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A numerical study of atrium fires using deterministic models
Fire Safety Journal 33 (1999) 213}229
A numerical study of atrium "res using deterministic models J.S. Rho, H.S. Ryou* Department of Mechanical Engineering, 221 Heuksuk-Dong, Dongjak-ku, Chung-Ang University, Seoul 156756, South Korea Received 1 September 1998; received in revised form 29 April 1999; accepted 10 May 1999
Abstract The smoke "lling process for the three types of atrium space containing a "re source are simulated using the two types of deterministic "re model; zone model and "eld model. The zone model used in this simulation is CFAST (Version 3.1) developed at the Building and Fire Research Laboratories, NIST in the USA. The "eld model is a self-developed CFD model based on full consideration of the compressibility and k}e modeling for the turbulence. This article is focused on "nding out the smoke movement and temperature distribution in atrium spaces. A computational procedure for predicting velocity and temperature distribution in "re-induced #ow is based on the solution of three-dimensional Navier}Stokes conservation equations for mass, momentum, energy, species etc. using a "nite volume method and non-staggered grid system. Since air is entrained from the bottom of the plume, total mass #ow in the plume continuously increases. Also, the ceiling jet continuously decreases in temperature, smoke concentration and velocity; and increase in thickness with increasing radius. The "re models, i.e. zone models and "eld models, predicted similar results for the smoke layer temperature and the smoke layer interface heights. This is important in "re safety, and it can be considered that the required safe egress time in three types of atrium used, in this paper is about 5 min. 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction With increasing population in our major cities, large high rise buildings are being constructed. Many of these contain atria. The smoke generated from "res in such
* Corresponding author. Tel.: 00-782-282-05280; fax: 00-782-2816-4972. E-mail address: [email protected] (H.S. Ryou) 0379-7112/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 3 7 9 - 7 1 1 2 ( 9 9 ) 0 0 0 2 6 - 0
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Nomenclature C ,C ,C " g G h k P Q S,S . t ¹ u ,u ,u < x ,x ,x
empirical constants in the turbulence model gravitational acceleration buoyancy source term clear height turbulent kinetic energy pressure, Pa heat release rate, W component of source term time, s temperature, K velocity component of x, y and z directions in the Cartesian coordinate volume Cartesian coordinates
Greek symbols e turbulent energy dissipation rate
general dependent variable C exchange coe$cient k viscosity, Ns/m o density, kg/m p Prandtl number
Subscripts B P nb av e! t
buoyancy node point at the entry of the cell node point at the neighbor cell average value e!ective turbulent
Superscript o value at the previous time step
buildings may cause people to panic and interfere with evacuation. Not only does the smoke generated from modern synthetic materials lead to disorientation and death of the occupants, but large quantities of smoke become an obstacle to "re extinction. Therefore "re safety is an important issue which must be considered by Architects and
J.S. Rho, H.S. Ryou / Fire Safety Journal 33 (1999) 213}229
215
Engineers when they design the "re protection systems such as sprinklers and smoke control systems, etc. There are very few "re safety design guides based on sound scienti"c principles that are suitable for use by the industry. There are notable exceptions. For example, CFD simulations have been used to predict the hot air temperatures and the smoke layer interface for the design of the smoke control systems in the new airport project in Korea. It is very important to predict the smoke movement associated with a "re in an atrium. Many of the space characteristics of an atrium di!er from traditional buildings and di!er from atrium to atrium. For example, if a "re occurs in the atrium, #ame and smoke will spread vertically rather than horizontally to those parts of the building surrounding the atrium. The "re products are driven upwards within the interior of the atrium on account of buoyancy. It is di$cult to control smoke movement in such a case with the conventional ventilation designs available [1]. There have been several papers published on this topic [2,3]. Also, as the smoke movement by the "re-induced #ow is e!ected by a large number of inter-dependant processes including the stack e!ect and wind pressure, it is di$cult and expensive to perform experimental studies with full scale models. The alternative is to use computer simulation methods to determine the important physical perimeters. There are two types of simulation method, using zone models [4] or "eld models [5]. In the zone models, the interior of the "re compartment is divided into a uniformly heated upward gas layer and a lower layer of cool gas of uniform properties. The conservation laws are then solved in their full di!erential form as a set of coupled ordinary di!erential equations. Thus, it is computationally fast but yields no information on the internal structure of the smoke movement. On the other hand, in the "eld models the "re compartment is divided into a very large number of elements, and the basic equations expressing the conservation as mass, momentum, etc. are solved numerically. Such models provide a more detailed look at the phenomena which control the growth and spread of smoke, but the detail is restricted by the speed and storage capacity of the computer. Nevertheless, "eld models have been developed successfully with the rapid development of computational #uid dynamics(CFD) and considerable work has been done regarding "re environments [6}8]. There have been many zone models developed for smoke movement in o$ce and compartment "res most of which have been validated as reported in the literature [9}11]. Chow [3] has shown that zone models can be applied to an atrium "re by comparing the results with various zone models and "eld models for the three types of atrium space. He also points out that there are at least two problems which have to be considered with zone models. The "rst is whether a stable smoke layer can be formed in the upper layer region of a tall atrium space. Smoke layer instability may occur if the "re is small and the atrium space large. The second problem relates to the entrainment equations for the "re plume. The entrainment characteristics are greatly in#uenced by the degree of con"nement of the "re and it is not yet well quanti"ed in conventional plume equations. In most of the research mentioned above, it is not clear if the results from the sound models describe the details of smoke movement in an appropriate manner because the smoke layer interface is not obtained by using smoke concentration. Rho and Ryou [12] have described the physical phenomena leading to smoke movement
216
J.S. Rho, H.S. Ryou / Fire Safety Journal 33 (1999) 213}229
by considering smoke concentration within the "eld model. They were able to predict hot layer temperature and smoke layer interface height which are most important in "re safety considerations for atrium "res and o!er data on required safe egress time [13,14]. The purpose of this research is to predict smoke movement and the subsequent environmental conditions induced by di!usion and buoyancy, and compare the results with the zone models CFAST (Version 3.1) and Chow's "eld model. It is hoped to o!er Engineers and Architects essential data for smoke movement in the event of a "re in an atrium.
