application of computational fluid dynamics for simulating fire … · 2010. 12. 23. · the fire...

International Journal on Architectural Science, Volume 5, Number 1, p.20-34, 2004

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APPLICATION OF COMPUTATIONAL FLUID DYNAMICS FOR SIMULATING FIRE-INDUCED AIR FLOW IN A LARGE TERMINAL HALL Y.F. Li College of Architecture and Civil Engineering, Beijing University of Technology, Beijing, China, 100022 W.K. Chow Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong, China (Received 1 August 2003; Accepted 28 October 2003) ABSTRACT Application of computational fluid dynamics (CFD) for simulating fire-induced air flow in a large terminal hall will be discussed. The selected CFD model is based on Reynolds Averaging Navier-Stokes (RANS) equations method with k-ε based turbulence model. The fire is taken as a volumetric heat source and buoyancy effects are included in equations for the vertical momentum and turbulent parameters. Air velocity, pressure and temperature distribution are then predicted. The large terminal hall has a curved ceiling and so body-fitted coordinate (BFC) technique is required to divide the computational region into cells. Different fire scenarios are calculated. 1. INTRODUCTION Space of height taller than two stories without compartmentation is usually regarded as a large space. Smoke generated from a fire inside or in a nearby communicating space can move and fill up the space rapidly [1]. Examples of large space are atria, terminal halls, theaters, assembling rooms and indoor arenas. In designing fire safety provisions for those large spaces, achieving the life safety objective by protecting occupants against smoke hazards is important. In halls with a large space volume, large amount of smoke can be accumulated under the ceiling. The time taken for the smoke layer to descend to the occupant zone might be long enough for evacuation. To ensure that the evacuation time is shorter than the smoke filling time, smoke management systems should be designed for controlling smoke spreading in typical scenarios. It is far too expensive to carry out full-scale burning tests to study the fire environment in a large space building [2,3]. There are great differences among fire scenarios and so not all the field measured data are useful for hazard assessment. Therefore, an alternative is to use the computer fire models to better understand the fire environment in a large space. There are two types of fire models, zone and field models for studying fire. Zone models [4,5] were developed to study fire and smoke spreading in a single or multi-compartments. Predicted results are well validated by experiments in smaller

enclosures such as offices or industrial units [6,7]. However, zone models are not suitable for buildings with a large length to width or height to width ratio, because the two-layer assumption might not work in these buildings [8,9]. Field modeling, or application of computational fluid dynamics (CFD), is based on solving a set of transient, three-dimensional equations derived from conservation laws on mass, momentum and energy. The Reynolds Averaging Navier-Stokes (RANS) equations method is commonly used to deal with turbulence. The building concerned is divided into a large number of cells for solving key equations on mass, momentum and species numerically. Apart from the number of cells, there is no difference in dealing with large or small spaces volume. Therefore, this technique is commonly used by fire engineers in designing smoke management system in atria and tunnels. The flow fields in enclosure fires were attempted to be solved by CFD in the past twenty years [10]. Approaches include laminar models incorporating the Boussinesq approximation; the stream function-vorticity formulation; and the variable density turbulence models with recirculation using the primitive variable formulation [11-13]. Whether the CFD predicted results for building fire are accurate is an important issue in using these models. The models become more complex by incorporating the physical and chemical processes in an enclosure fire to the coupled system of partial differential equations. As the combustion process during a fire is very complicated among many

International Journal on Architectural Science

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intermediate reactions, realistic treatment of combustion in a fire field model has not yet been simulated realistically [14-15]. A simplified approach for practical design of smoke management systems is to take the fire as a spatially distributed heat source. The hot object is put into the computational domain in a CFD model to predict flow and temperature fields [16]. Buoyancy must be induced to change the mean flow and its fluctuating motions. Such an approach has been applied [17,18] to study fire scenarios in atrium, terminal hall and indoor arena in many projects. Most of the numerical simulations were on buildings with rectangular geometry. In this paper, CFD is applied to study fire-induced air flow in a terminal hall as shown in Fig. 1. Since the horizontal length is much longer than the ceiling height, a two-dimensional mathematical field model is good enough to predict the movements of airflow pattern in the terminal hall.

