Trans. Tianjin Univ. 2008, 14: 434-440DO|10.1007/s12209-008-0075versity and Springer-Verlag 2008Mechanical Model of Domestic Gas Explosion LoadHAN Yongli(韓永利), CHEN Longzhu(陳龍珠)(Institute of Engineering Safety and Disaster Prevention, Shanghai Jiaotong UniversityShanghai 200240, China)Abstract: With the increase of domestic gas consumption in cities and towns in China, gas explosion accidents happened rather frequently and many structures were damaged greatly. Rationalphysical design could protect structures from being destroyed, but the character of explosion loadmust be learned firstly by establishing a correct mechanical model to simulate vented gas explo-sions. The explosion process has been studied for many years towards the safety of chemical industry equipments The key problem of these studies was the equations usually involved some adjustable parameters that must be evaluated by experimental data, and the procedure of calculationwas extremely complicated, so the reliability of these studies was seriously limited. Based on thesestudies, a simple mathematical model was established in this paper by using energy conservationmass conservation, gas state equation adiabatic compression equation and gas venting equationExplosion load must be estimated by considering the room layout the rate of pressure rise wasthen corrected by using a turbulence factor, so the pressure-time curve could be obtained. by usingthis method, complicated calculation was avoided, while experimental and calculated results fittedfairly well. Some pressure-time curves in a typical rectangular room were calculated to inves-tigate the influences of different ignition locations, gas thickness, concentration, room size andventing area on the explosion pressure. The results indicated that: it was the most dangerous condition when being ignited in the geometry centre of the room, the greater the burning velocity, theorse the venting effect; the larger the venting pressure, the higher the peak pressure; the largerthe venting area, the lower the peak pressureKeywords: gas explosion; mechanical model; venting; peak pressure, turbulence factorollananPoapartment caused by gas explosion in 1968, the influ- 1 Introductionence of these accidents and how to protect civil buildingsfrom being destroyed have aroused people's attention In 1.1 Gas explosion mechanismChina, with the increase of domestic gas consumptionGas explosion, in essence, is a rapid combustion ofgas explosion disasters arise more often than before, the mixed gas. Flame surface is created after igniting atsome even destroyed the structure of buildings and a point in the room and expands continuously duringbrought tremendous disaster to human beings. For ex- this chemical reaction process. Released energy by theample, several walls and slabs were destroyed by the gas combustion products makes the pressure and temperexplosions that happened in Dalian(Dec. 2006), Ying- ture increase with the time in the room. Discharged gaskou(Feb. 2007)and Jilin (an. 2008), resulting in some will carry away a lot of energy after venting; then, pres-casualty and great property lossessure rise in the room is determined by the differenceWe can protect buildings from being destroyed between released energy during combustion and disthrough rational physical design, but the properties of charged energythe gas explosion load must be fully understood at firstExperiments showed that the surface of the flameSo, this needs to establish a reasonable mechanics model grows smoothly and regularly only in the early stageto simulate the whole process of the gas explosionWith the development of combustion, the flame front中國(guó)煤化工Accepted date: 2008-07-15CNMHGHAN Yongli, born in 1981, male, doctorate studentCorrespondencetoHANYongli,E-mail:hanyongli01@sjtu.edu.cnHAN Yongli et al: Mechanical model of Domestic gas Explosion loadarea can be affected by many different physical processes: gineering of Dalian University of Technologyl6l didinitial turbulence, development of cellular structure, many theoretical and experimental studies about theelongation of flame front towards the vent, buoyancy venting process of gas explosion. Some safety vent ruleseffect, Taylor flame instability, internal obstacles. Such have been formed and already used in project designsinstability and turbulence mainly result in shape distorMoen, hijertager et al i8 believed that internal ob-tion as well as the acceleration of the flame front. So, stacles will make the turbulence even bigger, and makethese factors affecting the turbulence must be considered the burning velocity increase. Canu et all) introducedin the model, and many domestic and foreign scholars two empirical parameters in the closed and vented situahave done a vast amount of research on thistions separately to represent the flame wrinkling caused1. 