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Large eddy simulations for studying tunnel smoke ventilation
Tunnelling and Underground Space Technology incorporating Trenchless Technology Research
Tunnelling and Underground Space Technology 19 (2004) 577–586
www.elsevier.com/locate/tust
Large eddy simulations for studying tunnel smoke ventilation P.Z. Gao a, S.L. Liu a, W.K. Chow
b,*
, N.K. Fong
b
a
b
College of Power and Nuclear Engineering, The Harbin Engineering University, Harbin, China Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong, China Received 30 June 2003; received in revised form 10 January 2004; accepted 26 January 2004 Available online 11 March 2004
Abstract Computational fluid dynamics are applied to simulate the smoke movement in a ventilated tunnel fire through large eddy simulation (LES). Several scenarios with different ventilation rates are considered by taking the fire as a volumetric heat source. Results predicted by LES are compared with those from a k–e model. These include temperature fields, flame shape and the smoke movement pattern. It is found that thermal stratification and smoke backflow can be predicted successfully by LES. The possibility of applying LES as an engineering tool to smoke management system design in tunnels is discussed. 2004 Elsevier Ltd. All rights reserved. Keywords: Fans; Research and development; Fire safety systems
1. Introduction Fires occurring in mine headings or transport tunnels would lead to a loss of human lives in many cases (Leitner, 2001; Kirkland, 2002). Smoke, not heat, was identified to be the most hazardous factor to human beings as it can spread throughout the tunnel rapidly. Smoke management systems (SMS) for smoke control should therefore be installed in the tunnels with effective ventilation systems. The longitudinal ventilation (or one-way ventilation) system operated by blowing smoke towards a tunnel exit is commonly designed to prevent backlayering. However, system performance is not effective if the ventilation rate is low and the buoyancy of smoke is strong enough. The fire plume would impinge on the ceiling and spread against the discharged ventilation flow. It is very important to understand when a smoke backflow will occur. Results are useful for SMS design and development of the associated fire codes. Both physical experiments (Apte et al., 1991, 1998; Oka and Atkinson, 1995; Vauquelin and Megret, 2002; Wichman et al., 2002) and numerical simulations with *
Corresponding author. Tel.: +852-2766-5111; fax: +852-2765-7198. E-mail address: [email protected] (W.K. Chow).
0886-7798/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2004.01.005
fire models (Fletcher et al., 1994; Beard et al., 1995, 1996; Chow, 1996; Woodburn and Britter, 1996a,b; Kunsch, 1998; Kunsch, 2002; Megret and Vauquelin, 2000; Wu and Bakar, 2000; Li and Chow, 2003) were reported on tunnel fires. It is far too expensive to design SMS with full-scale burning tests. Fire models are used as engineering design tools. In view of the large aspect ratio of the tunnel, zone models are not too suitable because a smoke layer of uniform thickness is assumed to form at the ceiling. This assumption might not hold in a tunnel as the ceiling jet is moving as a wave front. The field model (or application of Computational Fluid Dynamics CFD) has been applied but there are also limitations. Very few physical experiments such as those in a full-scale mock-up of a mine roadway by Apte et al. (1991) were carried out to verify the predicted field modelling results. Smoke movement in that experiment was simulated by Fletcher et al. (1994) with results compared with experimental data. Their field model included sub-models for combustion and thermal radiative heat transfer. The turbulent flow was simulated by the two equations k–e model. Adequacy of the chosen physical models was investigated. On the other hand, the large eddy simulation (LES) is starting to be more popularly used as an engineering tool. LES can give a more complete description of the
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Nomenclature A Cp d D Fr gi G k L Ls m_ p Prt q_ c Q_ Sij t T T0 ui , u j us
area specific heat capacity distance diameter Froude number acceleration of gravity in the co-ordinate directions x, y and z filter function turbulent kinetic energy; thermal conductivity characteristic length mixing length for subgrid scales fuel release rate pressure turbulent Prandtl number heat release rate per unit volume total heat release rate local large-scale rate of strain tensor time temperature ambient temperature velocity components in the co-ordinate directions x, y and z shear velocity
transient turbulent flow structure, leading to better understanding of smoke spreading. The underlying theory of LES including subgrid-scale models and numerical schemes developed rapidly. Some works on the simulation of fire and smoke movement (McGrattan et al., 1996, 1998; Wang et al., 2002; Liu et al., 2002a,b) were reported. Scenarios on the tunnel fires similar to those reported by Fletcher et al. (1994) will be simulated with LES in this paper. Air flow induced by taking fire as a simple heat source will be simulated. Results are also compared with experimental data and the earlier simulations by Fletcher et al. (1994). There are three objectives in this study: • To investigate whether LES can be used as a fire simulation tool. • To compare LES with the Reynolds averaged Navier–Stokes equations (RANS) approach such as the k–e model. • To study smoke movement in a tunnel fire and performance of longitudinal ventilation system. Note that LES and RANS (such as k–e) models are different methods in dealing with turbulent flows using spatial and temporal averaging. Basically in LES, largerscales of turbulence were simulated with smaller-scale motions modeled as discussed later. RANS had been applied to solve practical engineering problems. A two-
V ~ x x xi , xj y z
cell volume ðx, y, zÞ Cartesian coordinate streamwise co-ordinate co-ordinate directions x, y and z cross-stream co-ordinate vertical co-ordinate
Greek symbol b thermal expansion coefficient dij Kronecker delta e dissipation of the turbulent kinetic energy l dynamic viscosity lt subgrid-scale turbulent viscosity m kinematic viscosity q air density q0 ambient air density D filter width / general variable / large-scale component /0 subgrid-scale component X domain of interest sij stress tensor sij;S subgrid-scale Reynolds stress
equation k–e model is commonly used to give the averaged flow fields.
2. Experiment Experimental studies (Apte et al., 1991; Fletcher et al., 1994) were carried out in a tunnel of 130 m length, 5.4 m width and 2.4 m height. The geometry of the tunnel is shown in Fig. 1. A pool fire was located 40 m further down the tunnel. The fuel burnt was aviation fuel (octane) contained in a circular tray with diameter of 1 m. Airflow with speeds up to 2 m s1 was induced by two exhaust fans installed at one end. Instruments such as thermocouples, bi-directional velocity probes and video cameras were installed in different positions for measuring the parameters concerned.
