基于物理学的城市火灾蔓延模型的发展和改进.pdf

Fire Safety Journal 43 2008 477 494 Development and validation of a physics based urban fi re spread model Keisuke Himotoa Takeyoshi Tanakab aPioneering Research Unit for Next Generation Kyoto University Gokasho Uji Kyoto 6110011 Japan bDisaster Prevention Research Institute Kyoto University Gokasho Uji Kyoto 6110011 Japan Received 1 May 2006 received in revised form 31 March 2007 accepted 18 April 2007 Available online 4 March 2008 Abstract A computational model for fi re spread in a densely built urban area is developed The model is distinct from existing models in that it explicitly describes fi re spread phenomena with physics based knowledge achieved in the fi eld of fi re safety engineering In the model urban fi re is interpreted as an ensemble of multiple building fi res that is the fi re spread is simulated by predicting behaviors of individual building fi res under the thermal infl uence of neighboring building fi res Adopted numerical technique for the prediction of individual building fi re behavior is based on the one layer zone model Governing equations of mass energy and chemical species in component rooms are solved simultaneously for the development of temperature concentrations of chemical species and other properties As for the building to building fi re spread three mechanisms are considered as contributing factors of fi re spread i e I thermal radiation from fi re involved buildings II temperature rise due to wind blown fi re plumes and III fi rebrand spotting As for the model verifi cation fi re spread simulations were carried out in a hypothetical urban area where 2500 buildings of identical confi guration were aligned at constant separations Calculated fi re spread rates were then compared with that of the Hamada model and reasonable agreements were obtained The model was further verifi ed with the record of a past urban fi re which took place in the city of Sakata in 1976 Although the general features of the fi re spread were similar there were certain discrepancies in the eventual burnt area The reasons for these discrepancies were discussed and issues for future refi nements were stated r 2007 Elsevier Ltd All rights reserved Keywords Urban fi re Fire spread External fl ame Fire plume Firebrand Zone model 1 Introduction When a fi re initiates in a densely built urban area it easily propagates to adjacent buildings one after another Especially in the case of large earthquake when multiple fi res break out simultaneously hazard of fi re spread is likely to overwhelm ability of fi re fi ghting and enlarge damage area Such urban fi re involves as many as thousands or even more building fi res at a time Historically cities especially in the United States and Japan have frequently experienced such fi res and have suffered substantial damage Some of the well known urban fi res are as follow 1 4 Chicago Fire 1871 which lasted for 3 days burnt over 17 000 buildings and caused 300 fatalities San Francisco Earthquake Fire 1906 burnt area of 1 200 000m2and caused 700 fatalities Kanto Earthquake Fire 1926 burnt area of 38 000 000m2 in which almost 70 of buildings existed in the city area were destroyed and caused over 100 000 fatalities mostly by fi re Hakodate Fire 1934 in which the rate of fi re spread reached as fast as 1000m hr due to spotting of numerous fi rebrands burnt 23 000 buildings and caused 2100 fatalities Sakata Fire 1976 burnt 1700 buildings in spite of considerable effort made by fi re fi ghters Oakland Hills Fire 1991 which took place at the urban wildland interface burnt over 2300 buildings and Hanshin Awaji Earthquake Fire 1995 which involved concurrent fi res in multiple places burnt 7000 buildings in total and caused 500 fatalities Several attempts have been made in developing models for prediction of urban fi re spread behaviors Such a model was fi rstly proposed by Hamada in 1951 4 5 in which the rate of fi re spread was formulated empirically as functions of macroscopic parameters of the environment such as wind speed building scale building to building separation construction types etc The model was designed to take ARTICLE IN PRESS resaf 0379 7112 see front matter r 2007 Elsevier Ltd All rights reserved doi 10 1016 j fi resaf 2007 12 008 Corresponding author Tel 81774384481 fax 81774384044 E mail address himoto kupru iae kyoto u ac jp K Himoto a form of a system of algebraic equations so that it can calculate the rate of fi re spread without an aid of numerical