2. Fire 5eld model 2.1. The physical problem The con"gurations and dimensions of the three atrium spaces are shown in Fig. 1. These have the same volume, 16,000 m, and in each case there is a 5 m;3 m high opening. A 3 m;3 m "re was located at the centre of the #oor. The #ow induced by this "re source is turbulent because the inertial force due to the density di!erence between the hot smoke and the ambient air is much greater than the viscous force. In this simulation, the standard k}e turbulent model is used.
Fig. 1. Con"gurations and dimensions for the three types of atrium.
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2.2. The governing diwerential equation The "re "eld described by the air #ow and temperature, can be predicted by solving the following set of the time-averaged equations for continuity, velocity components, temperature, smoke concentration, and turbulence variables in tensor form. Continuity equation: *o * # (ou )"0, (1) G *t *x G where i"1, 2 and 3 denote x, y and z (vertical direction) directions, respectively, in the Cartesian coordinate system. Momentum equation:
* *o *p * *u G . (ou )# (ou u )"! #og # k (2) G H G G *x *x *t *x *x H G H H General transported yuid scalar equation (e.g. smoke concentration, temperature):
* * * *
(o )# (ou )" C #S. H ( *x *t *x *x H H H The equation of state for the ideal gas is assumed to be
(3)
P"oR¹,
(4)
where stands for the velocity components, temperature and smoke concentration; k is the e!ective viscosity; and C is the e!ective exchange coe$cient for the ( transport of property, ; S is the source term. The two-equation k}e model of ( turbulence is used to estimate the local value of k and C . The eddy viscosity is ( then determined from the local value of k and e as C ok k" " , e
(5)
k "k#k . The e!ective exchange coe$cient is then de"ned by
(6)
k k C " # , (7) p p where p, p are the laminar and turbulent Prandtl numbers, respectively. R k and e themselves can be solved from the transport equation derived from the Navier}Stokes equation and expressed as
*k *k * #ou " H *t *x *x H H *e *e * o #ou " H *x *t *x H H
o
k *k *u *u *u G G# H , k# R !oe#G #k (8) p *x R *x *x *x I H H H G k *e e *u *u *u e G # H #G !C o , k# #C k G p *x k R *x *x *x k C H H H G (9)
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where G is the buoyancy source term and is expressed as follows [15]: 1 *o G "k g . o *y
(10)
The above model contains six constants, which were assigned the following values: C "1.44, C "1.92, C "0.99, p "1.0, p "1.3. " 3. Numerical method 3.1. Grid system The three atrium spaces were divided into 56;25;32, 45;23;30 and 50;22; 40 cells along the x, y and z (vertical direction) directions of a Cartesian coordinate system as shown in Fig. 2. Finer grids were used in the areas where strong local gradient of properties were anticipated. This included the area above the "re source and those regions near the solid wall. Since the geometry of atrium spaces are symmetric across the central plane, only half of the space was simulated to reduce the computing time. 3.2. The discretization equation The di!erential equations described above can be expressed in a general form as * (o )#div(ou )"div(C grad )#S . ( ( *t
(11)
As there is no analytical solution for the set of equation, they are discretized into "nite di!erence forms by the integral of the governing equation over the control volume and are solved numerically at those nodal points. Eq. (11) can be discretized with the following form [16]: a " a #b, . . where
(12)
*< a " a #o !S , . . *t *< b"S #o- , ! . . *t
(13)
with nb denoting a neighbor node, and the summation is to be taken over all the neighbors. The system of discretization equation for individual variable was then solved with Stone's implicit procedure (SIP) and SIMPLE algorithm.
