 We now turn to the descrpton of the lamnar flame speed s L. s L vares wth the fuel-ar mass rato (or equvalently the mxture fracton Z ), the unburnt gas temperature T u and the bulk pressure p. The varatons of s L wth T u and p are descrbed usng closure expressons proposed n Ref. [8]: γ β s L = sl ref Z ) ( Tu / Tu ref ) ( p / p ) where s L ref ( ) s the value of s L obtaned at normal temperature, (, ref, Z and pressure condtons ( T u = T u, ref = 98 K and p = p ref = kpa ), and where γ and β are model coeffcents that are functons of the local fuel-ar mass rato: γ = ( φ 1) and β = ( φ 1) wth φ = ( 1 Z st ) Z / Z st /(1 Z ). The varatons of s L, ref wth Z are descrbed va an ad-hoc analytcal expresson parametrzed n terms of four nput varables, called Z LFL, Z UFL, Z st and s L,st. Z LFL and Z UFL are the values of mxture fracton Z at the lower and upper flammablty lmts; Z st and s L,st are the stochometrc values of Z and. We use here a pecewse second-order polynomal s L, ref functon that vanshes at Z LFL, Z UFL,, s maxmum at Z st, and features a peak value equal to s L,st [3-5]. Refs. [3-5] present a detaled dscusson of the grd resoluton requrement of the PPC model formulaton when used n non-homogeneous confguratons (.e., confguratons wth varatons n mxture fracton) and show that n addton to the flter-to-grd length scale rato constrant dscussed above, there s a requrement that the LES premxed flame remans thn n mxture fracton space. Ths requrement s qute demandng and corresponds to an mportant lmtaton of the present PPC model. To overcome ths dffculty, a modfed PPC formulaton s proposed n Ref. [5] and s also adopted here. The modfed * ** * ** formulaton s based on a two-speed treatment ( s L, s L ) where s L s used n Eq. (1) and s L n Eq. (), and where s * L = s ** L = sl wthn the flammable regons, whle ** * s L < sl < sl near the edges (.e., at locatons where Z s close to Z LFL or Z UFL ). Ths scheme has proven successful at elmnatng spurous premxed burnng near the flammablty lmts and at provdng a clean descrpton of the burn out phase after premxed burnng s completed (see Ref. [5] for addtonal detals). Dffuson Flame Modelng We adopt n the present study the combuston modelng framework proposed n FDS Verson 5 [1]. Ths framework s lmted to a descrpton of non-premxed burnng and corresponds to a one-step or two-step global combuston model, wth or wthout flame extncton due to ar vtaton. We lmt our dscusson heren to the one-step verson of the combuston model. We start from the global combuston equaton: C n H m m + ν O O ( n ν ) CO H O CO C ( R1) CO ν soot + + ν CO + ν soot (3) where ν O = ( n + ( m / 4) ( ν / ) ) CO ν soot and where combuston products nclude CO, H O, and also CO and soot (treated as pure carbon). The stochometrc coeffcents n reacton (R1) are smply obtaned from the fuel chemcal composton and user-specfed carbon monoxde and soot yelds. In FDS, the mxture composton s descrbed usng two reactve scalars, called Z 1 and Z. These scalars are based on the followng decomposton of carbon mass: WC H WC H W n m n m CnH m Z = YC H + ( ) YCO + ( ) Y ( ) CO + Ysoot (4) n m nwco nw CO nwsoot Z 1 Z where Z 1 represents the carbon mass fracton contaned n the fuel, and Z the carbon mass fracton contaned n CO, CO and soot, and where Y k and W k are the mass fracton and molecular weght of speces k. It can be shown that the entre mxture composton can be reconstructed from the knowledge of Z 1 and Z va state relatonshps. 1058

5 The correspondng governng equatons are: ( ρz1) + t t ( ρz ) + ν t Z1 ( ρuz1) = ( ρ ) ωr 1 Sct ν t Z ( ρu = + Z ) ( ρ ) ωr1 Sct x (5) where ω R 1 s the mass reacton rate of the global combuston reacton (R1). In FDS, combuston s treated usng a closure expresson known as the Eddy Dsspaton Concept model [9], ω 1 = ω ; we wrte: mn( YF ; YO / ) ω [1 ] ρ rs d = FEF (6) τ R d where r s s the stochometrc oxygen-to-fuel mass rato, τ a characterstc combuston tme scale, and where FEF s a flame extncton factor that takes values 0 or 1, and s determned accordng to a dffuson flame extncton model. Consstent wth the classcal dea that n the absence of flame extncton, chemstry s fast, the tme