Fire computation: The ‘flashover’ phenomenon

ds

-

K~yT4 KI + - Ir

Special Practicesfor Fires: The application of the above modelling to fires entails some special practices which will now be described.

The Turbulence Model: (1)

where d~ stands for any one of the above mentioned variables and S+ is a source term which, in the momentum equation (6 = u, v and w) for example, accommodates the influences of the pressure gradient and mean buoyancy, The thermal radiation is governed by the fundamental transfer equation: dI

where I,+1 and I, are the intensities at successive stations separated by the discretised distance 8s. Eq. (3) is applied to discretised solid angle elements within which the intensity value is presumed uniform. This solution technique, known as the 'discrete transfer' method, is exact, economical and applicable to arbitrary geometrical shapes. It is fully described in. 16

The fluid motion in room fires is dominated by mean buoyancy effects. We have found that the standard k-~ turbulence model requires modification for the satisfactory prediction of hot ceiling layers. A buoyancy production term GD, recommended by Rodi 17 in the light of experience with plume prediction, is appended to the source term for the k equation: Ixt aT GB = 13 g - -

(2)

where I is the radiation intensity in the direction of s, K is the absorption coefficient, ~r is the Stefan Boltzman constant, and T is the temperature. As smoke particles are generally small enough for scattering to be negligible, both the in-scattering and out-scattering terms have been neglected from this equation. Equation (2) also implies that the fire may be treated as a gray body. This point will be further addressed below.

Numerical Solution Technique: The differential Eq. (1) is integrated over a finite difference control volume to yield a conservative finite difference expression. 'Upwind' or 'donor cell' differencing of the convection terms is employed. A staggered grid is utilised for the velocity and scalar variables. A Poisson-form pressure correction equation, deduced from the mass continuity equa-

(4)

(lk. t OZ

where 13 is the coefficient of thermal expansion, g is the gravitational constant, i~t is the turbulent viscosity, crk.t is the Schmidt number and ~T/Oz is the temperature gradient in the vertical direction. This term, which has also been used with effect by Cox et al2-4As in studies of room fires, arises naturally in the derivation of the k equation. Rodi also proposes a corresponding modification to the source term S, of the ~ equation. The term becomes:

if_2 s. = c , ~ (G~ + C./(1 + C~ R ~ / - ca p ~

/5/

where Gk is the standard shear production term of the k equation, C3 is a model constant, R3 is the Richardson number and the term Ca p (2/k is standard. This modification is based on physical arguments and is not an outcome of derivation.

FLASHOVER PHENOMENON

The Free Boundary Conditions: The specification of the flow boundary condition at an open door or window poses special problems. A simple expedient is to expand, the computational domain into the quiescent atmosphere outside the compartment door or window. In the present study of the SNTI room fires we spread the calculation domain some 3 metres into the free surroundings. Experience has shown that carefully formulated specifications do not always guarantee convergence across a range of problem conditions. In order to secure computational stability we calculate the velocities normal to the plane of the free boundary from individual mass balances, the velocities parallel to the plane being zero. These are subsequently adjusted at each iteration to ensure an overall mass balance, Pressure is taken to be fixed at the free boundary. Other variables are given free stream values when the velocities are directed into the compartment, for example, k = e = 0, while a zero gradient condition is imposed when the flow is outwardly directed, For the thermal radiation calculations, openings to the surroundings are considered to act as cold black bodies.

The Wall Boundary Conditions: Standard wall functions are employed at the walls for the flow equations. For thermal radiation purposes a wall emissivity of 0.8 is assumed. For the steady state simulations the wall temperatures are updated presuming one dimensional heat conduction through the walls given the calculated total heat flux (convective and radiative) on the fire side from the previous iteration. For developing fires, the full solution of the transient heat conduction in the wall has proved uneconomic. Following Bagnaro et a114 a polynomial temperature profile is presumed within the material of the wall:

1321

Here Ti and To are the inside and outside wall temperatures and qtot is the calculated total heat flux. In practice, the prevailing qtot is determined using the Ti from the previous iteration, and an updated T~ is then determined with the aid of the preceding Eqs. (7) and (8) and is carried forward to the next iteration.