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Fig. 2. The grid system for three types of atrium.
3.3. Boundary and initial condition The initial temperature and pressure were assumed to be 293 K and 101,325 Pa. In the "re plume region, a greater initial velocity in buoyant air was expected. In this simulation the magnitude of air velocity in the "re plume region is 1.0 m/s according to the plume theory. Adiabatic wall boundary was assumed on all of the side walls except the opening door. The Neumann condition is applied at the door opening as shown in Fig. 1. Since the geometry of the space is symmetric about central plane, for a central plane symmetric condition is applied as *
"0. (14) *n The heat release rate of the "re, Q (in W), was increased as the square of the time t (in s) as Q"47t and kept constant at 1.5 MW after 178.6 s as shown in Fig. 3.
(15)
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Fig. 3. Heat release rate for the "re simulation.
The time step of 1 s was used and the simulation was performed up to 5 min as this was considered su$cient time for people to evacuate the atrium safely. With regard to computing time, this was less than 40 h by IBM, PC-586. The convergence criterion was taken as 10\.
4. Results Calculation of the unsteady "re-induced #ow was performed by the "nite volume method using the non-staggered variables arrangement. The transient #ow pattern and temperature and smoke concentration contours for half of the simulated type 3 atrium are shown in Figs. 4}8. Fig. 4 shows velocity vectors at 30 s in the type 3 atrium after the start of the "re. Like all the other cases of "re simulation, air was entrained from bottom of the plume as shown in this "gure. Figs. 5 and 6 are temperature and smoke concentration contours at 30 s. Because of the elevated temperature, buoyancy forces drive gases upwards from the "re area towards the ceiling. In this way a plume is formed above the "re and relatively quiescent and cool gases at its periphery are laterally entrained and mixed with the plume gases. As a result of this entrainment the total mass #ow in the plume continuously increases. Figs. 7 and 8 show temperature and smoke concentration contours at 120 s. As depicted in Figs. 7 and 8, when the hot plume gases impinge on the ceiling, they spread across it forming a relatively thin radial jet and move outward under the ceiling surface. The hot gases transfer energy by convection and are retarded by frictional forces from the ceiling surface above, and by turbulent momentum transfer to the
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221
Fig. 4. Velocity vectors for type 3 atrium at 30 s.
entrained air from below. As a result of all this #ow and heat transfer, the ceiling jet continuously decreases in temperature, smoke concentration and velocity; and increase in thickness with increasing radius. Because of the wall con"ning e!ect, the hot gases moved along the edge between the ceiling and the wall. The hot gases propagated outwards below the ceiling with a maximum ceiling jet velocity of about 2.5 m/s. The results of calculations in the present "re "eld model were compared with the zone model CFAST (Version 3.1) and Chow's "eld model in order to test the present "re "eld model and numerical method used in this simulation. From the predicted air #ow pattern and temperature and smoke concentration "eld, the smoke layer interface height was determined by inspecting the positions where smoke concentration is 0.01. The upper region above this interface height is regarded as the upper hot smoke layer and the average smoke layer interface height is determined by the following equation: *q h " G. Area of floor
(16)
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Fig. 5. Temperature contours for type 3 atrium at 30 s.
Fig. 6. Gas concentration contours for type 3 atrium at 30 s.
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Fig. 7. Temperature contour for type 3 atrium at 120 s.
Fig. 8. Gas concentration contours for type 3 atrium at 120 s.
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Fig. 9. (a) Predicted smoke layer temperatures in the type 1 atrium; (b) Predicted smoke layer interface heights in the type 1 atrium.
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Fig. 10. (a) Predicted smoke layer temperatures in the type 2 atrium; (b) Predicted smoke layer interface heights in the type 2 atrium.
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Fig. 11. (a) Predicted smoke layer temperatures in the type 3 atrium; (b) Predicted smoke layer interface heights in the type 3 atrium.