3. Mathematical model 3.1. Governing equations It is very complicated to simulate a pool fire realistically because combustion, radiation and turbulence have all to be included. A volumetric heat source
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Fig. 1. The experimental and computational geometry.
(VHS) without chemical reactions is assumed. The heat release rate per unit volume q_ c from the VHS represents that generated from the pool fire. The main theme of the study is on simulating the smoke movement described by the predicted hot gas flow pattern and the temperature field. Species transport equations are not included and so the species concentration distribution will not be predicted. The air surrounding the VHS is entrained, heated up with its density reduced and then rises up. Buoyancy is included in the momentum equation by means of a Boussinesq approximation to calculate the density differences. A gas flow with a Mach number below 0.3 can be regarded as incompressible (e.g., Ferziger and Peric, 1996). This criterion holds for a fire-induced flow as the air velocity is less than 10 m s1 and the ventilation rate is lower than 2 m s1 . For an incompressible gas flow at low velocity, the thermal energy due to viscous shear in the flow is small. The viscous dissipation term in the energy equation can be neglected. With the above assumptions, the governing equations on fire-induced air flow can be written in the following form: ouj ¼ 0; oxj oui oðui uj Þ 1 op 1 osij þ ¼ þ gi bDT ; oxj q oxi q oxj ot oT oðTuj Þ o k oT q_ c þ ¼ þ : ot oxj oxj qCp oxj Cp
ð1Þ
ð2Þ
differential equations numerically. The effect of smallscale motions will be represented by stress terms similar to Reynolds stresses called subgrid-scale Reynolds stresses to be modelled (Shi, 1994). The first step of LES is filtering which decomposes a x; tÞ and variable /ð~ x; tÞ into a large-scale component /ð~ a small-scale component (subgrid-scale component) x; tÞ þ /0 ð~ x; tÞ, i.e., /ð~ x; tÞ ¼ /ð~ x; tÞ . The large-scale /0 ð~ component, /ð~ x; tÞ is obtained by taking a function Gð~ x ~ x0 ; DÞ as the filter kernel Z x; tÞ ¼ /ð~ Gð~ x ~ x0 ; DÞ/ð~ x0 ; tÞ d~ x0 ð4Þ X
where X is the domain of interest; D is the filter width, given by D ¼ V 1=3 Q; 3and V is the volume of a computational cell, V ¼ i¼1 Dxi ¼ DxDyDz , where Dxi is the grid interval along the xi direction. The filter function is ( 1=V for ~ x0 2 V ; 0 Gð~ x ~ x ; DÞ ¼ ð5Þ 0 otherwise: Filtering each term in Eqs. (1)–(3) would give the following: ouj ¼ 0; oxj
ð6Þ
j Þ oui oðui u 1 op 1 þ ¼ þ oxj q oxi q ot
osij osij;S þ oxj oxj
!
gi bDT ; ð3Þ
3.2. Large eddy simulation In LES, the turbulent motion is decomposed as large- and small-scale motions by filtering. The largescale flow structures are calculated by solving the
oT oðT uj Þ o þ ¼ ot oxj oxj
k oT qCp oxj
ð7Þ ! þ
oRj q_ c þ ; oxj Cp
ð8Þ
where the overbar denotes the filtered variable. The large-scale eddies are computed directly at the resolved scale. The scales of motions unresolvable on the computational mesh are removed. In most fire simulations, the primary momentum transport and turbulent
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diffusion are sustained by large-scale eddies. Smallerscale eddy motion are not accounted for. The subgrid-scale (SGS) motions are represented by an eddy viscosity with the length scale related to the grid size in the computing domain. The time scale is determined by the local resolvable dissipation. The SGS motion is calculated by the Smagorinsky–Lilly model where the unknown SGS Reynolds stresses, sij;S are related to the local large-scale rate of strain, S ij , by sij;S 1skk;S dij ¼ 2lt Sij ; ð9Þ
As reported by McGrattan et al. (1998), adequate resolution would be achieved by assigning ten computing cells for L. With hardware limitation taken into account, the heat source is discretized into 8 8 3 cube cells, about 0.11 m on a side. The whole computing domain is composed of 108,416 cells, with 176 parts along the tunnel, 28 parts across it and 22 parts in the vertical direction. Finer grids are used in the heat source and regions near to it.
sij;S and S ij are defined, respectively, as
4.2. Boundary conditions
3
j ; sij;S qui uj þ q ui u ! 1 o u o u i j þ : Sij 2 oxj oxi
ð10Þ ð11Þ
The subgrid-scale turbulent viscosity lt is used to provide the role of modelling the dissipative behavior of the unresolved small scales. The eddy viscosity is modeled by lt ¼ qL2s jSij j; ð12Þ where qffiffiffiffiffiffiffiffiffiffiffiffi jSij j ¼ 2Sij Sij ð13Þ Ls ¼ min k1 d; Cs V 1=3 ;
ð14Þ
where k1 ¼ 0:42; d is the distance to the closest wall; Cs is the Smagorinsky constant, lying between 0.1 and 0.23, taken as 0.1 in this paper. The subgrid heat flux, qRj is based on the eddy viscosity approach, l oT Rj ¼ Tuj þ T uj ¼ t ; ð15Þ qPrt oxj Prt is the turbulent Prandtl number of values lying between 0.2 and 0.9, and is taken as 0.85 in this paper. 4. Numerical simulations
A tunnel segment of length 90 m is taken out with boundary shown in Fig. 1. The pool fire is located 40 m from the tunnel entrance. To simplify the computation, the pool fire was taken as a heat source of 0.89 m2 with height 0.33 m. The height 0.33 m was selected after some simulation tests. The total heat is assumed to be released uniformly throughout the whole source. The computing mesh was assigned with a suitable grid resolution by considering the characteristic length scale L for a fire plume related to the total heat release rate Q_ by L¼
!2=5 :
ui ¼ hui i þ Iwjuj;
ð16Þ
ð17Þ
where I is the intensity of the fluctuation, w is a Gaussian random number satisfying w ¼ 0 , and ffiffiffiffiffi q w0 ¼ 1 . The wall shear stress is obtained from the logarithmic law of the wall, u 1 us y ; ¼ ln E u s k2 m
ð18Þ
where y is the distance to the wall, k2 ¼ 0:418 and E ¼ 9:793. The tunnel wall is assumed adiabatic. The total heat release rate of the pool fire is _ Q_ ¼ qm Am;
4.1. Grid system
Q_ pffiffiffi q0 T0 Cp g
The differential pressure at the tunnel inlet, which is defined as the difference of pressure drop at the entrance from the atmospheric pressure (Fletcher et al., 1994), is used as the operating pressure of the computing region. The velocity boundary is used at the tunnel outlet with values taken from the experimental data (Fletcher et al., 1994). The stochastic components of the flow at the velocityspecified boundaries are accounted for by superposing random perturbations on individual velocity components as
ð19Þ
where qm is the calorific value of the fuel, 44.4 MJ/kg for octane (Fletcher et al., 1994); A is the fuel pool area, A ¼ pD2 =4; and m_ is the fuel release rate, see Table 1. 4.3. Numerical solution In applying LES for solving transient problems, computing starts from some initial conditions in a fine enough grid system with an appropriate time step. Computing must be run long enough to get results independent of the initial conditions. In the simulation, the second-order implicit formulation is used for temporal discretization with the time step size set to 0.1 s. The fully implicit scheme is unconditionally stable with respect to time step size.
