CFD simulations of a tunnel fire—Part I

ELSEVIER

Pll:

Fire Safety Journal 16 (1996) 35-62 Copyright ~) 1996 Elsevier Science Limited Printed in Northern Ireland. All rights reserved 0379--7112/96l$15.00 $0379-7112(96)00018-5

C F D Simulations o f a T u n n e l Fire

Part I

P. J. Woodburn* & R. E. Britter Engineering Department, Cambridge University, Trumpington Street, Cambridge CB2 1PZ, UK (Received 20 July 1995; revised version received 30 January 1996; accepted 23 February 1996)

ABSTRACT

Thi~ paper concerns sensitivity studies o f computational fluid dynamics (CFD) simulations of a fire in a tunnel. The simulations were o f an experimental fire in a tunnel carried out by the Fire and Thermofluids Section o f the Health and Safety Executive, Buxton, UK. The fuel used in t,~e experiment was kerosine, the heat output rate was 2.7 M W and the tunnel was longitudinally ventilated. During the period o f the experiment studied in the simulations, there was an upstream layer of approximate length 11 m . Simulations were carried out for two areas o f i~.he tunnel: the area around the fire and the area downstream of the [ire. This paper describes the simulations of the area around the fire, whilst the accompanying Part H paper describes the area downstream of the fire. In the fire area simulations, the upstream propagating smoke layer length was found to be sensitive to the ventilation velocity, the ventilation velocity profile, the turbulence model used and the heat input rate. This case, in which the fire did not extend over the width of the tunnel, gave an upstream layer at higher ventilation velocities than those found in the literature. While reduction o f the heat input rate to allow for radiative heat transfer from the flame caused a significant change in results, neither radiative heating of the tunnel ceiling nor the distribution o f the fuel across the fuel pan had a significant effect on the results. Copyright ~) 1996 Elsevier Science Ltd.

* Now at Fire Safety Engineering Group, Department of Civil and Environmental Engineering, Edinburgh University, Edinburgh, UK. 35

36

P. J. Woodburn, R. E. Britter

NOTATION

D F g H lr k rh O T

va U

Constant in k-E turbulence model Diameter of fuel pan Froude number given by eqn (1) Gravitational acceleration Height of tunnel Upstream layer length Turbulence energy Mass flow rate Heat input rate Temperature Ventilation velocity Vertical velocity fluctuations

Greek symbols Rate of dissipation of turbulence energy Turbulent viscosity Vt Density P Ambient density Pa Or Stefan-Boltzmann constant Prandtl number Ort 'Prandtl number' for turbulence energy Ork 'Prandtl number' for dissipation rate Or~

1 INTRODUCTION This work describes a sensitivity study of computational fluid dynamics (CFD) simulations of an experimental fire in a tunnel. Simulation sensitivity studies were carried out for the area around the fire (the fire area) and the area downstream of the fire (the downstream area). The fire area sensitivity study is described in this paper, whilst the downstream area sensitivity study is described in the accompanying Part II paper. CFD simulations are increasingly used to estimate the effects of fires in tunnels and corridors. However, little work has been done to assess the accuracy of these simulations, or to investigate which aspects of the simulation process cause the greatest uncertainties. The objective of this work was to assess the errors and uncertainties which occur in

CFD simulations o f a tunnel f i r e - - I

37

simulations of tunnel fires. By assessing the uncertainties due to several factors individually, the most important factors can be identified. 2 PREVIOUS R E S E A R C H Previous research in which the sensitivity of simulations to input parame.ters was tested includes that by Brandeis and Bergman, 1 who carried out two-dimensional simulations of a forced ventilated tunnel under various ventilation schemes. Simcox et al. 2 carried out 13 documented simulations investigating the King's Cross fire. The effect of varying heat release rates, heat release area, and different boundary conditions was investigated. Kumar and Cox carried out threedimensional simulations of the Zwenberg tunnel experiments, and investigated the effects of wall roughness and the modelling of the effects of radiation, both of which significantly lowered the temperatures downstream of the fire. Chass63 simulated a naturally ventilated tunnel in two and three dimensions. Apte, Green and Kent 4 and Fletcher et al. 5 investigated the effects of varying ventilation velocities and fuel pan sizes on a mine gallery mock-up, and compared the simula'tion results with their experiments. They further investigated the effects of grid refinement, fuel inflow profile, upstream smoke layer radiative heat transfer, and radiation modelling downstream of the fire on sirrmlation results of the mine gallery. They found that the grid refinement, fuel inflow profile and modelling of the radiative heat transfer from the upstream layer had little effect on the results, but including the modelling of the radiative heat transfer from soot downstream of the fire caused a significant lowering of downstream temperatures. 3 THE EXPERIMENT The UK Health and Safety Executive (H.S.E.) carried out a series of experi'ments at their facility at Harpur Hill, Buxton, in which sufficient data were recorded to provide a comprehensive test of CFD simulations. The work described in these two papers is based on one of the experiments in the 'interim validation of consequence models for tunnel fires' series. The data from test 4, phase 1 were u s e d . 6 The data set from this test was chosen because it showed a clear steady-state burning period. The test tunnel at the H.S.E., Buxton is arched, 366 m long, 2.5 m

