A new model on simulating smoke transport with computational fluid dynamics

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Building and Environment 39 (2004) 611 – 620

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A new model on simulating smoke transport with computational $uid dynamics W.K. Chow∗ , R. Yin Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong, China Received 8 February 2001; received in revised form 1 August 2002; accepted 11 December 2003

Abstract A new model is proposed for simulating smoke movement induced by a 1re. Smoke is taken as a collection of particles with size described by a certain distribution function. Movement of the particles will be studied by dividing the physical problem into two parts: solid phase and air phase. The Lagrangian approach is used for studying motion of the solid phase, with the air $ow simulated by computational $uid dynamics (CFD). Interaction between the air phase and the solid phase will be described by the particle-source-in-cell method. k– types of turbulence models are used in the simulation of air $ow. Some of the results are also compared with the 1re dynamics simulator model based on large eddy simulation developed at the Building and Fire Research Laboratory, National Institute of Standards and Technology, USA. Application of the model for designing smoke management system is also illustrated. This model should be useful for designing smoke management system as it describes an intermediate step while using CFD. ? 2004 Elsevier Ltd. All rights reserved. Keywords: Smoke management; Computational $uid dynamics; Smoke transport; Building 1re model; Fluid modeling

1. Introduction Smoke transport due to a 1re should be well understood for designing practical smoke management system. Apart from full-scale burning tests, 1re 1eld model or application of computational $uid dynamics (CFD) [1,2] is now a popular method to study smoke transport. In those 1re models, smoke is taken as the variation of one parameter set by a threshold level of a scalar marker such as the smoke-volume fraction. This might give a similar pattern as the temperature contours by taking smoke as a continuous phase with the Eulerian method [3]. But the interactions such as the dragging e>ect and heat transfer among smoke particles and the surrounding air $ow would not be included. This approach was applied to study the optical density and the detector response without including the smoke ageing processes [4]. Structures and shapes of the smoke particles are critical factors in activating the detectors. The particle size distribution would be changed if the ageing processes are included. The response time of the smoke detectors predicted without considering smoke ageing would not be accurate enough. ∗

Corresponding author. Tel.: +852-2766-5843; fax: +852-2765-7198. E-mail address: [email protected] (W.K. Chow).

0360-1323/$ - see front matter ? 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2003.12.012

Smoke coagulation and aggregation were included in studying the response time of the smoke detectors and the $amelet-based smoke properties [5,6]. Field modelling technique was applied to predict the optical properties of smoke with coagulation and its detection. But the property of smoke was only considered as a single factor with the simpli1ed soot formation model incorporated into the CFD model to describe coagulation, nucleation and aggregation. Fractal aggregate structure of soot aerosol was considered [5] to improve the study on smoke detectors’ response time. But doing this would not give a real physical picture of smoke. Smoke can be visualized as small solid or liquid particles resulting from combustion or pyrolysis [7]. The Lagrangian method seems a more reasonable way to describe motion of the smoke particles. Fire models with the Lagrangian method have been applied to study the deposition of large particles from warehouse 1re plumes [8], wildland 1res [9,10], simulations of 1re plumes [11], and brand propagation from large-scale 1res [9]. Recently, smoke was taken as a large number of small particles emitted from a 1re [12,13]. The motion of the smoke particle was calculated from Newton’s second law and the surrounding air $ow was calculated from the 1re 1eld model. Smoke particles were assumed to be

