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Comparison of different combustion models in enclosure fire simulation
Fire Safety Journal 36 (2001) 37}54
Comparison of di!erent combustion models in enclosure "re simulation H. Xue*, J.C. Ho, Y.M. Cheng Department of Mechanical and Production Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 Received 26 July 1999; received in revised form 10 July 2000; accepted 17 July 2000
Abstract In this study, three combustion models, the volumetric heat source (VHS) model, the eddy break-up model and the presumed probability density function (prePDF) model, are examined in enclosure "re simulation. The combustion models are compared and evaluated for their performance in predicting three typical enclosure "res, a room "re, a shopping mall "re and a tunnel "re. High Reynolds number turbulence k}e model with buoyancy modi"cation and the discrete transfer radiation model (DTRM) are used in the simulation. Corresponding experimental data from the literature are adopted for validation. The results show satisfactory prediction in #ow patterns and features in the complex enclosure "res. However, it is shown that these combustion models are not able to show consistent performance over the di!erent locations and enclosure "res. The needs for adequate turbulent combustion models in enclosure "res are discussed. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Combustion model; Fire; Simulation; Smoke concentration
1. Introduction Accurate prediction of the "re-induced air velocity, temperature, and smoke concentration in enclosure "res become more and more important for designing e$cient "re protection systems. Much e!ort has been made in "re modeling which deals with the development of quantitative descriptions of the "re phenomena in terms of the physical and chemical processes as functions of the ignition source, space geometry, and material content. Jones [1], Duong [2], Dembsey et al. [3] and Peacock et al. [4] * Corresponding author. Tel.: #65-874-6479; fax: #65-779-1459. E-mail address: [email protected] (H. Xue). 0379-7112/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 3 7 9 - 7 1 1 2 ( 0 0 ) 0 0 0 4 3 - 6
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Notation a C ,C ,C C,C E B C I f f Y g h , I i J k M m P p(f) Q R T ; u u
absorption coe$cient constants of the k}e model constants of the prePDF model constant of the k}e model mixture fraction mixture fraction variance gravitational acceleration height of the neutral layer total hemispherical intensity chemical species di!usion #ux of species i turbulence kinetic energy molecular weight of species i mass mean pressure probability density function heat release rate of the "re source mass rate of creation or depletion by chemical reaction mean temperature mean velocity of the cross section mean velocity component #uctuating velocity component
Greek letters b C e k k l o p p ,p I C p
thermal expansion coe$cient exchange coe$cient turbulence energy dissipation dynamic viscosity coe$cient turbulent viscosity molar stoichiometric coe$cient air density Stefan}Boltzmann constant turbulent Schmit number turbulent Prandtl number general scalar quantity
Subscript k P R
reaction product reactant
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investigated a number of "re models and conducted intensive comparison and evaluation with "re experimental data. But only zone models were dealt with in their reviews. Yang [5] studied several "eld models including PHOENICS (CHAM of North America, Inc.) and UNDSAFE developed at the University of Notre Dame. Beard [6] evaluated "eld models like JASMINE [7] and FLOW3D (UK AEA Technology) and discussed the limitations and capabilities of the "re models. However, their studies focused on the comparison and evaluation of overall ability of the CFD code. Details on the e!ect of combustion sub-models in the code are usually lacking. An enclosure "re is a complex phenomenon. In "eld modeling, sub-models of combustion, turbulence and radiative heat transfer are needed to describe an enclosure "re. Great complexity arises in view of the fact that there are strong interactions among these three e!ects. At present, there are many shortcomings in the existing "eld models in accounting for such complicated interactions. While current sub-models for buoyancy, compressibility, turbulence, and thermal radiation are quite adequate [5], the inability of turbulent combustion model is outstanding. This is due to the nature of enclosure "re phenomena where pyrolysis and gasi"cation are inherent and extremely di$cult to model. In addition, it is not easy to accurately know the reaction kinetics and combustion rate in enclosure "res. Consequently, the detailed combustion chemistry in coupling turbulence and radiation are left unknown even though the turbulent combustion sub-model might be included in the computational algorithm. It is not surprising to see the selection of combustion models among researchers varies in their application to di!erent types of enclosure "res at this stage. The aim of the present study is to examine the performance of three commonly used combustion models. The "rst is the volumetric heat source (VHS) model, which does not take chemical reaction into account, instead, it sets the heat release rate equivalent to that of the assumed "re. The VHS model is the simplest "re model and easy for implementation. The second is the eddy break-up model presented by Magnussen and Hjertager [8], who attempted to simultaneously account for mixing and "nite chemical reaction rates. The third is a mixture fraction approach using presumed PDF (prePDF) model, where an assumed shape probability density function (PDF) is generally used to take into account of turbulence}chemistry interaction. Although these models have been intensively compared and evaluated in combustors [9,10], studies of these combustion models in the context of enclosure "res are rare. We selected three typical cases of enclosure "re, namely, a room "re, a shopping mall "re and a tunnel "re for the study. The results of di!erent combustion models are compared and evaluated with available experimental data.
2. The mathematical models 2.1. Flow xeld model Heated air movement is the key concern in an enclosure. The turbulent buoyant #ow is governed by the equations expressing the conservation of mass, momentum,
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energy and concentration of species. When steady-state process is considered, the governing equations can be written in a Cartesian tensor form as continuity equation: *(ou ) G "0; *x G
(1)
momentum equations:
*(ou u ) *P * *u G H "! # k G !ou u #og ; G H G *x *x *x *x H G H H
(2)
general purpose transport equations:
*(ou ) * *
H " C !ou #S , G ( *x *x *x H G G
(3)
where denotes enthalpy, concentration of species i , respectively. The term S stands ( for the appropriate source or sink of the variable concerned. For enthalpy and species transport equations, the source term S is the rate of heat release and ( creation/destruction of species i in the combustion, respectively. The change of density is only related to the temperature of the air through the equation of state o"o(¹).
(4)
For the closure of the governing equations, the two-equation k}e model of turbulence is used [11]. According to eddy viscosity concept, the turbulent kinetic energy k and dissipation e equations can be derived:
* k *k *(ou k) H " #S , I *x *x p *x H G I G
(5)
*(ou e) * k *e H " #S , C *x *x p *x H G C G
(6)
k k "oC . Ie
(7)
The #uid motion in enclosure "res is a!ected by mean buoyancy force. Rodi [11] modi"ed the source terms S and S as I C S "G #G !oe, I I
(8)
e e S "C (G #G )(1#C R )!C o D k C k I
(9)
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where G and G denote the contributions of stress and buoyant force, respectively, I and R is #ux Richardson number. D *u *u *u H# G H, G "k (10) I *x *x *x G H G k *¹ G "!bg . (11) G p *x G The coe$cients used in the k}e model are standard [11]. It is noted that in simulating compressible turbulent buoyant #ow, the value of buoyancy constant C is controversial. The controversy has to do with the de"nition of the #ux Richardson number R to which C is a multiplier. In our previous study [12], C was revised to D be an empirical function of ventilation Reynolds number and densimetric Froude number. But the e!ectiveness is limited. In the present study, C "0.8 was chosen for the general enclosure "re, as suggested by Hossain [13].