38

P.J. Woodburn, R. E. Britter

high, and horizontal. One end of the tunnel is longitudinally ventilated by fans and the fire was placed 94 m from this end. The other end is open to the atmosphere. The walls are made of concrete, varying from 0.41 to 0.57 m thick. The fuel pan, which was approximately 1 m 2 in area, was m o u n t e d on a load cell platform, the fuel used was kerosine. The walls were insulated using fire-proofing between 89 and 114 m from the fan end, i.e. over the area around the fire. The test lasted about 35 min, during which time the ventilation velocity was varied several times between steady states. During the test, there was a quasi-steady period between 700 and 1200 s after ignition, the simulations are of this period. During this period the total heat output rate from the fire was measured by the experimental team using measurements of oxygen concentration downstream of the 2.3 MW fire; the ventilation velocity was calculated from the average of measurements taken at an upstream measuring rake as 1.72 m/s. The most noticeable feature of this stage of the experiment was an upstream propagating layer of smoke which extended approximately 11 m upstream of the fire. Temperature measurements were made at 91 points in 26 stations at different distances from the fire, both upstream and downstream. Eleven of these stations had six thermocouples distributed over the tunnel height. All measurements were made on the tunnel centreline. The thermocouples were accurate to 2.5°C or 0.75% of actual temperature, whichever was the greater. Velocity measurements were also made at 31 points in five stations. The data obtained from these measurements were not considered reliable by the experimental team, and will only be used in a few instances here; where the velocity data are consistent within themselves, they will be used.

4 SIMULATION STRATEGY The simulation of the experiment was split into two regions. The fire area included the first measurement rakes upstream and downstream of the fire in the experiment. The downstream area extended from 20 m downstream of the fire (the downstream end of the fire area) to the downstream exit to the tunnel. A schematic layout of the tunnel is shown in Fig. 1. Only half of the tunnel's cross-section was simulated; a symmetry boundary condition was specified at the centreline. This boundary condition set the gradients of variables to be zero perpendicular to the

CFD simulations of a tunnel fire--I 94ra

39

272m

q

[

.........

-'-'- . . . . . . . . .

c rNo

i ..........................

!

%.

ii

I

FAN FIRE A R E A 40m

DOWNSTREAM AREA 252m

Fig. 1. The configuration of the Buxton tunnel experiments.

wall. 7 The code used was FLOW3D, written by C.F.D.S., A E A Technology, Harwell Laboratory, UK. The division of the tunnel into separate simulations was not ideal, but was made to allow a greater number of simulations to be carried out. The division was only valid if the conditions in the downstream area did not affect the conditions in the fire area. This is not necessarily true, for example if the flow is controlled by conditions at the tunnel exit. In this case, the conditions within the tunnel were not found to be dependent on the conditions around the tunnel exit (as will be discussed in the second part of this study). Using Turner's analysis 8 for the speed of waves in a stratified flow of fixed velocity within a channel, together with the measured ventilation velocity and the maximum density gradient within the tunnel, no waves would have a velocity greater than the ventilation velocity. Therefore no waves pass upstream from this position of maximum density gradient. Furthermore, since the density gradient at this position was greater than that at any position downstream, no waves downstream of this position will move upstream either. In these simulations the ventilation flow rate was fixed, so there was no possibility of the flow changing sufficiently that this result did not always hold, unless the flow regime changed. It was expected in this case that the profiles of pressure each side of the fire area/downstream area boundary would be the same except for a constant pressure difference, which proved to be correct. The flow was therefore controlled from upstream, and division of the problem into two regions was valid. Examination of the fluid mechanics of this situation, which revealed that the simulation could be split in two, resulted in a better use of the computing resources.

40

P.J. Woodburn, R. E. Britter

The grid used in each region was the same across the tunnel section; all the variables were specified directly across the boundary between the fire area and the downstream area. Two factors caused significant reductions in the C P U time required for the simulations of the downstream area. Not simulating the fire area meant that the problem was approximately half the size of that of simulating the whole tunnel at once; and the fuel, oxidant and products equations were not solved in the downstream area.

5 THE FIRE AREA

The physical layout of the fire area is shown in Fig. 2. The grid used for the fire area simulations was 14 × 30 × 24 cells in the tunnel's width,

Fig. 2. Fire area--geometry--figure scaled lengthwise by a factor of 0.15.

CFD simulations of a tunnel fire--I

41

Fig. 3. Fire area--grid--tunnel cross-section. The outer two cells form the wail. height: and length directions. The grid is shown in cross-section in Fig. 3 and in profile in Fig. 4. The walls were simulated using one cell each for the wall and insulation. Grid refinement over the inside of the tunnel did not yield any appreciable difference in results. Although the grid could not be made doubly fine over the whole geometry due to hardware limitations, simulations were carried out in which the grid in the area around the fire and in the region of the hot layer was made twice as fine to test the effects of grid refinement. The results were not significantly d e p e n d e n t on the grid refinement in these areas. The following conditions were applied to all runs. 1.

2. 3.

The upstream boundary was a developed inlet. The profiles of velocity and the turbulence variables were obtained from an isothermal simulation of a 30 m length of empty tunnel. The downstream boundary to the fire area was specified as an outflow boundary (the mass flow rate was the same as the inlet). The walls of the tunnel were modelled as fully conducting

42

P. J. Woodburn, R. E. Britter

!!! !!!! mmlP~ IN|l~ Ill|ll Illll llll~ Dill

II | l i d illmiN I l l i l I l l l l IIi I I

iiiJ tJiii nail, Illll IIiii IIIii gill] llll~ Illll limit

I l l n l illlll iiilll iIIIll ~lllll qlllll ,I I l l l

Fig. 4. Fire area--grid--tunnel centreline profile. Figure scaled lengthwise by 0.15. The outer two cells form the wall.