The Thermal Radiation Properties: Fires, especially those involving modern plastic materials, generate large quantities of smoke or soot which may significantly augment the absorption coefficient. A balance equation for soot of the general form of Eq. (1) is solved with d~ standing for the soot mass fraction, m~. Source terms Sf and Sc appear in this equation representing, respectively, the soot formation and consumption rates. The simulation of soot production has to a large extent defied modelling efforts. We use the simple kinetic expression reported in: 19

Sf = Cfpf~ (b" exp ( - Ef/RT)

(9)

where Cf is a constant which depends on the fuel type and the Richardson number, pj~ is the fuel partial pressure, ~b is the local equivalence ratio, n is a model constant, E is the activation energy, and R is the universal gas constant. This expression allows for all the known major factors influencing soot production. Two relations are able to control soot burnout rate, a kinetic one similar to Eq. (9), and another which presumes that the burnout rate is controlled by the turbulence mixing rate. Both are calculated and the lesser of the two is used. The gaseous products of combustion are highly non-gray. It is possible to solve Eq. (1) spectrally using a wide band approximation. In many predictions of furnace radiation heat transfer we have found that a pseudo-gray treatment based on the 'mixed gray gases' concept of Hottel x9 works well. This approach is retained here: n

T (x, t) = a(t) + b(t)x + c(t)x 2

(6)

~g = 2

ag,i [1 -- exp (-Kg,( Pg,i - K~,i C)L]

(10)

i=0

The penetration depth 8 is calculated and the coefficients are evaluated from the known boundary conditions for two cases: 1) ~ < wall thickness which leads to: qtot T, = To + - ~ 2 k

(7)

and 2) 8 = wall thickness which results in: dTi L dqtot . . . .

dt

3k dt

(8)

where Pg,i is the partial pressure of an absorbing and participating gas (here i = fuel, H20, or CO~), Kg,i is the absorption coefficient of the gas i, Ks,i is volumetric soot absorption coefficient per concentration unit, C is the soot concentration per unit volume, and L is the mean radiation path length which is here equal to the discretised distance ~s in each application of the recurrence relation (3) The quantitity ag.i is a temperature dependent weighting coefficient which may be viewed as prescribing the fraction of black body emissive powers within a gray radiation band for which kg,i is constant. The coefficients a~,i, Kg.i and Ks.i are those specified by

FIRE CHARACTERIZATION

1322

Truelove. 21 The pseudo-gray absorption coefficient K for use in recurrence relation (3) is extracted from: E =

1 -- e -KL

(11)

The Applications

Lawrence Livermore National Laboratory Fire Test Cell: Experiments s have been performed on the LLNL force ventilated full scale fire test cell shown in Fig. l(a). The tests were initially started at ambient conditions and conducted until steady state was achieved. We have selected test MOD8 for simulation and have confined interest to the steady state results. Useful numbers of wall and flow temperature data are reported, but the heat transfer measurements are insufficiently certain to assist the code validation exercise. We have used a grid of 14 x 13 x 12 which, although less than ideally fine, is compatible with what must be considered as an embryonic study.

(a)

240

Burner

Swedish National Testing Institute Room Fire: The room geometry, which is again full scale, is sketched in Fig. l(b) This compartment is lined with flammable test materials. The facility is particularly well instrumented and the test procedure has resulted in useful data on the flashover phenomenon. The 100 kW burner is ignited at time zero and flashover is presumed to have occurred when flames appear at the doorway. The transient computations are obviously time consuming. We have utilised a grid mesh of 20 x 13 x 10 nodes of which 5 x 13 x 10 lie outside the door in the free surroundings. Two test cases, numbered 1 and 5 in the original report 9 are considered here. In test 1 the walls were lined with insulating fibre board, while in test 5 the walls were lined with PVC wall covering on plaster board. Calculation of the flame spread over the wall coverings is an inherent difficulty in the proper simulation of these test results. We have made some exploratory studies on the modelling of flame spread. It has proved to be a demanding area in need of a concerted specialized study and one which is outside the scope of this paper. Fortunately the total compartment heat release is reported for the Swedish tests and we have approximated flame spread by adding this quantity to the burner heat input. The experimental results of test 5 showed little flame spread prior to flashover and were particularly suited to the present study, the primary purpose of which was to examine the simulation of flashover in the absence of the parallel and major influences of the separate phenomenon of flame spread.

