COMPUTATION OF SMOKE SPREAD IN A BUILDING FIRE BY MULTI-LAYER ZONE MODEL

Transcription

1 COMPUTATION OF SMOKE SPREAD IN A BUILDING FIRE BY MULTI-LAYER ZONE MODEL K. Suzuki Institute of Technology, Shiizu Construction Corporation Etchuia Koto-ku, Tokyo , Japan T. Tanaka Disaster Prevention Research Institute, Kyoto University, Gokasho, Ui, Kyoto 6-, Japan K. Harada Departent of Architecture and Architectural Engineering, Graduate School of Engineering Kyoto University, Katsura Capus C2-46, Nishikyo-ku, Kyoto , Japan ABSTRACT The ulti-layer zone fire soke oveent siulation odel (called as MLZ odel), a new zone odeling approach, was addressed to predict vertical distributions of the physical properties, such as teperature and cheical species concentration in a building fire. The odel still retains the advantage of other zone odels in ters of light coputational load, so it is expected to be useful for a practical application for fire safety design of a building. In this study, the verification against a fire experient in a ulti-roo area is presented. As the result, the predicted teperatures and gas velocity generally show satisfactory agreeent. Additionally, a GUI tool which decreases the user s load for calculation settings and which displays calculation results by color on a two-diensional plane was introduced. KEYWORDS: Multi-layer zone odel, Soke oveent, Fire experient, GUI tool INTRODUCTION A ulti-layer zone odel, a new zone odeling approach, was applied to predict vertical distributions of the physical properties in a building fire. As illustrated in Fig., the space volue of each roo is divided into an arbitrary nuber of ultiple layers as the control volues in which the physical properties are assued to be unifor. The boundary walls are also divided into segents in accordance with the layer divisions, and the convection and radiation heat transfer aong the layers and the wall segents are calculated. In this way, the vertical distributions of the physical properties in each roo are calculated. However the odel still retains the advantage of two-layer zone odels, such as CFAST and BRI22, in ters of light coputational load, so it is expected to be useful for a practical application for fire safety design of buildings. These basic concepts of the MLZ odel for a single roo and for a tunnel were introduced 2,3. In this study, the odel is extended to a ulti-roo configuration and iproveents are ade on the influence of ventilation flow to fire plue, the prediction of the ceiling et, the entrainent of the opening et plue and the radiation heat transfer fro the flae. The results of the validation against a fire experient in a building are deonstrated. THE MODEL The iage of the fluid oveent in the MLZ odel is deonstrated in Fig.. One of the notable differences of the concept fro the existing two-layer zone odels is that the fire plue flow does not ix with the upper layer the instant it penetrates the layer interface but continues to rise until it hits the Copyright International Association for Fire Safety Science

2 ceiling, after which it pushes down the gases in the top layer while flowing horizontally as a ceiling et. The iage of teperature prediction in a fire roo by the MLZ odel relative to that by a two-layer zone odel is on the left side of Fig.. The two-layer zone odel predicts the layer interface height and only two teperature values, i.e. those of upper and lower layers. In the case of the MLZ odel, the distribution of teperature can be predicted by calculating the teperatures of the ultiple layers of which positions are arbitrarily pre-fixed. () Governing Equation for Zone Properties The zone governing equation for the teperature of each layer is derived fro the conservation equations of ass and internal energy for each horizontal layer as follows: dti, = hi, + hi, Cpl,, i + Ti, + Cpl,, i Ti, + hop,, i + h, i + Qcw,, i + Q rl,, i dt C ρ V p i, i, [] h i, ( l,, i ) ( l,, i ) C p li,, Ti, = C p li,, Ti, < [2] where li,, and h i, are the vertical ass and enthalpy flow rate through the boundary between the th layer and the (+) th layer outside of the fire plue, respectively. Q cw,, i is the convection heat gain fro wall and Q rl,, i is the net radiation heat gain. Subscript i eans roo i. The enthalpy of the fire plue, h, i, is added only when entering the top layer of the fire roo, and in the other layer it equals zero. The enthalpies of ventilation flow are transferred to the ceiling or floor by buoyancy through the opening et plue, then the enthalpy of it, h op,, i, is added only to the layer in which the opening et plue reached. Likewise, the zone governing equations for ass fraction of species l (i.e. CO 2 ) in each layer can be derived. FIGURE. Iage of MLZ odel (a graph of left side shows coparison with teperature prediction iage of MLZ and 2-layer zone) 2