Body-fitted coordinate (BFC) technique is used to generate the grid system because the ceiling is not rectangular. The volumetric heat source model is employed to represent fire source as hot air with a certain thermal power. In dealing with CFD, there are at least three parts to consider: • Turbulence. • Discretization of the set of partial differential

equations into finite difference form. • Solving the velocity-pressure linked equations. The RANS method based on k-ε model was commonly used in the CFD literatures in the past twenty years. The advantage of RANS is that the computing effort is not so demanding and so affordable by the industry. The RANS technique is used for the CFD study in this paper.

a) Pictorial view of the terminal hall

b) Sectional plane

Fig. 1: Terminal hall

y x

A

B

C

2703

9.5

63

81

99

Fire

3.5

180

183

Sectional plane


22

2. GEOMETRY OF THE HALL The schematic diagram of the airport terminal hall is shown in Fig. 1. The horizontal width of the hall is much longer than its height and its length is much longer than the horizontal width. The building is of width 366 m, and the ceiling geometry is an arc of radius of 2703 m, a height of 9.5 m at the center. The fire is taken as a heat source of length 1.8 m and height 2.4 m. Its depth is 1.5 m normal to the x-y plane. The fire is situated on the right side at about 80 m from the central line of the building. Since this building is very wide, the main concern in fire scenario should be focused on the region near the fire. A region of interest is selected and shown in Fig. 1. This region is 36 m wide and the fire source is located at its center. The predicted results of this special region will be described and discussed in this paper. Smoke management systems are designed to maintain the smoke layer high enough above the height of the walking level for a certain time period. In evaluating the performance of the system, either static or dynamic smoke exhaust systems, the worst case giving out the biggest smoke production rate would be considered. Two-dimensional simulations

with a steady burning fire were carried out. This scenario is justified as: • There is sufficient air in the hall to give

steady burning. • The terminal hall has a large width to height

ratio, and so a zone model is not suitable for simulating the fire scenario.

3. GOVERNING EQUATIONS In this paper, the air movement field model treats the flow primarily as a natural convection problem without thermal radiation. Flow is dominated by buoyancy and turbulence would give faster rates of mass, momentum and heat transfer. The prediction of air flow in a building with fire is based on the solution of general transport equation for a flow variable Φ such as velocity components (u and ν):

[ ] ΦΦ +ΦΓ=Φ+Φ∂∂ SgaddivVdivt

)()()(r

ρρ (1)

where ΦΓ and ΦS are the exchange coefficient and source term for Φ respectively as shown in Table 1 [19].

Table 1: Effective exchange coefficient and source terms for variables in the turbulent