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hard spheres with a certain distribution of particle size. This approach should be valid for smoke produced from pyrolysis and smoldering combustion [14]. This method is now further applied to study smoke management system. The problem on studying smoke transport is divided into two parts [12,13]: • The ‘solid phase’ where smoke particles are taken as hard spheres without evaporation e>ect. • The ‘air phase’ with the air $ow induced by the 1re being simulated by CFD. Momentum and heat transfer of the two phases are described through the source term of the key equations describing air $ow, i.e., particle-source-in-cell (PSI-CELL) method [15]. This approach has been applied [16] in studying the convective heat transfer and dragging e>ects between the sprinkler water droplets and the hot-air layer induced by a 1re with a self-developed CFD package. This was also used in studying particle deposition and distribution for indoor ventilation design [17] with the commercial package FLOW3D/CFX [18]. As the 1re-induced buoyancy $ow is turbulent, the k– types of turbulence models [1,2] were widely used in most of the practical design tools based on CFD. They were applied to predict the smoke movement in compartments [1], tunnels [19], atria [20] and uncon1ned pool 1res [21] in the past years. Further, the modi1ed k– turbulence model can be applied for studying a wide range of 1re problems with results well veri1ed by experiments [22,23]. In this paper, the concept [12,13] was further extended as described in later sections for modelling the smoke transport phenomenon better. This intermediate step is an important development of the use of CFD in understanding smoke movement and, consequently, in designing smoke management system. Two sets of simulations C1 and C2 were carried out to illustrate this modi1ed concept: • C1: On the simulation of a smoke plume induced by a 1re. • C2: On the application of the approach to design a smoke management system for a building. The CFD software CFX4.3 [18] with the modi1ed k– model was used as the simulator. Further investigational work will be on studying smoke particle distribution, coagulation and response time of the smoke detectors with the developed transport models. Criticisms were made in using the k– model for 1re simulations as it was derived by substituting the sum of a time-average term plus a $uctuating term for the instantaneous quantities. A fundamental limitation lies on the averaging of the model equations. The predicted results appeared to be ‘smoothed’ out even with a 1ne grid system. The k– model would be a reasonably good approach for isotropic turbulent $ow but the air $ow induced by a 1re is not isotropic. Evolution of large eddies of a 1re plume

cannot be predicted as this is a local transient phase. There are proposals on using large eddy simulation (LES) [24,25] for 1re simulations [26–29] and other areas such as computational wind engineering [30,31]. There, larger scales of turbulent motion were simulated, with the smaller ones being approximated by some spatial functions. Recently, a 1re 1eld model, 1re dynamics simulator (FDS) [29], was developed based on LES at the Building and Fire Research Laboratory, National Institution of Standards and Technology (NIST). This model is readily available in the website of NIST and can be downloaded for use. Part of the results simulated by CFX [18] was compared with those predicted by FDS [29] based on LES. 2. Brief review on the approach In a 1re 1eld model with modi1ed k– model, the air $ow induced by the 1re can be predicted by solving the Reynold-averaged Navier–Stokes (RANS) equation [1–3] for the mean $ow variables  in the form ˜  −  grad ) = S : div(a U

(1)

For a k– model, there are six equations in the form of Eq. (1) with  includes air velocity components ˜ , enthalpy h, the two turbuu; v; w of the air vector U lence parameters on turbulence kinetic energy k and its rate of dissipation . a is the air density, S is the source term and  is the total di>usivity in the equation for $ow variable . The 1re is taken as a heat source with speci1ed volume appeared in the source team of the conservation equation for enthalpy. The e>ects of the smoke particles on the air $ow are described in the source term for the momentum and enthalpy equations. Further, a pressure equation has to be solved. The Lagrangian method was used to track the movement of smoke particles [12,13,16]. Smoke particles were divided into sets of individual particles which would be tracked separately through the $ow domain by solving the equations of motion. The following assumptions are made to simplify the model: • All particles are considered hard spheres produced from pyrolysis and smouldering combustion [14]. • Combustion is not included for the particles so that the diameter of particles would not change. • There is no mass transfer between the particles and the surrounding air. • Particles would lose 20% of their momentum after hitting on the solid walls. • Forces on the particles due to pressure gradient are not included as the particles are quite small. The equation of motion for a particle moving with ˜ p is described by Newton’s second velocity V

W.K. Chow, R. Yin / Building and Environment 39 (2004) 611 – 620

law as: md

The eddy lifetime and the eddy characteristic size along the particle trajectory are estimated from the local turbulence properties. A general expression for these two scales in isotropic turbulent $ow has the form