2 Related research achievementsby instability combustion and vent. The parameters wereThe phenomenon of vented gas explosion has been fitted through a collection of about 160 experimentalstudied for more than 100 years. Studies showed that the data. Dobashi u did some gas explosion experimentalevolution of pressure with time depends on the nature studies of the methane-air mixture in a closed rectanguand state of the initial explosive mixture, such as com- lar vessel. It was shown that the gas flow turbulence irposition, initial pressure and temperature, vessel charac- creased the flame propagating velocity and made theteristics, position of the ignition, size and strength of the pressure rise rapidly. Molkov ,2 achieved a reasonablevent, presence of obstacles. However, while the physics comparison with experimental data for very high valuesbehind this process seems to be quite well known, many of the deflagration-outflow-interaction number x /ubasic problems have not been solved. For example, the results showed that internal obstacles, mixed gas concenaccurate estimation of the turbulent burning velocity is tration and vessel volume all had influence on the flameone of the most important contents in current research 2. surface. Kobiera et ala gave a new phenomenologicalTheoretical approaches to modeling gas explosions model in a closed vessel, which is based on the assumpare either CFD models or the so-called multi-zone mod- tion that the burning velocity of a turbulent wrinkledels. The explosion process in the latter is usually divided flame could be determined by the flame surface. Qian etinto two stages: closed gas explosion and vented gas ex- all3 analyzed the process of indoor gas explosion withplosion, and they are treated by different burning veloc- AutoReaGas explosion simulator. The result showedity models; an instability factor is introduced in the for- that the higher the venting pressure is, the more seriousmer stage and a turbulence factor in the latter stage The the hazard consequence will be, peak pressure wasfactors are often generated by fitting some experimental greatly affected by the ignition location. Bradley et al4data, and depend on too many factors, such as flame believed that the volume of burned gas inside the idealReynolds number, outflow coefficient, viscosity, expan- sphere is equal to that in the wrinkled flame surface, andsion ratio, Bradley number, sound speed as well as the the turbulent burning velocity was studied based on thisinternal obstacles, the calculation process is extremely theory. By comparing the predictive ability of 1l empiri-complex, and these models are only able to predict with cal and semi-empirical equations for venting of gas ex-good accuracy vessels with simple geometries, so they plosions, Razus et all found that there was great differare very limited in terms of scope and usageence among the calculation results, even to hundreds ofLu Jie et alsl studied the acceleration mechanism of timesflame propagation of city coal gas-air mixture in a closed 1.3 Application in domestic buildingsvessel. It was found that obstacles made the maximurVenting remains the main cost-effective techniqueexplosion pressure increase by 20%, gas concentration to mitigate the impact of gas explosions on equipmentsand blockage ratio all had effects on flame velocity and and buildings. but related research showed that the inoverpressure. The same conclusions were obtained by Yu crease of venting area is not always effective to mitigateLixin et all, who studied the turbulent flame accelera- gas explosions to a safe level. Domestic buildings aretion of the hydrogen-air mixture in a semi- open ob- different from the chemical equipments, they have thestructed tube by experiment. Wang Zhirong I analyzed characteristics of large venting area and internal obstadrical vessel by numerical simulation, especially the fea- engendered at differences of actual conditions will bethe process of gas deflagration and discharge in a cylin- cles. Fairly gre中國(guó)煤化工 d researchtures of pressure development. School of Chemical En- to calculate gasCNMHGin a domestic435Transactions of Tianjin University Vol 14 No 6 2008buildings directly. So far there have been little re- remain locally spherical, as shown in Fig. 1arches on the multi-zone models about gas explosion6) Only unburned gases are vented; especiallyhappened in the domestic buildings, and nobody put when igniting near the window only burnt gas areforward the correction method for turbulent burning ventedNow, in field investigation on gas explosion acci-Windowdents, the peak pressure is usually estimatedto the destruction situation and resistance of structuralmembers. By comparison, it is feasible to estimate thepeak pressure by the calculation formulas proposed byBurntDragosavic and rasbash in the sixties and the seventiesof the last centuThe aim of this paper is to simulate the pressure-(a) Ignited in the closed endtime behavior of the gas explosion accident happened incivil buildings by using a turbulence factor n to modifythe burning velocity, and experimental and calculatedT, P, Vresults fitted fairly well. The peak pressure must be estimated by room layout at first, then the calculated peakT PVpressure is made to fit the estimated one by regulatinthe value of a thus the whole