transport governing equations

Equation Φ ΦΓ ΦS

Continuity 1 0 0

u momentum u effµ

∂∂

∂∂

+

∂∂

∂∂

+∂∂

−xv

yxu

xxp

effeff µµ

v momentum v effµ )( 0ρρµµ −−

∂∂

∂∂

+

∂∂

∂∂

+∂∂

− gyv

yyu

xyp

effeff

Temperature T t

t

σµµ

+Pr

pfire cq&

Kinetic energy k keff σµ G-ρε

Dissipation rate ε εσµ eff )( 21 ρεε CGCk

−

yg

xv

yu

yv

xuG

t

tt ∂

∂+

∂∂

+∂∂

+

∂∂

+

∂∂

=ρ

ρσµµ

222

2

teff µµµ +=

ερµ µ /2kCt =


23

The above model contains six constants. Constants 1C and 2C in ε-equation are given as 1.44 and 1.92 respectively. εσ is the effective Prandtl number for the diffusion of turbulence dissipation and given as 1.3; kσ is the effective Prandtl number for the diffusion of turbulent energy; and tσ is the effective Prandtl number for the diffusion of heat. It was reported that tσ and µC are the two parameters which were varied to improve agreement with the experiment. In standard k-ε model, µC and tσ are given as 0.09 and 1.0 respectively. A test case for jet flow with µC = 0.109 and tσ = 0.614 was reported in ref. [13]. It shows that the results for a pure jet was somewhat improved by changing the values of these two constants, but the spread rates of buoyant plumes were still significantly underpredicted. In ref. [15], µC and tσ were taken to be 0.18 and 0.85 respectively in simulating thermal plume. However, there is no generally accepted standard for choosing the values of these two parameters. In this paper, the values of µC and tσ in the standard k-ε model are chosen. Here, the k-ε model is adopted to incorporate the effect of buoyancy so as to account for the unstable stratification in the rising plume and stable stratification in the hot ceiling layer. The combined laminar and turbulent stresses are then expressed by means of effµ .

teff µµµ += (2)

ερµ µ /2kCt = (3)

where µ is dynamic viscosity and µt is local turbulent viscosity. The generation term G is defined as follows:

xv

yu

yv

xuGGG tBk

∂∂

+∂∂

+

∂∂

+

∂∂

=+= µ222

2

y

g

t

t

∂∂

+ρ

ρσµ (4)

The first term on the right-hand side, kG , is the shear production. The second term, BG , is the buoyancy production through which the influence of buoyancy on turbulent quantities is included. Since buoyancy would play an important role in the rising plume and ceiling layer, it is important to

introduce buoyancy in the k-ε equation. It represents an exchange between the turbulent kinetic energy and the potential energy. In the stable stratification in the hot ceiling layer, this term becomes a sink term so that the turbulent mixing is reduced while the potential energy increases. In unstable stratification in the rising plume, buoyancy will enhance the turbulent mixing [14]. 4. BOUNDARY CONDITIONS AND

INITIAL CONDITIONS For this problem, the non-slip condition on the velocity components is employed on a solid boundary. For the temperature equation, adiabatic side walls, floor and ceiling are considered. For the kinetic energy of turbulence, the zero diffusive flux at the wall is used. For the dissipation rate, the empirical evidence that a typical length scale of turbulence varies linearly with the distance from the wall is used to calculate ε at the near-wall point. In the no-slip condition on a solid wall, friction is calculated by the invoking ‘wall-functions’ [20], the scaled velocity component parallel to the wall is:

≥

<=

+++

+++

+

0

0

)ln(1 yyEy

yyyu

κ

(5)

kC 2/1µρτ = (6)

ykC

κε µ

2/34/3

= (7)

where, u+ and y+ are scaled variables, they are expressed as follows:

( )ρτ

µ

/

2/14/1

w

kCuu =+ (8)

( )

νµ

2/14/1 kCuy =+ (9)

Here, +0y is the cross-over point between the

viscous sub-layer and the logarithmic region, +0y is a constant given the value 11.63, τ is the turbulent shear stress, κ is the von Karman constant taken to be 0.4187, and E is a constant given the value 9.0.


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The air temperature in the space is set initially as 300 K. A uniform pressure field is also set for the initial condition and the pressure is 1.0 × 105 Pa. 5. GRID GENERATION WITH BODY-

FITTED COORDINATE Since the ceiling of the terminal hall has the geometry of curvilinear form, the most important factor to the success of the numerical simulation is how to specify the curvilinear physical model as the boundary condition in the computation. An approximation of the boundaries of a curvilinear physical system with the orthogonal grids may introduce large errors [21,22]. In this study, body-fitted coordinate (BFC) technology is employed to divide the irregular domain into cells and boundary fitted grids are used to solve the governing equations in transformed coordinates. The procedure of generating the curvilinear coordinate system is followed through the numerical solution of partial differential equations. The terminal hall considered is divided into 204 × 20 cells. Regions A and C are divided into 2 × 20 cells, region B is divided into 200 × 20 cells uniformly and the width of each cell is 1.8 m. The heat source is distributed over 1 cell in the x co-ordinate (1.8 m) and 6 cells in the y co-ordinate (2.4 m). The other part of the region above the heat source in the y-co-ordinate is also divided into 14 cells uniformly. The heat power is uniformly distributed over a depth of 1.5 m. One cell with a width of 1.5 m is adopted in the direction normal to the plane of calculation. The computational cell in the special region is shown in Fig. 2. In a two-dimensional physical domain, the Cartesian coordinates x and y are used. If a BFC grid system is employed, the original governing equations in the physical space are transformed to the computational space through coordinate transformation. Then the scalar variables (p, ρ, T, k, ε, etc.) are located at the arithmetic center of the