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Table 1 Measured and calculated flame angles under different simulation conditions Case
Fuel release rate (kg s1 m2 )
Air flow speed (m s1 )
Measured flame anglea ()
Predicted flame anglea ()
Predicted (k–e) flame angle ()
Predicted (LES) flame angle ()
a b c
0.070 0.065 0.058
0.50 0.85 2.00
46 56 66
49 62 78
40 45 67
32 56 67
a
Results from Fletcher et al. (1994).
However, the time step would be set to be at least one order of magnitude smaller than the smallest time constant in the system. Time step size can be adjusted by observing the number of iterations required for getting converged results. Optimum number of iterations per time step is 10–20. The assigned time step is too large if more than 20 iterations was used. Wider time step can be used if converged results can be achieved with several iterations. For spatial discretization, the second-order central differencing and QUICK scheme are used. Excessive diffusive schemes such as the first-order upwind or power law scheme are not used. The pressure-velocity linked equations are solved by the PISO scheme. Velocity components at selected locations are monitored to check whether the flow is fully-developed. Computing will be carried on until the flow becomes steady. The solution will be started again with sampling instantaneous data during the calculation, and continued until stable data are obtained. With these sample data, time-averaged values and root-mean-square values can be computed. All the flow field figures are processed by time averaging. Residuals are checked for judging convergence. The convergence criterion is selected as that the scaled residuals decreased to 106 for the energy equation and 103 for all others. In addition, values of other relevant quantities such as drag coefficient on the tunnel ceiling are also judged. Parameters in this paper are set as: Cp ¼ 1006 J kg1 1 K , ambient temperature T0 ¼ 300 K, air density at 300 K q0 ¼ 1:2 kg m3 , acceleration due to gravity g ¼ 9:81 m s2 .
5. Results and discussion 5.1. Comparison of different turbulence models The k–e model and LES are used to simulate the same cases of tunnel fires. Results predicted by LES are similar to those by the k–e model. Two different initial conditions have been chosen for running LES: (1) the converged steady flow field obtained by k–e model; (2) the flow field with the airflow rate.
Table 2 Simulation time for LES
Initial condition (1) Initial condition (2)
Case a
Case b
Case c
4 days –
20 h 8 days
15 h 5 days
It is observed that final results predicted by LES are not affected by the two initial conditions. However, the simulation times are quite different. Only a few iterations are needed to get converged results for initial condition (1). More iterations are needed for initial condition (2). Since 105 grid cells are involved in this study, the transient calculation for LES required about 7 s of CPU time per iteration in a personal computer of 1.90 GHz CPU and 512 MB of RAM. An unsteady simulation for one case would require a few days of CPU time as shown in Table 2. The lower the ventilation rate, the longer is the required simulation time. When using k–e model for case c with ventilation rate of 2 m s1 , convergence is much faster as the problem is dominated by convection. But for cases a and b (the ventilation rates are 0.5 and 0.85 m s1 , respectively), backflow occurs and it is difficult to get converged results. Suitable under-relaxation factors have to be selected for reducing the computing effort. Common approach to flow simulations employs RANS (such as k–e model) in modelling turbulent motions. Predicted results are average values of the flow field. LES can describe the transient structure of the turbulent flow, and give the propagation process of smoke. Development of the flame and smoke movement pattern of case b are shown in Fig. 2. Instantaneous temperature and velocity field at different times are shown in Fig. 2(a) and (b). 5.2. Flame shape Flame shape and smoke movement predicted by LES can be compared with the experimental results and the predicted results by Fletcher et al. (1994). The temperature contours predicted by LES (after post-processing by time-averaging) in region close to the heat source are shown in Fig. 3. The flame shape
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Fig. 2. Fire environment for case b: (a) transient temperature; (b) transient velocity vectors.
can be defined by taking the region with the maximum temperature gradient (i.e., the region with dense temperature contour). Results of the flame angle for the three cases are listed in Table 1. The experimental values in Table 1 are based on the time averaged values derived from video data and are accurate to 10 (Fletcher et al., 1994). The flame angles based on the flame shape agree well with the experimental data. It is shown clearly from the figure that the flame behavior is affected by the ventilation rate. Temperatures above the pool fire predicted by Fletcher et al., 1994) were high, but much higher values were predicted by LES in this study.