2.2. Combustion models Three representative combustion models, namely the VHS, the eddy break-up and the prePDF models are selected. Their basic principles and features are discussed below. 2.2.1. Volumetric heat source (VHS) model The volumetric heat source model is the simplest model for combustion. The "re source is modeled as a volumetric heat source, which is patched into the computational domain. For the case of tunnel "re, a mass and a momentum source are also patched to account the gas mixture entering to the tunnel from a gas burner. In the VHS model, the direct contribution of combustion species is neglected. The VHS model excludes the species transport equation and cannot predict the species concentration distribution. 2.2.2. Eddy break-up model The eddy break-up model is based on the solution of species transport equations for reactant and product concentrations. The reaction mechanism must be explicitly de"ned and it can be simple or multi-stage reactions. The reactions are assumed to be in"nitely fast whenever fuel and oxidant simultaneously exist at a point. The e!ects of combustion on #ow are estimated in the source terms in species transport equation and energy equation. The conservation equation of species is written as following: * * (ou m )"! J #R #S (12) G GY GY GY *x GY G *x G G where R is the mass rate of creation or depletion by chemical reaction, R " R , GY GY I GY I which can be estimated by the eddy break-up model [8]; S is the rate of creation by GY addition from the dispersed phase; J is the di!usion #ux of species i , which arises GY G
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due to concentration gradients, and is written as
k *m Y G J "! oD # GY G GY K Sc *x G
(13)
where Sc is the e!ective Schmidt number. Sc "0.7 is used in the calculation. In the eddy break-up model of Magnussen and Hjertagar [8], the e!ects of turbulence on the chemical reaction rates are accounted for. The model relates the rate of reaction to the dissipation rate of turbulent eddies containing products and reactants. The dissipation rate of turbulent eddies is assumed to be proportional to the ratio of the turbulent kinetic dissipation and turbulent kinetic energy, e/k [14]. The rate of reaction R is given by the smallest of the two GY I expressions below: e m 0 , R "!l M G Ao GY I GY I G k l M 0 I 0
(14.1)
e m . . , R G "!l M G ABo G I GY I G k l M . . I .
(14.2)
where m is the mass fractions of any product species, P, and m represents the mass . 0 fraction of a particular reactant, R, which is the reactant species giving the smallest value of R . A and B are empirical constants, A"4.0 and B"0.5. GY I 2.2.3. Presumed PDF (prePDF) model The prePDF model [15,16] is based on the solution of transport equations for one or two conserved scalars (the mixture fractions and/or its variance). The chemistry is modeled by equilibrium model, which assumes that the chemistry is rapid enough for chemical equilibrium to exist at the molecular level. It computes species from mixture fraction by an algorithm based on the minimization of Gibbs free energy. Individual component concentrations for the species of interest are derived from the predicted mixture fraction distribution. The prePDF model can account for the interaction of turbulence and chemistry. For a simple fuel/oxidizer system, the mixture fraction can be de"ned as m $ f" m #m $ -
(15)
where f is a conserved quantity. In turbulent #ow, its mean (time averaged) value is obtained by solving the following conservation equation:
* * k *fM (ou fM )" #S G K *x *x p *x G G G where S is due solely to phase change. S "0, if there is no phase change. K K
(16)
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In addition, a conservation equation for the mixture fraction variance (f Y) is introduced as
* * * k *f *fM e (of )# (ou f )" #C k !C o f G E *x B k *t *x *x p *x G G G G
(17)
where the constants p , C and C take the values 0.7, 2.86 and 2.0, respectively [16]. E B The mixture fraction variance is used in the closure model describing turbulencechemistry interactions. After this single conserved scalar f in the "eld is determined, other important scalars of interest can be derived from it without solving individual transport equation according to the equilibrium model. However in turbulent reaction #ow, not only the instantaneous values but also the time-averaged values of #ow scalars are widely concerned, a probability density function (PDF) is introduced to account for the turbulence-chemistry interaction. This PDF describes the fraction of time that the #uctuating variable f takes on a value between f and f#*f; it can be written as 1 p( f )*f" lim q G ¹ 2 G
(18)
where q is the fraction of time that f spends in the *f band. The shape of the function G p( f ) depends on the nature of the turbulent #uctuations in f. The PDF describes the temporal #uctuation of f in the turbulent #ow. When the p( f ) is determined at each position, it can be used as the weighting function to calculate the time-averaged mean values of species concentrations, density and temperature using the integral equation as follows
" G
p( f ) ( f ) df G
(19)
Generally, p( f ) is represented by the b-function, which is given by following functions: f ?\(1!f )@\ p( f )" f ?\(1!f )@\ df
(20)
where a"fM
fM (1!fM ) f Y
!1
and
b"(1!fM )
fM (1!fM ) f Y
!1 .
(21)
The prePDF model allows intermediate species formation, dissociation e!ects and the coupling between turbulence and chemistry to be accounted for. The solutions of the transport equations of many species are omitted, which can save a lot of computations.
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2.3. Radiative heat transfer To account for the radiative heat transfer in enclosure "res, the Discrete Transfer Radiation Model (DTRM) [17] is incorporated into the turbulence k}e model together with three combustion sub-models. Heating or cooling of surfaces due to radiation and/or heat sources can be included in the model. Based on the e!ective gray gas approximation and the concept of the absorption coe$cient, the change in radiant intensity, dI, along a path, ds, can be written as dI ap¹ #aI" ds n
(22)
where a is absorption coe$cient, p is Stefan}Boltzmann constant, T is local temperature, and I is total hemispherical intensity. As smoke particles are generally very small for scattering e!ects, both in-scattering and out-scattering terms are neglected.
3. Numerical solution The computations were carried out using Fluent [18], a commercial computational #uid dynamics (CFD) code. The governing equations are solved using the "nitevolume method in a staggered grid system. The algorithm employed is the SIMPLEC. Power-law scheme is used for the numerical simulation. Although high-order discretization scheme such as QUICK [19] is available in the code, sensitivity tests in room and tunnel "re showed that the results were not unduly tainted by numerical errors. For the case of shopping mall "re, #uctuation in convergence was detected with QUICK scheme. As the convergence criterion, the sum of the normalised absolute residuals in each control volume for all the variables is controlled to be less than 10\.
4. Enclosure 5res considered To examine the performance of the combustion models, they are applied to three representative enclosure "res. 4.1. Room xre Steckler et al. conducted a benchmark compartment "re experiment in 1982 [20]. The dimension of the compartment room is 2.8;2.8;2.18 m with a 0.74;1.83 m door as shown in Fig. 1. The "re was located at the center of the room and occupied an area of 0.45;0.45 m and had heat release rate of 62.9 kW. For the VHS model, the heat source was uniformly distributed in a volume of 0.45 m;0.45 m;1.2 m. For the eddy break-up and prePDF model, chemical reaction was assumed to take place in the "re area with a height equivalent to two-grid size (0.1 m). An average outdoor temperature of 302 K was assumed.
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Fig. 1. Sketch of the Steckler's room "re.