four adjacent grids marked by the circle. Both u and U are located at the midpoint of the east and west faces of the control volume. Both v and V are located at the midpoint of the north and south faces of the control volume. Their equations are approximated by a finite difference method based on a collected grid where the Cartesian velocity components and pressure are defined at the center of cell, while the volume flux components are defined at the mid-point on the corresponding cell surfaces, as shown in Fig. 3 [22]. The coordinates in the computational domain are denoted by ξ and η.

Fig. 3: Configuration of a staggered grid system

[20] 6. DISCRETIZATION OF CONSER-

VATION EQUATION The governing conservation equation typically can be written in two-dimensional Cartesian coordinates for dependent variable in the following form:

)()()(yv

xu

t ∂Φ∂

+∂Φ∂

+∂Φ∂ ρρρ

),( yxSyyxx

+

∂Φ∂

Γ∂∂

+

∂Φ∂

Γ∂∂

= (10)

Fig. 2: Computational cell of the region of interest in the terminal hall


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Equation (10) can be rewritten in (ξ, η) coordinate as follows:

( ) ( )Φ∂∂

+Φ∂∂

+∂Φ∂ 11)( ρ

ηρ

ξρ V

JU

Jt

Φ−ΦΓ

∂∂

= )(1 ηξ βαξ JJ

( )ηξγβη ηξ

,)(1 RJJ

+

Φ+Φ−Γ

∂∂

+ (11)

where

22ηηα yx += (12a)

ηξηξβ yyxx += (12b)

22ξξγ yx += (12c)

ξηηξ yxyxJ −= (12d)

ηη vxuyU −= (12e)

ξξ uyvxV −= (12f) R(ξ, η) is the source term in ξ, η coordinates. A staggered grid system is adopted [20] as shown in Fig. 4. In terms of the notation shown in Fig. 3 for a typical grid node P enclosed in its cell and surrounded by its neighbors N, S, E, and W, the finite difference approximation to the conservation laws can be performed by taking the integral of

equation (11) over the control volume and discretizing it, as done in Cartesian coordinate. It is noted that, after suitable interpolations for variables whose values are unknown on the control surface, a relation between the neighboring variables can be written as follows:

AAAAA SSNNWWEEpP Φ+Φ+Φ+Φ=Φ BA PP +Φ+

00

(12) where B represents all the terms that cannot be approximated by values of Φ at the five points.

[ ] [ ]0,eeeE FPADA −+= (13a)

[ ] [ ]0,wwwW FPADA −+= (13b) [ ] [ ]0,nnnN FPADA −+= (13c)

[ ] [ ]0,sssS FPADA −+= (13d)

0PSNWEP AAAAAA ++++= (13e)

tA PP ∆

∆∆=

ηξρ0 (13f)

∆ΦΓ

−

∆ΦΓ

+∆∆=we JJ

RJB ηβηβηξ ηη

∆ΦΓ

−

∆ΦΓ

+sn JJ

ξβξβ ξξ (13g)

a) Physical plane b) Transformed plane [22]

Fig. 4: Finite difference grid representation


26

where the term in square bracket of equation (13g) is an additional term resulting from non-orthogonality. If the grid is orthogonal, this term becomes zero. F is the convection intensity, D is the diffusion conductance, P is Peclet number, [ ]0,F− are the maximum value of -F and 0, ( )PA is the difference scheme, ∆ξ and ∆η denote

distances between two adjacent control faces in ξ and η directions respectively, and δη and δξ denote distances between two adjacent nodes in ξ and η directions respectively. The subscripts e, w, n, and s represent east, west, north, and south control faces respectively.