˜p 1 dV ˜ −V ˜ p )|U ˜ −V ˜ p| = Cd d2 a (U dt 8 +

1 3 d (d − a )g; 6

(2)

where md is the mass of the particle, d is the particle diameter, and d is the particle density. The drag coeNcient Cd is given by the following correlation relation: Cd =

24(1 + 0:15Re0:687 ) : Re

(3)

The Reynolds number Re of the particle is de1ned through the viscosity  as Re =

˜ −V ˜ p |d a |U : 

(4)

Eq. (3) holds only for Re 6 1 × 105 . Temperature of the particle Tp can be described by the convective heat transfer Qc with air: Qc = d Nu (Ta − Tp );

(5)

where  is the thermal conductivity of the air$ow, Ta is the air temperature predicted from CFD and the Nusselt number Nu is given by 1=3
Cp Nu = 2 + 0:6Re0:5  : (6)  As the particle size is quite small, i.e. about 100 m, the effect of turbulence must be included within the particle transport. Common models are the stochastic-separated-$ow (SSF) model [23] and Thomson’s random $ight model ˜ in [32,33]. The SSF model is applied in this paper. U Eq. (2) is taken to be the mean air $ow velocity plus a term due to turbulence. A collection of random eddies was used to describe turbulence. These eddies interacted with the particles are described by a $uctuating velocity u
(in m s−1 ), the eddy lifetime te (in s) which is a time scale, and the eddy characteristic size le (in m) which is a length scale. The particle is assumed to be interacting with an eddy for a time interval (i.e. the interaction time tint in s) with minimum value of the eddy lifetime and the eddy transit time tc (in s). Thus, the expression for the time step Ot is given by Ot = tint = min(te ; tc );

(7)

where tc is the time taken for a particle to travel through an eddy of size le :   le tc = − p ln 1 − ; (8) ˜ ˜ p |U − V P | where p

=

1 md : 3d (1 + 0:15Re0:687 )

613

te = 1:51=2 C2=3

k 

(9)

and le = C3=4

k 2=3 : 

(10)

For normal turbulent $ow, the variance of the speed of the eddies is taken to be twice the turbulent kinetic energy 2k. The diameter and density of particles generated from a 1re are important parameters. Smoke generated by a 1re depends on the burning behaviour of the materials. For example, the relative amount of gases, liquid and solid matter generated is a>ected by the fuel and burning mode such as $aming or smoldering. Di>erent results were found in measuring the particle size. 0:01 m for normal agricultural burning and wildland 1res [9,34], and up to 18 mm for large pool 1res with wind e>ect [35]. Smoke particles of diameters between 10 and 90 m were selected in this study. The range was not too large nor too small, and is a representative value for smoke in a 1re plume burning in an atrium [8]. Smoke particles were divided into 10 mean particle diameters from 10 to 90 m with intervals of 10 m. Smoke particles emitted at di>erent positions were distributed uniformly above the 1re. Initial velocities of the smoke particles are set to zero. Particles of the same size were uniformly distributed in each cell centre of the 1re source horizontally with the initial height Z0 given by [35] 2




dg Zc 4 d 1 ; (11) Z0 = 2 2:13 Uc 3 Cd a where Uc is the central velocity of the 1re plume and Zc is given in terms of the ambient temperature T0 and the heat release rate of 1re Q˙ 0 : 2=5
Q˙ 0 ; (12) Zc = √ a C p T 0 g where Cp is the speci1c heat of air. The particle density d is assumed to be a constant of value 1800 kg m−3 [8] and the particle speci1c heat is taken as 800 J kg−1 K −1 for calculating the heat transferred to the particle.

3. Simulations C1 A relatively simple scenario C1 was selected to illustrate the application of this model. A plume generated by a pool 1re under a ceiling was considered. A 1re of heat release rate 500 kW, with length 1 m, width 1 m and height 0:5 m,

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Fig. 1. Geometry for C1 simulations.