curve can be obtained. Forit avoids the complicated calculation of/, the model isgreatly simplified(b) Ignited in the centerFig 1 Model of gas explosion flame front in room2 Mechanical model2.2 Governing equationsThe mass of the mixed gas flowing into the flameBased on energy conservation equation, mass con- surface in unit time is expressed ason equation, gas state equation, isentropic com-Aspression equation and the gas discharging rate equation,Pu STwhole process, then flame position, pressure and other Constant overall volume constraint isresults can be obtainedVess =v+vh(2)2.1 Basic assumptionswhere v indicates the vessel volumeThe process of vented gas explosion is very complex,The mass conservation equations areinvolving the knowledge of chemical thermodynamics,aerodynamics, combustion theory, fluid mechanics etc.0order to describe the main features of this processsome assumptions have to be made to reduce the com- where the first term and the second one are the massplexity of the systemconservation before and after vent opening, respectively.The temperatures of the gases are calculated by us-(1)The premixed gas in room meets the ideal gas ing the following equationsstate equation(2) The vessel can be regarded as adiabatic, heatT=T(p/Po)7u, T=T'(p/Pm)transfer between the gas and the cold wall is ignoredState equation for ideal gas behavior isB) The pressure remains uniform in the whole ves-PV=nR Tsel during the explosion(4)The flame surface is spherical, and the thicknessEq (5)applies to both burnt and unburnt gases, thatis not considered(5) Walls cut off the flame surface, while other partsTH中國(guó)煤化工CNMHG436HAN Yongli et al: Mechanical Model of Domestic Gas Explosion loadThe laminar burning velocity is calculated by using flame surface velocity equation as followsthe following equation:dvh polV dp,(p-po)dTdTS=S0(T/T)(p/p)°dt (T-Tp dt T-l)p dawhere So is the fundamental burning velocity; a and B(17)are empirical parameters, &=2.0, B=-025For example, when the ignition location is in theTurbulent burning velocity is expressed ascenter of a spherical vessel, dv,/dt=4 r2dr/dt(8)Thus, a mechanical model based on the above equa-For ideal gases, the energy conservation equation tions is set up By combining the boundary conditions(Bernoulli equation)isand using the numerical method, the development lawh2+-= Const(9)of tne pressure and the flame surface in the room can beobtainedAnd the ideal gas isentropic compression equation 2.3 Boundary conditions2.3.1 Initial and final statespV=p, v2(10)Initial statewhere h is the gas enthalpy, v is the velocity of gas flowt=0,p=p,5=0,Vb=0,A=0,7=7through the vent And the relationship between gas en-thalpy and gas state is as followsFinal state.h(11)p=p3.2 GeometriroomSo the volume of the gas flow through the ventWalls cut off the flame surface, but other parts ofunit time 1sthe flame remain spherical. The flame area A and theIm, Ao(12) volume of the burned gas Vhare the function of flameradius, ignition location and room shapeFlow status equation of the gas flow through theA=f(, xi, yu)(18)vent in subsonic speed is given by eqs.( 9)-(12)f2(5,x1,y)(19)an,_,p 2r P2'_P2dMr"Ry-1\n丿(內(nèi)(13) For example, when igniting in the center of a sphericalessel, Vh=4rr/3, A=4r, and A is a ConThe governing equations of the pressure rate in a stant for a tube vessel,Vb=Avented vessel can be achieved after summation of the 2.4 Example verificatioaboveWe can use the test data in Ref [17 to verify the ac-Before ventingcuracy of the model in this paper. Experiments weredp Rn(n-n)dT R(Tb-1) dn,, rmn, dTconducted at initial temperature of 295 K and near-atmospheric pressure (about 100 kPa), the volume of theAfter ventingspherical vessel is 6.85 m,yu=1. 4 and yb=1. 25, otherdp Rm(n-n)dT, R(T-T) dn,shown in tab. 1 The wholeretical computation results accords with the experimen-Rm n, dT rT(15)well(see Fig. 2)Experiments proved that the venting area has littleffect on ththExperimental dataout considering the effect of venting area on explosion2.0relationship between Vb andVh=fC)(p-PolTV(Th-Tup(16)中國(guó)煤化工After derivation calculus to Eq (16), we can get theFig. 2CNMH Results437Transactions of Tianjin University Vol 14 No 6 2008Tab. 1 Experimental data on vented deflagrationsPressure-time curvep(H2)/%A,/m2pypoP/pM=(g·mol)So/mS")0.0177model. The window is composed of 3 pieces of glass, the3 Gas explosion simulation in a kitchendimension of one glass is 0.6 mx 1.5 m, and the thickness is 4 mm, so venting pressure py is 5.3 kPall6l.The3. 1 Basic calculation parametersfundamental burning velocity So reaches maximura kitchen room with total area of 20 m" square 0.84 m/s when the volume percentage of coke oven gas tofilled with coke oven gas-air mixture is taken as the mixture is 20%. Other parameters are shown in Tab. 2Tab. 2 Relative calculation parametersPo/kPaR/-(kg.K))307.23.2 Computational results3.2.3 Effect of ventingareaThe influences of ignition location, concentrationThe peak pressure reaches 27 kPa, 20 kPa and 15venting area, venting pressure, and room size on the kPa when the venting area is 1. 