computation Accuracy of the model was supplemented by adjusting the involved empirical constants so that the simulated fi re spread rate agrees well with that of the past incidents Basic concepts of the models developed later on are similar to those of the Hamada model in which they describe the macroscopic behaviors of fi re spread with empirical relations 4 6 12 The advantage of such an approach of modeling is that it can simulate the rate of fi re spread with a fairly simple procedure However as fi re spread mechanisms are not explicitly incorporated in these models there are diffi culties in evaluating the hazard of fi re spread quantitatively as a function of a variety of factors involved As a result they have not always been made effi cient use of designing countermeasures ARTICLE IN PRESS Nomenclature Alphabets Asurface area m2 Bwidth of opening m B dimensionless number defi ned in Eq 40 dimensionless brhalf width of plume with regard to temperature rise m CW wind pressure coeffi cient dimensionless cpheat capacity of gas kJ kgK Drepresentative scale of heat source m D fl shortest distance between window fl ame and exterior wall m dwidth m Fview factor dimensionless F dimensionless number defi ned in Eq 30 dimensionless gacceleration due to gravity m s2 Hheight of opening m DHheat of combustion kJ kg L fl height of window fl ame m LMheat of burn through kJ kg m mass fl ow rate kg s mFmass loss rate of combustible kg s m O mass supply rate of oxygen kg s NB number of fi rebrands released from a fi re involved building dimensionless pprobability dimensionless p0reference pressure at the ground level Pa Dppressure difference Pa Q apparent heat release rate of window fl ame kW QBheat release rate kW P QLheat loss rate kW q 00 heat fl ux kW m2 Q00cumulative heat absorbed per unit surface area kJ m2 sdistance between gravitational points of win dow fl ame and exterior wall m Ttemperature K TPpyrolysis temperature K DTtemperature rise K ttime s UNwind velocity m s u0maximum vented velocity of hot gas at the opening m s Vvolume of compartment m3 wFdensity of movable combustible kg m2 Ymass fraction rate of chemical species dimen sionless ZNheight of neutral plane m Greeks a mass fl ow rate coeffi cient dimensionless aBconstant invoked in Eq 37 dimensionless aFheat growth rate m2 s2 bBconstant invoked in Eq 41 kJ 1 eemissivity dimensionless yangle rad mmean value pcircumference ratio dimensionless rdensity kg m3 sStefan Boltzmann constant kW m2K4 stan dard deviation wRrate of heat loss due to radiation dimension less C defi cit rate of structural member due to burn through dimensionless C0 rate of initial exposed surface area of fi xed combustible dimensionless Odimensionlessnumber defi nedinEq 35 dimensionless Suffi x B fi rebrand crcritical for ignition Dopening F combustible gasifi ed fuel fl window fl ame fl oor fl oor Lmovable combustible M compartment boundary fi xed combustible Ooxygen P fi rebrand Rthermal radiation Standard ISO 834 standard fi re curve Tinterior surface of compartment Nreference ambient K Himoto T Tanaka Fire Safety Journal 43 2008 477 494478 So the purpose of this study is to develop a quantitative model for urban fi re spread with the physics based knowledge of the phenomena to explore effective solutions to the above problem A number of attempts have been made for the identical purpose in the last few years 13 14 This paper rearranged the recent development of the author s model and carried out a number of simulations for the model verifi cation 2 Outline of the urban fi re spread model Schematic diagram of the present model is shown in Fig 1 In the model spread of fi re in urban area is describedbysimulatingthebehaviorsofindividual building fi res under the infl uence of neighboring building fi res as urban fi re is nothing but an ensemble of multiple building fi res Thus the model consists of two major sub models one that describes fi re behaviors inside buildings and another that describes building to building fi re spread As to the building fi re model each room of a building is considered as a control volume with uniform physical properties and transient development of internal fi re behaviors are calculated by solving the governing equa tions for the properties of control volumes simultaneously This uniformity assumption is appropriate as vigorous phase of fi re occupies a large portion of compartment fi res and building to building fi re spread takes place mostly within this particular