5.3. Backflow of smoke Backflow of smoke should be considered carefully for a ventilated tunnel. If the air flow rate is low, the buoyancy induced by the fire would drive smoke to flow upstream. But for higher ventilation rates such as 2 m s1 , there is no backflow as predicted by LES (see Fig. 3(c)). Backflow occurs for a lower ventilation rate. Smoke can move back to the tunnel entrance for two cases as in Fig. 4 for LES results. These predictions agreed well with experiments. The steady calculation results of k–e model show that under the ventilation rate of case a (0.5 m s1 , the
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Fig. 3. Flame shapes calculated by LES: (a) case a – low ventilation rate (0.5 m s1 ); (a) case b – medium ventilation rate (0.85 m s1 ); (a) case c – high ventilation rate (2.0 m s1 ).
backflow can be simulated and reach the entrance. However, for case b of ventilation rate of 0.85 m s1 , although the backflow can be simulated, it does not reach the entrance as shown in Fig. 4 for k–e results. This shows that the backflow simulated by LES is better than by k–e model. 5.4. Flow behavior in the fire zone Results for case b are used to analyze the flow pattern near the fire with the velocity profile displayed in the vertical center plane of the tunnel shown in Fig. 5. The three-dimensional nature of the flow is evident, with the heated air rising due to buoyancy and being deflected at the roof to form a ceiling jet. The ceiling jet then reaches the corner of the tunnel and is deflected downwards, producing a circulation flow pattern. This three-dimensional flow is confined to a
region a few meters upstream and downstream of the fire. Outside these regions, the flow is almost onedimensional. Further, predicted air speeds induced by the fire are checked for whether the Mach number is less than 0.3. The maximum value is 5.6 m s1 for case a, 4.8 m s1 for cases b and c. Taking the speed of sound as 340 m s1 in normal atmospheric conditions, the Mach number in this study is much lower than 0.3. 5.5. Temperature distribution in the tunnel The hot air generated by the fire flows in a complex three-dimensional manner. The calculated temperature distributions by LES at 20 m downstream of the fire are shown in Fig. 6. Based on the predicted vertical temperature profiles, a clear thermal stratificated layer was identified.
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Fig. 4. Backflow of smoke: (a) LES results; (b) k–e model results.
Fig. 5. The velocity distribution in the tunnel for case b – LES results.
The vertical temperature distributions on the axis of the tunnel at various locations calculated by LES are shown in Fig. 7. It is shown that the calculated results and the experimental results (Fletcher et al., 1994) are in good agreement in the general shape of the temperature profile, but the calculated values are higher. 5.6. Other verifications Fig. 6. The temperature distribution for case b – LES results, 20 m downstream of the fire.
For a discussion of the mentioned discrepancy between experimental and predicted temperature values,
Fig. 7. Vertical temperature profiles at different positions from the fire for case b – LES results.
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Fig. 8. Time-averaged centerline temperature for a 2.3 MW pool fire in open air.
additional calculations were performed. A free plume in an open environment under the same pool fire as in this paper was simulated to check the LES results. The same assumptions and computing procedures are used with results shown in Fig. 8. The centerline temperature profile predicted are higher than those computed from the correlation of Heskestad (NFPA/SFPE, 2002). Note that the free plume simulated by McGrattan et al. (1998) agreed better with the correlation. Excluding radiation might explain the discrepancy, but the use of the Boussinesq approximation is another reason. This model is applicable for solving both steady and transient natural convection problems with small temperature changes. It is not suggested to be used with combustion. Special treatment of Boussinesq approximation for fire simulations (McGrattan et al., 1994, 1996; Baum et al., 1994) might be considered. Density differences should be reconsidered in our study. Other factors such as radiation and combustion should be considered. In the study of McGrattan et al. (1998), the motion of the fluid induced by buoyancy is governed by the equations written in a form suitable for low Mach number applications. This approach might be applicable for further studies. 5.7. Application to SMS CFD is now a useful engineering tool in many advanced countries including Hong Kong. This had been used for quite a long time locally, say for at least five years, while the fire engineering approach started
in 1998 to deal with new architectural features, such as green or sustainable buildings where prescriptive fire codes cannot be followed. This had also been considered in some local tunnel projects by the Authority in approving the fire safety design. For tunnels, SMS is one of the most important fire protection systems and should be designed carefully. CFD can be applied to consider different fire scenarios, estimate their consequences by predicting the temperature and air flow fields in a ‘microscopic’ view. With the predicted CFD results, locations of critical zones such as stagnant flow regions upon activation of the SMS can be identified. Both mechanical system like the longitudinal ventilation as demonstrated above, and to some extent, natural vents (applicable also for atria) can be designed properly with the aid of CFD. There are problems in using CFD, particularly if the users do not have a good understanding on the physical basis, numerical schemes and computer structure inside. Commercial packages would come with a preprocessor, most probably integrated with popular Computer-Aided-Design-Drafting packages for the geometrical model of the building; and post-processors for analyzing the large volume of predicted data (very huge for LES!). The industry hopes to see dealing with CFD is similar to use drafting software as 10 years ago! However, it is quite impossible if the engineers concerned do not have adequate training. Most likely, there are at least three parts to understand:
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• Turbulence. • Algorithms for solving velocity and pressure linked equation. • Selection of the finite difference scheme. There are points to consider in applying CFD, and particularly LES, for tunnel SMS design: • Results predicted by LES and RANS are fairly similar. • LES is far more expensive than RANS in terms of computing time. That will be a hinder for a general application on engineering consultancy firms.
6. Conclusion Large eddy simulation has been applied to studying pool fire in a ventilated tunnel with a field model. The results show that the model can well predict the flame shape and the smoke backflow. Note that large eddy simulation is not yet popular to solve practical engineering problems unless for projects of higher cost. This study shows the possibility of applying the technique on simulating smoke movement in a ventilated tunnel. Results predicted by large eddy simulation can be applied for selecting design alternatives. For example, smoke backflow cannot be prevented by low ventilation rate, and so high ventilation rate should be used. Both approaches using large eddy simulation and Reynolds averaged Navier–Stokes methods can get good results for simple problems. Although higher-level computer configuration and more computing time are required for carrying out large eddy simulation, more complex flow structures can be simulated. Taking tunnel study as an example, a good prediction on smoke backflow can be achieved. This point is important in dealing with smoke ventilation design in tunnels.
Acknowledgements The project is funded by President of The Hong Kong Polytechnic University and Departmental Earnings Account of Department of Building Services Engineering; and partly funded by the China NKBRSF project, No. 2001CB409604.