3 (2) Flow through the Openings Suing up the energy conservation equations in each roo of the atospheric pressure, the following equation could be written, x x x x C p T T Q Q Q nb i, nb, i nb, i, + cw,, i + + = rl,, i c nb = nb = = = [3] where Q c, the convective heat fro the fire source, which equals zero except for in the fire roo. The horizontal ass flow rates through the openings, i and nb, nb, are calculated fro Eq. [4] and i, Eq. [5]. ( ) ( ) = α B Δz 2ρ P P P P v i nb, i nb, i, i, nb, i, nb, ( ) = α B Δz 2 ρ ( P P ) P P < v nb i, i nb, nb, nb, i, i, nb, [4] i, i, i, k k = P = P g ρ Δz [5] Here, Eq. [3] can be solved for the value of the pressure of roo i at the floor height, P i,, by an appropriate iteration ethod, because it includes P i, iplicitly, i.e. starting fro an initial value of P i, and calculating i and nb, nb by Eq. [4], next substituting the into the left hand side of i, Eq. [3], then odifying P i, iteratively until the value of the left hand side of Eq. [3] becoes close enough to zero. This process is repeated to all roos by the Gauss-Seidel ethod, thus P i, of all roos and horizontal ass flow rates are calculated iplicitly. The flows that have passed through openings becoe opening et plues by buoyancy. They change direction upward or downward, depending on their teperature relative to the environent, entraining the gas around it. The teperature, the velocity, the half-width and the trace of the axis are calculated by arranging the conservation equations of ass, energy, and oent for two-direction. (3) Fire Plue Entrainent The ass entrainent rate into the fire plue fro the th layer,, and the enthalpy transported through fire plue into the top layer, h fp, are assued to be given 4 : ( ) /3 5/3 5/3 e, c = C Q z z [6] where the entrainent coefficient of fire plue, C e,, is estiated as 8 in the windless condition, while the value increases by the influence of the draft fro the openings on the fire plue. The plots in Fig. 2 shows the relation of the ratio of divided by the entrained ass flow rate in windless condition,, and the ratio of the ventilation velocity, U, divided by the velocity of the fuel, w* 5. Thus in this study, shown as the thick line in Fig. 2, it is assued to have a linear relation in * 833 U W.25 as follows: U = [7] 8.33 * w 3

4 Qg C w* = DρTC [8] p * Fro Eqs. [6], [7] and [8], the equation for C e, is given as 8 2U W. When U is too * * high, U W >.25, or U is too low, U W < 833, then C e, is decided as.24 and 8, respectively. C U * W U U = 8 2 < 2 3 * W < W U e, * 8 2 * W [9] Upper liit windless condition lower liit FIGURE 2. Relation of horizontal flow and entrainent increase rate (4) Teperature of Ceiling Jet FC The teperature rise of ceiling et under an unconfined ceiling under cal conditions, Δ T c, and Δ, can be calculated by the following equations 6 : FC T c, r 2/3 FC FC Q c, c, 5/3 r Δ T T T = [] H H 2/3 2/3 FC FC Q r r c, r c, r = < 5/3 Δ T T T [] H H H To apply Eqs. [] and [] to a fire in a copartent with a confined ceiling, consideration should be ade of the following issues: a) the entrainent of a fire plue increases by the draft fro openings as discussed in section (2), b) the enthalpy of the fire plue increases due to the entrainent of the hotter gas fro the layers at elevated teperature and c) the enthalpy into the ceiling et increases by 4

5 the sae reason. Hence, the calculation ethod for the teperature rise of ceiling et in a copartent fire, Δ T c, and Δ T c, r, is introduced as follows: a) Increase of the fire plue entrainent by draft The teperature rise of ceiling et adapted for the increase of the ass flow rate fro to, FC by draft, T FC Δ, and Δ T,, can be obtained as follows: letting the adusted ceiling height, or c entrainent height H be: c r fp 3/5 x x H = H = = [2] Substituting H for H in Eqs. [] and [] yields: 2/3 FC Q r c, = /3 Δ T [3] H H 2/3 2/3 FC Q r r c, r = /3 < Δ T H H H [4] b) Influence of plue entrainent fro layers at elevated teperature into the fire plue Fro the energy conservation of the fire plue, Δ T c, is calculated as: x = ( ) Tf, T FC = r Δ Tc, =Δ T c, +.8 x H [5] c) Influence of hot gas entrained into the ceiling et Considering the energy conservation for the ceiling et under unconfined ceiling without wind, the ass flow rate entrained by the ceiling et at radial distance r fro the ipinging point, c, r, is found to be: ΔT FC x 2/3 x c, r c, r = = 3.4 FC ΔT c, r = H = [6] Assuing that c, r can be obtained by Eq. [6] in an unconfined ceiling configuration, the equation for Δ T c, r is obtained by cobining the energy conservation of the ceiling et and Eq. [6] as follows: 5