Front View

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Dimensions in mm

(b) FIG. 1. (a) Schematic diagram of the Lawrence Livermore National Test Laboratory Fire Test Celt. (b) Swedish National Testing Institute Fire Test Room.

Results Lawrence Livermore National Laboratory Fire Tests: Panel (a) of Fig. 2 shows a comparison between the measured and predicted variations of the gas temperature in the vertical direction in the eastwest symmetry plane of the room (thermocouple rake TR1 east and TR2 west). The agreement is remarkably good. The absence of a pronounced ceiling layer is due to the fact that the results are for the steady state regime reached after prolonged op-

FLASHOVER PHENOMENON I

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(b} FIG. 2. (a) Room Temperature Distribution: LLNL Test Cell, Test MOD8. (b) Wall surface temperatures: LLNL Test Cell, Test MOD8 eration of the spray pool fire. Panel (b) compares the measured and predicted surface temperature variations for the south wall along its vertical symmetry axis, and for the ceiling along its east-west symmetry axis. Given the scatter in the test data, the agreement is reasonable. In any attempt to simulate the flashover phenomenon it is critical that the heat transfer rates to solid surfaces are correctly

predicted. Unfortunately, it is not possible to interpret the surface heat transfer data of the LLNL tests in a manner suitable for the predictive needs of the present work. The present comparisons of t e m p e r a t u r e and similar evidence of other studies2'3'4'13 indicate that reasonable predictions of a steady state fire are possible using available field model techniques.

1324

FIRE CHARACTERIZATION

Swedish National Testing Institute Room Fire Tests: Here we examine the more interesting case of transient fires for which the measurement of the time to flashover was a focal point of the observations. This time interval was defined as that required for flames to emerge from the doorway. The many different tests were distinguished by the different materials used to line the walls of the test cell and by the locations of these linings. In almost all cases, flashover is preceded by flame spread across the lining from an ignition location near the burner. Flame spread is obviously a key process in fire growth. Nonetheless, with regard to field modelling this complex process is under-researched and demanding of specialized study. The results of the SNTI test number 5 are of particular interest for our more limited present purpose: the assessment of the ability to predict the heat transfer to solid surfaces for a specified fire, a key factor in fire growth consequent of flash over. For this case the wall lining was PVC wall covering on plaster board. An early ignition near the burner quickly extinguished itself with no detectable subsequent ignition or flame spread during the first 10 minutes of the test for which the burner output was maintained at the standard value of 100 kW. At the elapsed time of 10.0 minutes the burner output was increased to 300 kW, a sudden flashover occurred at 10.1 minutes. Fig. 3 shows the development with time of the gas temperature variation with height when the experimental thermocouple rake was placed at location A, the position of which is indicated in Fig l(b), see Ref. 22 for details. The predictions and the data are in good agreement. The ceiling layer thickens' with time and grows rapidly between 10.0 and 10.1 minutes to a thickness well below the top of the doorway. Panel (b) of Fig. 4 shows a comparison between the measured and predicted heat fluxes at the sole measuring location, the centre point of the floor. The measured and predicted heat flux rise sharply at t = 10 min when the burner input is increased. The measured flux increases faster than the predicted flux due to a small amount of material ignition which is not accounted for in the simulation. Panel (a) of Fig. 4 shows the variation of the surface temperatures of the ceiling at several locations, 22 with the highest temperature being recorded for a location immediately above the burner. The agreement between the predictions and the data is reasonably good. The temperature above the burner initially rises faster than the predicted one for reasons which are not very clear. One reason would be reactions in the acumulated layer above the burner, or it could be due to ignition of surface materials at initial stages when sufficient oxygen is available.

