Fire driven flow in an inclined trench

ELSEVIER

Fire Safety Journal 25 (1995) 141-158 1996 Elsevier Science Limited Printed in Northern Ireland. All rights reserved 0379-7112/95/$09-50 0379-7112(95)00039-9

Fire D r i v e n Flow in an Inclined Trench G. T. A t k i n s o n Health and Safety Laboratory, Harpur Hill, Buxton, Derbyshire, SK17 9JN, UK D. D. D r y s d a l e & Y. W u * Department of Civil Engineering and Building Science, University of Edinburgh, The Kings Buildings, Edinburgh EH9 3JL, UK (Received 10 June 1995; revised version received 24 August 1995; accepted 22 September 1995) ABSTRACT Measurements are presented of flow velocity and temperature in an inclined trench of square cross-section;flame lengths and flow velocities have been measured for trench fires with a rate of heat release per unit width of between 10 and 1500 kW/m. For all of the fires studied, and for angles of inclination of between 20 and 45°, the flow is dominated by large, buoyancy-driven, plume-like structures that are convected up the trench. The results suggest that time-dependent calculations that capture the development o f such large structures would greatly increase the accuracy of numerical simulations of the flow. 1 INTRODUCTION A disastrous fire in the King's Cross underground station in L o n d o n , U K on 18 November 1987 drew attention to a previously unrecognised mechanism by which fire can spread rapidly upwards in an inclined trench with combustible linings. This has become known as the trench effect, and has been demonstrated on a n u m b e r of occasions. 1,2 A n u m b e r of experimental studies have investigated the effect: Drysdale and Macmillan 3 measured the rate of fire spread on inclined surfaces with and without sidewall confinement, and Smith 4 reported flame lengths and angles in an inclined trench. The investigation of the King's Cross fire also included c o m p u t e r simulations of the flow of hot gas. 5'6 These simulations revealed that the * Present address: Department of Mechanical and Process Engineering, Sheffield University, Sheffield,UK. 141

142

G.T. Atkinson et al.

flow remained attached to the base of the trench, in qualitative agreement with observations of flames under similar circumstances, although no quantitative comparison between computational fluid dynamics (CFD) predictions and experimental measurements of temperatures and velocities have been possible as there has been no systematic survey of the flow dynamics associated with this scenario. The purpose of this paper is twofold. 1.

2.

To demonstrate the importance of a strong buoyancy-driven instability in the trench flow. Large plume-like structures are produced by this instability. These structures--rather than shear driven vortices--dominate entrainment into the flow. To guide the development of appropriate computational methods for trench flows and for the more general problem of flame attachment to unconfined, upward facing, inclined surfaces. The data presented will provide a check on the output of such computations. 2 EXPERIMENTAL DETAILS

A model trench with a square cross-section of 276 mm × 276 mm was constructed from mineral fibre insulation board--Fig, l(a)-(d). Its length was 2440 mm, but this could be extended to 4440 mm for tests to assess the effects of finite aspect ratio. The trench was supported on a steel frame at a series of different angles to the horizontal [angle 0 in Fig. l(a)]. The apparatus was located well clear of laboratory walls and floor and all tests were carried out in still air. The fire sources were placed near the lower end of the inclined trench as shown in Fig. l ( a ) - ( c ) . Three fire sources were used, as follows. 1.

2.

3.

A perforated-plate gas burner supplied with high-purity propane gas for a heat release rate of 3 kW. The position and dimensions of the burner are shown in Fig. l(b). In this case, the total length of the visible flame was around 200 mm. The above burner supplied with a higher gas flow to give a heat release rate of 18 kW. In this case, the total length of the visible flame was around 600 mm. Three lengths of asbestos tape 50 mm × 1000 mm x 2 mm, soaked in a measured quantity of cyclohexane [Fig. l(c)]. The heat release rate for this fire (400 kW) was estimated from the mass burning rate (10 g/s) and the average heat of combustion o f analogous hydrocarbons. 7 The visible flame extended the whole of the length of the smaller trench and to a length of around 4000 m m in the longer trench.