8 m, 2.7 m and 3.6 mpressure-time curve are analyzed, and some useful re- separately, as shown in Fig. 5. As it considers the turbusults are obtained as shown in Figs. 3--7lence, there is still very large overpressure in the room3. 2. 1 Effect of ignition locationthough the venting area is already big enough. The lessThe highest peak pressure is obtained when ignit- the venting area, the more effect of the venting on peaking in the center(curve 1), as shown in Fig 3; the devel- pressureopment of the flame surface is more limited when igniting in the other conditions (curve 2), so the peak pressure is lower. It is the lowest one when the ignition loca一0-30%tion is near the window(curve 3), because more energyby the burnt gas vents to the atmosphere.1.101.2591.210095Fig 4 Effect of ctration on the pressure-timecurve2002503001.20me after ignition/ms1.5Fig3 Effect of ignition location on the pressure-timecurye1.053.2.2 Effect of concentrationWhen the volume concentration is 30%, the burn-050100150200250300ing velocity reaches about 0.62 m/s, and it is only 0.45Fig 5 Effect of venting area on the pressure-timem/s when the volume concentration is 10%. The influence of the concentration on the pressure-time curve isshown in Fig 4, the lower the burning velocity, the3.2.4 Effect of venting pressurelonger the explosion time and the better the venting ef-Venting pressure is 3kPa.53 kPa and 8.6 kPa re-pectively, when中國(guó)煤化工nm,4 mm and5 6, ventingCNMHG, So the pres-438HAN Yongli et al: Mechanical Model of Domestic Gas Explosion loadsure-time curves are shown in Fig. 6. The higher the tion and venting gas all have influence on the pressureventing pressure is and the longer the time before vent time curve.ing, the higher the peak pressure will be.(2)The lower the burning velocity and the longer3.2.5 Differeom sizesthe explosion time the better the vent effect. The volExplosion curves in three rooms with different sizes ume concentration of the mixture has great influence on(2.7m×2.7m×2.7m,2.7m×2.0m×3.6m,2.7m× the burning velocity. For most gas explosion accidents,2.4 mx3.0 m) but with the same volume are analyzed; the gas mixtures do not reach the best mix proportionignition location is in the geometric center of the room. Maybe this is the main reason why most accidents do notThe development of flame surface is more limited in the produce very high pressureroom with high length width ratio, so the peak pressure (3)The larger the venting area, the lower the peakis lower than the others, but the effect is not very big, as pressure. For the laminar model, this is very obviousshown in Fig.7.But actually, because of the big turbulence effect in akitchen room, the increase of venting area is not alwayseffective to reduce the peak pressure. This explains whythe peak pressure is still so large in some accidents while1.15the window is already large enough(4)The larger the venting pressure and the longerthe time before venting, the higher the peak pressure益1.00e∈The limiting case is that, when the venting pressure is00150250300big enough, the vented vessel becomes a closed one.Time after ignition/Burning velocity is modified by using a constant aFig6 Effect of venting pressure on the pressure-time thus the calculation procedure is much simplified whilethe result obtained still remains relatively high accuracy2.7m×2.0m×3.6after disaster, the press1.20-。-27m×24m×30-2,7mx2.7m×2,7curve can be obtained as long as the peak pressure isestimated correctly. And for the explosion-proof designin the future, it should be strengthened to research therational calculation method to estimate the peak pres-that happens in arational method to calculate the turbulence factorthrough a laFig. 7 Effect of room size on the pressure-time curveNomenclaturep--pressure, Pa;4 ConclusionsTtemperature, K;The gas explosion that happens in a room has theV volume of enclosure. m3.specialty of large venting area, big turbulence factor, lowA-surface area, m.peak pressure, uncertain ignition location, etc. But itstill follows the general rules of gas explosion. In this n--molar masspaper, a simplified model is presented that has beenM--average molecular mass, kg/molproved itself as a useful tool in modeling gas explosionRm--ideal gas constant, Rm=8.314 J/(molK)n a kitchen room and some useful conclusions are oby— specific heat ratiotained(1) Pressure rise in the room is determined by the2-turbulence factdifference between released energy during combustionSubscriptsand discharged energy. So the room shape ignition locainitial si中國(guó)煤化工v--venCNMHG439Transactions of Tianjin University Vol 14 No 6 2008L--laminar[8 Hijertager B h, Fuher K, Parker sJ et al. Flame acT-turbulentceleration of proir in a large scale obstructedburnt gastube [C]. In: Progress in Astronautics and AeronauticNew york: AIAA Inc, 1984. 94: 504-5229] Canu P, Rota R, Carra S. Vented gas deflagrations: Am--maximum value,1, 2-upper and lower reaches of the venting lodetailed mathematical model tuned on a large set ofexperimental data []. 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