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Tunnelling and Underground Space Technology 19 (2004) 577–586
www.elsevier.com/locate/tust
Large eddy simulations for studying tunnel smoke ventilation P.Z. Gao a, S.L. Liu a, W.K. Chow
b,*
, N.K. Fong
b
a
b
College of Power and Nuclear Engineering, The Harbin Engineering University, Harbin, China Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong, China Received 30 June 2003; received in revised form 10 January 2004; accepted 26 January 2004 Available online 11 March 2004
Abstract Computational fluid dynamics are applied to simulate the smoke movement in a ventilated tunnel fire through large eddy simulation (LES). Several scenarios with different ventilation rates are considered by taking the fire as a volumetric heat source. Results predicted by LES are compared with those from a k–e model. These include temperature fields, flame shape and the smoke movement pattern. It is found that thermal stratification and smoke backflow can be predicted successfully by LES. The possibility of applying LES as an engineering tool to smoke management system design in tunnels is discussed. 2004 Elsevier Ltd. All rights reserved. Keywords: Fans; Research and development; Fire safety systems
1. Introduction Fires occurring in mine headings or transport tunnels would lead to a loss of human lives in many cases (Leitner, 2001; Kirkland, 2002). Smoke, not heat, was identified to be the most hazardous factor to human beings as it can spread throughout the tunnel rapidly. Smoke management systems (SMS) for smoke control should therefore be installed in the tunnels with effective ventilation systems. The longitudinal ventilation (or one-way ventilation) system operated by blowing smoke towards a tunnel exit is commonly designed to prevent backlayering. However, system performance is not effective if the ventilation rate is low and the buoyancy of smoke is strong enough. The fire plume would impinge on the ceiling and spread against the discharged ventilation flow. It is very important to understand when a smoke backflow will occur. Results are useful for SMS design and development of the associated fire codes. Both physical experiments (Apte et al., 1991, 1998; Oka and Atkinson, 1995; Vauquelin and Megret, 2002; Wichman et al., 2002) and numerical simulations with *
Corresponding author. Tel.: +852-2766-5111; fax: +852-2765-7198. E-mail address: [email protected] (W.K. Chow).
0886-7798/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.tust.2004.01.005
fire models (Fletcher et al., 1994; Beard et al., 1995, 1996; Chow, 1996; Woodburn and Britter, 1996a,b; Kunsch, 1998; Kunsch, 2002; Megret and Vauquelin, 2000; Wu and Bakar, 2000; Li and Chow, 2003) were reported on tunnel fires. It is far too expensive to design SMS with full-scale burning tests. Fire models are used as engineering design tools. In view of the large aspect ratio of the tunnel, zone models are not too suitable because a smoke layer of uniform thickness is assumed to form at the ceiling. This assumption might not hold in a tunnel as the ceiling jet is moving as a wave front. The field model (or application of Computational Fluid Dynamics CFD) has been applied but there are also limitations. Very few physical experiments such as those in a full-scale mock-up of a mine roadway by Apte et al. (1991) were carried out to verify the predicted field modelling results. Smoke movement in that experiment was simulated by Fletcher et al. (1994) with results compared with experimental data. Their field model included sub-models for combustion and thermal radiative heat transfer. The turbulent flow was simulated by the two equations k–e model. Adequacy of the chosen physical models was investigated. On the other hand, the large eddy simulation (LES) is starting to be more popularly used as an engineering tool. LES can give a more complete description of the
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Nomenclature A Cp d D Fr gi G k L Ls m_ p Prt q_ c Q_ Sij t T T0 ui , u j us
area specific heat capacity distance diameter Froude number acceleration of gravity in the co-ordinate directions x, y and z filter function turbulent kinetic energy; thermal conductivity characteristic length mixing length for subgrid scales fuel release rate pressure turbulent Prandtl number heat release rate per unit volume total heat release rate local large-scale rate of strain tensor time temperature ambient temperature velocity components in the co-ordinate directions x, y and z shear velocity
transient turbulent flow structure, leading to better understanding of smoke spreading. The underlying theory of LES including subgrid-scale models and numerical schemes developed rapidly. Some works on the simulation of fire and smoke movement (McGrattan et al., 1996, 1998; Wang et al., 2002; Liu et al., 2002a,b) were reported. Scenarios on the tunnel fires similar to those reported by Fletcher et al. (1994) will be simulated with LES in this paper. Air flow induced by taking fire as a simple heat source will be simulated. Results are also compared with experimental data and the earlier simulations by Fletcher et al. (1994). There are three objectives in this study: • To investigate whether LES can be used as a fire simulation tool. • To compare LES with the Reynolds averaged Navier–Stokes equations (RANS) approach such as the k–e model. • To study smoke movement in a tunnel fire and performance of longitudinal ventilation system. Note that LES and RANS (such as k–e) models are different methods in dealing with turbulent flows using spatial and temporal averaging. Basically in LES, largerscales of turbulence were simulated with smaller-scale motions modeled as discussed later. RANS had been applied to solve practical engineering problems. A two-
V ~ x x xi , xj y z
cell volume ðx, y, zÞ Cartesian coordinate streamwise co-ordinate co-ordinate directions x, y and z cross-stream co-ordinate vertical co-ordinate
Greek symbol b thermal expansion coefficient dij Kronecker delta e dissipation of the turbulent kinetic energy l dynamic viscosity lt subgrid-scale turbulent viscosity m kinematic viscosity q air density q0 ambient air density D filter width / general variable / large-scale component /0 subgrid-scale component X domain of interest sij stress tensor sij;S subgrid-scale Reynolds stress
equation k–e model is commonly used to give the averaged flow fields.
2. Experiment Experimental studies (Apte et al., 1991; Fletcher et al., 1994) were carried out in a tunnel of 130 m length, 5.4 m width and 2.4 m height. The geometry of the tunnel is shown in Fig. 1. A pool fire was located 40 m further down the tunnel. The fuel burnt was aviation fuel (octane) contained in a circular tray with diameter of 1 m. Airflow with speeds up to 2 m s1 was induced by two exhaust fans installed at one end. Instruments such as thermocouples, bi-directional velocity probes and video cameras were installed in different positions for measuring the parameters concerned.