143

Fire driven flow in an inclined trench

angleof inclination 0 ~ " ~

~

~

Gas burner ~ ~~

L

'

~

Asbestos tape j

~276

|_

2~Omm

I

(a)

_

~ 1000mm

/

mlll

(b)

I

(c)

12 ram thick mineral fibre board (d)

276 mmI q

276 ram

h

""-

24 nun thick mineral fibre board

Fig. 1. Experimental layout: (a) side view of the inclined trench showing the position of the gas burner relative to the lower end of the trench; (b) top view of the trench and gas burner; (c) top view of the trench showing positions of the cylclohexane-soaked asbestos strips used to fuel the 400 kW fire; (d) cross-section of the trench. Errors in the m e a s u r e m e n t of the fuel consumption rate and assumptions about convective heat release rates mean that the quoted heat release rates may be in error by around 3% for the gas burners and up to 20% for the liquid fuel fires. To allow the flow to be photographed, some tests were carried out in a trench 2000 m m long with a transparent side. Some of these tests used fire source (3) above, which p r o d u c e d luminous flames in the whole

144

G. 7/'. A t k i n s o n et al.

length of the trench (Fig. 2). Other tests used a small mineral fibre wick 10 mm x 276 m m x 2 mm soaked in xylene. This wick was laid across the width of the trench, 200 mm from the open lower end. The rate of convective heat release in this case was around 5 kW. Smoke flow in the trench was illuminated through a 90 mm transparent slot in the base, with a series of flashlamps triggered by the camera shutter (Fig. 3).

3 INSTRUMENTATION T e m p e r a t u r e and pressure m e a s u r e m e n t s were made near the base of the trench on the centreline, between 450 and 2100 m m from the lower end. The positions of all reported measurements of temperature and pressure are shown in Fig. 4(a). Total pressures were tapped through open-ended copper tubes

(a)

TP SP Fr T

SP T

SP T

SP T

SP T

SP T

SP T TT /

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I t t t t t t ttt Wi i!ow0rend I b~

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o

~,

0

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N

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o

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(DPT) Fig. 4. (a) Location of instrumentation used for reported measurements. Distances measured from the lower end of the trench. Total pressure taps and thermocouples 15 mm from trench base. T, thermocouple (1-5 mm diameter); FT, fine thermocouple (0.25 mm diameter); SP, static pressure tap; TP, total pressure tap. (b) Geometry of static and total pressure taps close to the trench base.

Fire driven flow in an inclined trench

Fig. 2. 400 kW cyclohexane fire--self illuminating flames.

Fig. 3. 5 kW xylene fire--smoke illuminated from below.

145

147

Fire driven flow in an inclined trench

parallel to the trench base [Fig. 4(b)]. The tubes' exterior and interior diameters were 4 and 2 mm respectively. Static pressures at the base were tapped through similar tubes with open ends set flush with the trench floor [Fig. 4(b)]. Separate measurements of total and static pressure were made with all reference pressures taken at the same point outside the trench. There was no flow or heating effect at the position of the reference tap and all results were independent of its position or orientation. The dynamic head of the flow was then obtained by subtracting the static from the total pressure at the measurement point. [For details of the total and static pressure taps see Fig. 4(b).] Pdynamic = Pro,a,- Pstatic

1 where p = fluid density and v = fluid velocity. The differential pressure transducer used had a time constant of 25 ms. It was considered that any attempt to measure the total pressures away from the base of the trench would produce misleading results because of the large vertical velocities and corresponding variations in flow direction. Average temperature measurements were made with stainless-steelsheathed K-type thermocouples (o.d. 1.5 mm). Some partially timeresolved temperature measurements were made with fine-sheathed thermocouples, o.d. 0.25 mm (Fig. 5). 1

BOO

-1

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~ ~

0

\/

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// v

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2

" o

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Time (seconds) Fig. 5. Static pressure (negative) and dynamic head (positive). Measurement point 2100 mm from lower end of trench. Angle of inclination 30°. Rate of heat release: (a) 400 kW; (b) 18 kW; and (c) 3 kW.