scale τ s smply set equal to the computatonal tme step, τ = Δt. The flame extncton model descrbes the effects of ar vtaton (.e. ar mxed wth recrculatng combuston products; see Refs. [1] and [30] for addtonal detals): FEF = 0 at flame locatons that are well-ventlated, whereas FEF = 1 at locatons that are suppled wth super-crtcal levels of vtated ar. Couplng Interface We now turn to a descrpton of the couplng nterface between the premxed and non-premxed flame models dscussed above. The nterface formulaton provdes a generalzed expresson for the global combuston reacton ω R 1. Ths generalzed expresson s based on an dentfcaton of the locally domnant combuston mode (premxed versus non-premxed) usng the concept of a LES-resolved flame ndex FI [18-19]. Followng Ref. [18], we defne the flame ndex as: 1 YF. YO FI = ( + 1) (7) Y Y F O where Y F and Y O are the grd-resolved fuel and oxygen mass fractons (determned as functons of Z 1 and Z va state relatonshps). Note that ths expresson dffers slghtly from that n Ref. [18]: the FIexpresson n Ref. [18] ncludes a subgrd-scale contrbuton; ths contrbuton s neglected n Eq. (7). As seen n Eq. (7), FI s a non-dmensonal feld quantty that vares between 0 and 1: nert mxng between cross-dffusng fuel and oxygen corresponds to FI = 0; a dffuson flame confguraton n whch fuel and oxygen penetrate the dffusve/reactve layer from opposte drectons also corresponds to FI = 0; n contrast, a premxed flame confguraton corresponds to FI = 1. In regons where the fuel or oxygen mass s homogeneously dstrbuted (.e. n regons where Y = 0 or Y O = 0 ), FI s set to 0. F We adopt n the followng the PPC closure model of Ref. [18] and descrbe ω R 1 as a weghted average between the premxed and non-premxed contrbutons, usng FI as a weght coeffcent: ω ) R1 = FI ω p + (1 FI fgn ωd (8) 1059

6 where f gn s an ad hoc gnton factor. f gn s ntroduced n Eq. (8) so that the dffuson flame model remans nactve wherever nert mxng s takng place (f gn = 0 when c = 0 ), and s only actvated as a postpremxed-flame event ( f = 1 when c = 1 ). We use the expresson: f gn = tanh(( c 0.6) / 0.05). gn Enhanced by the couplng scheme n Eqs. (7)-(8), Eqs. (1)-(6) correspond to a combuston model wth a partally-premxed combuston capablty. Ths model has been mplemented n an n-house verson of FDS (Verson 5). We focus n the remander of the paper on a seres of smulatons amed at evaluatng the overall performance of the PPC/FDS model aganst prevously obtaned expermental data. The test confguraton corresponds to explosve combuston n a confned envronment and features sgnfcant bulk pressure varatons. Snce much of the evaluaton of the PPC/FDS model performance wll rely on comparsons between measured and smulated pressure tme hstores, we frst address n the next Secton ssues assocated wth the bulk pressure algorthm of FDS. We then proceed n the Secton that follows to a dscusson of the valdaton study. Bulk Pressure Modelng We start from the bulk pressure equaton [1]: dp dt = γ 1 T q t R j u, jn jds + ( ( ρ c p ) + q c CS CV γp Sct dv CV γp ν ) dv (9) where c p s the specfc heat (at constant pressure), γ the rato of specfc heats, T the temperature, the x j -component of the radaton heat flux vector (n unts of W/m ), and q c the combuston heat release rate (W/m 3 ), q c = ω R 1 ΔH F wth Δ H F the heat of combuston (per unt mass of fuel). The ntegral terms n Eq. (9) are calculated as volume ntegrals over the arbtrary control volume CV, or surface ntegrals over ts control surface CS (n j s the x j -component of the unt vector normal to CS and pontng outward). In the followng, CV denotes the exploson chamber. The frst term n the numerator of the RHS of Eq. (9) represents the effects of convectve transport across vents: an nflow of mass ( u jn j < 0 ) tends to ncrease the compartment pressure, whereas an outflow ( u jn j > 0 ) decreases t. The second term represents the effects of convectve/radatve heat transfer across CS (predomnantly wall heat losses) as well as those of combuston: heat losses tend to decrease the pressure whereas heat release tends to ncrease t. Eq. (9) s an ordnary dfferental equaton that can n prncple be