ee J

D

∆Γ=

δξηα , ( )ee UF ηρ ∆= ,

e

ee D

FP =

(14a)

ww J

D

∆Γ=

δξηα , ( )ww UF ηρ ∆= ,

w

ww D

FP =

(14b)

nn J

D

∆Γ=

δηξγ , ( )nn VF ξρ ∆= ,

n

nn D

FP =

(14c)

ss J

D

∆Γ=

δηξγ , ( )ss VF ξρ ∆= ,

s

ss D

FP =

(14d) The continuity equation can be written in a discretized form over each control volume as follows:

( ) ( )[ ]0 ∆

Φ−Φ+∆∆∆−

JUU

t wePP ηρρηξ

ρρ

( ) ( )[ ] 0=∆Φ−Φ+J

UU snξρρ (15)

The momentum equation can only be solved if the pressure field is given. The velocity field cannot satisfy the continuity equation unless the pressure

is correct. The pressure gradient xp∂∂ and

yp∂∂

should be separated from the source term. Because these two terms not only produce the corresponding term but also produce the cross-derivative terms, for example

)(11 ξηηξξη ηξypyp

Jypyp

Jxp

−=

∂∂

−∂∂

=∂∂ (16)

In this study, the ‘SIMPLEST’ algorithm is used for solving the velocity-pressure linked equations. The correct pressure p is obtained from

ppp ′+= * (17) where p′ is called the pressure correction. It is assumed that *u and *v are the velocities that satisfy the momentum equations with a given distribution p*, the corresponding velocity corrections u′ v′ could be introduced in a way:

uuu ′+= * (18a)

vvv ′+= * (18b) The significant difference between ‘SIMPLEST’ and the well-established ‘SIMPLE’ algorithm is that the finite-domain coefficients for momenta contain only diffusion contributions in the former scheme, the convection terms are added to the linearized source term of equations. In the physical plane, the momentum equation for eu is expressed as [20]:

−

++

= ∑∑ ua

cabu

adu nb

e

nb

enb

e

nbe

− −

x

pp

axy PE

e δ

δ∆ (19)

where nbd is diffusion contribution and nbc is convection diffusion. The sum of them is nba which is the total neighbors contribution. The subscript nb means neighbor points. Similar to the physical plane, *u and *v in computational plane are obtained from:

( )**,,,,,,

*ηξ PCpBucDudu

uu

SNWEii

ui

u

SNWEii

uiP ++

++= ∑∑

==

(20a)

( )**,,,,,,

*ηξ PCpBvcDvdv

vv

SNWEii

vi

v

SNWEii

viP ++

++= ∑∑

==

(20b) where Du and Dv are the cross derivation viscous terms in the momentum equations of u and ν respectively, B and C can be calculated by:

ηδξη ∆−= uP

u

Ay

B , ηδξξ ∆= uP

u

Ay

C (21a)


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ξδηη ∆= vP

v

Ax

B , ξδηξ ∆−= uP

v

Ax

C (21b)

Here, the velocity components are assumed to be corrected by the following formula:

( )ηξ pCpBuu uu ′+′+= * (22a)

( )ηξ pCpBvv vv ′+′+= * (22b) The correct form for U and V are obtained by substituting equations (22a) and (22b) to equations (12e) and (12f).

( ) ηηηξηη pxCyCpxByBUU vuvu ′−+′−+= )(* (23a)

( ) ηξµξξξξ pyCxCpyBxBVV vuv ′−+′−+= )(* (23b)

where U* and V* are calculated based on *u and

*v . Since the U and V points are located on the east-west and north-south respectively, equation (11) is formally of the same form as the finite-difference equation derived in Cartesian coordinate. Because of this similarity, the SIMPLEST solution procedure, which has been successfully used for flow calculation in Cartesian coordinate, can also be extended to the present body-fitted coordinate system. 7. SOLUTION FOR PRESSURE FIELD Pressure is obtained from the pressure-correction equation which yields the pressure change needed to procure velocity changes to satisfy mass continuity. In equations (23a) and (23b), it can be found that derivative terms of the pressure correction both in the same direction and cross direction are included. This means more than four unknown points (NE, NW, SW, SE) should be contained in the pressure correction equation. The successive line under relaxation (SLUR) method would be used to solve the system of finite-difference equations. The ηp′ term in equation (23a) and ξp′ in equation (23b) are omitted. Hence, the pressure correction equation will still be of the nature of five-point approximation. The effect of this neglect will be discussed later. Therefore, the velocity correction in the transformed plane is:

( ) ξηη pBxByUU vu ′−+= * (24a)

( ) ηξξ pCyCxVV uv ′−+= * (24b) It should be noted that both u and ν momentum equations contribute to U and V terms. This is different from the case in Cartesian coordinates. By substituting equation (24) to the continuity equation (15), an alternative formulation of pressure correction equations can be obtained:

bpApApApApA SSNNWWEEPp +′+′+′+′=′ (25) where

SNWEP AAAAA +++= (26a)

eE BBA

∆=

δηξρ ,

wW BBA

∆=

δηξρ ,

nN CCA

∆=

δξηρ ,

sS CCA

∆=

δξηρ (26b)

ξρξρηρηρ ∆−∆+∆−∆= VVUUb snwe**** )()()()(

ηξρρ

∆∆∆−

+ Jt

PP0

(26c)

( )ηη xByBBB vu −= , ξµξ yCxCCC v −= (26d)

The boundary condition in the transformed plane can be divided into two conditions: 1) The pressure of the boundary is known, this means pressure correction p′ = 0. 2) The velocity is known, then the velocity correction value is zero. According to equation (24), the pressure correction derivation in the direction perpendicular to the boundary ( ξp′ or ηp′ ) is zero. After the pressure correction is obtained, u, ν, U and V can be calculated by equations (22) and (24) respectively. The solution procedure is described as follows. • The momentum equations are first solved to

obtain the velocity components *u , *v , U* and V* with an assumed pressure field. Conservation equations for T, k, ε are solved at the same time. The equations are solved by a line-by-line procedure which is similar to the Stone’s Strongly Implicit Method but free from parameters requiring case-to-case adjustment. As a result, the solution is less complex and slower. Under-relaxation parameters are used in different subroutines to control the advancement of the solution field.


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• The pressure-correction equation (25) is solved in a whole-field manner. The mass errors that have been calculated during the first step are used.

• The velocity field u , v , U, V are updated by using equations (22) and (24) accordingly.

• The coefficients in the momentum discretized equation is replaced by the updated velocity and the corrected pressure is also used to start the next iterative cycle. This sequence is repeated until convergence is attainted.

Here, the effect of omission in equation (23) is discussed. When the iteration is convergent, both the velocity correction and pressure correction will tend to be zero. Therefore, the final convergent value of variable will not be affected when neglecting cross derivation term in equation (23). This simplified method has been adopted in the literature [e.g. 23].

8. CONVERGENCE CRITERIA It is important to define the convergence criteria since they are related to the accuracy of solution. The residuals are selected as the quantities used to monitor the convergence procedure in this paper. The convergence criteria for the Gauss-Seidel iteration method were used by checking the coefficient PA at point P and its neighbor points coefficients nbA ( nb is N, S, E or W) in the computational plane through a sum of absolute residues FVsumR for flow variables FV ( p′ and Φ are usually separated):

∑ ∑ −+=volume

control all SW,E, N,nbA pPnb

FVsum FVAbFVR (27)

The convergence criterion for pressure correction equation is:

FVFVsumR ε≤ (28)

Values for pε and Φε used in this simulation are 10-3. The relaxation factors, Φα , are introduced in the correction equation for flow variables Φ in order to get the converged computational results. The correction equation is then expressed by:

Φ′+Φ=Φ Φα* (29)

where Φ′ is the correction term for flow variable Φ , and *Φ is the incomplete term for flow variable. In this study, the relaxation factor for pressure is taken as 1.0 and the relaxation factors for u, ν, k and ε are all taken as 0.075. For temperature, the relaxation factor is taken as 0.1. It is found that these values of relaxation factors could allow the computational case to converge in a reasonable time. Simulations are performed with a PⅢ 500 MHZ personal computer. The number of iterations of the whole field for convergence varies from 1500 to 3000. Execution time for each iteration is about 1.32 s. Upwind difference was used in discretizing the convective terms in this study. The integrated source term is linearized. These practices are widely used to enhance numerical stability. However, upwind differencing used in nonlinear advection term results in computational damping, leading to false diffusion. This is a multidimensional phenomenon, resulted from evaluating multi-dimensional flow on each cell boundary as one-dimensional flow. In this study, values of the effective thermal diffusion are relatively large in the turbulent buoyant flow. For example, for a 1.0 MW fire, the effective diffusion coefficient, effµ , in the heat source region, is about 0.16, while the laminar diffusion coefficient is 2.53 × 10-5, the ratio of

effµ to µ is about 6.32 × 103. The effective

thermal diffusion coefficient (µ/Pr + µt/σt) is about 0.178 which is about 3.75 × 103 times the laminar thermal diffusion coefficient µ/Pr. The effect of false diffusion should be small in turbulent buoyant flows. 9. NUMERICAL RESULTS As mentioned earlier, the more difficult case of establishing a genuine steady state is attempted in order to aid the design of smoke control in a large space. The simulations are carried out for four fire scenarios where the heat release rates of fire are 0.5, 1.0, 2.0 and 5.0 MW respectively. In the calculation, the air pressure, temperature and velocity are given. The process of air entrainment into the fire, buoyant vertical acceleration of the plume, formation of ceiling jet and the establishment of recirculation in the cell are clearly evident. The predicted velocity vector, room air temperature, and pressure in the special region are shown in Figs. 5 to 7 respectively. Predicted velocity vectors of


29

special region under four conditions are illustrated in Fig. 5. It can be seen clearly that the airflow from the heat source impinges on a ceiling, and then spreads out radially to form a so-called ceiling jet. By comparing the velocities under different conditions, it can be found that as the heat power increases, the centerline velocity of plume also increases and the ceiling jet velocities also increase. In addition, the entrainment velocities of airflow to thermal plume also become larger with a higher heat release rate. The room air pressure fields are illustrated in Fig. 6. By comparing the air pressure in the stagnant region above the plume, it can be found that with the increase of heat source power, the stagnant pressure in the region above the heat source also increases. The reason is that centerline velocity increases with a higher heat release rate of fire and this could result in a higher stagnant pressure in the region above the plume. The neutral pressure plane is also described in this figure. It can be found that the height of neutral pressure plane would decrease with the increase of heat release rate. For example, at the position where x is 246 m, the heights of neutral plane are 4.82 m and 4.38 m when heat release rates are 0.5 MW and 2.0 MW respectively. Since the velocity on the neutral plane is almost zero, this tendency is also shown in Fig. 7. The neutral plane heights in the special region under four conditions show that the smoke layer will take a longer time to descend for small size fire in this large span building. The evacuees would have long enough time to evacuate after fire alarming. The predicted air contour in the special region is shown in Fig. 7. A stratified hot layer can be seen to flow under the ceiling. There is a steady increase of gas temperatures in the fire compartment from the floor to the ceiling. As the heat source power increases, the temperature ceiling jet temperature increases. The temperature near the heat source also increases. For example, the temperature of ceiling air is about 340 K for a heat release rate of 1 MW while the value is about 650 K for a heat release rate of 5 MW. 10. CONCLUSION Application of CFD for simulating indoor air movement induced by a fire is demonstrated. A computer code capable of simulating the flow field and taking into account the shape of boundary without rectangular feature is described. Although the codes have been used in the transient mode, the more difficult case of establishing a