Simulation of the Steckler's room "re was carried out with grid size of 48;48;41 grids. The "re was simulated by combustion of CH in the prePDF and the eddy break-up models. Gas #ow velocity was estimated to be 0.00803 m/s. E!ect of radiation was taken into account using discrete transfer radiation model (DTRM). Floor, ceiling, and walls were assumed as adiabatic. To compare with the experimental data [20], both pro"les of velocity and temperature at the middle of the opening are plotted in Fig. 2. It is seen that none of the models can give a close prediction in velocity and temperature pro"les. The VHS model predicts velocity and temperature pro"les well at the region where the ceiling height is less than 0.7 m. But it fails to follow the slope of the increase in velocity and temperature as the height is above 0.7 m. The prePDF model can predict the maximum velocity and temperature near the ceiling, but it shows large discrepancies in the rest of the region. All three models disagree with the experimental data particularly in the region around the height of 0.8 to 1.3 m, where the rapid changes of velocity and temperature were experienced. The neutral layer of the #ow "eld (u"0 m/s) was situated at the height of 1.03 m in the experiment approximately while it is predicted at the height around 0.745}0.824 m in the numerical simulations. The reason for the discrepancies in the numerical prediction of room "re can be complicated. On one hand, the turbulent combustion models may be incapable of predicting the velocity and temperature near the "re source. The large gradients in velocity and temperature occurred at the middle of the room height are the results of the complicated interaction between "re plume and air entrainment. Although the interaction of energy and turbulence is included in the turbulence k}e model, modelling of turbulence-chemistry interaction is inadequate. This is because the chemistry or reaction kinetics for actual combustion process in the Steckler's room "re was not known. The de"ciency of turbulent combustion models become more obvious when
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Fig. 2. Results of the Steckler's room "re case: (a) temperature distribution; (b) velocity distribution.
the velocity and temperature "elds in the region near to the "re source are concerned. On the other hand, it may be a result of numerical errors. The grid density or assumption of adiabatic walls are the possible causes. We compare the results with that obtained by Lewis et al. [21]. Table 1 lists the comparison between prediction of the height of the neutral layer h (relative to that of the doorway h ), the respective , in#ow and out#ow mass #uxes, and the upper layer temperature along the middle plane of the doorway. The numerical simulation of Lewis et al. [21] were based on a speci"cally developed CFD code SOFIE for building "re prediction. They used turbulent k}e model with buoyancy modi"cation. Eddy break-up combustion model is incorporated and radiative heat transfer was considered using the DTRM. A "ne grid density of 140944 was employed. Obviously, the results obtained by Lewis et al. predict the Steckler's room "re much better than any of the present combustion models. 4.2. Shopping mall xre The experiment on shopping mall "re was described by Markatos and Cox [22]. The experimental compartment was 3 m high, 6 m wide and 9 m long with an
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Table 1 Comparison between models and with experiment
VHS Eddy breakup PrePDF Lewis et al. [21] Experiment [20]
h /h ,
In#ow (kg/s)
Out#ow (kg/s)
Temperature (3C)
0.418 0.407 0.450 0.546 0.561
0.568 2.112 1.165 0.521 0.554
1.266 1.117 1.209 0.523 0.571
137 117 113 128 129
Fig. 3. Sketch of shopping mall "re.
adjustable so$t depth between 1 and 1.5 m. Although the aspect ratio of 2 for the testing shopping mall was not su$cient to justify the two-dimensional assumption, e!ort had been made on design of a strip "re source, which contained 3 rectangular pans in an area of 0.5;2 m each and was laid across the width of the mall 1.25 m from the rear wall to approximate a two-dimensional heat and #uid #ow. The fuel used was industrial methylated spirit and the heat output calculated from the weight loss of the central pan was 2.04 MW. The geometry of the shopping mall is shown in Fig. 3. To simulate the shopping mall "re, a computational grid size of 96;24 grids were adopted. Ambient temperature was 293 K. The heat input used in the simulation was 324 kW/m being product of the measured rate of mass loss of the fuel. For the VHS model, the heat source was uniformly distributed on an area of 0.45;1.70 m. For the eddy breakup and the prePDF model, the chemical reaction was assumed to take place in the "re area with a height equivalent to two-grid size (0.25 m). Walls were assumed to be adiabatic. Fire was simulated by combustion of industrial methylated spirit in the eddy breakup and prePDF models and the assumed gas #ow velocity was 0.01516 m/s. The results of numerical simulation are shown in Fig. 4. Fig. 4a shows the velocity vectors in the shopping mall. Multiple #ow layers of air movement are observed. Particularly, a large eddy at the corner of the shopping mall above the "re source is predicted, which agrees with the #ow pattern in the experiment observed by Markatos and Cox [21]. Temperature distributions are compared with experimental data at three columns situated at 2.56, 5.76 and 8.96 m from the rear wall as shown in Figs. 4b}d respectively. At the column x"2.56 m (Fig. 4b), which is the nearest to the "re
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Fig. 4. The shopping mall "re case: (a) #ow pattern; (b) temperature pro"les at column 1 (x"2.56 m); (c) temperature pro"les at column 2 (x"5.76 m); (d) temperature pro"les at column 3 (x"8.96 m).
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source, the results of the prediction are poor. The result of the VHS model predicts well the large gradient of the temperature pro"le up to the height around 1 m, where the neutral plane (u"0 m/s) exists. But it fails to predict the temperature above 1.5 m. On the other hand, the results of the eddy breakup and the prePDF models are close to the experimental data at the region above the neutral plane, but perform badly at the region below 1.5 m. At the column 2, which is 5.76 m from the rear wall (Fig. 4c), the VHS and eddy breakup models over-predict the experimental results in most of the region. The prePDF model shows a reasonable agreement except at the region where large temperature gradient occurred. At the column 3, which is 8.96 m away from the rear wall (Fig. 4d) and therefore relatively far from the "re source, the prePDF model performances well. However, the VHS and eddy breakup model resulted in large discrepancies at the region above 1.5 m. The results of the numerical prediction in the shopping mall "re show that the all three combustion models can predict reasonably on temperature pro"les. Among the combustion models tested, none of them can perform well in all measuring stations compared. 4.3. Tunnel xre The experiment of tunnel "re was conduced in a small-scale tunnel in the laboratory. The detailed description can be found in our recent report on the experiment [23]. The basic con"guration and coordinate system of the main test section is shown in Fig. 5. The main test section is 6 m long with rectangular cross section 0.3 m high and 0.9 m wide. The "re source is located 1.5 m from the inlet of the test section at central of the #oor level. The burner occupies an area of 0.18;0.15 m with longer side set along the tunnel axis. Lique"ed petroleum gas (LPG) is used as fuel. The majority of the test section is made of perspex with a thickness of 8 mm. Silica glass and aluminium are partially used at the ceiling and #oor areas close to the "re source. Longitudinal ventilation is simulated by an axial fan located at the end of the di!user. The speed of the fan can be varied by supplying di!erent voltages to it. In the experimental study, two heat release rates, 3.15 and 4.75 kW were studied under four di!erent ventilation #ow velocities at 0.13, 0.31, 0.52 and 0.61 m/s, respectively. Since heat release rates were well controlled by the burner in tunnel "re experiments, for all three combustion models, "re source were simulated in the burner surface with a height equivalent to two-grid size (0.01 m). The temperatures are measured at three cross-sections. Station 1 is located upstream at x"0.9 m and stations 2 and 3 are located downstream at x"3.3 m and x"5.1 m, respectively. The numerical simulation of tunnel "re was carried out in half of the tunnel with 150;40;15 (length;height;width) grids due to the symmetric structure of the tunnel. Relatively large number of grids are allocated in the direction of height to account for the rapid change in velocity and temperature due to the buoyancy force. Ambient temperature is assumed to be 300 K. Heat loss through conduction in the tunnel wall is taken into account by applying conducting wall boundary condition in the computation.