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Also, the predicted hot layer temperature is the average value over all at the control volumes in the smoke layer with each cell having a volume *q and temperature ¹ G G [3]: ¹ *q ¹ " G G. (17) *q G Results for the transient development of the smoke layer temperature ¹ and the interface height h predicted by the zone model CFAST (Version 3.1) and Chow's "eld model and present "eld model for the three types of atrium are plotted in Figs. 9}11 for the three types of atrium space. For the type 1 atrium, the smoke layer temperatures predicted by the zone model CFAST (Version 3.1) and "eld models are similar as shown in Fig. 9(a); di!erence in the temperature calculated with the three models was found to be less than 5 K. Regarding the smoke layer interface height, the results predicted by the zone model CFAST (Version 3.1) and the two "eld models matched quite well. The smoke layer interface heights are predicted by the three models to be about 5 m at 5 min, with an initial rate of increase with a rate of approximately 0.067 m/s. For the type 2 atrium, the smoke layer temperatures predicted by the zone model CFAST (Version 3.1) and two "eld models have similar trends but the temperature predicted by "eld models was approximately 5 K higher than that predicted by zone model. The results of the smoke layer interface height show signi"cant di!erences after 7 min, CFAST (Version 3.1) and the present "eld model predict similar heights which are about 7 m less at 5 min, than that predicted by Chow's model. This di!erence seems to come from the di!erence of the smoke layer interface de"nition. Chow obtained the smoke layer interface height from the change in the gradient temperature in the vertical direction, although there is a small temperature gradient within the thermally strati"ed layer. As mentioned above, the smoke layer interface heights in the present "eld model was obtained by inspecting the position where smoke concentration is 0.01. Like the type 1 atrium, the smoke layer temperatures predicted for the type 3 atrium by the zone model CFAST (Version 3.1) and "eld models are similar, di!ering by less than 7 K. Regarding the smoke layer interface height, the heights predicted by the two "eld models and zone model are similar, although the zone model predicts a height which is 5 m below the average of the heights predicted by the "eld models. This may be because the zone model assumes that a stable and homogeneous smoke layer is formed, even in tall spaces. Regarding the smoke layer temperatures in the three types of atria, the results predicted by "eld model are, in general, higher than those by zone model and the results predicted are approximately linear because of the means by which the smoke layer interface heights are obtained.
5. Conclusions Numerical calculation of smoke movement is performed in three types of atrium "re and transient smoke movement is predicted and compared with zone model CFAST
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(Version 3.1) and Chow's "eld model. The following conclusions are obtained. 1. Field models provide a more detailed look at the phenomena such as development of the plume, the plume}ceiling interaction and the ceiling jet}wall interaction. 2. The results for the smoke layer temperature and clear heights, predicted by CFAST (Version 3.1), Chow's "eld model and present "eld model are very similar. 3. The "eld model is proposed to substitute the zone model for predicting the smoke layer temperature and clear heights because zone models assume that a stable and homogeneous smoke layer is formed, even in a large atrium spaces. 4. It can be thought that present "eld model appropriately describes the smoke movement by solving smoke concentration equation for predicting the smoke layer temperatures and smoke layer interface heights. 5. The smoke interface heights is about 5 m at 5 min for the three types of atrium after starting the "re. Therefore, the required safe egress time in the three types of atrium is about 5 min.
Acknowledgements The research was supported by the Chung-Ang University Research grants in 1997.
References [1] Kim WJ, Yang SH, Choi KR. The experimental study of "re properties in atrium space of high-rise buildings. J Korea Inst of Fire Sci Eng 1993;7(2):13}23. [2] Chow WK, Wong WK. On the simulation of atrium "re environment Hong Kong using zone model. J Fire Sci 1993;11:3}51. [3] Chow WK. A comparison of the use of "re zone and "eld models for simulating atrium smoke-"lling process. Fire Safety J 1995;25:337}53. [4] Jones WW. Multi-compartment model for the spread of "re, smoke and toxic gases. Fire Safety J 1985;9:55}79. [5] Baum HR, Rehm RG. Calculation of three dimensional buoyant plumes in enclosures. Combustion Sci Technol 1984;40:55}77. [6] Chow WK, Leung WM. Solid-wall boundary e!ect on a building "re "eld model. Combust Sci Technol 1990;71:77}93. [7] Markatos NC, Malin MR, Cox G. Mathematical modeling of buoyancy-induced smoke #ow in enclosures. Int J Heat Mass Transfer 1982;25:63}75. [8] Cox G, Kumar S, Cumber P, Thomson V. Fire simulation in the design evaluation process: an exemplication of the use of a computer "eld model. Inter#am'90. Interscience Communications Ltd, 1990 p. 55-66. [9] Thomas PH. Modeling of compartment "res. Fire Safety J 1983;5:181}90. [10] Klote JH. Computer modeling for smoke control design. Fire Safety J 1985;9:181}8. [11] Peacock RD, Forney GP, Reneke PA, Portier RM, Jones WW. CFAST, the consolidated model of "re growth and smoke transport. NIST Technical Note 1299. [12] Rho JS, Ryou HS, Kim CI, Yoon MO. Smoke movement by a "re in an enclosure. J Korea Inst Fire Sci Eng 1996;10(3):10}8.
J.S. Rho, H.S. Ryou / Fire Safety Journal 33 (1999) 213}229
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[13] Rho JS, Ryou HS. A numerical study of smoke movement in atrium "res. Proceedings of '97 the Korea Institute of Industrial Safety. [14] Rho JS, Ryou HS. The numerical study of smoke movement by a "re in an enclosure. Transport Phenomena in Thermal Science and Process Engineering, Kyoto, Japan, 1997, Nov 30}Dec 3. [15] Zhou Lixing. Theory and numerical modeling of turbulent gas-particle #ows and combustion. Science press. CRC press. INC. [16] Patankar SV. Numerical heat transfer and #uid #ow. Washington, DC: McGraw Hill, 1980.