4. 5.

6. 7.

solids. The insulation on the inside wall of the tunnel was modelled. The outer wall boundary condition was a constant ambient temperature. The walls were assumed to be smooth. The combustion was modelled using an 'eddy break-up' combustion model, with infinite-rate chemistry. The fuel vapour supply rate was calculated from the experimental measurements of heat release rate, and the fuel was supplied uniformly over all the cells immediately above the fuel pan. The fuel pan and supports were modelled as solid. The simulation was carried out as a fully transient calculation progressing towards a steady state. The differencing schemes used were a second-order scheme for

CFD simulations of a tunnel fire--1

43

all velocity equations and a hybrid upwind/central (first/second-order) scheme for all turbulence, enthalpy and combustion equations.

6 F I R E A R E A SENSITIVITIES The effects on the results of three factors: the ventilation velocity, the turbulence model, and the heat input rate were investigated over the runs carried out in this area. These factors will be briefly outlined below, after which the results from the simulations will be discussed. The two features of the experiment used to assess the results from the simulations were the length of the upstream layer and the velocity and temperature profiles at the first measuring rake downstream of the fire.

6.1 Ventilation velocity The length of an upstream propagating smoke layer is very sensitive to the ventilation velocity.9-12 The length of an upstream layer from a fire is of gxeat importance for safety in fires 1°,5 The existence of an upstream layer means that there is no smoke-free escape from the area of the fire, and no completely smoke-free access to the fire for the safety services. The; presence of an upstream layer about 11 m long in the experiment provided a demanding test of the simulation of this region. Thomas 11,~2 found that the length of an upstream layer lr from a fire which spanned the entire width of a tunnel was dependent on a Froude number F as: lr H

0.6(F-5)

(1)

F - gH(p. -/if) 2 V~O. In these equations, no upstream layer is formed for F < 5; if a layer is formed, its length is strongly dependent on the ventilation velocity. A partially developed ventilation velocity profile was specified over the inlet rather than a uniform profile. The profile used was obtained from an isothermal run on a 30 m length of empty tunnel. This gave a velocity profile which was constant over most of the cross-section, but significantly lower near the walls, so this was a partially developed

44

P. J. Woodburn, R. E. Britter

rather than fully developed profile. The values of the turbulence variables were also specified using data from the same isothermal run. It was not possible to calculate exactly the correct profile as the experimental data did not contain measurements of velocity close to the wall, nor was it possible to simulate the interaction of the fans and tunnel at the upstream end of the tunnel. 6.2 Turbulence model The turbulence model used for most fire simulations is the standard k - ~ model. 13 The standard k - ~ model is a two-equation eddy viscosity turbulence model which uses transport equations for two variables: k the turbulence energy, and E the rate of viscous dissipation of turbulence energy. It is the most widely used turbulence model because of its robustness and simplicity. The uncertainties introduced by using this model were assessed by comparing the results from a simulation using the standard k - e model with results from a simulation using a modified k - ~ model. The turbulent shear stress and the turbulent diffusion of heat are important processes in the physics of the upstream layer and the models within the code must represent the physics of these processes accurately for the simulation to give results acceptably close to the experimental measurements. The modified k - e model used was based on models developed by Rodi) 4 The modified k - ~ model outlined here is one derivation from the process carried out by Rodi and co-workers for hydraulic applications. Earlier work on stratified channel flows was carried out by Hossain and Rodi, 15:6 while Ljuboja and Rodi 17:8 derived a slightly different version of the model for application to plane buoyant and non-buoyant wall jets. The model used here was developed specifically for near-horizontal, stratified flows. A full description of the model can be found in the literature) 9 The modified k - e model was applied over the whole flow except for the area close to the fire where the flow is not near-horizontal. The standard k - e model was applied over this area. The k - e model is an eddy viscosity model, the turbulent viscosity of vt is found from k2 vt =

(2)

where C,, is a constant in the standard model of value 0.09. 20 While eqn (2) gives good results for isothermal free shear flows, there is a large number of data which suggest that the value of the C,, 'constant' should vary significantly with stratification and wall proximity.

CFD simulations of a tunnelfireII

45

Further, in the standard k - ¢ model, the turbulent viscosity is assumed to be the same in all directions, and is an 'average' of the viscosity in each direction. In stratified flows the vertical component of the turbulence, and hence the vertical turbulent viscosity, is reduced compared to that in the other two directions; this reduction is not reflected in the standard k-E model. In the modified k - e model, the vertical turbulence intensity itself is calculated and the turbulent viscosity made a function of this vertical turbulence intensity. The justification for this is that in near-horizontal, stratified flows, the vertical direction is the only one in which transport is diffusion dominated; advection will dominate the transport in the other directions and diffusive transport is negligible. In the standard k - e model, the Prandtl number (the ratio of the diffusivity of momentum to the diffusivity of heat) is assumed constant. In strongly stratified flows this is not the case, the value of the Prandtl number can vary by a factor of more than two. This is due to the fact that momentum can be transported in the form of waves, whereas heat energy cannot. In the modified k - ¢ model, the Prandtl number is made a function of the stratification. Lastly, walls reduce the turbulence intensity in the direction normal to the wall (and hence the turbulent diffusion normal to the wall) which is not reflected in the standard model. The modified k-E model takes this reduction into account. This derivation results in a modified k-E model, in which the k and E equations remain the same as in the standard model, but with the following additional equations: ~2