6 x ( ) Tf, T c, r ( T FC f, x T = ) r Δ Tc, r =Δ T c, r + + >.8 x x H + + c, r c, r = = [7] (5) Radiation Heat Transfer In the odel, the radiation heat flux is assued to consist of three directional coponents between layers or layer and wall, i.e. the upward, the downward and the horizontal one fro each layer. The upward, downward and horizontal heat fluxes, q& ru,, i, q& rd,, i and q& rw,, i are calculated as follows: ( ) ( ) ( ) { } q& = α F q& + α σt + α F α q& + α σt [8] 4 4 ru,, i g,, i LU,, i ru,, i g,, i i, g,, i WU,, i w,, i rw,, i w,, i ws,, i ( ) + ( ) ( ) { } q& = α F q& + α σt + α F α q& + α σt [9] 4 4 rd,, i g,, i UL,, i rd,, i g,, i i, g,, i WL,, i w,, i rw,, i w,, i ws,, i 4 ( α )( + ) α σ q& = F q& + F q& + T + Q A [2] rw,, i g,, i LW,, i ru,, i UW,, i rd,, i g,, i i, rfw, w,, i where α wi,, are the radiation absorptivity, which is the sae as the eissivity, of the wall surface. Only in the fire roo, radiation fro the flae of the fire source to walls, partially absorbed in layers, is considered, as shown as broken lines in Fig. 3. The fraction of radiation heat fro the flae directing to the surface of the th wall segent, Q rf,, is given as: Q = Q F [2] rf, r FW, where Q r is the radiation heat eitted fro the fire source and FW, F is the ratio of radiation heat fro the fire source directing to the th wall. The fraction of Q rf, reached th, Q rfw,, is calculated by Eq. [22,] subtracted the radiation heat absorbed by the layers ( st - th ) fro Q rf, : Q ( α )( α ) ( α ) = L Q [22] rfw, g, f, g, f, g, f, rf, where α gi,,, the radiation absorptivity of the th layer of the i th roo, changes according to the gas teperature and ass fractions of CO 2, H 2 O and soot, of which the spectra are not unifor. In this odel, the Fortran progra ABSORB, developed by Modak 7, is used to calculate α gi,,. In the other hand, the total radiation absorbed in the th layer fro the fire point, Q x ( ) ( ) = α α L α Q [23] rfl, f, f, f, rf, k k= Thus the net radiation heat gain of the th layer of the i th roo, Q rl,, i, is: (& & ) ( & & + + ) 4 {( α ) & α σ } Q = A q q + A q + q rl,, i f,, i ru,, i rd,, i f,, i ru,, i rd,, i + A q& q + T + Q wi,, rwi,, wi,, rwi,, wi,, wi,, rfl, [24] 6

7 (6) Calculation Flow Fig. 4 shows the flow chart of this odel. (-α w,f, )q rw,f, +α w,f, σ(τ ws,f, ) 4 q rw,f, Q rfl, q rd,f,+ + layer T ws,f, q ru,f, T f, q rd,f, layer Wall - layer Q rfw, Q rf, fire q ru,f,- Point q rd,f,2 2 layer q rw,f, T ws,f, Q rfw, q ru,f, T f, q rd,f, layer Q rf, T ws,f, q ru,f, Area f FIGURE 3. Iage of radiation transfer in fire roo Reading setting file Initial condition t=t+δt t= Heat release rate Cobustion gas calc. Opening flow and pressure calc. Opening et plue calc. Fire plue calc. Ceiling et calc. Vertical flow calc. Radiation heat transfer calc. Convective heat transfer calc. Wall teperature calc. Gas teperature calc. Gas concentration calc. Output data no Tie finish? yes end FIGURE 4. Flow chart 7

8 COMPARISON WITH EXPERIMENTAL RESULTS () Experiental Data In this section, the results of teperature and velocity easureents in 4 cases of the fire experients are copared with the predictions by the odel for validation. The experiental setup of the roo of the fire origin, the plane of the whole experiental structure layout and a picture of the fire roo are shown in Figs. 5, 6 and 7, respectively. The experiental fields, adusted by the openings, and the fire source conditions are shown in Table. The total heat release rate data of the fire sources was obtained by easuring the weight loss of the fuel (n-heptane) and ultiplying the heat of cobustion per unit fuel (44.4 MJ/kg), as shown in Fig. 8. The vertical distributions of gas and wall surface teperature were easured by therocouples and the velocity distributions at the openings were easured by Pitot tubes and differential pressure gauges. As the ceiling et, the teperature at the point 2 below the ceiling at 2 distance fro the center of the fire source was easured by therocouple. FIGURE 5. Scheatic of fire roo FIGURE 6. Plane of experient field 8