Finally in Fig. 5 we show the predicted total heat flux (convective plus radiative) contours for the ceiling at the flashover time of 10.1 minutes. No ceiling heat transfer data is available, but these predictions are nonetheless of interest since they show that the critical heat fluxz3 of 15 kW/m 2 is attained over the most of the ceiling layer. On t h e basis of this criterion alone the prediction of the flashover is assured. We have also predicted the SNTI test number 1 for which the walls were lined with insulating fibre board. In this case there was considerable fire spread prior to flashover at a time of 1.07 minutes. As stated before we have been forced to account for this by augmenting the burner output by the measured increase in heat release. The agreement between the predictions and the measurements is similar to that for test number 5. They permit no new conclusions to be drawn and are not presented in the interest of brevity.

Concluding Remarks Field models suffer certain limitations when applied to fire problems. One results from the need to specify suitably fine finite difference grids to the extent that the cost of calculating geometrically complex building fires can be prohibitive. Another is that the field models, having for the most part been developed for combustor applications, are not sufficiently validated for the specialized circumstances of fires. Nonetheless, field models, because of the amount of detailed physics they incorporate, provide valuable insights into the mechanisms governing the behaviour of fires. The validation studies themselves, as already demonstrated by previous applications, can be very illuminating in this respect. The present study makes apparent the insufficiency of heat transfer measurements in compartment fire tests, a surprising observation in the view of the obvious importance of heat transfer to fire propagation. The need of field modellers to address the specific problem of flame spread across a combustible surface is also made evident. The available flame spread experiments have not been designed to satisfy the particular needs and conveniences of field modellers. A full self consistent and universal description of the factors controlling flashover will be possible only when a good and tested flame spread model, which properly simulates the diffusion, convection, and radiation transport processes, has been constructed and incorporated in a transient and three dimensional computational procedure to predict, say, the SNTI room fires. Flashover is a broad phenomenon which involves some other processes such as sudden i~gnition of hot unburnt gases and themal instability and further work

1325

FLASHOVER PHENOMENON i

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FIG. 3. Room temperature distribution with time: Swedish Room Test 5.

is required to describe the complete phenomenon by fundamental physical processes, The present study has nonetheless demonstrated that, for the special circumstances of the absence of a significant role of flame spread, or alternatively, when the data are used to specify the effect of flame spread as an input, the compartment aerodynamics, convection, thermal radiation heat transfer and, importantly, the time to flashover can be well predicted. Nomenclature ag,i E f g h I i, j k K L P p

weighing factor for i th band blackbody emissive power (trT 4) mixture fraction gravitational constant specific enthalpy radiation intensity tensor designates turbulence kinetic energy; thermal conductivity absorption coefficient wall thickness and path length pressure partial prerssure

S s T t u v w x, y, z

source term distance temperature time velocity in x-direction velocity in y-direction velocity in z-direction direction coordinates

Greek Symbols

F

p ~r 4)

exchange coefficient penetration depth turbulence dissipation rate viscosity density Prandtl Schmidt number; Stefan Boltzman constant dependent variable solid angle

Subscripts

c eft fu g

carbon dioxide effective fuel gas

1326

FIRE CHARACTERIZATION

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We wish to thank the United Kingdom Home Ofllce for the financial support for this study. We wish also to thank the United Kingdom Fire Research Station. and particularly Dr. G. Cox for his technical advice.