used as a closure model for p. It turns out, however, that ths equaton s numercally stff and requres specal care for numercal ntegraton (see for nstance past studes of the equaton for pressure conducted n the context of zone modelng [31-33]). Ths pont s overlooked n FDS, where the same explct predctor-corrector tme ntegraton scheme s used for the flow/fre varables and for p [1]. In the absence of a proper treatment, the ntegraton of Eq. (9) can lead to the development of numercal nstabltes and to a computatonal crash. Ths analyss was confrmed n a seres of FDS tests that also revealed that numercal problems are lmted to confguratons wth vents and do not occur n sealed compartments ( u n ds = 0 ). Ths s an nterestng result snce n the presence of vents, the bulk pressure equaton may be bypassed entrely by adoptng a classcal zone modelng strategy. For nstance, assumng steady state and usng a Bernoull 1/ expresson for the outflow veloctes, u j = (Δp / ρ eq ) wherever u jn j > 0, wth Δp eq = ( p p ) the compartment over-pressure and p the external atmospherc pressure, one obtans: CS j j q R, j 1060

7 Δp eq CS, u jn j < 0 u n j j ds + CV γ 1 ν t ( ( ρ c γp Sct 1/ ( ) ds ρ CS, u jn j > 0 p T q R, ) j + q ) dv c (10) where the surface ntegrals over the vent openngs of CS are condtoned on nflow or outflow state. The pressure algorthm n FDS has been modfed accordng to the observatons above. We assume a scenaro n whch the fre compartment s ntally sealed, and the pressure p rses, untl a vent bursts open at tme t = t O because a crtcal value of p has been reached. The followng scheme s proposed: (1) for 0 t t O (sealed confguraton), calculate p (t) from Eq. (9) and store the value p ( t = to ) ; () for t O < t (vented confguraton), use Eq. (10) and wrte: ( p p ) = ( p( t = t ) p ) exp( ( t t ) / τ ) + Δp (1 exp( ( t t ) / τ )) (11) O O eq O where τ s a relaxaton tme scale assumed to be fast (τ s set to a value that s a few tmes larger than the computatonal tme step). Eq. (11) allows for a smooth transton from the ordnary dfferental equaton model n Eq. (9) to the quas-steady state expresson n Eq. (10). Note that whle the modfcatons proposed n Eqs. (9)-(11) provde a valuable soluton to the problem of calculatng the bulk pressure n FDS, other problems reman and have yet to be resolved. For nstance, the velocty feld n FDS remans nsenstve to the over-pressure ( p p ) and prelmnary attempts to modfy the velocty boundary condtons at open flow boundares (n order to fully couple the velocty algorthm to that of p ) have proven unsuccessful. Because of ths unresolved problem, the outflow veloctes at vent openngs n an over-pressurzed compartment are lkely to be sgnfcantly underestmated. NUMERICAL SIMULATIONS OF EXPLOSIVE COMBUSTION Our n-house verson of FDS Verson 5, enhanced by both a partally-premxed combuston model and a modfed bulk pressure algorthm, s now evaluated va detaled comparsons wth an expermental database prevously developed by FM Global Research. The confguraton corresponds to controlled gnton followed by explosve combuston n an enclosure flled wth vertcally-stratfed mxtures of propane n ar, both wth and wthout ventng, and wth and wthout obstacles [34-36]. Ths database was orgnally developed for analyss of exploson hazards assocated wth flammable lqud splls or releases of heavy flammable vapors n enclosures. Confguraton The FM Global exploson chamber s a rectangular-shaped 63.7 m 3 enclosure wth a m (15 15 ft ) square base and a 3.05 m (10 ft) heght. The walls of the enclosure are made of 38 mm (1.5 n) plywood panels that are steel-faced (0.41 mm, or n), whle the floor s made of concrete materal. The enclosure s made as tght as possble by coverng all the jonts wth a bead of slcone sealant. Rectangular openngs ( m or 0 44 n ) are avalable on the roof of the chamber for exploson ventng. A few of the avalable roof vents are used durng some tests: the vents are then covered wth a sheet of polyethylene that bursts open at known over-pressure levels. In addton, a sgnfcant number of tests are conducted wth obstacles that are ntroduced to study the effect of blockages; the obstacle array corresponds to m (.5.5 ft ) steel plates nstalled horzontally n a checkered pattern 0.46 m (1.5 ft) above the floor; the array provdes a 50% blockage to vertcal flow/flame expanson (but less resstance to horzontal motons). 1061