C,, = ~o k

(3)

o.J o-, = O~

(4)

(

1-C3 1-C=raB ~ (1 - C2 + 3/2C2C~f) 1 - 1 - C2 + 3/2C2C~f C,r / 1 - C3 1 ) ( C l + 312C[f) 1 + C, + 3/2C;fC, r B v~

2 [C~ - 1

k

3

+ -P- + G

-

2c c f) + c_ (3 -

- 2 c , + 2c

c

(5)

f)]

E

P+G C, + 2C~f + - -

1

)

E

(6)

46

P.J. Woodburn, R. E. Britter

a

1

C,r + C;rf + 2(1 - C3r)RB

(7)

k 2 OT

--OU OY

P =

G

(8)

- uv ~

=

v'-'!'g

Op

O"t p

Oy

d

f

=

k3~/~

trk =

to -Ck

(9)

o)

C,

where o-, is the Prandtl number, v is the vertical velocity fluctuation, trk and tr, are the Prandtl number equivalents for k and E, f is the wall damping parameter, and d is the normal distance to the wall. TABLE 1 The Values of the Constants in the Modified k - ¢ Model

C,~ C.2 C,.~ Ci C2 C3 Cw irk

0", C; C~ Cir C2r C3T C;r R

1.44 1.92 0.2 1.8 0.6 0.6 3.72 0.24 0.15 0.6 0.3 3.0 0.5 0.5 0.5 0.8

CFD simulations of a tunnel fire--1

47

The values of the constants in the modified k - ~ model are given in Table 1. The constants contained in the standard k - , model are retained and keep their non-buoyant values.

6.3 Heat input Radiative heat transfer was not modelled in the fire area runs, and all the heat released from combustion was transported away in the plume. The proportion of heat released in the flame transferred by radiation to the total heat output varies considerably for different fuels and sizes of fuel pan, but mostly falls within the range 1/5 to 1/3. 21~2 The size of the fuel pan in this experiment meant that the proportion was likely to be towards the upper end of this range. The heat release rate of the fire was therefore reduced in runs 3 and 4 by a factor of 1/3, from 2.3 to 1.5 MW. 7 F I R E A R E A RESULTS The specified conditions and results from the four full simulations of the fire area are summarised in Table 2. The results from run 3 were selected to provide the boundary conditions for the downstream area because the conditions at the measuring rake at +12 m (positive distances were measured downstream from the fire) were the closest to the experimental measurements, and the length of the upstream layer was approximately correct. Run 3 had the correct ventilation velocity, 1.72 m/s, and the heat input from the fire was adjusted to account for the heat transferred from the flames by radiation. The velocity vectors and temperature contours on the tunnel centreline for run 3 are shown

TABLE 2 Fire Area Simulation Specifications and Hot Layer Length

Run no.

Heat input rate (MW)

Ventilation velocity (m/s)

Turbulence model

Upstream layer distance

(m) 1 2 3 4

2.3 2.3 1.5 1.5

1.85 1.85 1.72 1.85

Modified Standard Modified Modified

k-e k-e k-, k-¢

11 0 11.5 3

48

P. J. Woodburn, R. E. Britter

~

-4

---*

~

~

---4

Fig. 5. Fire area--run 3--final state: tunnel centreline velocity vectors, temperature contours (303-703 K in 40 K intervals ). Figure scaled lengthwise by 0.15. Ventilation is from left to right.

in Fig. 5. T h e ventilation velocity in this figure is f r o m left to right, as for all figures. Table 2 shows that the length of the u p s t r e a m layer was extremely sensitive to the inlet velocity, the turbulence m o d e l used in the simulation, and, to a lesser extent, the heat input rate. T h e i m p o r t a n t features of these results for run 3 are as follows. 1. 2.

3.

T h e presence of an u p s t r e a m layer of about 11 m in length. T h e effect of this u p s t r e a m hot layer c o m b i n e d with the blocking effect of the fire tray base on the velocities a r o u n d and d o w n s t r e a m of the fire, in particular on the velocity profile d o w n s t r e a m which had a m a x i m u m close to the floor, shown in Fig. 11. T h e velocities at low-level are shown in Fig. 7. T h e hot layer was thin, but hot, and e m e r g e d f r o m a stagnation region above the fire.

CFD simulations of a tunnel fire--I

49

2.5

i

'

210~97

'

8~

Ix 35(~B8 2001106 I

• 310/17O

' 200/196 I

I 170/202

10/13 •

160/21 m

8/10

180/198 !

•

i 150/205

300/150

1.5 ~r-

I 8/10

12011 g3

8/10

100/181

8/10

56/162

@

:1-. 1

0.5

8/10 I

- 10

I

I

I

"5

0

5

33/63

110

15

Distance from fire (m)

Fig.

6.