phase Such an approach is generally called zone modeling which is widely adopted in building fi re safety engineering A reliable fi re spread model will effectively be developed by extending such established numerical techniques As to the building to building fi re spread following mechanisms are considered as contributing factors I thermal radiation heat transfer from fi re involved buildings II temperature rise due to wind blown fi re plumes III spotting of fi re brands to the downwind of fi re involved buildings As an urban area is composed of substantial number of buildings in general it is indispensable to minimize the load of fi re spread computation Thus we adopt experimentally verifi ed similarity relations for the prediction of these phenomena instead of taking fi ne modeling approach such as CFD techniques Under the infl uence of the above phenomena occurrence of fi re spread is determined when one of the following conditions are met A incident heat fl ux through opening exceeds a critical value q00 cr B surface temperature of exterior wooden wall exceeds a critical value Tcr C fi rebrands at high energy states are fallen upon combustibles 3 Building fi re model 3 1 Governing equations Following the defi nition of the one layer zone model a room of building is assumed as a control volume in which the properties of compartment gases are uniform regardless of spatial position Then the conservation equations of mass energy and chemical species subscripts O and F denote oxygen and gasifi ed fuel respectively for an arbitrary control volume is expressed as follows respectively d dt riVi mF i X j mij mji 1 d dt cPriTiVi QB i cP m F iTP X QL i X j cP m ijTi cP m jiTj 2 d dt riViYX i GX i X j mijYX i mjiYX j X O F 3 ARTICLE IN PRESS U T B Q B Q B Q T R q m L Q Firebrand spotting Temperature rise due to wind blown fire plume Thermal radiation heat transfer from fire involved building m m m m mm m m m m m R q R q R q B Q B Q L Q L Q U R Fig 1 Schematic of the urban fi re spread model K Himoto T Tanaka Fire Safety Journal 43 2008 477 494479 The state equation of gas is given by rT ffi 353 4 In above Eqs 1 4 cPis the gas heat capacity r is the gas density T is the gas temperature TPis the pyrolysis temperature of combustible V is the volume of control Y is the mass fraction of chemical species mFis the mass productionrateof gasifi edfuelduetopyrolysisof combustibles m is the mass fl ow rate through opening QB is the heat release rate P QLis the sum of heat loss rate through openings and walls and G is the mass production rate of chemical species Subscripts ij and ji denote the direction of mass fl ow between compartments i and j Transient change of gas temperature density and mass fraction of chemical species are calculated by solving these equations simultaneously 3 2 Mass production rate of gasifi ed fuel In a room fi re combustibles receive heat from fl ame and hot gas accumulated in the upper layer Thereby they start pyrolyzing to produce gasifi ed fuel Assuming that mass pyrolysis rates of these combustibles are same regardless of their positions the mass production rate of gasifi ed fuel mF is calculated by multiplying the surface area of burning combustible AFand the mass pyrolysis rate per unit area m 00 F as m F AF m 00 F 5 It is generally acknowledged that the mass pyrolysis rate of solid materials m F can be modeled as a proportional function of the incident heat fl ux However as wooden materials which is the most commonly used materials in dwellings form char layers at their irradiated surfaces it is not easy to estimate the net incident heat fl ux necessary to calculate the mass loss rate Thus we adopt the following formula derived from an experimentally obtained expres sion for the mass loss rate 15 m 00 F 0 86 m00 O m00 Op0 0082 0 007 0 0082o m00 Op0 0117 0 003 1 03 m00 O exp 94 4 m00 O 0 0117o m00 O 8 6 where m00 O is the mass infl ow rate of oxygen per unit surface area of the combustible The combustibles can be divided into following cate gories with regard to their modes of combustion movable combustibles such as furniture or clothing designated by L and fi xed combustibles such as lining or structural member designated by M The storage conditions of the movable combustibles can be seen in the report of an existing survey 16 Following the results exposed surface area of movable combustibles in each room AF Lis given as AF L 0 70w1 3 F LAfloor 7 where wF Lis the mass density of movable combustibles and A