8 (a) (b) (c) (d) Fg. 3. Tme varatons of the smulated heat release rate. The plots show the total heat release rate (crcles) as well as ts premxed (dashed lne) and dffuson flame (sold lne) components. (a) case 6; (b) case 6; (c) case 7; (d) case 14. We focus n the present study on 4 expermental cases: case 6 that s unvented and wthout obstacle; case 6 that s unvented and wth obstacles; case 7 that s vented (1 roof vent) and wthout obstacle; case 14 that s vented (1 roof vent) and wth obstacles. In all cases, a quas-one-dmensonal, vertcally-stratfed layer of flammable gas s produced pror to gnton by controlled, floor-level, low-velocty, njecton of propane. The mxture composton s montored n tme by a gas analyss system. Ignton s trggered n the center of the chamber usng an arrangement known as a Jacob s ladder. The lst of expermental dagnostcs nclude vdeo observatons of the flames and measurements of the tme hstory of the chamber pressure. Because of the presence of uncontrolled leaks, the pressure measurements are corrected to provde an estmate of the pressure that would have been obtaned n the absence of leaks and wall heat losses [34-36]. Ths corrected pressure wll be the man dagnostc used for comparsons wth FDS results. The FDS computatonal doman corresponds to the exploson chamber. The smulatons start at gnton tme and use the (case-dependent) measured dstrbuton of propane n ar for ntal condtons. The computatonal grd corresponds to a unform rectangular mesh; the sze of the mesh s adjusted to adequately resolve the floor-level flammable porton of the propane-ar layer; the mesh corresponds to cubc grd cells wth a Δ spacng: Δ =.5 cm n cases 6 and 14, Δ = 1.5 cm n case 7 and Δ = 0.8 cm n case 6. The flame speed model parameters are: Z LFL = 0.03, Z UFL = 0.153, Z st = 0.06 and s L,st = 0.44 m/s. The flter-to-grd length scale rato s equal to 5, (Δ c /Δ) = 5. Based on tral and error, the flame wrnklng factor s fxed at a relatvely hgh values, Ξ = 4. Smulatons are performed on a mult-processor Lnux cluster avalable at the Unversty of Maryland, usng the parallel MPI-based verson of FDS. 106

9 Results The smulatons provde valuable nsghts nto the transent combuston dynamcs that follow gnton. Fg. 3 presents the tme varatons of the smulated spatally-averaged heat release rate as well as those of ts premxed and dffuson flame components, as obtaned usng the PPC formulaton (Eq. (8)). The heat release rate s maxmum shortly after gnton (at t = 0.5 s n case 6, at t = 1. s n case 6) and reaches a peak value that ranges from 15 MW (cases 7 and 6) to more than 5 MW (cases 6 and 14). In all cases, the combuston phase s short and lasts between 1.5 and s; combuston ceases because of fuel depleton. An analyss of the dfferent smulatons reveals that the flame expands from the centrally-located gnton pont n both horzontal and (upward) vertcal drectons. The horzontal spread s assocated wth the premxed flame (the flash fre), whereas the vertcal spread s assocated wth a buoyancy-drven dffuson flame (a freball). The ntensty of both flames depends strongly on the state of the propane-ar mxng feld found at gnton tme [34-36]. For nstance, n case 6, the bulk of the propane cloud s flammable fuel-lean and combuston s predomnantly premxed (Fg. 3(a)). In contrast, n case 6, the propane cloud features a large ultra-rch layer and combuston s n that case predomnantly non-premxed (Fg. 3(b)). Fnally, n cases 7 and 14, the bulk of the propane cloud s flammable fuel-rch/fuel-lean and combuston s partallypremxed (Fgs. 3(c)-(d)). In all cases, premxed burnng peaks when the deflagraton mpnges on the vertcal sde walls of the chamber, whle dffuson burnng peaks when fuel depleton effects become domnant. Fg. 4 compares the expermental and smulated tme hstores of bulk pressure. As mentoned earler, the expermental data are corrected for the presence of leaks and wall heat losses. In cases 6 and 6 (unvented), the pressure