Safe Separation Distance Calculation Model with Changing Area of Fuel Packages in Large Space

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1 Avilble online t Pocedi Engineeing 11 (011) The 5 th Confeence on Pefomnce-Bsed Fie nd Fie Potection Engineeing Sfe Seption Distnce Clcultion Model with Chnging Ae of Fuel Pckges in Lge Spce ZHANG Ji-qing, LU Shou-xing *, YUAN Mn, LI Chng-hi, LI Qing Stte Key Lbotoy of Fie Science, Univesity of Science nd Technology of Chin, Hefei 3006, Chin Abstct In pefomnce-bsed fie potection design, the sfe seption distnce of fuel pckges is usully clculted by NFPA model, i.e., setting cetin het elese te nd consideing the fuel pckge s point. The distnce between djcent fuel pckges is tken s the distnce between the two centl points, which includes the equivlent dius of the fuel pckges. Howeve, thee e mny poblems in pctice. This ppe intoduced the pinciple of chnging e to clculte the sfety distnce between djcent fuel pckges, combined with the lgoithm of point souce, line souce nd e souce. Results show tht it my diectly get the coeltion between the equied sfety distnce nd cceptble fie development time by using the chnging e model of the fuel pckges, which cn meet both the functionl nd economic demnds of buildings nd void the unsfe esults clculted by NFPA 9B model. Clcultion esults of point, line nd e souce model e vey close to ech othe, thus simple model like point souce model nd line souce model would be moe pplicble in engineeing pplictions. 011Published by Elsevie Ltd. Open ccess unde CC BY-NC-ND license. Keywods: pefomnce-bsed mesues; fie sfety engineeing; fuel pckge; sfe distnce 1. Intoduction As the ppence of moe nd moe novel design methods, pesciption fie potection design my not meet the needs of moden building technology ny moe[1]. Thee e often something exceeded cuent stndd in lge spce especilly. Relted sttistics[-4] show tht moe nd moe counties begn to dopt pefomnce-bsed design methods to optimize nd evlute the fie sfety of new buildings. Fo exmple, due to the building functionl equiements nd othe fctos, fcilities such s fie wlls nd fie esistnt shuttes often cnnot be set in lge spce buildings. In pefomnce-bsed fie potection design, it my use some spces such s vilble ods nd spces without fuel s seption zones. We need to evlute the sfety of these seption zones by clcultion. * Coesponding utho. Tel.: ; fx: E-mil ddess: sxlu@ustc.edu.cn Published by Elsevie Ltd. Open ccess unde CC BY-NC-ND license. doi: /j.poeng

2 ZHANG Ji-qing et l. / Pocedi Engineeing 11 (011) Moeove, in ode to povide theoeticl bsis of foming mesues to contol the sped of fie, we need to cy out sfety distnce clcultion fo some stoge sites such s the oil tnk fm[5] in open spce. With the incese of distnce nd diminishing of het elese te, the het dition intensity fom fie deceses shply[6,7]. Fie my not sped even without the spinkle systems so long s to limit the fie lod nd keep sufficient distnce between combustibles. Then thee will be some fuel pckges, fie seption zones foms between the fuel pckges. NFPA 9B[6,8] povides the clcultion eqution of shotest distnce tht it suely cnnot ignite djcent fuel pckges. Q R = 1π q 1/ (1) whee R is sfe seption distnce, m; Q is het elese te fom fie, KW; q is incident dint het flux equied fo piloted ignition, kw/m. When pplying this eqution, we cn conside the fuel pckge s point souce nd clculte the sfety distnce by setting cetin het elese te nd tke R s the distnce between the two centl points, which includes the equivlent dius of fuel pckges s the distnce between djcent fuel pckges. Howeve, thee e mny poblems in pctice. Fistly, thee is no need to set so long seption distnce s sfety distnce when thee e sufficient fie sfety fcilities nd the development nd sped of fie cn be contolled within cetin time. Fie will be contolled befoe speding to the entie fuel pckge in most cses if the e of fuel pckge is lge enough in some degee. Then if we still clculte the fie size ccoding to the size of entie fuel pckge, too long distnce nd too lge septed occuption will be set nd it my not meet the functionl nd economic equiements of lge spce buildings. Secondly, in cetin cicumstnce the distnce clculted by NFPA 9B is not sfe ctully when tking the equivlent dius of the fuel pckges into ccount. An exteme sitution is: we cn get R when the het elese te of fuel pckge (with dius ) is smll enough, then the djcent fuel pckge will be teted s sfe, which does not mtch with the ctul sitution, becuse thee is no seption zone between djcent fuel pckges ctully. This ppe intoduced the pinciple of chnging e to clculte the sfety distnce between djcent fuel pckges, combined with the lgoithm of point souce, line souce nd e souce. It is impotnt to note tht models discussed in this ppe did not tke smoke lye dition into considetion. When the cold lye is high nd the tempetue of hot lye is low, the model cn be used diectly by ignoing the dition of smoke lye. Moeove, models in this ppe cn be used diectly to clculte the sfe distnce of fuel pckge in open spce. Fo the clcultion of fuel pckge sfety distnce in lge spce whee the dition of smoke lye cnnot be ignoed, models cn be used to clculte the dition of fie plume pt.. Sfe Seption Distnce Model In lge spce buildings, especilly in some lge wehouses, goods e often lid in cubic stcking. It is ssumed tht thee e two sque stcking fuel pckges with side length b. We cn use eqution (1) diectly, which is the sfety distnce clcultion model in NFPA 9B. But if the stcking e is too lge, the sfe septe distnce my not meet functionl nd economic equiements of the buildings, since the sfe septe distnce incesed with the stcking e. When the e is lge enough, it needs to expeience long peiod of time fo fie fom beginning to buning ll ove the fuel pckge. If thee e some effective mesues to contol the development nd the sped of fie duingthis peiod of time, thee is no need to set the septe distnce ccoding to the clculted esult of eqution (1). This ppe intoduces the pinciple of chnging e, combined with the lgoithm of point souce, line souce nd e souce, to clculte the sfety distnce between djcent fuel pckges unde diffeent cceptble development time of fie.