G.T. Atkinson et al.

148 250 i

e-

~

,

~100~ E 5O I.•

-

0

•

0

•

-

500

1000

1500

2000

Distance from lower edge of burner (mm) Fig. 6. A v e r a g e temperatures measured 15 mm above the trench base on the centreline. Angle of inclination 30 °. Rate of heat release: (a) 3 kW; and (b) 18 kW.

Flow measurements have been presented as dynamic heads because the fully time-resolved temperature measurements necessary to make fully time-resolved estimates of the density were not available. For the two smaller fires, the velocity can be estimated with reasonable accuracy by assuming that the temperature and density are always equal to their average values (Fig. 6). Results from a time-dependent computation would include both temperature and velocity, so that a direct comparison of measured and predicted dynamic head should be straightforward. All data were logged at a rate of 100 Hz using a Microlink 3000 system.

4 RESULTS The basic character of the flow is clearly illustrated by Fig. 7(a)-(c), which shows the variation of dynamic head and static pressure at a distance 2100 mm from the lower end of the trench for each of the 3, 18 and 400 kW fires. For all of the fires, the burning rate was steady but flow was regularly disturbed by the passage of the large plume-like structures visible in Figs 2 and 3. At the base of each of these 'travelling plumes' was an area of low static pressure which drew fluid into the base of the plume. It is these strong secondary flows which produce the oscillations in dynamic head (flow speed) that characterise the results in Fig. 5. Minima in static pressure correspond to places in the flow where

149

Fire driven flow in an inclined trench

o . I~

-2

-

-4 1

2

3

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Time (seconds)

'I g z ~ m ~

bl ,

1 0.5 0 -O.5 -1 1

2

3

4

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Time (seconds) °" 1

c 1

0... n

-11.2

.0.4 0

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2

3

4

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Time (seconds) Fig. 7. Time variation of (a) static pressure and (b) temperature. Measurement point close to the trench base and 2100 mm from the lower end. Rate of heat release 400 kW. Angle of inclination 30°.

the dynamic pressure (flow s p e e d ) is increasing rapidly. Characteristic values for the dynamic head and estimates of m a x i m u m and minimum flow speeds are shown in T a b l e 1. Simultaneous m e a s u r e m e n t s s h o w e d that the flow at 2100 m m from the lower end of the trench was closely similar across the width of the trench: the flow had a quasi-two-dimensional character. This is to be e x p e c t e d as the variations in velocity are caused by structures that are m a n y times longer than the trench width. Closer to the base of the fire,

G.T. Atkinson et al.

150

TABLE

1

Summary of Flame Lengths and Flow Measurements on Base Of Trench, 2100 mm from Lower End

Flame length (mm) Maximum dynamic head (N/m2) Maximum velocity (m/s) Minimum velocity (m/s) Convection rate (m/s) Frequency (Hz) Characteristic plume size (m) (convection rate/frequency)

3 kW gas fire

18 kW gas fire

400 kW cyclohexane fire

200 0.45 0-9 ~0 0.65-0.8 0.48 1.3-1.6

600 1.7 1.9 - 0 1.3-1.7 0-73 1.7-2.3

4000 7 4.6 0-1-0 2.5-3.0 1.4 1.7-2.2

the size of the structures was comparable to the trench width and the flow was visibly t h r e e - d i m e n s i o n a l in character. The rate at which these plume-like structures travel up the trench can be m e a s u r e d by c o m p a r i n g the records from relatively closely spaced static t a p s a s e e Fig. 8. Characteristic values for this convection rate for all of the fires studied are given in Table 1. These results m a k e it clear that because the variations in velocity and t e m p e r a t u r e are d o m i n a t e d by very large structures, it is not possible to use a correlation technique s to m e a s u r e the average fluid velocity. This point is discussed in detail in Atkinson. 9

4 0 0 kW

o

18 kW

os

3 kW

o

o

o

.1

4).25

.e I

2

3

Time (seconds)

4

0

1

2

Tlme

3

(seconds)

4

5

0

I

2

3

4

Time (seconds)

Fig. 8. Convection of large structures shown by variations in static pressure on the trench base. Angle of inclination 30°. Distance of measurement point from the lower end of the trench: (a) 2100 ram; (b) 1850 ram; (c) 1600 mm; (d) 1350 mm; and (e) 1100 mm.