3. Mathematical model 3.1. Governing equations It is very complicated to simulate a pool fire realistically because combustion, radiation and turbulence have all to be included. A volumetric heat source
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Fig. 1. The experimental and computational geometry.
(VHS) without chemical reactions is assumed. The heat release rate per unit volume q_ c from the VHS represents that generated from the pool fire. The main theme of the study is on simulating the smoke movement described by the predicted hot gas flow pattern and the temperature field. Species transport equations are not included and so the species concentration distribution will not be predicted. The air surrounding the VHS is entrained, heated up with its density reduced and then rises up. Buoyancy is included in the momentum equation by means of a Boussinesq approximation to calculate the density differences. A gas flow with a Mach number below 0.3 can be regarded as incompressible (e.g., Ferziger and Peric, 1996). This criterion holds for a fire-induced flow as the air velocity is less than 10 m s1 and the ventilation rate is lower than 2 m s1 . For an incompressible gas flow at low velocity, the thermal energy due to viscous shear in the flow is small. The viscous dissipation term in the energy equation can be neglected. With the above assumptions, the governing equations on fire-induced air flow can be written in the following form: ouj ¼ 0; oxj oui oðui uj Þ 1 op 1 osij þ ¼ þ gi bDT ; oxj q oxi q oxj ot oT oðTuj Þ o k oT q_ c þ ¼ þ : ot oxj oxj qCp oxj Cp
ð1Þ
ð2Þ
differential equations numerically. The effect of smallscale motions will be represented by stress terms similar to Reynolds stresses called subgrid-scale Reynolds stresses to be modelled (Shi, 1994). The first step of LES is filtering which decomposes a x; tÞ and variable /ð~ x; tÞ into a large-scale component /ð~ a small-scale component (subgrid-scale component) x; tÞ þ /0 ð~ x; tÞ, i.e., /ð~ x; tÞ ¼ /ð~ x; tÞ . The large-scale /0 ð~ component, /ð~ x; tÞ is obtained by taking a function Gð~ x ~ x0 ; DÞ as the filter kernel Z x; tÞ ¼ /ð~ Gð~ x ~ x0 ; DÞ/ð~ x0 ; tÞ d~ x0 ð4Þ X
where X is the domain of interest; D is the filter width, given by D ¼ V 1=3 Q; 3and V is the volume of a computational cell, V ¼ i¼1 Dxi ¼ DxDyDz , where Dxi is the grid interval along the xi direction. The filter function is ( 1=V for ~ x0 2 V ; 0 Gð~ x ~ x ; DÞ ¼ ð5Þ 0 otherwise: Filtering each term in Eqs. (1)–(3) would give the following: ouj ¼ 0; oxj
ð6Þ
j Þ oui oðui u 1 op 1 þ ¼ þ oxj q oxi q ot
osij osij;S þ oxj oxj
!
gi bDT ; ð3Þ
3.2. Large eddy simulation In LES, the turbulent motion is decomposed as large- and small-scale motions by filtering. The largescale flow structures are calculated by solving the
oT oðT uj Þ o þ ¼ ot oxj oxj
k oT qCp oxj
ð7Þ ! þ
oRj q_ c þ ; oxj Cp
ð8Þ
where the overbar denotes the filtered variable. The large-scale eddies are computed directly at the resolved scale. The scales of motions unresolvable on the computational mesh are removed. In most fire simulations, the primary momentum transport and turbulent
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diffusion are sustained by large-scale eddies. Smallerscale eddy motion are not accounted for. The subgrid-scale (SGS) motions are represented by an eddy viscosity with the length scale related to the grid size in the computing domain. The time scale is determined by the local resolvable dissipation. The SGS motion is calculated by the Smagorinsky–Lilly model where the unknown SGS Reynolds stresses, sij;S are related to the local large-scale rate of strain, S ij , by sij;S 1skk;S dij ¼ 2lt Sij ; ð9Þ
As reported by McGrattan et al. (1998), adequate resolution would be achieved by assigning ten computing cells for L. With hardware limitation taken into account, the heat source is discretized into 8 8 3 cube cells, about 0.11 m on a side. The whole computing domain is composed of 108,416 cells, with 176 parts along the tunnel, 28 parts across it and 22 parts in the vertical direction. Finer grids are used in the heat source and regions near to it.
sij;S and S ij are defined, respectively, as
4.2. Boundary conditions
3
j ; sij;S qui uj þ q ui u ! 1 o u o u i j þ : Sij 2 oxj oxi
ð10Þ ð11Þ
The subgrid-scale turbulent viscosity lt is used to provide the role of modelling the dissipative behavior of the unresolved small scales. The eddy viscosity is modeled by lt ¼ qL2s jSij j; ð12Þ where qffiffiffiffiffiffiffiffiffiffiffiffi jSij j ¼ 2Sij Sij ð13Þ Ls ¼ min k1 d; Cs V 1=3 ;
ð14Þ
where k1 ¼ 0:42; d is the distance to the closest wall; Cs is the Smagorinsky constant, lying between 0.1 and 0.23, taken as 0.1 in this paper. The subgrid heat flux, qRj is based on the eddy viscosity approach, l oT Rj ¼ Tuj þ T uj ¼ t ; ð15Þ qPrt oxj Prt is the turbulent Prandtl number of values lying between 0.2 and 0.9, and is taken as 0.85 in this paper. 4. Numerical simulations
A tunnel segment of length 90 m is taken out with boundary shown in Fig. 1. The pool fire is located 40 m from the tunnel entrance. To simplify the computation, the pool fire was taken as a heat source of 0.89 m2 with height 0.33 m. The height 0.33 m was selected after some simulation tests. The total heat is assumed to be released uniformly throughout the whole source. The computing mesh was assigned with a suitable grid resolution by considering the characteristic length scale L for a fire plume related to the total heat release rate Q_ by L¼
!2=5 :
ui ¼ hui i þ Iwjuj;
ð16Þ
ð17Þ
where I is the intensity of the fluctuation, w is a Gaussian random number satisfying w ¼ 0 , and ffiffiffiffiffi q w0 ¼ 1 . The wall shear stress is obtained from the logarithmic law of the wall, u 1 us y ; ¼ ln E u s k2 m
ð18Þ
where y is the distance to the wall, k2 ¼ 0:418 and E ¼ 9:793. The tunnel wall is assumed adiabatic. The total heat release rate of the pool fire is _ Q_ ¼ qm Am;
4.1. Grid system
Q_ pffiffiffi q0 T0 Cp g
The differential pressure at the tunnel inlet, which is defined as the difference of pressure drop at the entrance from the atmospheric pressure (Fletcher et al., 1994), is used as the operating pressure of the computing region. The velocity boundary is used at the tunnel outlet with values taken from the experimental data (Fletcher et al., 1994). The stochastic components of the flow at the velocityspecified boundaries are accounted for by superposing random perturbations on individual velocity components as
ð19Þ
where qm is the calorific value of the fuel, 44.4 MJ/kg for octane (Fletcher et al., 1994); A is the fuel pool area, A ¼ pD2 =4; and m_ is the fuel release rate, see Table 1. 4.3. Numerical solution In applying LES for solving transient problems, computing starts from some initial conditions in a fine enough grid system with an appropriate time step. Computing must be run long enough to get results independent of the initial conditions. In the simulation, the second-order implicit formulation is used for temporal discretization with the time step size set to 0.1 s. The fully implicit scheme is unconditionally stable with respect to time step size.