steady state is attempted in order to aid the smoke control design. The volumetric heat source method is used to represent the fire. Detailed numerical analyses of airflow velocity, temperature, pressure in the full-sized terminal hall with different heat release rates of fire are made in this paper. Note that even two-dimensional simulations would be useful for some applications. The results have demonstrated the capability of CFD technique in modeling fire-induced smoke movement in big halls of this type. It is encouraging to see that the computed results indicate the correct trends, and the buoyancy modification improves the realism of the prediction of fire scenario in a large space. Entrainment into the fire, buoyant vertical acceleration of the plume, and formation of ceiling jet can be expressed clearly in the simulation. As the fire heat release rate increases, the ceiling jet velocity and temperature also increase. The height of the neutral pressure plane would decrease when the heat release rate increases. The problem of false diffusion with upwind scheme used in the convective terms of the governing equation is also discussed. False diffusion should have very slight effect in simulation because the effective thermal diffusion value is relatively large for the turbulent buoyant flow. However, there are not much discussions on the key points to note in the numerical works: • Relaxation and convergence criteria. • False diffusion in the turbulent buoyant flow. • Sudden changes in the flow parameters across

the heat source. The above key point will be reported in another paper. There are many criticisms on using RANS for simulating fire-induced flow. However, if the parameters are properly tuned with the relaxation factor and convergence criteria selected carefully, this technique can be used to study fire-induced flow. The more demanding analysis on designing smoke management system can be carried out within a reasonable computing time. Developing the CFD preprocessor and postprocessor in the computer-aided design in fire simulation is a critical part in implementing engineering performance-based fire code. Obviously, relevant training on CFD is still required and continued professional development lectures should be offered to the engineers.


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3 ms-1

a) fireQ& = 0.5 MW

3 ms-1

b) fireQ& = 1.0 MW

3 ms-1

c) fireQ& = 2.0 MW

6 ms-1

d) fireQ& = 5.0 MW

Fig. 5: Velocity vectors of the special region under different conditions


31

a) fireQ& = 0.5 MW (reference pressure = 100005 Pa)

b) fireQ& = 1.0 MW (reference pressure = 100008 Pa)

c) fireQ& = 2.0 MW (reference pressure = 100005 Pa)

d) fireQ& = 5.0 MW (reference pressure = 100010 Pa)

Fig. 6: Pressure contours of the special region (P0 = 1.0 × 105 Pa)

15 105

0

-5

9 7 5 0

-3

25 155

0

-5

30

1020

0

-12


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a) fireQ& = 0.5 MW

b) fireQ& = 1.0 MW

c) fireQ& = 2.0 MW

d) fireQ& = 5.0 MW

Fig. 7: Absolute air temperature contours (K) in the special region

380360

340

320 320

360

340

440

420

380 400

380

500

340330

310

300 300

330

310 380

340

650550 550

450

750

450


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NOMENCLATURE A coefficient in the discretized equation b a constant term

pc specific heat (Jkg-1oC-1)

D diffusion conductance F convection intensity g gravitational acceleration (m2s-1) k turbulent kinetic energy (m2s-2) p pressure (Pa)

*p incomplete pressure p′ pressure correction (Pa)

P Peclet number of grid Pr Prandtl number

fireq& power density of the heat source (Wm-3)

fireQ& fire heat release rate (W)

ΦS source term in general transport equation T absolute temperature (K) u,ν velocity components in x and y direction

respectively (ms-1) +u scale velocity in wall function

Vr

velocity vector (ms-1) x, y special coordinates in physical plane (m)

+y scaled distance in wall function Greek Symbols α transformation constant in BFC system β transformation constant in BFC system

ΦΓ effective diffusivity coefficient ε dissipation rate of the turbulent kinetic

energy (m2s-3) µ dynamic viscosity (kgm-1s-1) µt turbulence dynamic viscosity (kgm-1s-1) ν kinematical viscosity (m2s-1) ξ, η coordinate in computational plane ρ density (kgm-3)

tσ turbulence Prandtl number Φ variable in general transport equation Subscripts e, w, n, s east, west, north and south for an

elementary cell E, W, N, S east, west, north and south elementary

cell, respectively REFERENCES

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