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Acknowledgments

,"/4 REFERENCES

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(b) FIG. 4. (a) Ceiling Temperatures: Swedish Room Test 5. (b) Heat Flux ( k W / m 2) to center of the floor: Swedish Room Test 5 i o t tot w qb

inside outside turbulent total water relative to d e p e n d e n t variable

FIG. 5. Predicted total heat flux (kW/m2): Swedish Room 5

1. THOMAS, P. H.: Fire Safety J. 3, 67 (1980) 2. Cox, G. riND KUMAR, S.: Comb. Sci. Tech. 52, 7 (1986). 3. Cox, G.: Proc. CSNI specialist meeting of interaction of fire and explosion with ventilation systems in nuclear facilities, CSNI Report No. 83, Los Alamos Report LA-9911-C, p 199, 1983. 4. Cox, G., KUMAR, S., AND MARKATOS, N. C.: Proc. First International Symposium on Fire safety science, p 159, Hemisphere, 1986. 5. SATOH, K., Report of Fire Research Institute of Japan 59, 45 (1985) 6. Ku, A. C., DORIA, M. L. AND LLOYD, J. R.: Sixteenth Symposium (Internatinal) on Combustion, p. 1976, The Combustion Institute, 1977. 7. MAO, C. P., FERNANDEZ-PELLO, A. C., AND HUMI'HEBEY, J. A. C.: J. Heat Transfer 106, 221 (1984). 8. ALVERAZ, N. J., FOOTE, K. L. AND PAGNI, P. J.! Comb. Sci. Tech. 39, p 55 (1984). 9. SUNDSTBOME, B.: Full Scale Fire Testing of Surface Materials, Swedish National Testing Institute, Fire Technology, Technical report SPRAPP 1986: 45, 1986. 10. LOCKWOOD, F. C.: Comb. Flame 29, 111 (1977) 11. PATANKA, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington D.C., 1980. 12. GOSMAN, A. D., LOCKWOOD, F. C., MEGAHED, I. E. A. : The prediction of the flow, reaction and heat transfer in the combustion chamber of a glass furnace, Proceedings of AIAA Aerospace Sciences Meeting, paper 80-0016, 1980 13. ABBAS, A. S., LOCKWOOD, F. C., AND SALOOJA, A. P.: Comb. Flame 58, 91 (1984) 14. BAGNARO, M., LAOUISSET, M., AND LOCKWOOD, F. C.: "Fire D y n a m i c s and H e a t transfer', Quintiere, J. editor, HTD-Vol 25, Amer. Soc. Mech. Engrs., New York, p 107, 1983. 15. LOCKWOOD, F. C., AND SALOOJA, A. P.: Comb Flame 54, 23 (1983). 16. LOCKWOOD, F. C., AND SHAH, N. G.: Eighteenth Symposium (International) on Combustion, p. 1405, The Combustion Institute, 1981. 17. Rom, W., Turbulence Models and Their Applications in Hydraulics, International Associa-

FLASHOVER P H E N O M E N O N tion for Hydraulics Research, Delft, Netherlands. 18. MARKATOSN. C., MALIN M. R., AND COX, G.: Int. J. Heat and Mass Transfer 25, 63 (1982). 19. ABBAS, A. C., AND LOCKWOOD, F. C.: J. of the Institute of Energy, p 112, Sept 1985. 20. HO'FI'EL, H. C., AND 8AROFIM, A. F., Radiative Transfer, McGraw-Hill, New York 1967.

1327

21. TRUELOVE, J., U. K. AERE Harwell Report, H L76/3448, 1976. 22. "Room Fire Tests in Full Scale for Surface Products, NORD TEST Fire test m e t h o d , Swedish National Testing Institute, Technical Report NT FIRE 025. 23. DRYSDALE, D., An Introduction to Fire Dynamics, John Wiley and Sons, Chischester, 1985.

COMMENTS A. K. Kulkarni, Pennsylvania State Univ., USA. In the problem you presented, vertical flame spread along the sidewalls of the compartment should play an important role in determining time to flashover. How did you model (or take into account) the vertical flame spread?

Author's Reply. Flame spread is a critical factor for flashover. But in the particular test we have considered, the experimental data does not indicate considerable flame spread prior to flashover. We have not considered the modelling of flame spread in the present study.

The treatment used here has been used for the prediction of various compartment fires, see for example Ref. 1. We think the combustion model used in the present study is good enough to predict the overall properties of fires. The k-~ model of turbulence has been tested for many flow situations and has proved successful in predicting flows in fires. 2'3 For the calculation of radiation properties, the mixed grey gas concept of Hottel has worked very well in various combustor applications, see for example references listed below. Velocity data were not available for the present experiments.