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Fig. 5. Sketch of tunnel "re.
There is a good agreement in predicting general #ow patterns of "re-induced air#ow in a ventilated tunnel. Fig. 6 plots the results of #ow visualization in the tunnel "re experiment at mean ventilation velocity U "0.13 m/s and heat release rate Q" 3.15 kW. It is seen that a signi"cant upstream back #ow is formed near the entrance of the main test section. Despite the longitudinal ventilation in the tunnel, a thin layer of recirculating #ow near the #oor brings smoke back against the ventilation. The recirculating #ow becomes more evident at section 2 downstream, which is further away from the "re source. The corresponding result simulated by the prePDF model is shown in Fig. 7a. The main features of the "re-induced air #ow at relatively low ventilation velocity: upstream back #ow, temperature/smoke strati"cation, and recirculating #ow downstream, are reproduced. The results of the VHS and the eddy breakup models in the prediction of #ow pattern are similar to that of the prePDF model. This indicates that there is little e!ect on di!erent combustion models in predicting qualitative patterns of the air#ow in the tunnel "re. Predicted temperature distributions along verticals on the centerline of the tunnel are compared with the experimental measurements in Figs. 7b}d. For the case at U "0.13 m/s and Q"3.15 kW, it is observed that the temperature pro"les predicted by the eddy breakup model and the prePDF model di!er only slightly. The predicted temperature pro"les are reasonable in most of the region at station 1 upstream and station 3 downstream. However, all three combustion models show poor performance at station 2 downstream, a location near the "re source. The predicted temperature rise from the height of 0.15 m to 0.28 m is 55C, while experimental data shows that the temperature rise only reaches 553C at the height of 0.26 m. The predicted temperature distribution at di!erent heat release rates and ventilation velocities in the tunnel "re are shown in Figs. 8a and b. In Fig. 8a, the heat release rate was changed from 3.15 to 4.75 kW. The corresponding temperature rise in the tunnel was increased. It can be seen that with the increase of the heat release rate, the di!erence in prediction of temperature between the prePDF and the eddy breakup models appear. The prePDF model performs the best among the combustion models. The prePDF model also shows its performance superior than other two models when the ventilation velocity is increased to 0.61 m/s. At the large ventilation velocity, the #ow downstream tends to become more mixed and the temperature gradient along the direction of height become #at.
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Fig. 6. Tunnel "re case: visualized #ow pattern at U "0.13 m/s and Q"3.15 kW.
5. Conclusions Numerical simulation of "re-induced air#ow in enclosures were conducted to test the performance of three combustion models in typical cases of enclosure "re: room
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Fig. 7. The tunnel "re case (U "0.13 m/s, Q"3.15 kW): (a) #ow pattern; (b) temperature pro"les at station 1 (x"0.9 m); (c) temperature pro"les at column 2 (x"3.3 m); (d) temperature pro"les at column 3 (x"5.1 m).
"re, shopping mall "re and tunnel "re. The prediction of general #ow patterns is satisfactory. The main features, such as, recirculating #ow and temperature strati"cation in room and shopping mall "re, upstream back #ow and circulating #ow downstream in tunnel "re are characterized. The predictions of velocity and temperature distribution by the three combustion models were compared with experimental data. None of the combustion model gives consistent performance in prediction of temperature and velocity "elds in all the cases
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Fig. 8. The tunnel "re case: (a) temperature pro"les at station 1 (x"0.9 m, Q"4.75 kW, U "0.13 m/s); (b) temperature pro"les at station 3 (x"5.1 m, Q"3.15 kW, U "0.61 m/s).
tested. For the Steckler's room "re, the performances of the VHS model and the prePDF model are similar, while the eddy breakup model is poor. The VHS model performs well at the measuring station close to the "re for the shopping mall "re, while the prePDF model appears to perform best at the station upstream and relatively far away from the "re source. For the tunnel "re, the eddy breakup model and prePDF model perform equally well. The performance of the prePDF model is further improved at high heat release rate and high ventilation velocity. In general, the performance of prePDF model is more consistent, although there is no distinct performance which can be commented as a good combustion model for enclosure "re simulation, especially at the #ow region where "re source is nearby and large temperature gradient exists. This indicates the current turbulent combustion models are inadequate to account for the interaction of combustion, turbulence, radiative heat transfer of participating media including smoke and soot. In addition, numerical errors may be contributing to the observed discrepancies with experimental data. However, this does not deter the application of "eld model in enclosure "res. As demonstrated in the present and many previous studies, one can give a good prediction to an enclosure "re, provided that good estimation can be made on the heat release rate and its spatial distribution. Our study suggests that more adequate turbulent combustion models are required for simulating general enclosure "res for which the chemistry or reactive kinetics for
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actual combustibles is described. In this direction, the results of recent work by Moss and Stewart [24] are encouraging. References [1] Jones WW. A review of compartment "re models. NBSIR 83-2684, 1983. p. 1}38. [2] Duong DQ. The accuracy of computer "re models: some comparisons with experimental data from Asutrlia. Fire Safety J 1990;16:415}31. [3] Dembsey NA, Pagni PJ, Williamson RB. Compartment "re experiments: comparison with models. Fire Safety J 1995;25:187}227. [4] Peacock RD, Reneke PA, Forney CL, Kostreva MM. Issues in evaluation of complex "re models. Fire Safety J 1998;30:103}36. [5] Yang KT. Recent development in "eld modelling of compartment "res. JSME Int J Ser B 1994;37(4):702}17. [6] Beard AN. Fire models and design. Fire Safety J 1997;28:117}38. [7] Cox G, Kumar S. Fielding modeling of "re in forced ventilated enclosures. Combustn Sci Techol 1987;52:7}23. [8] Magnussen BF, Hjertager BH. On mathematical models of turbulent combustion with special emphasis on soot formation and combustion. 16th Symposium (International) on Combustion, Cambridge, MA, 1976. p. 719}29. [9] Goldin GM, Menon S. A comparison of scalar PDF turbulent combustion models. Combust Flame 1998;113:442}53. [10] Eaton AM, Smoot LD, Hill SC, Eatough CN. Components, formulations, solutions, evaluations, and applications of comprehensive combustion models. Prog Energy Combust Sci 1999;25:387}436. [11] Rodi W. Turbulence models and their applications in hydraulics * a state-of-the-art review. Book Publication of International Association for Hydraulic Research, Delft, Netherlands, 1984. [12] Xue H, Hihara E, Saito T. Modeling of air#ow in a "re tunnel (1st report, study of two-dimensional turbulence model). Trans Jpn Soc Mech Eng 1991;57(536):1457}62 ((in Japanese)). [13] Hossain MS. Mathematische Modellierung von Turbulenten Auftruebsstromun-gen. PhD thesis, University of Karlsruhe, Germany, 1980. [14] Spalding DB. Mixing and chemical reaction in steady con"ned turbulent #ames. 13th Symposium (International) on Combustion, Salt Lake City, UT, 1970. [15] Sivathann YR, Faeth GM. Generalized state relationship for scalar properties in non-premixed hydrocarbon/air #ame. Combust Flame 1990;82:211}30. [16] Jones WP, Whitelaw JH. Calculation methods for reacting turbulent #ows: a review. Combust Flame 1982;48:1}26. [17] Carvalho MG, Farias T, Fontes P. Predicting radiative heat transfer in absorbing, emitting, and scattering media using the discrete transfer method. Fund Radiat Heat Transfer, ASME HTD 1991;160:17}26. [18] Fluent Inc. Fluent 4.4 user's guide. Lebanon, NA, 1996. [19] Leonard BP. A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput Methods Appl Mech Engng 1979;19:59}98. [20] Steckler KD, Quintiere JG, Rinkinen WJ. Flow induced by "re in a compartment. National Bureau of Standards, Center for Fire Research, NBSIR 82-2520, 1982. [21] Lewis MJ, Moss MB, Rubini, PA. CFD modeling of combustion and heat transfer in compartment "res. Proceedings of the 5th International Symposium on Fire Safety Science, IAFSS, 1997. p. 463}74. [22] Markatos NC, Malin MR, Cox G. Mathematical modelling of buoyancy-induced smoke #ow in enclosures. Int J Heat Mass Transfer 1982;25:63}74. [23] Xue H, Chew TC, Tay KL, Cheng YM. Control of ventilation air#ow for tunnel "re safety. Combust Sci Technol 2000;152:179}96. [24] Moss JB, Stewart CD. Flamelet-based smoke properties for the "eld modelling of "res. Fire Safety J 1998;30:229}50.