Fire driven flow in an inclined trench

151

0.2'3

(a) 0.2 U)

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0.1

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2

4

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Frequency (Hz) 025

(b) 0.2 g,)

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Frequency (Hz) 0.25

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Fre( luency (Hz) Fig. 9. Power spectrum of variations in static pressure on the trench base. Rate of heat release 3 kW. Angle of inclination 30°. Distance from the lower end of the trench: (a) 450ram; (b) 850 ram; and (c) 2100 ram. Figures 9 and 10 show h o w the p o w e r spectra of the variations in static pressure develop along the length of the trench.¢ Each of these spectra was obtained from a 20.48 s time series weighted with a Hanning w i n d o w to reduce spectral leakage. The t The word thousandths in the units of power in Figs 9, 10 and 13 indicate that the quantity plotted is the periodogram estimate of the power spectral density multiplied by 1 0 3.

152

G.T. Atkinson et al.

(a)

¢-

i

!

o. o

S

2

4

Frequency(Hz)

(b)

2

1

3

4

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Frequency(Hz) Fig. 10. Power spectrum of variations in static pressure on the trench base. Rate of heat release 18 kW. Angle of inclination 30°. Distance from the lower end of the trench: (a) ll00mm and (b) 2100 mm. characteristic frequencies with which large structures pass a measurem e n t point can be o b t a i n e d from the spectra. Results for the measurem e n t point 2100 m m up the trench are summarised in Table 1. Figure 11 shows the effect of increasing the length of the trench from 2400 to 4400 mm. The passing frequency of large-scale structures is not significantly affected by this increase. These results, as shown in Table 1, are likely, therefore, to be characteristic of all trenches with lengths greater than 2400 mm. Figure 12 shows the variations in dynamic head for trenches at different angles to the horizontal b e t w e e n 20 and 90 °. The m e a s u r e m e n t point is again 2100 m m f r o m the lower end of the trench and the fire is the 18 k W gas flame described previously. Figure 13 shows p o w e r spectra of 20.48 s of records of these variations.

153

Fire driven flow in an inclined trench 12,

Ioi zv ":

6 4

w

0

1

2

3

4

Time (seconds)

b

lo

Z 4

0

1

2

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Time (seconds)

Fig. 11. Dynamic head close to the trench base, 2100 mm from the lower end. Rate of heat release 400 kW. Angle of inclination 30°. Total trench length: (a) 2440 mm; and (b) 4440 mm.

For the trench at an angle of 20 ° to the horizontal, the flames were attached to the base of the trench, but the hot flow lifted out of the trench about 1000 mm from the lower end. For larger angles between 25 and 45 °, the flow Was dominated by the strong buoyancy-driven variations described in this~paper. For higher angles, shear driven vortices produced velocity variations with higher frequencies and lower amplitudes relative to the mean.