fl oor is the fl oor area Whereas for the fi xed combustibles we tentatively assume that the surface area AF Mis identical to the internal surface are of the room AT that is AF M AT 8 However the overall surface area of burning combustibles AFcannot be evaluated by just summing AF Land AF M since the burning area enlarges along with the development of fi re Firstly considering that the development of fi re inside a room is often described as a time squared model in the growth phase we adopt a similar model for the development of burning area of the movable combustibles Secondly we assume that the exposed surface area of the fi xed combustibles is given by a sum of the area that is initially exposed the ratio of the initially exposed area to the internal surface area is designated as C0 and the area exposed after the burn through of compartment bound aries the ratio of the burn through area to the internal surface area is designated as C Thus AFis expressed as AF minfaF t tig 2 AF Lg minf C0 C AT AF Mg 9 where aF is the growth coeffi cient and tigis the time of ignition 3 3 Heat release rate inside the fi re room In the ventilation controlled fi re combustion in the fi re room is restricted by the supply of oxygen Assuming that the rate of chemical reaction is fast heat release rate inside the fi re room is governed by the mass fl ow rate of oxygen coming into the fi re room QB O DHO X j mjiYO j 10 where DHOis the heat produced when unit mass of oxygen is consumed While in the case of the fuel controlled fi re heat release rate inside the fi re room is governed by the supply rate of gasifi ed fuel QB F DHF m F X j m jiYF j 11 where DHF is the heat of combustion of gasifi ed fuel Considering that the rate of heat release inside the fi re room QBchanges continuously at the transition between the ventilation controlled fi re and the fuel controlled QB minf QB O QB Fg 12 The rates of oxygen and gasifi ed fuel consumed in the combustion are calculated by dividing the heat release rate QBwith their heats of combustion respectively Thus the mass production rate of oxygen GO and that of gasifi ed fuel GFare given with the following equations respectively GO QB DHOand GF mF QB DHF 13 ARTICLE IN PRESS K Himoto T Tanaka Fire Safety Journal 43 2008 477 494480 3 4 Mass transfer through openings When combustibles start burning pressure difference Dp will be built between the burn room i and its adjacent space j which causes the mass transfer through openings between the rooms When the neutral plane exists between the upper and the bottom edges of the opening the mass fl ow rates mijand mjiwill be calculated with the following well known formulae respectively m ij 2 3 aB ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffiffi 2griDr p Hu ZN 3 2 m ij 2 3 aB ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi 2grjDr q ZN Hb 3 2 14 where a is the mass fl ow rate coeffi cient B is the width of the opening g is the acceleration due to gravity Dr is the density difference Huis the upper edge height of the opening Hbis the bottom edge height of the opening and ZNis the height of the neutral plane Yet as the pressure profi le at opening changes signifi cantly with the develop ment of thermal conditions in the facing spaces we need to assume additional pressure profi les Thus all of the mass fl ow rate equations of possible pressure profi les are provided in the model in addition to Eq 14 The height of the neutral plane ZNis the height at which the pressure difference between two contiguous spaces becomes zero In obtaining ZN hydrostatic pressure gradient is assumed for the pressure inside a room that is p z p0 rgz CW1 2rU 2 1 15 where p0is relative pressure of the space to the atmospheric pressure at the ground level CWis the wind pressure coeffi cient and UNis the wind speed The third term in the right hand side of Eq 15 represents the wind pressure which becomes zero when the concerning opening is not on the exterior wall The wind pressure coeffi cient CWis expressed as a function of the attack angle of the wind into the wall y as follows which is based on the existing wind tunnel experiment 17 CW 0 75 1pcos yp 0 866 0 45 1 38 cos y 0 866pcos yp0 0 45 0pcos yp1 8 16 As the relative pressure p0in Eq 15 cannot be described explicitly it is evaluated by implicitly solving the mass conservation equation of the compartment gas However as there are mass conservation equations as many as the number of rooms in the building and the mass conserv