Comparison of di!erent combustion models in enclosure "re simulation H. Xue*, J.C. Ho, Y.M. Cheng Department of Mechanical and Production Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 Received 26 July 1999; received in revised form 10 July 2000; accepted 17 July 2000
Abstract In this study, three combustion models, the volumetric heat source (VHS) model, the eddy break-up model and the presumed probability density function (prePDF) model, are examined in enclosure "re simulation. The combustion models are compared and evaluated for their performance in predicting three typical enclosure "res, a room "re, a shopping mall "re and a tunnel "re. High Reynolds number turbulence k}e model with buoyancy modi"cation and the discrete transfer radiation model (DTRM) are used in the simulation. Corresponding experimental data from the literature are adopted for validation. The results show satisfactory prediction in #ow patterns and features in the complex enclosure "res. However, it is shown that these combustion models are not able to show consistent performance over the di!erent locations and enclosure "res. The needs for adequate turbulent combustion models in enclosure "res are discussed. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Combustion model; Fire; Simulation; Smoke concentration
1. Introduction Accurate prediction of the "re-induced air velocity, temperature, and smoke concentration in enclosure "res become more and more important for designing e$cient "re protection systems. Much e!ort has been made in "re modeling which deals with the development of quantitative descriptions of the "re phenomena in terms of the physical and chemical processes as functions of the ignition source, space geometry, and material content. Jones [1], Duong [2], Dembsey et al. [3] and Peacock et al. [4] * Corresponding author. Tel.: #65-874-6479; fax: #65-779-1459. E-mail address: [email protected] (H. Xue). 0379-7112/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 3 7 9 - 7 1 1 2 ( 0 0 ) 0 0 0 4 3 - 6
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Notation a C ,C ,C C,C E B C I f f Y g h , I i J k M m P p(f) Q R T ; u u
absorption coe$cient constants of the k}e model constants of the prePDF model constant of the k}e model mixture fraction mixture fraction variance gravitational acceleration height of the neutral layer total hemispherical intensity chemical species di!usion #ux of species i turbulence kinetic energy molecular weight of species i mass mean pressure probability density function heat release rate of the "re source mass rate of creation or depletion by chemical reaction mean temperature mean velocity of the cross section mean velocity component #uctuating velocity component
Greek letters b C e k k l o p p ,p I C p
thermal expansion coe$cient exchange coe$cient turbulence energy dissipation dynamic viscosity coe$cient turbulent viscosity molar stoichiometric coe$cient air density Stefan}Boltzmann constant turbulent Schmit number turbulent Prandtl number general scalar quantity
Subscript k P R
reaction product reactant
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investigated a number of "re models and conducted intensive comparison and evaluation with "re experimental data. But only zone models were dealt with in their reviews. Yang [5] studied several "eld models including PHOENICS (CHAM of North America, Inc.) and UNDSAFE developed at the University of Notre Dame. Beard [6] evaluated "eld models like JASMINE [7] and FLOW3D (UK AEA Technology) and discussed the limitations and capabilities of the "re models. However, their studies focused on the comparison and evaluation of overall ability of the CFD code. Details on the e!ect of combustion sub-models in the code are usually lacking. An enclosure "re is a complex phenomenon. In "eld modeling, sub-models of combustion, turbulence and radiative heat transfer are needed to describe an enclosure "re. Great complexity arises in view of the fact that there are strong interactions among these three e!ects. At present, there are many shortcomings in the existing "eld models in accounting for such complicated interactions. While current sub-models for buoyancy, compressibility, turbulence, and thermal radiation are quite adequate [5], the inability of turbulent combustion model is outstanding. This is due to the nature of enclosure "re phenomena where pyrolysis and gasi"cation are inherent and extremely di$cult to model. In addition, it is not easy to accurately know the reaction kinetics and combustion rate in enclosure "res. Consequently, the detailed combustion chemistry in coupling turbulence and radiation are left unknown even though the turbulent combustion sub-model might be included in the computational algorithm. It is not surprising to see the selection of combustion models among researchers varies in their application to di!erent types of enclosure "res at this stage. The aim of the present study is to examine the performance of three commonly used combustion models. The "rst is the volumetric heat source (VHS) model, which does not take chemical reaction into account, instead, it sets the heat release rate equivalent to that of the assumed "re. The VHS model is the simplest "re model and easy for implementation. The second is the eddy break-up model presented by Magnussen and Hjertager [8], who attempted to simultaneously account for mixing and "nite chemical reaction rates. The third is a mixture fraction approach using presumed PDF (prePDF) model, where an assumed shape probability density function (PDF) is generally used to take into account of turbulence}chemistry interaction. Although these models have been intensively compared and evaluated in combustors [9,10], studies of these combustion models in the context of enclosure "res are rare. We selected three typical cases of enclosure "re, namely, a room "re, a shopping mall "re and a tunnel "re for the study. The results of di!erent combustion models are compared and evaluated with available experimental data.