Fig. 2. Smoke movement for C1 simulations.

was located at the centre of $oor. The computation domain concerned was of length 10 m, width 10 m and height 8 m as in Fig. 1. For using CFX4.3, a coarser grid system, i.e. 30 × 30 × 20 along the x- , y- and z-directions, could be used. Simulations up to 100 s were carried out with time steps is taken as 0:2 s.

Transient positions of the smoke particles at 2, 4, 6 and 8 s are shown in Figs. 2a–d. Note that di>erent temperatures of the smoke particles were predicted at di>erent positions. These diagrams would give a pictorial presentation on how smoke moves in a building. For example, smoke particles were observed to

W.K. Chow, R. Yin / Building and Environment 39 (2004) 611 – 620

615

Fig. 3. Temperature for C1 simulations.

move up and hit the roof, then $ow under the roof to give a ceiling jet. After that, particles would spread out of the room geometry concerned. In this way, smoke movement induced by a 1re can be visualized. This approach on studying smoke movement is different from the particle tracing methods as there are interactions between particles and the surrounding air $ow through the momentum and enthalpy conservation equations. The temperature contours across the central z-plane at 2, 4, 6 and 8 s are shown in Figs. 3a–d. It was observed that the plume oscillated about the vertical axis above the 1re centre. This is consistent with the computed smoke movement pattern as shown in Fig. 2. Similar oscillations were observed in carrying out experiments with the full-scale burning facility, PolyU/USTC Atrium [36], and earlier simulations with the CFD software UNSAFE [37].

500 kW heat source as in CFX4, the heat release rate in FDS would be determined by the thermal elements that liberate heat to the surrounding air through a simple combustion model. Therefore, the input heat release rate has to be adjusted carefully. A more detailed description of the simulation with FDS is reported elsewhere [13]. Transient temperatures predicted by CFX at 6 m above the 1re centre are shown in Fig. 4. Here, the results from FDS are also plotted. It is observed that the temperature predicted by FDS $uctuated from 20◦ C to 270◦ C. Average temperatures for both models at that position are about 105◦ C. Excess temperature OT0 and velocity u0 above the $ames at a vertical height y above the 1re centre can be 1tted by the following relations [38]:  OT0 = 9:1

4. Comparison with LES and plume expressions Part of the results was compared with the FDS [29] model. In this model, a relatively 1ner grid system (64 × 64 × 64) was used due to the inherent requirement of LES as shown in Fig. 1. The time step for the FDS was 0:05 s at the beginning. Later, time intervals would be adjusted by the program itself to satisfy the convergence criterion during the calculation. Unlike setting the convective heat release rate of 1re to be a


u0 = 3:4

T∞ gCp2 2∞

T0 T∞

1=3 Qc2=3 (y − y0 )−5=3 ;

(13)

1=2 (y − y0 );

(14)

where Qc is the convective heat release rate (in kW), and y0 is virtual origin height given by the total heat release rate Q (in kW) and the e>ective 1re diameter D (in m): y0 = −1:02D + 0:083Q2=5 :

(15)

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Fig. 4. Temperature at 6 m above the 1re centre for C1 simulations.

Fig. 5. Vertical air velocity above the 1re centre for C1 simulations.

The $ame height L under normal atmospheric conditions is L = −1:02D + 0:23Q

2=5

:

(16)

Pro1les for u0 and OT0 predicted by CFX and FDS are shown in Figs. 5 and 6. Correlation relations given by the above equations are also shown. Instantaneous values predicted by FDS oscillated due to the vortices generated by the 1re. However, the time-averaged results from both CFX and FDS model show good agreement with the engineering correlations above the $ame height of 2 m. Based on a similar approach [38], there is an expression in NFPA 92B [39] on calculating the plume mass $ow rate mp (in kg s−1 ) at a height y (in m) for a 1re placed under

Fig. 6. Air temperature rise above the 1re centre for C1 simulations.

a roof of height H :  0:071Qc1=3 y5=3 + 0:0018Qc ; mp = 0:032Qc3=5 y;

y ¿ y‘ ; y ¡ y‘ ;

(17)

where y‘ = 0:166Qc2=5 :

(18)

Air velocity and density predicted by CFX and FDS were used to calculate mp which is plotted against y in Fig. 7. Very good agreement between the two models and Eq. (17) was found.