3 668 ZHANG Ji-qing et l. / Pocedi Engineeing 11 (011) Thee e sque stcking fuel pckges with side length b stoed in wehouse, the het elese te pe sque mete is Q. When het dition eceived by point F with distnce of R fom the side of the fuel stcking eches cetin theshold fte the fuel stcking is on fie, djcent fuel stcking cn be ignited. A minimum R tht cnnot ouse the ignition of djcent fuel is sfe seption distnce. Consideing the most dngeous cicumstnce, side length of ignited e is t time t, which foms fie e whose edge is coincided with AB side of fuel stcking. At this point, fie e nd the het elese te is Q = Q S. The het elese te cn be descibed s Q = αt. If the fie incesed by t sque model, the side length of ignited e is: = t α Q () whee is gowth fcto (often given in kilowtts pe second squed (kw/s )) nd t is the time fom estblished ignition, in seconds. Q is het elese te fom fie pe sque mete, kw/m..1. Point souce model of fuel pckge with chnging e At time t, consideing the whole ignited fuel stcking s point, the clculted distnce is composed of hlf the ignited e side length nd the distnce to the djcent stcking R, tht is =/+R. Fig. 1. Point souce model of fuel pckge with chnging e digm Accoding to eqution (1), t cn be substituted into the squed fie model nd clculte, then we get: α = 1π q 1/ t (3) Fom the model we know = /+ R, so the secuity seption distnce is: 1/ α α / Q R = t (4) 1π q whee R is the seption distnce between djcent fuel pckges, which is the shotest distnce between the edges of djcent fuel pckges excluding the equivlent dius of the fuel pckges, in metes. is the gowth te

4 ZHANG Ji-qing et l. / Pocedi Engineeing 11 (011) (often given in kilowtts pe second (kw/s)). q is incident dint het flux equied fo piloted ignition, kw/m Q is het elese te fom fie pe sque mete, kw/m... Line souce model of fuel pckge with chnging e At time t, dividing the het elese te poduced by fied stcking to the cente line eqully, fom which we tke fie mico-unit dx nd ssuming the dition to the point F of ny one is independent, then the dition of dx to F cn be obtined by integte the point souce model.. Fig.. Line souce model of fuel pckge with chnging e digm Accoding to the fuel pckge dition eceived by cetin point clcultion eqution fom NFPA9B[8,9], incident flux on point F fom dx cn be estimted fom the following: xq / b dq = dx (5) 4π Tking integtion on this eqution fom 0 to, the totl dition intensity of the fie pckge to the F point is: xq / b q = dx (6) 4π 0 Accoding to the model we know = x+ R the F point:, integting eqution (6) to get the dition het flux eceived by xαt q = α 4 π Rt ( + R) Q (7) Accoding to eqution (7), the sfe distnce between fuel pckges is: 1 α Q R = ( + 1) 1 Q t (8) 3π q