5 DISCUSSION The key features of the flow--for a 30° trench--to be compared with the output of a computation are summarised in Table 1. The variation of flame length with heat output is shown in Fig. 14 and compared with some previously suggested correlations for vertical wall fires by Hasemi 11 and for an open line fire by Steward 1°. The assumption made by both of these authors, that flame length varies with Q~3--where Q is the heat release ratemis approximately supported. In fact, these data closely match the findings of Smith 4 who found that

154

G.T. Atkinson et al. 5

a 4

d

4

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8

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-I 10

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1

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Time (seconds)

Time (seconds)

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Time (seconds)

Time (seconds)

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1

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4

5

0

1

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Time (seconds) Time (seconds) Fig. 12. Dynamic head close to the trench base, 2100 mm from the lower end. Rate of

heat release 18 kW. Total trench length 2440 mm. Angle of inclination: (a) 20°; (b) 25°; (c) 30°; (d) 45°; (e) 60°; and (f) 90°. flame length varied as Q0.62. Figure 14 shows the flame length to be intermediate b e t w e e n those expected for an open line fire and a vertical wall fire. This may reflect the fact that whilst e n t r a i n m e n t is considerably restricted, there are mechanisms for buoyancy-driven increases in flame volume and entrainment that are absent in the vertical wall fire. Figure 15 shows m e a s u r e m e n t s of m a x i m u m fluid velocity and characteristic convective velocities for large structures as a function of

155

Fire driven flow in an inclined trench 21

a

d

I

o 1.5

I

~ o.s

r 0

2 3 Frequency (Hz)

5

2

0

3

4

Frequency (Hz)

,1.5~

= 1.5

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1

3 Frequency (Hz)

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Frequency (Hz)

c = 1.5

2

l

== 1.5

]

f

~ o.s 0 3

Frequency (Hz)

0

1

2 3 Frequency (Hz)

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Fig. 13. Power spectra of dynamic head close to the trench base, 2100 mm from the lower end. Rate of heat release 18 kW. Total trench length 2440 mm. Angle of inclination: (a) 20°; (b) 25°; (c) 30°; (d) 45°; (e) 60°; and (f) 90°.

heat release. Previous studies of plumes by McCaffery ~2 and Alpert, ~3 amongst others, as well as dimensional analysis, suggest that beyond the limits of flaming, velocities should scale as Q1/3. I n the flames, the velocity becomes less sensitive to the rate of heat release. Hasemi and T o k u n a g a 14 and McCaffery 12 suggest that velocity becomes proportional to Q1~5. The current velocity m e a s u r e m e n t s are in line with this scaling with Q. T h e power spectra in Figs 9 and 10 show that smaller-scale, higher-frequency instabilities develop most rapidly, as is to be expected. T h e size of these smaller scale structuresmvisible in Fig. 3--is similar to the width of the trench. They then interact strongly, eventually coalescing into the larger plumes described above.

156

G.T. Atkinson et al. 10

o

0

m 0.1 U.

0.01

10

100 1000 Heat release rate per metre (KWlm)

10000

Fig. 14. Variation of flame length with heat release rate per unit trench width. II, present experiments; solid line, open line fire; I° dashed line, vertical wall fire. H

6 IMPLICATIONS FOR MODELLING In a conventional, well-developed turbulent shear flow, it makes sense in constructing a numerical model to divide the flow into two parts: (1) a time-independent mean flow; and (2) relatively small, time-dependent turbulent fluctuations. These fluctuations are typically irregular with energy spread over a range of (short) length scales. Where the turbulent velocities are small, the equations of motion can be cast to 10

!

b)

Plume 0.1

'

lO

'

'

'

' ' ' "

Flame '

'J

.

.

.

.

.

.

.

.

.

.

10o lOOO Heat releime rate per metre (KW/rn)

.

' ' ~

10000

Fig. 15. Variation of velocity with heat release rate at a measurement point 2100 mm from the lower end of the trench, (a) Maximum fluid velocity. (b) Characteristic convection velocity of large structures. Solid lines show gradients to be expected if the velocity is proportional to Q1/3 or Q1/5; the dashed line indicates the heat release rate above which flames extend past the measurement point.