W.K. Chow, R. Yin / Building and Environment 39 (2004) 611 – 620

617

Fig. 7. Mass $ow rate of plume for C1 simulations.

5. Simulations C2 This set of simulations was to demonstrate how smoke management system can be designed by visualizing the smoke movement pattern. A room of length 8 m, width 6 m and height 10 m as shown in Fig. 8 is considered. A 500 kW 1re of size 1 m × 1 m and height 0:75 m was placed at the centre. The e>ectiveness of natural vents and mechanical extraction system of smoke management systems [39–41] were demonstrated. Those were installed through two square ducts of dimensions 1 m × 1 m up to a height of 2 m. The following three sets of simulations were carried out: • C2a: No smoke management system was installed. • C2b: Two natural vents of size 1 m × 1 m were considered. • C2c: Mechanical ventilation system was installed, with two ventilation rates of 60 air changes per hour (ACH) and 225 ACH. The results on transient positions of smoke particles for simulation C2a are shown in Fig. 9; for C2b on the natural vents, the results are shown in Fig. 10; and for C2c on mechanical ventilation system, the results are shown in Figs. 11 and 12. For simulation C2a, since there were vertical walls at the side, smoke particles would move back to the ceiling jet to give a smoke layer. The smoke layer descended downward to the vertical opening below. For C2b with natural vents, the smoke layer interface height could be kept quite high. This gives a good demonstration that natural vents are useful. For C2c on mechanical ventilation system, the smoke layer could not be kept at high levels for typical ventilation rates

Fig. 8. Geometry for C2 simulations: (a) geometry of the simulation; (b) top view.

(up to 12 ACH) commonly used in local design. Only high ventilation rates from 60 to 225 ACH would have smoke extraction e>ect.

6. Conclusion A new model for simulating smoke movement pattern based on a previous approach [12,13,16] was developed. In this model, heat and momentum transfer between the smoke particles and the surrounding air are included. The model is useful in illustrating the smoke 1lling process in a building. From this, smoke management systems [39–41] can be designed. The k– type of turbulence model [1–3] is still a practical approach for simulating air $ow as the required CPU time is much shorter. There are commercial packages with good computer-aided-design (CAD) interfaces so that engineers can use it easily. Therefore, this approach of simulating 1re-induced 1re $ow is still the 1rst choice.

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Fig. 9. Smoke particles across the central z-plane for C2a simulation.

Fig. 10. Smoke particles across the central z-plane for C2b simulation.

Fig. 11. Smoke particles across the central z-plane for C2c simulation of 60 ACH.

W.K. Chow, R. Yin / Building and Environment 39 (2004) 611 – 620

619

Fig. 12. Smoke particles across the central z-plane for C2c simulation of 225 ACH.

The LES approach [24,25,27,31] would give more detailed information, but the computing time required would be much longer and so more expensive computer hardware are expected. More knowledge is also expected of the personnel concerned. Training should be provided to engineers carrying out the CFD works with LES. They should know how to interpret the results, and how to make adjustment on the di>erent coeNcients concerned. However, LES is not just limited for use in research types of projects [26–32]. LES options are starting to be included in some commercial CFD software. Perhaps, the government should consider using LES while approving the 1re safety design based on CFD. A more detailed feasibility study is suggested to be carried out. Acknowledgements The project was funded by Area of Strategic Development in Advanced Buildings Technology in a Dense Urban Environment, The Hong Kong Polytechnic University. The software FDS was downloaded from the website of Building and Fire Research Laboratory, National Institute of Standards and Technology, USA.

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