A numerical study of atrium "res using deterministic models J.S. Rho, H.S. Ryou* Department of Mechanical Engineering, 221 Heuksuk-Dong, Dongjak-ku, Chung-Ang University, Seoul 156756, South Korea Received 1 September 1998; received in revised form 29 April 1999; accepted 10 May 1999
Abstract The smoke "lling process for the three types of atrium space containing a "re source are simulated using the two types of deterministic "re model; zone model and "eld model. The zone model used in this simulation is CFAST (Version 3.1) developed at the Building and Fire Research Laboratories, NIST in the USA. The "eld model is a self-developed CFD model based on full consideration of the compressibility and k}e modeling for the turbulence. This article is focused on "nding out the smoke movement and temperature distribution in atrium spaces. A computational procedure for predicting velocity and temperature distribution in "re-induced #ow is based on the solution of three-dimensional Navier}Stokes conservation equations for mass, momentum, energy, species etc. using a "nite volume method and non-staggered grid system. Since air is entrained from the bottom of the plume, total mass #ow in the plume continuously increases. Also, the ceiling jet continuously decreases in temperature, smoke concentration and velocity; and increase in thickness with increasing radius. The "re models, i.e. zone models and "eld models, predicted similar results for the smoke layer temperature and the smoke layer interface heights. This is important in "re safety, and it can be considered that the required safe egress time in three types of atrium used, in this paper is about 5 min. 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction With increasing population in our major cities, large high rise buildings are being constructed. Many of these contain atria. The smoke generated from "res in such
* Corresponding author. Tel.: 00-782-282-05280; fax: 00-782-2816-4972. E-mail address: [email protected] (H.S. Ryou) 0379-7112/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 3 7 9 - 7 1 1 2 ( 9 9 ) 0 0 0 2 6 - 0
214
J.S. Rho, H.S. Ryou / Fire Safety Journal 33 (1999) 213}229
Nomenclature C ,C ,C " g G h k P Q S,S . t ¹ u ,u ,u < x ,x ,x
empirical constants in the turbulence model gravitational acceleration buoyancy source term clear height turbulent kinetic energy pressure, Pa heat release rate, W component of source term time, s temperature, K velocity component of x, y and z directions in the Cartesian coordinate volume Cartesian coordinates
Greek symbols e turbulent energy dissipation rate
general dependent variable C exchange coe$cient k viscosity, Ns/m o density, kg/m p Prandtl number
Subscripts B P nb av e! t
buoyancy node point at the entry of the cell node point at the neighbor cell average value e!ective turbulent
Superscript o value at the previous time step
buildings may cause people to panic and interfere with evacuation. Not only does the smoke generated from modern synthetic materials lead to disorientation and death of the occupants, but large quantities of smoke become an obstacle to "re extinction. Therefore "re safety is an important issue which must be considered by Architects and
J.S. Rho, H.S. Ryou / Fire Safety Journal 33 (1999) 213}229
215
Engineers when they design the "re protection systems such as sprinklers and smoke control systems, etc. There are very few "re safety design guides based on sound scienti"c principles that are suitable for use by the industry. There are notable exceptions. For example, CFD simulations have been used to predict the hot air temperatures and the smoke layer interface for the design of the smoke control systems in the new airport project in Korea. It is very important to predict the smoke movement associated with a "re in an atrium. Many of the space characteristics of an atrium di!er from traditional buildings and di!er from atrium to atrium. For example, if a "re occurs in the atrium, #ame and smoke will spread vertically rather than horizontally to those parts of the building surrounding the atrium. The "re products are driven upwards within the interior of the atrium on account of buoyancy. It is di$cult to control smoke movement in such a case with the conventional ventilation designs available [1]. There have been several papers published on this topic [2,3]. Also, as the smoke movement by the "re-induced #ow is e!ected by a large number of inter-dependant processes including the stack e!ect and wind pressure, it is di$cult and expensive to perform experimental studies with full scale models. The alternative is to use computer simulation methods to determine the important physical perimeters. There are two types of simulation method, using zone models [4] or "eld models [5]. In the zone models, the interior of the "re compartment is divided into a uniformly heated upward gas layer and a lower layer of cool gas of uniform properties. The conservation laws are then solved in their full di!erential form as a set of coupled ordinary di!erential equations. Thus, it is computationally fast but yields no information on the internal structure of the smoke movement. On the other hand, in the "eld models the "re compartment is divided into a very large number of elements, and the basic equations expressing the conservation as mass, momentum, etc. are solved numerically. Such models provide a more detailed look at the phenomena which control the growth and spread of smoke, but the detail is restricted by the speed and storage capacity of the computer. Nevertheless, "eld models have been developed successfully with the rapid development of computational #uid dynamics(CFD) and considerable work has been done regarding "re environments [6}8]. There have been many zone models developed for smoke movement in o$ce and compartment "res most of which have been validated as reported in the literature [9}11]. Chow [3] has shown that zone models can be applied to an atrium "re by comparing the results with various zone models and "eld models for the three types of atrium space. He also points out that there are at least two problems which have to be considered with zone models. The "rst is whether a stable smoke layer can be formed in the upper layer region of a tall atrium space. Smoke layer instability may occur if the "re is small and the atrium space large. The second problem relates to the entrainment equations for the "re plume. The entrainment characteristics are greatly in#uenced by the degree of con"nement of the "re and it is not yet well quanti"ed in conventional plume equations. In most of the research mentioned above, it is not clear if the results from the sound models describe the details of smoke movement in an appropriate manner because the smoke layer interface is not obtained by using smoke concentration. Rho and Ryou [12] have described the physical phenomena leading to smoke movement
216
J.S. Rho, H.S. Ryou / Fire Safety Journal 33 (1999) 213}229
by considering smoke concentration within the "eld model. They were able to predict hot layer temperature and smoke layer interface height which are most important in "re safety considerations for atrium "res and o!er data on required safe egress time [13,14]. The purpose of this research is to predict smoke movement and the subsequent environmental conditions induced by di!usion and buoyancy, and compare the results with the zone models CFAST (Version 3.1) and Chow's "eld model. It is hoped to o!er Engineers and Architects essential data for smoke movement in the event of a "re in an atrium.