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Table 1 Measured and calculated flame angles under different simulation conditions Case
Fuel release rate (kg s1 m2 )
Air flow speed (m s1 )
Measured flame anglea ()
Predicted flame anglea ()
Predicted (k–e) flame angle ()
Predicted (LES) flame angle ()
a b c
0.070 0.065 0.058
0.50 0.85 2.00
46 56 66
49 62 78
40 45 67
32 56 67
a
Results from Fletcher et al. (1994).
However, the time step would be set to be at least one order of magnitude smaller than the smallest time constant in the system. Time step size can be adjusted by observing the number of iterations required for getting converged results. Optimum number of iterations per time step is 10–20. The assigned time step is too large if more than 20 iterations was used. Wider time step can be used if converged results can be achieved with several iterations. For spatial discretization, the second-order central differencing and QUICK scheme are used. Excessive diffusive schemes such as the first-order upwind or power law scheme are not used. The pressure-velocity linked equations are solved by the PISO scheme. Velocity components at selected locations are monitored to check whether the flow is fully-developed. Computing will be carried on until the flow becomes steady. The solution will be started again with sampling instantaneous data during the calculation, and continued until stable data are obtained. With these sample data, time-averaged values and root-mean-square values can be computed. All the flow field figures are processed by time averaging. Residuals are checked for judging convergence. The convergence criterion is selected as that the scaled residuals decreased to 106 for the energy equation and 103 for all others. In addition, values of other relevant quantities such as drag coefficient on the tunnel ceiling are also judged. Parameters in this paper are set as: Cp ¼ 1006 J kg1 1 K , ambient temperature T0 ¼ 300 K, air density at 300 K q0 ¼ 1:2 kg m3 , acceleration due to gravity g ¼ 9:81 m s2 .
5. Results and discussion 5.1. Comparison of different turbulence models The k–e model and LES are used to simulate the same cases of tunnel fires. Results predicted by LES are similar to those by the k–e model. Two different initial conditions have been chosen for running LES: (1) the converged steady flow field obtained by k–e model; (2) the flow field with the airflow rate.
Table 2 Simulation time for LES
Initial condition (1) Initial condition (2)
Case a
Case b
Case c
4 days –
20 h 8 days
15 h 5 days
It is observed that final results predicted by LES are not affected by the two initial conditions. However, the simulation times are quite different. Only a few iterations are needed to get converged results for initial condition (1). More iterations are needed for initial condition (2). Since 105 grid cells are involved in this study, the transient calculation for LES required about 7 s of CPU time per iteration in a personal computer of 1.90 GHz CPU and 512 MB of RAM. An unsteady simulation for one case would require a few days of CPU time as shown in Table 2. The lower the ventilation rate, the longer is the required simulation time. When using k–e model for case c with ventilation rate of 2 m s1 , convergence is much faster as the problem is dominated by convection. But for cases a and b (the ventilation rates are 0.5 and 0.85 m s1 , respectively), backflow occurs and it is difficult to get converged results. Suitable under-relaxation factors have to be selected for reducing the computing effort. Common approach to flow simulations employs RANS (such as k–e model) in modelling turbulent motions. Predicted results are average values of the flow field. LES can describe the transient structure of the turbulent flow, and give the propagation process of smoke. Development of the flame and smoke movement pattern of case b are shown in Fig. 2. Instantaneous temperature and velocity field at different times are shown in Fig. 2(a) and (b). 5.2. Flame shape Flame shape and smoke movement predicted by LES can be compared with the experimental results and the predicted results by Fletcher et al. (1994). The temperature contours predicted by LES (after post-processing by time-averaging) in region close to the heat source are shown in Fig. 3. The flame shape
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Fig. 2. Fire environment for case b: (a) transient temperature; (b) transient velocity vectors.
can be defined by taking the region with the maximum temperature gradient (i.e., the region with dense temperature contour). Results of the flame angle for the three cases are listed in Table 1. The experimental values in Table 1 are based on the time averaged values derived from video data and are accurate to 10 (Fletcher et al., 1994). The flame angles based on the flame shape agree well with the experimental data. It is shown clearly from the figure that the flame behavior is affected by the ventilation rate. Temperatures above the pool fire predicted by Fletcher et al., 1994) were high, but much higher values were predicted by LES in this study.