Fire

area--comparison of experimental and (measured/calculated, °C).

simulated

temperatures

A comparison of the measured and calculated temperatures on the centreline of the fire area is shown in Fig. 6. The temperatures upstream of the fire are lower in the simulation than the experiment; downstream they are higher. Part of the reason for the high temperatures close to the fire in the experiment is because the thermocouples were not shielded from radiation. Simple calculations show that the radiative heat flux at the thermocouple nearest to the fire in the experiment was approximately 6 kW/m2; this would certainly cause a significant increase in the temperature measured by the thermocouples close to the fire. However, it is clear from Fig. 6 that the effect on the /hermocouples 10 m upstream of the fire, which measured ambient temperature, was small, so the effect of radiation on the temperature measurements was negligible except close to the fire. There were still significant differences between the measured and simulated temperatures, despite the fact that the flows were qualitatively very similar. This is partly due to the high temperature gradients in this area; small errors in the location of the bottom of the hot layer in the simulations will mean significant differences when the simulated and experimentally measured temperatures are compared. Thus a large difference when the two ternperatures are compared may be due to much smaller errors in the location of the bottom of the hot layer.

50

P. J. Woodburn, R. E. Britter

8 T H E U P S T R E A M SMOKE L A Y E R The length of the upstream layer was important for two reasons. Firstly, the measurement of the length of this layer under different ventilation velocities was a major objective in this experiment (during later periods of the experiment the ventilation velocity was reduced to 1.1 and 1.3 m/s on two separate occasions to investigate the effect of this on the length of the hot layer). Secondly, the sensitivity of this layer to many factors was a very sensitive test of the simulations. The length of the hot layer in each run is shown in Table 2. 8.1 Ventilation velocity

The sensitivity of the simulation results to the ventilation velocity is seen when runs 3 and 4 are compared. Both runs had a developed velocity profile. The only change between these runs was the velocity of the core of the velocity profile from 1.72 m/s in run 3 to 1.95 m/s in run 4, a change of 7.5%. The length of the upstream layer reduced from approximately 11 m in run 3 to approximately 3 m in run 4, a reduction of more than 70% in length. The velocity specified in Table 2 is the velocity over the core of the inflow. In the experiment, none of the upstream velocity measurements were made close to the walls, so the measured velocity was a measurement of the average velocity of the central core of the flow rather than an average over the whole cross-section. The measured ventilation velocity during the test was 1.72 m/s; the figure of 1.85 m/s used in some of the runs was the velocity obtained for the central core at inflow if an average velocity of 1.72 m/s over the whole inflow cross-section is assumed rather than just over the central core. The difference between the results for the two different velocities therefore reflects the likely errors due to the velocity being specified in a different way in the simulation from that in which it was measured. 8.1.1 Comparison with eqn (1) The changes calculated here are much greater than those predicted using eqn (1). Using the values for the density at the plume stagnation point at the tunnel ceiling and the ventilation velocity from run 3, the Froude numbers, F, calculated using eqn (1) were approximately 3 and 2.5 for runs 3 and 4, respectively. This implies that there should be no hot layer at all in either case. The reasons for this are as follows. 1.

The geometry. The most common geometry chosen for studies of upstream smoke flow is the case in which the fire spans the

CFD simulations of a tunnel fire--I

.

51

tunnel width, which is the case considered by Thomas, 11'12 and L e e et al. 1° In this case, the ventilation air must either force all the smoke downstream or must all be entrained into the plume. In the case considered here, the fire does not span the tunnel width, and there is a route for the ventilation air to pass around the plume and fuel tray at low level as shown in Fig. 7. The density at the ceiling. In eqn (1), the density at the ceiling is independent of the ventilation velocity. This was not the case in these simulations; the non-dimensional density differences (Pa --P)]lga at the ceiling stagnation points for runs 3 and 4 were 0.35 and 0.31 respectively, so ( p a - P)/Pa =f(Va).

The fact that both the experiment and simulations showed approximately the same layer length with other similar features shows that these differences are physical differences rather than features of the numerical model.

Fig. 7. Fire area--velocity vectors at low level. Figure scaled longitudinallyby 0.15.

52

P. J. Woodburn, R. E. Briner

8.1.2 Ventilation velocity profile It was also found here that the length of the upstream layer was influenced by the velocity profile at the inlet. Use of a partially developed velocity profile rather than a uniform profile caused a much longer upstream layer. The movement of the hot layer upstream occurred within the slow-moving air close to the wall, as seen in Fig. 5. The sensitivity of the upstream layer to the velocity profile is important both from an experimental point of view and in the assessment of results from the simulations. Experimentally, it means that the layer length is a function of the roughness and length of the tunnel upstream of the layer, which should be noted when the experiments are performed. 'In the Buxton experiment, the walls near the fire were covered with mineral wool insulation, which was unlaced. This is certainly rougher than a smooth wall, but it was not possible to estimate its roughness for these simulations. The presence of this insulation would certainly modify the ventilation velocity profile. Other factors which might affect the velocity profile in tunnels in general are the positioning and size of the fans, as well as any changes in tunnel geometry. For simulations such as this, in which there were no measurements to indicate the shape of the velocity profile in the tunnel in the experiment, the lack of information on the shape of the velocity profile is likely to introduce a significant uncertainty into the length of the hot layer in simulations. This uncertainty is not due to deficiencies or inaccuracies in the code, but is due to a lack of sufficiently accurate information with which to specify the problem. 8.1.3 Upstream layer sensitivity to the ventilation The results obtained here show that the ventilation velocity required to stop upstream flow was significantly higher than for the more standard case, that of a full-width floor fire. The upstream layer length is a function of the fractional width of the plume and the fractional height of the fuel pan from the floor, as well as the ventilation velocity. The sensitivity to ventilation velocity raises a further point, concerned with the comparison of numerical and experimental results. The sensitivity shown above, in which a 7% increase in ventilation velocity produced a reduction in upstream layer length of 70%, means that small errors in the measured value of the ventilation velocity mean large changes in hot layer length. Two causes of simulation errors other than errors due to the code can occur: the first is when an experimental error of a few per cent causes a large 'error' in upstream layer length in