2. Fire 5eld model 2.1. The physical problem The con"gurations and dimensions of the three atrium spaces are shown in Fig. 1. These have the same volume, 16,000 m, and in each case there is a 5 m;3 m high opening. A 3 m;3 m "re was located at the centre of the #oor. The #ow induced by this "re source is turbulent because the inertial force due to the density di!erence between the hot smoke and the ambient air is much greater than the viscous force. In this simulation, the standard k}e turbulent model is used.
Fig. 1. Con"gurations and dimensions for the three types of atrium.
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2.2. The governing diwerential equation The "re "eld described by the air #ow and temperature, can be predicted by solving the following set of the time-averaged equations for continuity, velocity components, temperature, smoke concentration, and turbulence variables in tensor form. Continuity equation: *o * # (ou )"0, (1) G *t *x G where i"1, 2 and 3 denote x, y and z (vertical direction) directions, respectively, in the Cartesian coordinate system. Momentum equation:
* *o *p * *u G . (ou )# (ou u )"! #og # k (2) G H G G *x *x *t *x *x H G H H General transported yuid scalar equation (e.g. smoke concentration, temperature):
* * * *
(o )# (ou )" C #S. H ( *x *t *x *x H H H The equation of state for the ideal gas is assumed to be
(3)
P"oR¹,
(4)
where stands for the velocity components, temperature and smoke concentration; k is the e!ective viscosity; and C is the e!ective exchange coe$cient for the ( transport of property, ; S is the source term. The two-equation k}e model of ( turbulence is used to estimate the local value of k and C . The eddy viscosity is ( then determined from the local value of k and e as C ok k" " , e
(5)
k "k#k . The e!ective exchange coe$cient is then de"ned by
(6)
k k C " # , (7) p p where p, p are the laminar and turbulent Prandtl numbers, respectively. R k and e themselves can be solved from the transport equation derived from the Navier}Stokes equation and expressed as
*k *k * #ou " H *t *x *x H H *e *e * o #ou " H *x *t *x H H
o
k *k *u *u *u G G# H , k# R !oe#G #k (8) p *x R *x *x *x I H H H G k *e e *u *u *u e G # H #G !C o , k# #C k G p *x k R *x *x *x k C H H H G (9)
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where G is the buoyancy source term and is expressed as follows [15]: 1 *o G "k g . o *y
(10)
The above model contains six constants, which were assigned the following values: C "1.44, C "1.92, C "0.99, p "1.0, p "1.3. " 3. Numerical method 3.1. Grid system The three atrium spaces were divided into 56;25;32, 45;23;30 and 50;22; 40 cells along the x, y and z (vertical direction) directions of a Cartesian coordinate system as shown in Fig. 2. Finer grids were used in the areas where strong local gradient of properties were anticipated. This included the area above the "re source and those regions near the solid wall. Since the geometry of atrium spaces are symmetric across the central plane, only half of the space was simulated to reduce the computing time. 3.2. The discretization equation The di!erential equations described above can be expressed in a general form as * (o )#div(ou )"div(C grad )#S . ( ( *t
(11)
As there is no analytical solution for the set of equation, they are discretized into "nite di!erence forms by the integral of the governing equation over the control volume and are solved numerically at those nodal points. Eq. (11) can be discretized with the following form [16]: a " a #b, . . where
(12)
*< a " a #o !S , . . *t *< b"S #o- , ! . . *t
(13)
with nb denoting a neighbor node, and the summation is to be taken over all the neighbors. The system of discretization equation for individual variable was then solved with Stone's implicit procedure (SIP) and SIMPLE algorithm.