REFERENCES

P. Mengiic, Univ. of Kentucky, USA. Considering that the radiation heat transfer is the dominant heat transfer mechanism in fires it is natural to expect a significant effect of the soot volume fraction distribution on your predictions, Did you need to "tune" any of your parameters related to soot formation in your calculations?

Author's Reply. We have tuned the parameters of the soot model with reference to experimental data on laboratory diffusion flames.

S. Bhattacharjee, Mississippi State Univ., USA. There are so many sources of error in modeling such a complicated phenomenon as flashover. In your mathematical formulation you n e g l e c t e d finitechemistry, turbulence/radiation interaction, spectral dependence of radiation properties. Accuracy of the turbulence and soot model is also not beyond questions. On top of these there could be numerical error due to false diffusion and inaccurate realization of boundary conditions. Yet, you got such good agreement with experiments. Did you compare any velocity data?

Author's Reply. The boundary conditions we used to formulate the problem are correct and accurate.

1. GOSMAN, A. D., LOCKWOOD, F. C. AND MEGAHED, I. E. A., J. of Energy, 6, 353 (1982). 2. ABBAS, A. S., LOCKWOOD, F. C. AND SALOOJA, A. P., Comb. Flame, 58, 91 (1984).

R. G. Gann, National Bureau of Standards, USA. I find this work quite interesting. I am, however, concerned about the unusually good agreement with the data. The assumptions in the model are quite severe and, when compounded, would be fortunate to predict absolute values to within a factor of two. I assume, therefore, that there are a number of adjustable parameters that you used to obtain the agreement. Would you comment on which parameters were varied and how you selected the values?

Author's Reply. The predictions are not surprising since the tests we selected for simulations were not severely influenced by fire spread. The constants of the soot model have been tuned with reference to experimental data,19 and as stated we used the experimentally measured heat release rates 9 as input for calculations. All the other constants of the modelling are retained at those values ascertained from many validation studies of both inert an reacting flows by many workers over several years.

1328

FIRE CHARACTERIZATION present simulations are those of the experiments, which were initiated from ambient conditions.

A. M. Kanury, Oregon State Univ., USA. In one instance in your presentation, you have mentioned your "'picture" of flashover as the radiantly driven rapid growth of fire in the compartment. In another juncture you spoke of a non-spreading fire (heat source) resulting in a flashover. In a third situation you talked about a critical heat flux at the floor or ceiling as a basis for your flashover. And in yet another context, you alluded to attainment of a certain prestated critical surface temperature as a signal for the impending flashover. Can you please briefy sort these various thoughts/statements/criteria out so as to help me see what it is precisely that you have identified the flashover with? Author's Reply. The only criterion we used to determine flashover was the critical heat flux on the ceiling. The ceiling temperature development of Fig. 4(a) is presented for the comparison of predictions with experimental data. A critical temperature was not used as a flashover criterion.

H. Takeda, Univ. of Tokyo, Japan. Flashover time is strongly affected by the initial condition. How did you decide the initial condition in your calculation to compare to the experimental results? Author's Reply. The initial conditions used in the

W. Grosshandler, Washington State Univ., USA. T,he agreement between your numerical calculations and limited experimental data is commendable, and one should be reluctant to quarrel with success. Cautionary statements are warranted, however, regarding the accuracy of different elements of your numerical scheme, including the turbulence, radiation, and soot formation models, and their general applicability to room fires and flashover. A significant conclusion from your calculations should be that the eei]ing heat flux and vertical temperature profiles are, fortunately, insensitive to the sophistication of the physical models chosen for the room fire situation investigated, An inappropriate conclusion would be that the individual soot, radiation, and turbulence models have been validated by the good agreement.

Author's Reply. We agree with your cautionary comments, We hope that we have not suggested that industrial modelling elements you cite have been validated by the work of the paper. The best we can say is that this modelling is good enough, and the predictions are insensitive enough to it, for purpose of the present kind. But this is nonetheless useful and positive statement.