CFD simulations of a tunnel fire--I

53

the simulation results; when the numerical results and experimental measurements are compared, any difference in upstream layer length is likely to be attributed to the simulation, though it was caused by small experimental errors. The second is the presence of errors in the specification of the ventilation velocity by the CFD operator, either because of a lack of knowledge of how the experimental measurements for the ventilation velocity were made, or because of insufficient information to be able to specify the correct ventilation velocity profile. With a system as sensitive as this, the difference between the average ventilation velocity over the whole tunnel and the ventilation velocity as measured over the middle of the tunnel section is significant, and will lead to errors similar to those shown here in the changes in ventilation velocity between 1.72 and 1.85 m/s. 8.2 Turbulence model

The modified k - e model was applied over the whole flow except for an area around the fire. The standard model was applied between the floor and a height of 1.35 m over a length of tunnel extending from 5.8 m upstream of the centre of the fire to 5 m downstream of the centre of the fire. Within this region, the plume had much greater vertical velocity than the rest of the flow, and the modified k - e model would not necessarily represent the state of the turbulence accurately in this region, as it was derived only for near-horizontal, stably stratified flows. Theretore the use of the standard model within this region was more appropriate. The effects of the two turbulence models on the upstream layer length are apparent from comparing runs 1 a n d 2 in Table 2; the only change,, between these two runs was the turbulence model used. The difference can be seen clearly in Figs 8 and 9, which show the temperature contours for runs 1 and 2 respectively. For run 1, the upstream layer was present, as in the experiment; for run 2, there was no upstream layer. 8.2.1 T u r b u l e n t shear stress The reason for this difference in results is due to the difference in turbulent shear stress on the lower side of the hot layer calculated using the two different turbulence models. In the steady-state results from run 3, the values of the 'constant' C,~ across the hot layer were between 0.05 and 0.08, as opposed to its standard value of 0.09, which results in a shear stress along the bottom of the layer of between 12% and 45% less than would be calculated by the standard k-E model. If the difference

54

P.J. Woodburn, R. E. Britter

Fig. 8. Fire area--run 1--final state: tunnel centreline, temperature contours (315615 K at 30 K intervals). Figure scaled lengthwise by 0.15.

in shear stresses stayed at these values, a reduction in layer length of between approximately 12 and 45% would be expected. This is because the main force opposing the buoyancy of the hot layer is the shear stress on the bottom of the layer. However, the increase in shear stress generates more turbulence, which in turn causes an increase in the shear stress. The result of this is that, although the initial difference in shear stresses calculated by each model is less than 50%, the difference increases rapidly with time, resulting in the complete removal of the hot layer when the standard k-~ model is applied. The use of different turbulence models caused a significant change in the simulation results. The standard k-~ model caused the results to underpredict seriously the upstream propagation of the hot layer.

CFD simulations of a tunnel fire--I

55

Fig. 9. Fire area--run 2--final state: tunnel centreline, temperature contours (315615 K at 30 K intervals). Figure scaled lengthwise by 0.15.

8.3 Heat input rate The effect of reducing the heat release rate on the simulation results is seen when runs 1 and 4 are compared. The result was a significant reduction, from 11 to 3 m, in the length of the upstream layer. This is contrary to experimental results which show that, over the range of heat release rates considered here, the upstream layer propagation distance is almost independent of heat release rate, because the temperatures in the continuous part of the flame are constant 23 and the flame is continuous to the roof. The difference in results is likely to be due to two factors. 1.

The m e t h o d of reducing the heat input. In experiments, the heat input rate is controlled by changing the area of the fuel pans. In the simulations the heat input rate was changed by altering the rate of fuel flow through the s a m e area fuel pan. Since the

56

P.J. Woodburn, R. E. Britter

.

m e t h o d of changing the heat input rate was fundamentally different from the experiments, it is not surprising that the effect on the hot layer was different in the simulations from the experiments. The combustion model. The combustion model used assumes infinite-rate, one-step chemistry, which will certainly overpredict the reaction rate compared with the experiment. More fuel will be burned close to the fuel tray and less further from the fuel pan than in the experiment, which will lead to a significantly different temperature distribution within the flame, and hence different temperatures at the tunnel ceiling. Runs 1 and 4 showed temperatures at the ceiling of 505 and 440 K, respectively, despite the fact that the flame would be continuous in both cases.

8.3.1 Specification o f heat input rate It is not immediately clear how a reduction of heat input rate could have been better specified in the simulation. Reducing the size of the fuel pan would have increased the free cross-sectional area around the sides of the fuel pan through which the ventilation air could pass. Maintaining the same size fuel pan and injecting fuel through just part of it would change the geometry close to the flame, which is likely to have important effects on the flame near its s o u r c e . 23 For the runs listed in Table 2, the fuel was supplied uniformly across the fuel pan. It is unlikely that the fuel is vapourised uniformly in the experiment. To test whether this had a significant effect on the results, one simulation was carried out (not listed in Table 2) in which the fuel was supplied at a greater rate in the middle of the pan than at the edge, while the total fuel flow rate was the same. This did not cause a significant change in conditions within the fire area, so a uniform fuel flow rate over the fuel pan was used in all other runs. This agrees with the conclusions of Fletcher et al. that the results were insensitive to the details of the fuel inflow rate. 5 It was also suspected that the heat supplied to the roof upstream of the fire by direct radiation from the fire might be a significant factor in the propagation of the upstream layer. A heat source equivalent to this radiative heating was applied along the roof, but was found to have no significant effect. This heat source, and the radiative heating of this area, was therefore neglected for the runs listed. This also agrees with the results of Fletcher et al., in which the upstream layer distance was relatively insensitive to their radiation heat transfer modelling.