ncreases to more than 60 kpa and reaches a plateau once the combuston s completed (Fgs. 4(a)-(b)). The good agreement between expermental data and numercal results when comparng the tmng of the pressure ncrease suggests that the rate of combuston s reasonably well predcted (n Refs. [34-36], the turbulent flame speed that characterzes the burnng ntensty of the deflagraton wave s estmated to be 1.75 ± 0.5 m/s). The far agreement when comparng the post-combuston pressure levels suggests that the total amount of propane mass consumed s predcted less accurately (wthn 0-30%). In cases 7 and 14 (vented), the pressure varatons feature two peaks (Fgs. 4(c)-(d)): the frst peak s assocated wth the sudden openng of the roof vent (at p 3 kpa ); the second peak corresponds to the tmng of maxmum heat release rate (Fg. 3(c)-(d)). The frst pressure peak s well predcted n case 14, but predcted wth some delay n case 7; the magntude of the second peak s under-predcted n both cases, whch suggests that the peak ntensty of the heat release rate mght also be under-predcted. As ponted out n the Bulk Pressure Modelng Secton, the vent outflow veloctes are not correctly descrbed n FDS, whch wll lead to ncorrect flow/flame predctons n the post-vent-openng phase n vented exploson scenaros. CONCLUSION The present study s amed at adaptng current large eddy smulaton capabltes to a descrpton of lowpressure explosons n fuel vapor clouds, wth an emphass on scenaros featurng delayed gnton followed by coupled deflagraton and dffuson burnng. The proposed model formulaton s based on a fltered reacton progress varable approach to treat premxed combuston, the Eddy Dsspaton Concept for nonpremxed combuston, and the flame ndex concept to provde a couplng nterface. The partally-premxed combuston (PPC) model s mplemented n the Fre Dynamcs Smulator (Verson 5) developed by the Natonal Insttute of Standards and Technology. Its performance s evaluated n a valdaton study usng an expermental database prevously developed by FM Global Research; the database corresponds to explosve combuston tests n an enclosure flled wth vertcally-stratfed mxtures of propane n ar, both wth and wthout ventng. The expermental database s well-suted to testng the PPC model snce t ncludes some cases n whch combuston s predomnantly premxed and other cases n whch t s essentally non-premxed. The unvented compartment cases develop bulk over-pressures up to approxmately 60 kpa (9 ps); the vented cases develop over-pressures up to 3 kpa (0.4 ps). These pressurzed combuston scenaros present a partcular challenge to the bulk pressure algorthm n FDS whch has robustness and accuracy ssues, n 1063

10 (a) (b) (c) (d) Fg. 4. Tme varatons of the bulk compartment pressure. Comparsons between expermental data (crcles) and numercal results (sold lne). (a) case 6; (b) case 6; (c) case 7; (d) case 14. partcular n vented confguratons. The FDS bulk pressure algorthm has been modfed n the present study n order to allow detaled comparsons between measured and smulated pressure tme hstores. Overall, the comparson between numercal results and expermental data ranges from far to good and confrms the feasblty of a numercal treatment of explosve combuston. Future work wll focus on some unresolved problems n FDS for applcatons to exploson scenaros, and n partcular the problem of couplng the open-flow velocty boundary condtons to the bulk pressure algorthm. ACKNOWLEDGMENTS Ths work was supported n part by the U.S. Natonal Insttute of Standards and Technology, Buldng and Fre Research Laboratory. Ths work also benefted from frutful nteractons and sharng of data wth Dr. F. Tamann from FM Global Research. The support of Dr. Robert Bll from FM Global Research s also gratefully acknowledged. REFERENCES [1] Strehlow, R.A., (1973) Unconfned Vapor Cloud Explosons an Overvew, Proceedngs of the Combuston Insttute 14: [] Baker, W.E., and Tang, M.J., Gas, Dust and Hybrd Explosons, Elsever, [3] Bradley, D., Cresswell, T.M., and Puttock, J.S., (001) Flame Acceleraton due to Flame-Induced Instabltes n Large-Scale Explosons, Combuston and Flame 14:

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