9 FIGURE 7. A picture of fire roo 4 total h.r.r 3 2 CASE3 CASE4 CASE2 CASE tie[s] FIGURE 8. Total heat release rate TABLE. Suary of experiental conditions (4 cases) Case Case 2 Case 3 Case 4 doain fire roo fire roo fire roo+ corridor fire roo+corridor + non-fire roo opening (height-width[] ) opening (.6x.4) opening (.6x.4) opening2(2.x.8) opening3(x.8) opening2(2.x.8) opening3(x.8) opening4(2.x.8) Firepan (area) pan (. 2 ) 2 pans (.22 2 ) 2 pans (.22 2 ) 2 pans (.22 2 ) peak H.H.R. 2 kw 32 kw 35 kw 3 kw (2) Condition of the Calculation The calculation doain consists of 4 spaces, i.e., the two roos and the corridor that is virtually divided into two at the center for better precision of the prediction. Each space is divided into 2 horizontal layers of equal thickness. The conditions, such as the areas of roos, the ceiling height, the 9

10 initial air teperature and the total heat release rate were deterined basically according to the experiental conditions for each case. In the experient, ost of the partition walls were assebly walls with 24 plaster board on both sides and 5 glass wool in between. However, in the calculation the walls were siplified as 48 plaster boards. The property of the ceiling and the floor were set as 2 plaster board and concrete according to the conditions of the experient. The calculation tie step was s. The flow coefficient, α v, was set to.7 on the openings and.95 on the virtual boundary of the center of the corridor. (3) Coputer Load The CPU tie of the calculation for each case was within 3 s for coputing 24 s by a PC with Pentiu4 2.4 GHz, hence it could be found that this odel has the advantage of coputing load. (4) Results and Discussion Fig. 9 shows the coparison between the experients and the calculations of the vertical distribution of the teperature in the fire roo, the corridor (case 3 and 4 only) and the non-fire roo (case 4 only) at 6, 2 and 8 s. The calculations in the fire roo generally show satisfactory agreeent with the experients. However, they were a little lower at.3 to.2 fro the floor, and especially at 6 s in case 4 the calculation was fairly lower. The ain reasons are suspected to be that the total heat release rate easured in the experient ight not be so accurate and that the experients are influenced by radiation heat of the flae. The calculations in the corridor were higher at.9 to.4 fro the floor in case 3 and at.2 to.4 fro the floor in case 4, because the influence of the diffusion and the entrainent into the opening et ight be calculated less. Fig. shows the coparison with the teperature on the wall surface in the fire roo and the sae conclusion can be found with Fig gas tep.[ ] gas tep[ ] gas tep.[ ] gas tep.[ ] Case (Fire roo) Case 2 (Fire roo) Case 3 (Fire roo) Case 3(Corridor) gas tep.[ ] gas tep.[ ] gas tep.[ ] Case 4 (Fire roo) Case 4 (Corridor) Case 4 (Non-fire roo) cal 2s cal 8s exp 6s 5 52 exp 2s exp 温度 8s [ ] 床面高さ []cal 6s FIGURE 9. Gas teperature in fire roo, corridor and non-fire roo

11 時間 [ 秒 ] Fig. shows the coparison of the teperatures easured under the ceiling and the ceiling et teperature predicted by Eq. [7], and for reference by Eq. [5] (r = ) and Eq. [] (r = 2, original Alpert s equation). Within 6 s in case to 3, the calculations were high. The reason is unclear, but Eq. [] was tuned for steady condition, hence the applicability ight be beyond the range for the quick increase of the heat release. In the other, the coparisons were slightly high. Fig. 2 shows the coparison with the velocity through the opening. The calculations were roughly coincident with the experients, but soe of the neutral heights were different. It sees that the experients were easured only along the centerline of the opening so they were different with the average value of the opening area. The influence of entering wind fro outside could also be considered. GUI TOOL FOR PRE AND POST PROCESS For quick and easy aking of setting files and iproveent of visibility of the result, the pre-post GUI (Grafic User Interface) tool of the MLZ odel was developed, referring to CFD software on the arket. Fig. 3 shows the flow of process for the prediction including the pre-post tool. hegiht[] wall surface tep.[ ] wall surface tep.[ ] wall surface tep.[ ] wall surface tep.[ ] Case Case 2 Case 3 Case 4 FIGURE. Wall surface teperature in fire roo 温度 [ ] cal 2 eq.7 exp 2 cal f.c. eq. eq.5 cal Ceilinget Tep.[ 3 2 Ceilinget tep.[ 3 2 Ceiling et tep. 3 2 Ceiliget tep.[ tie[sec] tie[sec] ti e[sec] ti e[sec] Case Case 2 Case 3 Case 4 FIGURE. Gas teperature under ceiling in fire roo