5 670 ZHANG Ji-qing et l. / Pocedi Engineeing 11 (011) whee L is the el sfe distnce between fuel pckges, m; is gowth fcto (often given in kilowtts pe second squed (kw/s )); is the potit width of the fie e to the tget stcking; is dil distnce fom cente of exposing fie to exposed fuel; Q is het elese te fom fie pe sque mete, kw/m ; q is incident flux on exposed fuel, kw/m..3. Ae souce model of fuel pckge with chnging e The fie souce is divided into numbe of mico-element fie dxdy, ssuming the ditions of mico-element fies to F e independent with ech othe, the point souce dition model cn be used to clculte the dition of mico-element fie dxdy to the point F. Fig. 3. Ae souce model of fuel pckge with chnging e digm xq dq = dxdy (9) 4π Integting eqution (9) in the ignited e, nd we get the totl dition intensity of ignited fuel pckge on point F. xq q = dxdy 4π 0 0 (10) By this model we know the distnce between the mico-element fie nd the tget point F is 1/ = [ x + ( y+ R) ], which is substituted into eqution (10) nd we get xq 1 q = π dxdy (11) x + ( y+ R) 0 0 whee q is incident flux on exposed fuel, kw/m ; x is the dition fcto, usully tke 1/3; Q is het elese te fom fie pe sque mete, kw/m. is the side length of the fied fuel stcking e, m; R is the distnce tht the djcent fuel stcking is fom the ignition, m. Accoding to eqution (11), we obtin the sfety distnce vying with time the MATLAB pogm.

6 ZHANG Ji-qing et l. / Pocedi Engineeing 11 (011) Results nd Compison 3.1. Model Results Bsed on the desciptions bove, compisons of esults of NFPA9B nd chnging e model e shown in Tb.1. Tble 1. The compison of the NFPA9B model nd the chnging e model Modeling pinciple Model q /( kw/m ) R /m Constnt e NFPA9B model xq 4π R Q 1π q 1/ chnging e Point souce model xαt 4 π ( R + ) 1/ α α / Q t 1π q chnging e Line souce model xαt α 4 π Rt ( + R) Q 1 α Q ( + 1) 1 t Q 3π q chnging e Ae souce model 1 xq dxdy π q = 0 0x + ( y+ R) π 0 0 xq 1 dxdy x + ( y+ R) 3.. Exmple In polyethylene wehouse, we tke the method of od seption between fuel pckges to obtin sfety distnce eltionship ove time which could be used fo setting the od seption distnce nd lyout of fie fighting fcilities. Moeove, the dint het flux of polyethylene incident flux is 9.4 kw/m, the fie gowth fcto of fuel pckge is 0.014kW/s while the het elese te of polyethylene fuel pckges is 3975 kw/m. Fig.4 shows the sfety distnce chnges with the side length of fuel pckges clculted by NFPA9B model. Fom Fig.4 we cn see tht the sfety distnce is only decided by the size of the fuel pckge. Accoding to the esults, the sfety distnce hs high equiement fo the fuel pckge size. Only to estict the fuel pckge size in cetin nge, cn we use shote sfe septe distnce. Fo exmple, when the side length of fuel pckges is 4.0m, the equied sfe distnce is no less thn 53.59m which is consideble distnce, leding to significntly effect on the functionl nd economic of the building ctully.

7 67 ZHANG Ji-qing et l. / Pocedi Engineeing 11 (011) R=53.59m R(m) R=30.14m R=1.40m b(m) Fig. 4. The esult of the NFPA point souce model Fig.5 shows the sfety distnce clculted by chnging e model ove cceptble fie development time. As cn be seen fom Fig.5, the esults obtined by point model, line model nd e model espectively e close to ech othe, nd esult of e model is close to the tue vlue but little bit complicted. In engineeing ppliction, we cn use simple model like point model nd line model. Results show if fie potection fcilities nd equipment efficiency llow the cceptble fie development time ech to 1800s befoe the fie ignites the djcent fuel pckge, the clculted sfety distnce is 9.6m by point model, 9.7m by line model while 9.75m by e model. R(m) point souce model line souce model e souce model R=9.6m,9.7m,9.75m R(m) R=9.75m R=9.7m R=9.6m T(s) 6 4 T=1800s T(s) Fig. 5. Results of the chnging e model Fig.6 shows the compison of the chnging e model nd the NFPA9B model. As cn be seen fom the figue, the sfety distnce of the NFPA9B model is only decided by the size of the fuel pckge, while the chnging size model llows us to use shote sfety distnce to septe the fuel pckge with cetin cceptble fie gowth time nd this method is moe conducive to buildings functionl nd economic equiements. Also, the sfe septe distnce is the shotest distnce between the edges of the djcent pckges, not including the equivlent dius of