2. The mathematical models 2.1. Flow xeld model Heated air movement is the key concern in an enclosure. The turbulent buoyant #ow is governed by the equations expressing the conservation of mass, momentum,
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energy and concentration of species. When steady-state process is considered, the governing equations can be written in a Cartesian tensor form as continuity equation: *(ou ) G "0; *x G
(1)
momentum equations:
*(ou u ) *P * *u G H "! # k G !ou u #og ; G H G *x *x *x *x H G H H
(2)
general purpose transport equations:
*(ou ) * *
H " C !ou #S , G ( *x *x *x H G G
(3)
where denotes enthalpy, concentration of species i , respectively. The term S stands ( for the appropriate source or sink of the variable concerned. For enthalpy and species transport equations, the source term S is the rate of heat release and ( creation/destruction of species i in the combustion, respectively. The change of density is only related to the temperature of the air through the equation of state o"o(¹).
(4)
For the closure of the governing equations, the two-equation k}e model of turbulence is used [11]. According to eddy viscosity concept, the turbulent kinetic energy k and dissipation e equations can be derived:
* k *k *(ou k) H " #S , I *x *x p *x H G I G
(5)
*(ou e) * k *e H " #S , C *x *x p *x H G C G
(6)
k k "oC . Ie
(7)
The #uid motion in enclosure "res is a!ected by mean buoyancy force. Rodi [11] modi"ed the source terms S and S as I C S "G #G !oe, I I
(8)
e e S "C (G #G )(1#C R )!C o D k C k I
(9)
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where G and G denote the contributions of stress and buoyant force, respectively, I and R is #ux Richardson number. D *u *u *u H# G H, G "k (10) I *x *x *x G H G k *¹ G "!bg . (11) G p *x G The coe$cients used in the k}e model are standard [11]. It is noted that in simulating compressible turbulent buoyant #ow, the value of buoyancy constant C is controversial. The controversy has to do with the de"nition of the #ux Richardson number R to which C is a multiplier. In our previous study [12], C was revised to D be an empirical function of ventilation Reynolds number and densimetric Froude number. But the e!ectiveness is limited. In the present study, C "0.8 was chosen for the general enclosure "re, as suggested by Hossain [13].
2.2. Combustion models Three representative combustion models, namely the VHS, the eddy break-up and the prePDF models are selected. Their basic principles and features are discussed below. 2.2.1. Volumetric heat source (VHS) model The volumetric heat source model is the simplest model for combustion. The "re source is modeled as a volumetric heat source, which is patched into the computational domain. For the case of tunnel "re, a mass and a momentum source are also patched to account the gas mixture entering to the tunnel from a gas burner. In the VHS model, the direct contribution of combustion species is neglected. The VHS model excludes the species transport equation and cannot predict the species concentration distribution. 2.2.2. Eddy break-up model The eddy break-up model is based on the solution of species transport equations for reactant and product concentrations. The reaction mechanism must be explicitly de"ned and it can be simple or multi-stage reactions. The reactions are assumed to be in"nitely fast whenever fuel and oxidant simultaneously exist at a point. The e!ects of combustion on #ow are estimated in the source terms in species transport equation and energy equation. The conservation equation of species is written as following: * * (ou m )"! J #R #S (12) G GY GY GY *x GY G *x G G where R is the mass rate of creation or depletion by chemical reaction, R " R , GY GY I GY I which can be estimated by the eddy break-up model [8]; S is the rate of creation by GY addition from the dispersed phase; J is the di!usion #ux of species i , which arises GY G
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due to concentration gradients, and is written as
k *m Y G J "! oD # GY G GY K Sc *x G
(13)
where Sc is the e!ective Schmidt number. Sc "0.7 is used in the calculation. In the eddy break-up model of Magnussen and Hjertagar [8], the e!ects of turbulence on the chemical reaction rates are accounted for. The model relates the rate of reaction to the dissipation rate of turbulent eddies containing products and reactants. The dissipation rate of turbulent eddies is assumed to be proportional to the ratio of the turbulent kinetic dissipation and turbulent kinetic energy, e/k [14]. The rate of reaction R is given by the smallest of the two GY I expressions below: e m 0 , R "!l M G Ao GY I GY I G k l M 0 I 0
(14.1)
e m . . , R G "!l M G ABo G I GY I G k l M . . I .
(14.2)
where m is the mass fractions of any product species, P, and m represents the mass . 0 fraction of a particular reactant, R, which is the reactant species giving the smallest value of R . A and B are empirical constants, A"4.0 and B"0.5. GY I 2.2.3. Presumed PDF (prePDF) model The prePDF model [15,16] is based on the solution of transport equations for one or two conserved scalars (the mixture fractions and/or its variance). The chemistry is modeled by equilibrium model, which assumes that the chemistry is rapid enough for chemical equilibrium to exist at the molecular level. It computes species from mixture fraction by an algorithm based on the minimization of Gibbs free energy. Individual component concentrations for the species of interest are derived from the predicted mixture fraction distribution. The prePDF model can account for the interaction of turbulence and chemistry. For a simple fuel/oxidizer system, the mixture fraction can be de"ned as m $ f" m #m $ -
(15)
where f is a conserved quantity. In turbulent #ow, its mean (time averaged) value is obtained by solving the following conservation equation:
* * k *fM (ou fM )" #S G K *x *x p *x G G G where S is due solely to phase change. S "0, if there is no phase change. K K
(16)
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In addition, a conservation equation for the mixture fraction variance (f Y) is introduced as
* * * k *f *fM e (of )# (ou f )" #C k !C o f G E *x B k *t *x *x p *x G G G G
(17)
where the constants p , C and C take the values 0.7, 2.86 and 2.0, respectively [16]. E B The mixture fraction variance is used in the closure model describing turbulencechemistry interactions. After this single conserved scalar f in the "eld is determined, other important scalars of interest can be derived from it without solving individual transport equation according to the equilibrium model. However in turbulent reaction #ow, not only the instantaneous values but also the time-averaged values of #ow scalars are widely concerned, a probability density function (PDF) is introduced to account for the turbulence-chemistry interaction. This PDF describes the fraction of time that the #uctuating variable f takes on a value between f and f#*f; it can be written as 1 p( f )*f" lim q G ¹ 2 G
(18)
where q is the fraction of time that f spends in the *f band. The shape of the function G p( f ) depends on the nature of the turbulent #uctuations in f. The PDF describes the temporal #uctuation of f in the turbulent #ow. When the p( f ) is determined at each position, it can be used as the weighting function to calculate the time-averaged mean values of species concentrations, density and temperature using the integral equation as follows
" G
p( f ) ( f ) df G
(19)
Generally, p( f ) is represented by the b-function, which is given by following functions: f ?\(1!f )@\ p( f )" f ?\(1!f )@\ df
(20)
where a"fM
fM (1!fM ) f Y
!1
and
b"(1!fM )
fM (1!fM ) f Y
!1 .
(21)
The prePDF model allows intermediate species formation, dissociation e!ects and the coupling between turbulence and chemistry to be accounted for. The solutions of the transport equations of many species are omitted, which can save a lot of computations.