Fire driven flow in an inclined trench

157

show the effect of turbulence as an enhancement to the diffusivity of the flow. For closure, such models also require the turbulent intensity to be defined, and this is usually done by relating turbulent intensity to the velocity gradients in the mean flow. There are a number of serious problems in applying such a method to the trench flows studied in this paper: the variations in this flow are very large in magnitude, highly regular and anisotropic, and are driven by buoyancy rather than shear forces. The large size and regularity of the structures in the flow suggest that it might be feasible to obtain time-dependent solutions for the mean flow, where the evolution of the large-scale structures is calculated explicitly. Smaller-scale variations within these large structures (which can more appropriately be described as turbulence) could be treated as increases in diffusivity as before. The main difficulty with this approach will probably be the modelling of processes of interaction and eventual coalescence between the smaller structures that develop first. 7 PRACTICAL IMPLICATIONS One practical consequence of the existence of the strong buoyancydriven instability shown in Figs 2 and 3 is that the hot gas layer broadens much more rapidly than would be the case for purely shear-driven entrainment. Smoke and heat escape from the trench a short distance from the lower extremity of the fire. This means that smoke detectors on a ceiling above the fire could be activated along almost the whole length of the fire or smoke flow. Most current computational methods would probably predict that detection was only possible some way up from the lower edge of the fire. One of the ultimate objectives of research in this area is the synthesis of rate of heat release data, computational fluid mechanics and combustion modelling to predict rates of flame spread in combustible trenches and on inclined combustible surfaces. The buoyancy-driven instabilities discussed here will have an important effect on flame length and heat transfer to surfaces by changing the flame shape and entrainment rate. ACKNOWLEDGEMENTS The authors wish to acknowledge the valuable contributions to this work made by staff at the Health and Safety Laboratory: the equipment used was built by Mr D. Bagshaw and Mr E. Belfield; Dr C. Lea and Dr R. Bettis provided help in data processing and analysis.

158

G.T. Atkinson et al. REFERENCES

1. Fennel, D., Investigation into the King's Cross Underground Fire. HMSO, London, UK, 1988. 2. Moodie, K. & Jagger, S. F., Results and analysis from scale model tests. Fire Safety J., 18 (1992) 83-103. 3. Drysdale, D. D. & Macmillan, A. J. R., Flame spread on inclined surfaces. Fire Safety J., 18 (1992) 245-54. 4. Smith, D. A., Measurements of flame length and flame angle in an inclined trench. Fire Safety J., 18 (1992) 231-44. 5. Simcox, S., Wilkes, N. S. & Jones, I. P., Computer simulation of flows of hot gases from the fire at King's Cross underground station. Fire Safety J., 18 (1992) 49-73. 6. Simcox, S., Wilkes, N. S. & Jones, I. P., Fire at King's Cross underground station, 18th November 1987: numerical simulation of the buoyant flow and heat transfer. Report No. AERE-G 4677, Harwell Laboratory, Harwell, UK, 1988. 7. Tewarson, A., The SFPE Handbook of Fire Protection Engineering, Ed. P. J. DiNenno. National Fire Protection Association, Quincy, MA, USA, 1988. 8. Motevalli V., Transient and steady state study of small scale, fire induced unconfined ceiling jets. ASME Thermophysics and Heat Transfer Conf., Vol. 141, Ed. J. G. Quintiere & L. Cooper. ASME Heat Transfer Division, June 1990. 9. Atkinson, G. T., Smoke movement driven by a fire under a ceiling. Fire Safety Journal (Submitted for publication). 10. Steward, F. R., Linear flame heights for various fuels. Combustion and Flame, 8 (1964) 171-8. 11. Hasemi, Y., Experimental wall flame heat transfer correlations for the analysis of upward wall flame spread. Fire Sci. Technol., 4 (1984) 75-90. 12. McCaffery, B., Purely buoyant diffusion flames: some experimental results. Report NBSIR 79-1910, National Bureau of Standards, Gaithersburg, MD, USA, 1979. 13. Alpert, R. L., Calculation of response time of ceiling mounted fire detectors. Fire Technol., 8 (1972) 181. 14. Hasemi, Y. & Tokunaga, T., Modelling of turbulent diffusion flame for the analysis of fire growth. Proc. 21st National Heat Transfer Conf. American Society of Mechanical Engineers, 1983.