5.3. Backflow of smoke Backflow of smoke should be considered carefully for a ventilated tunnel. If the air flow rate is low, the buoyancy induced by the fire would drive smoke to flow upstream. But for higher ventilation rates such as 2 m s1 , there is no backflow as predicted by LES (see Fig. 3(c)). Backflow occurs for a lower ventilation rate. Smoke can move back to the tunnel entrance for two cases as in Fig. 4 for LES results. These predictions agreed well with experiments. The steady calculation results of k–e model show that under the ventilation rate of case a (0.5 m s1 , the
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Fig. 3. Flame shapes calculated by LES: (a) case a – low ventilation rate (0.5 m s1 ); (a) case b – medium ventilation rate (0.85 m s1 ); (a) case c – high ventilation rate (2.0 m s1 ).
backflow can be simulated and reach the entrance. However, for case b of ventilation rate of 0.85 m s1 , although the backflow can be simulated, it does not reach the entrance as shown in Fig. 4 for k–e results. This shows that the backflow simulated by LES is better than by k–e model. 5.4. Flow behavior in the fire zone Results for case b are used to analyze the flow pattern near the fire with the velocity profile displayed in the vertical center plane of the tunnel shown in Fig. 5. The three-dimensional nature of the flow is evident, with the heated air rising due to buoyancy and being deflected at the roof to form a ceiling jet. The ceiling jet then reaches the corner of the tunnel and is deflected downwards, producing a circulation flow pattern. This three-dimensional flow is confined to a
region a few meters upstream and downstream of the fire. Outside these regions, the flow is almost onedimensional. Further, predicted air speeds induced by the fire are checked for whether the Mach number is less than 0.3. The maximum value is 5.6 m s1 for case a, 4.8 m s1 for cases b and c. Taking the speed of sound as 340 m s1 in normal atmospheric conditions, the Mach number in this study is much lower than 0.3. 5.5. Temperature distribution in the tunnel The hot air generated by the fire flows in a complex three-dimensional manner. The calculated temperature distributions by LES at 20 m downstream of the fire are shown in Fig. 6. Based on the predicted vertical temperature profiles, a clear thermal stratificated layer was identified.
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Fig. 4. Backflow of smoke: (a) LES results; (b) k–e model results.
Fig. 5. The velocity distribution in the tunnel for case b – LES results.
The vertical temperature distributions on the axis of the tunnel at various locations calculated by LES are shown in Fig. 7. It is shown that the calculated results and the experimental results (Fletcher et al., 1994) are in good agreement in the general shape of the temperature profile, but the calculated values are higher. 5.6. Other verifications Fig. 6. The temperature distribution for case b – LES results, 20 m downstream of the fire.
For a discussion of the mentioned discrepancy between experimental and predicted temperature values,
Fig. 7. Vertical temperature profiles at different positions from the fire for case b – LES results.
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Fig. 8. Time-averaged centerline temperature for a 2.3 MW pool fire in open air.
additional calculations were performed. A free plume in an open environment under the same pool fire as in this paper was simulated to check the LES results. The same assumptions and computing procedures are used with results shown in Fig. 8. The centerline temperature profile predicted are higher than those computed from the correlation of Heskestad (NFPA/SFPE, 2002). Note that the free plume simulated by McGrattan et al. (1998) agreed better with the correlation. Excluding radiation might explain the discrepancy, but the use of the Boussinesq approximation is another reason. This model is applicable for solving both steady and transient natural convection problems with small temperature changes. It is not suggested to be used with combustion. Special treatment of Boussinesq approximation for fire simulations (McGrattan et al., 1994, 1996; Baum et al., 1994) might be considered. Density differences should be reconsidered in our study. Other factors such as radiation and combustion should be considered. In the study of McGrattan et al. (1998), the motion of the fluid induced by buoyancy is governed by the equations written in a form suitable for low Mach number applications. This approach might be applicable for further studies. 5.7. Application to SMS CFD is now a useful engineering tool in many advanced countries including Hong Kong. This had been used for quite a long time locally, say for at least five years, while the fire engineering approach started
in 1998 to deal with new architectural features, such as green or sustainable buildings where prescriptive fire codes cannot be followed. This had also been considered in some local tunnel projects by the Authority in approving the fire safety design. For tunnels, SMS is one of the most important fire protection systems and should be designed carefully. CFD can be applied to consider different fire scenarios, estimate their consequences by predicting the temperature and air flow fields in a ‘microscopic’ view. With the predicted CFD results, locations of critical zones such as stagnant flow regions upon activation of the SMS can be identified. Both mechanical system like the longitudinal ventilation as demonstrated above, and to some extent, natural vents (applicable also for atria) can be designed properly with the aid of CFD. There are problems in using CFD, particularly if the users do not have a good understanding on the physical basis, numerical schemes and computer structure inside. Commercial packages would come with a preprocessor, most probably integrated with popular Computer-Aided-Design-Drafting packages for the geometrical model of the building; and post-processors for analyzing the large volume of predicted data (very huge for LES!). The industry hopes to see dealing with CFD is similar to use drafting software as 10 years ago! However, it is quite impossible if the engineers concerned do not have adequate training. Most likely, there are at least three parts to understand:
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• Turbulence. • Algorithms for solving velocity and pressure linked equation. • Selection of the finite difference scheme. There are points to consider in applying CFD, and particularly LES, for tunnel SMS design: • Results predicted by LES and RANS are fairly similar. • LES is far more expensive than RANS in terms of computing time. That will be a hinder for a general application on engineering consultancy firms.
6. Conclusion Large eddy simulation has been applied to studying pool fire in a ventilated tunnel with a field model. The results show that the model can well predict the flame shape and the smoke backflow. Note that large eddy simulation is not yet popular to solve practical engineering problems unless for projects of higher cost. This study shows the possibility of applying the technique on simulating smoke movement in a ventilated tunnel. Results predicted by large eddy simulation can be applied for selecting design alternatives. For example, smoke backflow cannot be prevented by low ventilation rate, and so high ventilation rate should be used. Both approaches using large eddy simulation and Reynolds averaged Navier–Stokes methods can get good results for simple problems. Although higher-level computer configuration and more computing time are required for carrying out large eddy simulation, more complex flow structures can be simulated. Taking tunnel study as an example, a good prediction on smoke backflow can be achieved. This point is important in dealing with smoke ventilation design in tunnels.
Acknowledgements The project is funded by President of The Hong Kong Polytechnic University and Departmental Earnings Account of Department of Building Services Engineering; and partly funded by the China NKBRSF project, No. 2001CB409604.
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