CFD simulations of a tunnel fire--I

57

9 THE FIRE AREA OUTFLOW In the experiment, a rake to measure temperature and velocity was placed 12 m downstream of the fire on the tunnel centreline. While all the velocity measurements should be treated with caution, the measurements made here are consistent within themselves; they are of reasonable magnitude for the experimental configuration and are similar to those found in the numerical results, so it is reasonable to use them for comparison. The profiles of temperature obtained from the experiment at the + 12 m measuring rake are compared with the results from runs 1 and 3 in Fig. 10. The profiles of velocity are shown in Fig. 11.

9.1 Temperature profile The temperatures at this downstream point are higher than those in the experiment. This is certainly partly due to the neglect of radiative heat transfer in the simulation. The reduction of the heat input rate between runs 1 and 3 caused a significant reduction of the downstream temperatures, and the reduction in the fire heat input rate was therefore

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150

200

250

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Fig. 111,. Fire a r e a - - t e m p e r a t u r e profile on centreline at +12 m: comparison of experimental measurements and simulation results.

P. J. Woodburn, R. E. Britter

58 1

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Fig. 11. Fire area--velocity profile on centreline at +12 m: comparison of experimental measurements and simulation results. justified. The rate of heat release was adjusted solely to take account of the radiation lost from the flame; there would also b e a significant heat loss from the hot layer by radiation between the flame and the + 12 m station. This heat loss was not accounted for here. Simple calculations (see the Appendix) show that the temperature drop between the +2 and +12 m measuring stations is consistent with the expected heat transfer to the walls by radiation alone over this section of the tunnel. The temperature rose within the plume over the downstream third of the fire area, as shown in Fig. 5. This was due to a very small a m o u n t of unreacted fuel which, because of the combustion model used here, continued to react and produce heat in this area. This is not physically realistic as this region is downstream of the flame and unburned fuel would be transported away in the plume without burning. This continuing reaction further increased the downstream temperatures in the simulation.

9.2 Velocity profile The velocity profiles are shown in Fig. 11. The bounds of the experimental velocities are shown rather than an average, because there were large fluctuations in the velocities. These bounds were estimated

CFD simulations of a tunnel fire--I

59

by eye from the experimental data. Both runs 1 and 3 showed an important feature of the experimental results, that 12 m downstream of the fire; the velocity is higher nearer the floor than the ceiling. While the magnitude of the difference in velocity across the height of the tunnel was not as high as that found in the experiment, it is still an important feature:. Two factors cause this velocity profile. The first, which can be seen in Fig. 5, is the deflection of the ventilation flow under the hot layer, causing an increased flow speed at lower levels. This feature was present even when no hot layer was formed in run 2, because the flow still formed a stagnation point at the ceiling. The second factor is the blocking effect of the fire and plume. The fire tray did not extend across the width of the tunnel, so there was a clear area between the fire tray apparatus and the tunnel side wall. This area to the side of the plume was not filled by the plume and provided a route for the ventilation air to pass around the plume. Hence a large proportion of the ventilation flow passed around the fuel pan, seen in Fig. 7. This results in the profile shown at the +12 m measuring point. Further down the tunnel, the velocity profile changed and the velocity maximum occurred close to the roof.

10 CONCLUSIONS--FIRE A R E A Conditions within the fire area were very sensitive to several different physical, modelling and problem specification factors. Simulation of this area required precise specification of velocity and heat input rate for the simulation, and realistic models of turbulence within the code. The length of the upstream layer, and to a lesser extent the downstream temperatures and velocities, are very sensitive to the ventilation velocity. This was in agreement with experimental results. The sensitivity to the heat input rate, not shown in the experiment, was thought to be due to the combustion model, together with the method used to change the heat input rate between simulations. The length of the upstream layer was very sensitive to the shear stress between the upstream layer and the ventilation air and hence to the turbulence model used in the simulation. The system magnified the differences between the results from standard and buoyancy modified k-E turbulence models. The

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P. J. Woodburn, R. E. Britter

•

•

•

differences in hot layer lengths found using the two different turbulence models were much greater than the initial difference in shear stress calculated by each model. The downstream temperatures were higher than the measured ones, because the radiative heat transfer from the smoke to the walls between the fire and the first measuring rake was not modelled. Without data for the ventilation velocity profile, the roughness of the tunnel walls and accurate measurement of the ventilation velocity, accurate simulation of the fire area is not possible, because conditions within the fire area are sensitive to all these factors. The results, while not exactly the same as those measured in the experiment, were close enough to allow the results to be used for the boundary conditions for the downstream area simulations.

in this paper, the objectives of the project were outlined, and the specification and results for the fire area were described. In Part II of this study, the sensitivity study on conditions downstream of the fire will be discussed, together with the conclusions for the project as a whole.

ACKNOWLEDGEMENTS The authors are grateful to Mr Ian Buckland, Health and Safety Executive, who funded this work and to Dr Stewart Jagger and Dr Chris Lea, also of the Health and Safety Executive, for their support of this project. The authors are also grateful to CFDS, A E A Technology for their support of this project.