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2.3. Radiative heat transfer To account for the radiative heat transfer in enclosure "res, the Discrete Transfer Radiation Model (DTRM) [17] is incorporated into the turbulence k}e model together with three combustion sub-models. Heating or cooling of surfaces due to radiation and/or heat sources can be included in the model. Based on the e!ective gray gas approximation and the concept of the absorption coe$cient, the change in radiant intensity, dI, along a path, ds, can be written as dI ap¹ #aI" ds n
(22)
where a is absorption coe$cient, p is Stefan}Boltzmann constant, T is local temperature, and I is total hemispherical intensity. As smoke particles are generally very small for scattering e!ects, both in-scattering and out-scattering terms are neglected.
3. Numerical solution The computations were carried out using Fluent [18], a commercial computational #uid dynamics (CFD) code. The governing equations are solved using the "nitevolume method in a staggered grid system. The algorithm employed is the SIMPLEC. Power-law scheme is used for the numerical simulation. Although high-order discretization scheme such as QUICK [19] is available in the code, sensitivity tests in room and tunnel "re showed that the results were not unduly tainted by numerical errors. For the case of shopping mall "re, #uctuation in convergence was detected with QUICK scheme. As the convergence criterion, the sum of the normalised absolute residuals in each control volume for all the variables is controlled to be less than 10\.
4. Enclosure 5res considered To examine the performance of the combustion models, they are applied to three representative enclosure "res. 4.1. Room xre Steckler et al. conducted a benchmark compartment "re experiment in 1982 [20]. The dimension of the compartment room is 2.8;2.8;2.18 m with a 0.74;1.83 m door as shown in Fig. 1. The "re was located at the center of the room and occupied an area of 0.45;0.45 m and had heat release rate of 62.9 kW. For the VHS model, the heat source was uniformly distributed in a volume of 0.45 m;0.45 m;1.2 m. For the eddy break-up and prePDF model, chemical reaction was assumed to take place in the "re area with a height equivalent to two-grid size (0.1 m). An average outdoor temperature of 302 K was assumed.
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Fig. 1. Sketch of the Steckler's room "re.
Simulation of the Steckler's room "re was carried out with grid size of 48;48;41 grids. The "re was simulated by combustion of CH in the prePDF and the eddy break-up models. Gas #ow velocity was estimated to be 0.00803 m/s. E!ect of radiation was taken into account using discrete transfer radiation model (DTRM). Floor, ceiling, and walls were assumed as adiabatic. To compare with the experimental data [20], both pro"les of velocity and temperature at the middle of the opening are plotted in Fig. 2. It is seen that none of the models can give a close prediction in velocity and temperature pro"les. The VHS model predicts velocity and temperature pro"les well at the region where the ceiling height is less than 0.7 m. But it fails to follow the slope of the increase in velocity and temperature as the height is above 0.7 m. The prePDF model can predict the maximum velocity and temperature near the ceiling, but it shows large discrepancies in the rest of the region. All three models disagree with the experimental data particularly in the region around the height of 0.8 to 1.3 m, where the rapid changes of velocity and temperature were experienced. The neutral layer of the #ow "eld (u"0 m/s) was situated at the height of 1.03 m in the experiment approximately while it is predicted at the height around 0.745}0.824 m in the numerical simulations. The reason for the discrepancies in the numerical prediction of room "re can be complicated. On one hand, the turbulent combustion models may be incapable of predicting the velocity and temperature near the "re source. The large gradients in velocity and temperature occurred at the middle of the room height are the results of the complicated interaction between "re plume and air entrainment. Although the interaction of energy and turbulence is included in the turbulence k}e model, modelling of turbulence-chemistry interaction is inadequate. This is because the chemistry or reaction kinetics for actual combustion process in the Steckler's room "re was not known. The de"ciency of turbulent combustion models become more obvious when
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Fig. 2. Results of the Steckler's room "re case: (a) temperature distribution; (b) velocity distribution.
the velocity and temperature "elds in the region near to the "re source are concerned. On the other hand, it may be a result of numerical errors. The grid density or assumption of adiabatic walls are the possible causes. We compare the results with that obtained by Lewis et al. [21]. Table 1 lists the comparison between prediction of the height of the neutral layer h (relative to that of the doorway h ), the respective , in#ow and out#ow mass #uxes, and the upper layer temperature along the middle plane of the doorway. The numerical simulation of Lewis et al. [21] were based on a speci"cally developed CFD code SOFIE for building "re prediction. They used turbulent k}e model with buoyancy modi"cation. Eddy break-up combustion model is incorporated and radiative heat transfer was considered using the DTRM. A "ne grid density of 140944 was employed. Obviously, the results obtained by Lewis et al. predict the Steckler's room "re much better than any of the present combustion models. 4.2. Shopping mall xre The experiment on shopping mall "re was described by Markatos and Cox [22]. The experimental compartment was 3 m high, 6 m wide and 9 m long with an
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Table 1 Comparison between models and with experiment
VHS Eddy breakup PrePDF Lewis et al. [21] Experiment [20]
h /h ,
In#ow (kg/s)
Out#ow (kg/s)
Temperature (3C)
0.418 0.407 0.450 0.546 0.561
0.568 2.112 1.165 0.521 0.554
1.266 1.117 1.209 0.523 0.571
137 117 113 128 129
Fig. 3. Sketch of shopping mall "re.
adjustable so$t depth between 1 and 1.5 m. Although the aspect ratio of 2 for the testing shopping mall was not su$cient to justify the two-dimensional assumption, e!ort had been made on design of a strip "re source, which contained 3 rectangular pans in an area of 0.5;2 m each and was laid across the width of the mall 1.25 m from the rear wall to approximate a two-dimensional heat and #uid #ow. The fuel used was industrial methylated spirit and the heat output calculated from the weight loss of the central pan was 2.04 MW. The geometry of the shopping mall is shown in Fig. 3. To simulate the shopping mall "re, a computational grid size of 96;24 grids were adopted. Ambient temperature was 293 K. The heat input used in the simulation was 324 kW/m being product of the measured rate of mass loss of the fuel. For the VHS model, the heat source was uniformly distributed on an area of 0.45;1.70 m. For the eddy breakup and the prePDF model, the chemical reaction was assumed to take place in the "re area with a height equivalent to two-grid size (0.25 m). Walls were assumed to be adiabatic. Fire was simulated by combustion of industrial methylated spirit in the eddy breakup and prePDF models and the assumed gas #ow velocity was 0.01516 m/s. The results of numerical simulation are shown in Fig. 4. Fig. 4a shows the velocity vectors in the shopping mall. Multiple #ow layers of air movement are observed. Particularly, a large eddy at the corner of the shopping mall above the "re source is predicted, which agrees with the #ow pattern in the experiment observed by Markatos and Cox [21]. Temperature distributions are compared with experimental data at three columns situated at 2.56, 5.76 and 8.96 m from the rear wall as shown in Figs. 4b}d respectively. At the column x"2.56 m (Fig. 4b), which is the nearest to the "re
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Fig. 4. The shopping mall "re case: (a) #ow pattern; (b) temperature pro"les at column 1 (x"2.56 m); (c) temperature pro"les at column 2 (x"5.76 m); (d) temperature pro"les at column 3 (x"8.96 m).