12 fire roo.6 outdoor fire roo.6 outdoor fire roo corridor.8 corridor 2.8 outdoor opening.4 opening.4 OPENING 2 2. opening velocity[/s] -2-2 velocity[/s] -2-2 velocity[/s] -2-2 velocity[/s] Case Opening Case 2 Opening Case 3 Opening 2 Case 3 Opening 3 fire roo corridor.8 opening 2 2. corridor 2.8 opening 3.96 outdoor cal 2s cal 8s exp 6s 5 52 exp 2s exp 温度 8s [ ] 床面高さ []cal 6s velocity[/s] velocity[/s] Case 4 Opening 2 Case 4 Opening 3 FIGURE 2. Gas velocity through openings Pre process Reading picture of plan Setting space condition Setting wall condition Setting openings condition Setting soke control condition Setting fire detections Setting fire sources Output setting file MLZ progra Calculation Post process Reading calculation result Displaying teperature on plan Displaying teperature on section FIGURE 3. Process of prediction 2

13 Firstly, the pre tool helps aking a setting file. Boundaries of roos are drawn by click and snap of ouse operation above an iage file of a plane of an obect space. Soe other conditions such as the heat release rate of a fire source, an opening type, walls type can be set by selection fro a pull-down box or by nueric input with key. Fig. 4 shows an iage where input of a shape and soe conditions of calculation area and a fire scenario was finished. As a suppleent, the default values were inputted as a heat release rate and an exhaust gas flow rate in the standard fire safety design of Japan, and it is possible to plan coparatively early and quickly. After the calculation of the MLZ progra using the setting file, the post tool can display the calculation results visually. Fig. 5 shows an exaple of visualizing horizontal gas teperature data by color. Any height and any tie can be selected or changed progressively like an aniation. Fig. 6 shows a vertical distribution of gas teperature on a section, which is selected fro any plane. In this version, only gas teperature and gas concentrations can be displayed by color. FIGURE 4. Drawing the boundaries of roos (pre) FIGURE 5. Display of gas teperature on the plane (post) 3

14 FIGURE 6. Display of teperature distribution on the section (post) CONCLUSION In this study, the forulation of a MLZ odel was extended to ulti-roo configuration, and also the refineents were ade of the coponent odels such as fire plue, opening et plue, ceiling et and radiation heat transfer. The validation was ade against the full-scale fire experient. Considerably satisfactory results were obtained fro the validation, so the odel present is considered to be a useful tool for fire protection design. However there is still roo for further study on coparison with various experients and confiration of accuracy and applicability. ACKNOWDGEMENT This study has been carried out by the support of the Grants-in-Aid for Scientific Research (No ). The authors thank Dr. Shigeru Yaada, Dr. Jun-ichi Watanabe, Dr Yuki Akizuki and Mitsuo Kadoya, Yoshitoo Kanai for their help and advice. REFERENCES. Tanaka, T. and Nakaura, K., Model for Predicting Soke Transport in Buildings - Base on Two Layer Zone Concept, Building Research Institute, No. 23, BRI, MOC, K. Suzuki, K. Harada and T. Tanaka, A Multi-Layer Zone Model for Predicting Fire Behavior in a Single roo, The 7th Syposiu of IAFSS, Jun, Suzuki, K., Harada, K. Tanaka, T. and Yoshida, H., An Application of a Multi-Layer Zone Model to a Tunnel Fire, 6th Asia-Oceania Syposiu on Fire Science and Technology, Zukoski, E.E., Soke Moveent and Mixing in Two-Layer Fire Models, The 8th UJNR Joint Panel Meeting on Fire Research and Safety, Tsukuba, May, J. G. Quintiere, The Effect of Roo Openings on Fire Plue Entrainent, Cobustion Science and Technology, Alpert, R.L., Calculation of Response Tie of Ceiling-Mounted Fire Detectors, Fire Technology, Modak, A.T., Radiation fro Products of Cobustion, Fire Research,, 978/79. 4