APPENDIX Assuming the smoke formed a cylinder of radius 0.6 m just downstream of the fire, and that the temperature was constant over any circular cross-section, the rate of heat transfer by radiation over a length of the cylinder 8x at a d i s t a n c e x from the upstream end of the cylinder is 8Q = 2~tr~r( T ~ - T4 )Sx

The rate at which heat energy was transported through any crosssection is Q = lilCp(T~ - T,,)

CFD simulations of a tunnel fire--I

61

so the following differential equation is obtained:

8ti~Cp( T~, -- T,~) 8x = 27rrtr(T~ - TL)

(A1)

Solution of this equation with the initial conditions T~ = 550 K at x = 2 gives T-460K a t x = 112 m. This is close to the m e a s u r e d t e m p e r a t u r e s at the +12 m measuring stations which are 443 and 423 K at heights 1.86 and 2.3 m, respectively.

REFERENCES 1. Brandeis, J. & Bergmann, D. J., A numerical study of tunnel fires. Combustion Sci. and Technol., 35 (1983) 133-155. 2. Simcox, S., Wilkes, N. S. & Jones, I. P., Computer simulation of the flows of hot gases from the fire at King's Cross Underground Station. In L Mech. E. Seminar: The King's Cross Underground Fire: Fire Dynamics and Organisation of Safety. MEP Publishing, Leamington Spa, UK, 1989. 3. Chass6, P., Sensitivity study of different modelling techniques for the computer simulation of tunnel fires, comparison with experimental measures. In C.F.D.S. International Users Conference. A E A Technology, UK, 1993. 4. Apte, V. B., Green, A. R. & Kent, J. H., Pool fire plume flow in a large-scale wind tunnel. In Fire Safety Science--Proceedings o f the Third International Symposium. Hemisphere, New York, 1991. 5. Fletcher, D. F., Kent, J. H., Apte, V. B. & Green, A. R., Numerical simulations of smoke movement from a pool fire in a ventilated tunnel. Fire Safety J., 23(3) (1994) 305-325. 6. Bettis, R. J., Hambleton, R. T. & Macmillan, A. J. R., Interim validation of ~tunnel fire consequence models: data from phase 1 test 4. Technical Report, Health and Safety Executive Research and Laboratory Services Division, Harpur Hill, Buxton, Derbyshire, UK, 1994. 7. C.F.D.S., FLOW3D Release 3.2 User Manual, Harwell Laboratory, Oxfordshire, UK, 1992. 8. Turner, J. S., Buoyancy Effects in Fluids. Cambridge University Press, UK, 1973. 9. Hwang, C. C. & Wargo, J. D., Experimental study of thermally generated reverse stratified layers in a fire tunnel. Combustion and Flame, 66 (1986) 171-180. 10. Lee, C. K., Chaiken, R. F. & Singer, J. M., Interaction between duct fires and ventilation flow--an experimental study. Combustion Sci. and Technol., 20 (1979) 59-72. 11. Thomas, P. H., Fire Research Note No. 351: the movement of buoyant fluid against a stream and the venting of underground fires. Technical Report, Fire Research Station, Borehamwood, Herts., UK, 1958.

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12. Thomas, P. H., Fire Research Note no. 723: the movement of smoke in horizontal passages against an air flow. Technical Report, Fire Research Station, Borehamwood, Herts., UK, 1968. 13. Launder, B. E. & Spalding, D. B., The numerical computation of turbulent flows, J. Computer Meth. Appl. Mech. Engng (1974) 269-289. 14. Rodi, W., Calculation of stably stratified shear layer flows with a buoyancy-extended k - e turbulence model. In Turbulence and Diffusion in Stable Environments, ed. J. C. R. Hunt. Clarendon Press Oxford, UK, 1985. 15. Hossain, M. S. & Rodi, W., Mathematical modelling of vertical mixing in stratified channel flow. In Second International Symposium on Stratified Flows. The Norwegian Institute of Technology, Trondheim, 1980. 16. Hossain, M. S. & Rodi, W., A turbulence model for buoyant flows and its application to vertical buoyant jets. In Turbulent Buoyant Jets and Plumes, ed. W. Rodi. Pergamon, UK, 1982. 17. Ljuboja, M. & Rodi, W., Calculation of turbulent wall jets with an algebraic Reynolds stress model. ASME J. Fluids Engng, 102 (1980) 350-356. 18. Ljuboja, M. & Rodi, W., Prediction of horizontal and vertical turbulent buoyant wall jets. ASME J. Heat Transfer, 103 (1981) 343-349. 19. Woodburn, P. J., Computational fluid dynamics simulations of firegenerated flows in tunnels and corridors. Ph.D. Thesis, Cambridge University, UK, 1995. 20. Rodi, W., Turbulence models and their application in hydraulics--a state of the art review. I A H R / A I R H Monograph, 3rd Edn. Balkema, Rotterdam, 1993. 21. Cox, G. & Chitty, R., A study of the deterministic properties of unbounded fire plumes. Combustion and Flame, 39 (1980) 191-209. 22. Mudan, K. S., Thermal radiation hazards from hydrocarbon pool fires. Prog. Energy Combustion Sci., 10 (1984) 59-80. 23. Cox, G. & Chitty, R., Some source dependent effects of unbounded fires. Combustion and Flame, 60 (1985) 219-232.