8 ZHANG Ji-qing et l. / Pocedi Engineeing 11 (011) the fuel pckges in chnging e model, thus the NFPA9B model will not ppe insecuity in cetin cicumstnces. R(m) 3 30 NFPA model(b=0.5m) point souce model 8 NFPA model(b=1.0m) line souce model NFPA model(b=1.5m) e souce model 6 NFPA model(b=.0m) 4 NFPA model(b=.5m) b=.5m b=.0m b=1.5m 6 4 b=1.0m 0 b=0.5m T(s) Fig. 6. The compison of the chnging e model nd the NFPA9B model Results of the chnging e model cn help clculte the equied time of contolling fie unde ppopite fie potection fcilities fte septing the fuel pckges by cetin sfety distnce, which is lso clled cceptble fie development time, poviding efeence fo nging necessy fie potection fcilities nd equipments to meet the time equiement of the building. A shote sfety distnce will be obtined by this model to septe fuel pckges befoe the fie speds to djcent fuel pckges, since the fie size is function of time nd it will be smll enough when fie potection fcilities nd equipments cn contol fie within cetin time. Howeve, ppopite ppliction of the esults is bsed on the ccucy of the time tht ppopite fie fcilities nd equipments cn contol the fie. The esults of the point model, line model nd e model e simil, so in the engineeing ppliction we cn use simple model like point model nd line model. 4. Conclusions This ppe intoduced the pinciple of chnging e to clculte the sfety distnce between djcent fuel pckges, combined with the lgoithm of point souce, line souce nd e souce. 1) Sfety distnce clculted by NFPA 9B model is only decided by the size of the fuel pckge, nd hs high equiement of contolling the fuel pckge size. Only to estict the fuel pckge size in cetin nge, cn we use the shote sfe septe distnce. The chnging e model llow us to use shote sfety distnce to septe the fuel pckge with cetin cceptble fie gowth time nd this method is moe conducive to building functionl nd economic equiements. ) Results of the chnging e model cn help clculte cceptble fie development time unde ppopite fie potection fcilities fte septing the fuel pckges by cetin sfety distnce, poviding efeence fo nging necessy fie potection fcilities nd equipments to meet the time equiement of the building. 3) Appopite ppliction of the esults is bsed on the ccucy of the time tht ppopite fie fcilities nd equipments cn contol the fie. The esults of the point model, line model nd e model e simil, so in engineeing ppliction we cn use simple model like point model nd line model. 4) The model discussed in this ppe did not tke the dition of smoke lye into considetion. In lge spce without consideing the smoke lye dition o in open spce, we cn use the model diectly to clculte the sfety distnce. To the clcultion of fuel pckge sfety distnce in lge spce whee the dition of smoke lye should be consideed, the model cn be used to clculte the dition of fie plume pt.

9 674 ZHANG Ji-qing et l. / Pocedi Engineeing 11 (011) Refeences [1] R.W. Bukowski, V. Bbusks. Developing tionl, pefomnce-bsed fie sfety equiements in model building codes. Fie nd Mteils 1994; 18: [] S.M. Lo, K.C. Lm, Z. Fng, K.K. Yuen. An investigtion on the building officils' peception fo the use of pefomnce-bsed fie engineeing ppoch in building design. Fie Technology 00;38: [3] S.M. Lo, C.M. Zho, M. Liu, etc. A simultion model fo studying the implementtion of pefomnce-bsed fie sfety design in buildings. Automtion in Constuction 008; 17: [4] P. A. Coce, W. L. Gosshndle, R. W. Bukowsk, et l. The Intentionl FORUM of Fie Resech Diectos: A position ppe on pefomnce-bsed design fo fie code pplictions. Fie Sfety Jounl 008;43: [5] S. Atllh, D. S. Alln. Sfe seption distnces fom liquid fuel fies. Fie Technology 1971;7: [6] P. J. DiNenno. The SFPE hndbook of fie potection engineeing. USA: Ntionl Fie Potection Assocition; 00. [7] T. Achibld. Combustion Efficiency nd Its ditive component. Fie Sfety Jounl 004;39: [8] NFPA 9B-009. Stndd fo Smoke Mngement Systems in Mlls, Ati, nd Lge Spces.