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Fig. 2. The grid system for three types of atrium.
3.3. Boundary and initial condition The initial temperature and pressure were assumed to be 293 K and 101,325 Pa. In the "re plume region, a greater initial velocity in buoyant air was expected. In this simulation the magnitude of air velocity in the "re plume region is 1.0 m/s according to the plume theory. Adiabatic wall boundary was assumed on all of the side walls except the opening door. The Neumann condition is applied at the door opening as shown in Fig. 1. Since the geometry of the space is symmetric about central plane, for a central plane symmetric condition is applied as *
"0. (14) *n The heat release rate of the "re, Q (in W), was increased as the square of the time t (in s) as Q"47t and kept constant at 1.5 MW after 178.6 s as shown in Fig. 3.
(15)
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Fig. 3. Heat release rate for the "re simulation.
The time step of 1 s was used and the simulation was performed up to 5 min as this was considered su$cient time for people to evacuate the atrium safely. With regard to computing time, this was less than 40 h by IBM, PC-586. The convergence criterion was taken as 10\.
4. Results Calculation of the unsteady "re-induced #ow was performed by the "nite volume method using the non-staggered variables arrangement. The transient #ow pattern and temperature and smoke concentration contours for half of the simulated type 3 atrium are shown in Figs. 4}8. Fig. 4 shows velocity vectors at 30 s in the type 3 atrium after the start of the "re. Like all the other cases of "re simulation, air was entrained from bottom of the plume as shown in this "gure. Figs. 5 and 6 are temperature and smoke concentration contours at 30 s. Because of the elevated temperature, buoyancy forces drive gases upwards from the "re area towards the ceiling. In this way a plume is formed above the "re and relatively quiescent and cool gases at its periphery are laterally entrained and mixed with the plume gases. As a result of this entrainment the total mass #ow in the plume continuously increases. Figs. 7 and 8 show temperature and smoke concentration contours at 120 s. As depicted in Figs. 7 and 8, when the hot plume gases impinge on the ceiling, they spread across it forming a relatively thin radial jet and move outward under the ceiling surface. The hot gases transfer energy by convection and are retarded by frictional forces from the ceiling surface above, and by turbulent momentum transfer to the
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Fig. 4. Velocity vectors for type 3 atrium at 30 s.
entrained air from below. As a result of all this #ow and heat transfer, the ceiling jet continuously decreases in temperature, smoke concentration and velocity; and increase in thickness with increasing radius. Because of the wall con"ning e!ect, the hot gases moved along the edge between the ceiling and the wall. The hot gases propagated outwards below the ceiling with a maximum ceiling jet velocity of about 2.5 m/s. The results of calculations in the present "re "eld model were compared with the zone model CFAST (Version 3.1) and Chow's "eld model in order to test the present "re "eld model and numerical method used in this simulation. From the predicted air #ow pattern and temperature and smoke concentration "eld, the smoke layer interface height was determined by inspecting the positions where smoke concentration is 0.01. The upper region above this interface height is regarded as the upper hot smoke layer and the average smoke layer interface height is determined by the following equation: *q h " G. Area of floor
(16)
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Fig. 5. Temperature contours for type 3 atrium at 30 s.
Fig. 6. Gas concentration contours for type 3 atrium at 30 s.
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Fig. 7. Temperature contour for type 3 atrium at 120 s.
Fig. 8. Gas concentration contours for type 3 atrium at 120 s.
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Fig. 9. (a) Predicted smoke layer temperatures in the type 1 atrium; (b) Predicted smoke layer interface heights in the type 1 atrium.
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Fig. 10. (a) Predicted smoke layer temperatures in the type 2 atrium; (b) Predicted smoke layer interface heights in the type 2 atrium.
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Fig. 11. (a) Predicted smoke layer temperatures in the type 3 atrium; (b) Predicted smoke layer interface heights in the type 3 atrium.