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source, the results of the prediction are poor. The result of the VHS model predicts well the large gradient of the temperature pro"le up to the height around 1 m, where the neutral plane (u"0 m/s) exists. But it fails to predict the temperature above 1.5 m. On the other hand, the results of the eddy breakup and the prePDF models are close to the experimental data at the region above the neutral plane, but perform badly at the region below 1.5 m. At the column 2, which is 5.76 m from the rear wall (Fig. 4c), the VHS and eddy breakup models over-predict the experimental results in most of the region. The prePDF model shows a reasonable agreement except at the region where large temperature gradient occurred. At the column 3, which is 8.96 m away from the rear wall (Fig. 4d) and therefore relatively far from the "re source, the prePDF model performances well. However, the VHS and eddy breakup model resulted in large discrepancies at the region above 1.5 m. The results of the numerical prediction in the shopping mall "re show that the all three combustion models can predict reasonably on temperature pro"les. Among the combustion models tested, none of them can perform well in all measuring stations compared. 4.3. Tunnel xre The experiment of tunnel "re was conduced in a small-scale tunnel in the laboratory. The detailed description can be found in our recent report on the experiment [23]. The basic con"guration and coordinate system of the main test section is shown in Fig. 5. The main test section is 6 m long with rectangular cross section 0.3 m high and 0.9 m wide. The "re source is located 1.5 m from the inlet of the test section at central of the #oor level. The burner occupies an area of 0.18;0.15 m with longer side set along the tunnel axis. Lique"ed petroleum gas (LPG) is used as fuel. The majority of the test section is made of perspex with a thickness of 8 mm. Silica glass and aluminium are partially used at the ceiling and #oor areas close to the "re source. Longitudinal ventilation is simulated by an axial fan located at the end of the di!user. The speed of the fan can be varied by supplying di!erent voltages to it. In the experimental study, two heat release rates, 3.15 and 4.75 kW were studied under four di!erent ventilation #ow velocities at 0.13, 0.31, 0.52 and 0.61 m/s, respectively. Since heat release rates were well controlled by the burner in tunnel "re experiments, for all three combustion models, "re source were simulated in the burner surface with a height equivalent to two-grid size (0.01 m). The temperatures are measured at three cross-sections. Station 1 is located upstream at x"0.9 m and stations 2 and 3 are located downstream at x"3.3 m and x"5.1 m, respectively. The numerical simulation of tunnel "re was carried out in half of the tunnel with 150;40;15 (length;height;width) grids due to the symmetric structure of the tunnel. Relatively large number of grids are allocated in the direction of height to account for the rapid change in velocity and temperature due to the buoyancy force. Ambient temperature is assumed to be 300 K. Heat loss through conduction in the tunnel wall is taken into account by applying conducting wall boundary condition in the computation.
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Fig. 5. Sketch of tunnel "re.
There is a good agreement in predicting general #ow patterns of "re-induced air#ow in a ventilated tunnel. Fig. 6 plots the results of #ow visualization in the tunnel "re experiment at mean ventilation velocity U "0.13 m/s and heat release rate Q" 3.15 kW. It is seen that a signi"cant upstream back #ow is formed near the entrance of the main test section. Despite the longitudinal ventilation in the tunnel, a thin layer of recirculating #ow near the #oor brings smoke back against the ventilation. The recirculating #ow becomes more evident at section 2 downstream, which is further away from the "re source. The corresponding result simulated by the prePDF model is shown in Fig. 7a. The main features of the "re-induced air #ow at relatively low ventilation velocity: upstream back #ow, temperature/smoke strati"cation, and recirculating #ow downstream, are reproduced. The results of the VHS and the eddy breakup models in the prediction of #ow pattern are similar to that of the prePDF model. This indicates that there is little e!ect on di!erent combustion models in predicting qualitative patterns of the air#ow in the tunnel "re. Predicted temperature distributions along verticals on the centerline of the tunnel are compared with the experimental measurements in Figs. 7b}d. For the case at U "0.13 m/s and Q"3.15 kW, it is observed that the temperature pro"les predicted by the eddy breakup model and the prePDF model di!er only slightly. The predicted temperature pro"les are reasonable in most of the region at station 1 upstream and station 3 downstream. However, all three combustion models show poor performance at station 2 downstream, a location near the "re source. The predicted temperature rise from the height of 0.15 m to 0.28 m is 55C, while experimental data shows that the temperature rise only reaches 553C at the height of 0.26 m. The predicted temperature distribution at di!erent heat release rates and ventilation velocities in the tunnel "re are shown in Figs. 8a and b. In Fig. 8a, the heat release rate was changed from 3.15 to 4.75 kW. The corresponding temperature rise in the tunnel was increased. It can be seen that with the increase of the heat release rate, the di!erence in prediction of temperature between the prePDF and the eddy breakup models appear. The prePDF model performs the best among the combustion models. The prePDF model also shows its performance superior than other two models when the ventilation velocity is increased to 0.61 m/s. At the large ventilation velocity, the #ow downstream tends to become more mixed and the temperature gradient along the direction of height become #at.
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Fig. 6. Tunnel "re case: visualized #ow pattern at U "0.13 m/s and Q"3.15 kW.
5. Conclusions Numerical simulation of "re-induced air#ow in enclosures were conducted to test the performance of three combustion models in typical cases of enclosure "re: room
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Fig. 7. The tunnel "re case (U "0.13 m/s, Q"3.15 kW): (a) #ow pattern; (b) temperature pro"les at station 1 (x"0.9 m); (c) temperature pro"les at column 2 (x"3.3 m); (d) temperature pro"les at column 3 (x"5.1 m).
"re, shopping mall "re and tunnel "re. The prediction of general #ow patterns is satisfactory. The main features, such as, recirculating #ow and temperature strati"cation in room and shopping mall "re, upstream back #ow and circulating #ow downstream in tunnel "re are characterized. The predictions of velocity and temperature distribution by the three combustion models were compared with experimental data. None of the combustion model gives consistent performance in prediction of temperature and velocity "elds in all the cases
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Fig. 8. The tunnel "re case: (a) temperature pro"les at station 1 (x"0.9 m, Q"4.75 kW, U "0.13 m/s); (b) temperature pro"les at station 3 (x"5.1 m, Q"3.15 kW, U "0.61 m/s).
tested. For the Steckler's room "re, the performances of the VHS model and the prePDF model are similar, while the eddy breakup model is poor. The VHS model performs well at the measuring station close to the "re for the shopping mall "re, while the prePDF model appears to perform best at the station upstream and relatively far away from the "re source. For the tunnel "re, the eddy breakup model and prePDF model perform equally well. The performance of the prePDF model is further improved at high heat release rate and high ventilation velocity. In general, the performance of prePDF model is more consistent, although there is no distinct performance which can be commented as a good combustion model for enclosure "re simulation, especially at the #ow region where "re source is nearby and large temperature gradient exists. This indicates the current turbulent combustion models are inadequate to account for the interaction of combustion, turbulence, radiative heat transfer of participating media including smoke and soot. In addition, numerical errors may be contributing to the observed discrepancies with experimental data. However, this does not deter the application of "eld model in enclosure "res. As demonstrated in the present and many previous studies, one can give a good prediction to an enclosure "re, provided that good estimation can be made on the heat release rate and its spatial distribution. Our study suggests that more adequate turbulent combustion models are required for simulating general enclosure "res for which the chemistry or reactive kinetics for
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