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Also, the predicted hot layer temperature is the average value over all at the control volumes in the smoke layer with each cell having a volume *q and temperature ¹ G G [3]: ¹ *q ¹ " G G. (17) *q G Results for the transient development of the smoke layer temperature ¹ and the interface height h predicted by the zone model CFAST (Version 3.1) and Chow's "eld model and present "eld model for the three types of atrium are plotted in Figs. 9}11 for the three types of atrium space. For the type 1 atrium, the smoke layer temperatures predicted by the zone model CFAST (Version 3.1) and "eld models are similar as shown in Fig. 9(a); di!erence in the temperature calculated with the three models was found to be less than 5 K. Regarding the smoke layer interface height, the results predicted by the zone model CFAST (Version 3.1) and the two "eld models matched quite well. The smoke layer interface heights are predicted by the three models to be about 5 m at 5 min, with an initial rate of increase with a rate of approximately 0.067 m/s. For the type 2 atrium, the smoke layer temperatures predicted by the zone model CFAST (Version 3.1) and two "eld models have similar trends but the temperature predicted by "eld models was approximately 5 K higher than that predicted by zone model. The results of the smoke layer interface height show signi"cant di!erences after 7 min, CFAST (Version 3.1) and the present "eld model predict similar heights which are about 7 m less at 5 min, than that predicted by Chow's model. This di!erence seems to come from the di!erence of the smoke layer interface de"nition. Chow obtained the smoke layer interface height from the change in the gradient temperature in the vertical direction, although there is a small temperature gradient within the thermally strati"ed layer. As mentioned above, the smoke layer interface heights in the present "eld model was obtained by inspecting the position where smoke concentration is 0.01. Like the type 1 atrium, the smoke layer temperatures predicted for the type 3 atrium by the zone model CFAST (Version 3.1) and "eld models are similar, di!ering by less than 7 K. Regarding the smoke layer interface height, the heights predicted by the two "eld models and zone model are similar, although the zone model predicts a height which is 5 m below the average of the heights predicted by the "eld models. This may be because the zone model assumes that a stable and homogeneous smoke layer is formed, even in tall spaces. Regarding the smoke layer temperatures in the three types of atria, the results predicted by "eld model are, in general, higher than those by zone model and the results predicted are approximately linear because of the means by which the smoke layer interface heights are obtained.
5. Conclusions Numerical calculation of smoke movement is performed in three types of atrium "re and transient smoke movement is predicted and compared with zone model CFAST
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(Version 3.1) and Chow's "eld model. The following conclusions are obtained. 1. Field models provide a more detailed look at the phenomena such as development of the plume, the plume}ceiling interaction and the ceiling jet}wall interaction. 2. The results for the smoke layer temperature and clear heights, predicted by CFAST (Version 3.1), Chow's "eld model and present "eld model are very similar. 3. The "eld model is proposed to substitute the zone model for predicting the smoke layer temperature and clear heights because zone models assume that a stable and homogeneous smoke layer is formed, even in a large atrium spaces. 4. It can be thought that present "eld model appropriately describes the smoke movement by solving smoke concentration equation for predicting the smoke layer temperatures and smoke layer interface heights. 5. The smoke interface heights is about 5 m at 5 min for the three types of atrium after starting the "re. Therefore, the required safe egress time in the three types of atrium is about 5 min.
Acknowledgements The research was supported by the Chung-Ang University Research grants in 1997.
References [1] Kim WJ, Yang SH, Choi KR. The experimental study of "re properties in atrium space of high-rise buildings. J Korea Inst of Fire Sci Eng 1993;7(2):13}23. [2] Chow WK, Wong WK. On the simulation of atrium "re environment Hong Kong using zone model. J Fire Sci 1993;11:3}51. [3] Chow WK. A comparison of the use of "re zone and "eld models for simulating atrium smoke-"lling process. Fire Safety J 1995;25:337}53. [4] Jones WW. Multi-compartment model for the spread of "re, smoke and toxic gases. Fire Safety J 1985;9:55}79. [5] Baum HR, Rehm RG. Calculation of three dimensional buoyant plumes in enclosures. Combustion Sci Technol 1984;40:55}77. [6] Chow WK, Leung WM. Solid-wall boundary e!ect on a building "re "eld model. Combust Sci Technol 1990;71:77}93. [7] Markatos NC, Malin MR, Cox G. Mathematical modeling of buoyancy-induced smoke #ow in enclosures. Int J Heat Mass Transfer 1982;25:63}75. [8] Cox G, Kumar S, Cumber P, Thomson V. Fire simulation in the design evaluation process: an exemplication of the use of a computer "eld model. Inter#am'90. Interscience Communications Ltd, 1990 p. 55-66. [9] Thomas PH. Modeling of compartment "res. Fire Safety J 1983;5:181}90. [10] Klote JH. Computer modeling for smoke control design. Fire Safety J 1985;9:181}8. [11] Peacock RD, Forney GP, Reneke PA, Portier RM, Jones WW. CFAST, the consolidated model of "re growth and smoke transport. NIST Technical Note 1299. [12] Rho JS, Ryou HS, Kim CI, Yoon MO. Smoke movement by a "re in an enclosure. J Korea Inst Fire Sci Eng 1996;10(3):10}8.
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[13] Rho JS, Ryou HS. A numerical study of smoke movement in atrium "res. Proceedings of '97 the Korea Institute of Industrial Safety. [14] Rho JS, Ryou HS. The numerical study of smoke movement by a "re in an enclosure. Transport Phenomena in Thermal Science and Process Engineering, Kyoto, Japan, 1997, Nov 30}Dec 3. [15] Zhou Lixing. Theory and numerical modeling of turbulent gas-particle #ows and combustion. Science press. CRC press. INC. [16] Patankar SV. Numerical heat transfer and #uid #ow. Washington, DC: McGraw Hill, 1980.