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2 FIRE MODELING BACKGROUND Over the past decade numerous computer-solved theoretical programs have evolved for modeling a fire in an enclosure (Figure 2-1~. The growth in activity has proceeded from the original treatment of a single chamber with a single event (Miller, 1985a), to the more recent undertaking of a multicompartment arrangement (including corridor linkage) for a single-story structure (Jones, 1 985), to FIGURE: 2-1. Schematic of the fire processes in a room. Sourec: Quintiere, 1988. efforts at treating a multicompartment, multistory structure. Very little of this effort is aimed at mass transit vehicles and none at such specific problems as fire in mass transit vehicles in a lengthy TRANSFER ~ \~7 tA ~ MIXING I RADIATION ~ _ TURBULENT' MIXING ~ ~ ~ . - ~ - ~ ,~ ~ , AO '~ ~ aim ,~oO\)G~< : >?) ~ ;' ~ -' ...... .r~ ... , _ .~;7' P. ~ _ ~ AIR _ FUEL 'A LOW SPEED BUOYANT FLOWS 11

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12 tunnel. Virtually all of the modeling is aimed at compartments whose length, width, and height are comparable, so that an essentially two-dimensional point of view suffices. However, the great length of a typical transit vehicle car (relative to its width and/or height) introduces important ~three-dimensional" aspects to the thickening of a ceiling contiguous layer comprised of hot vitiated air, unburned combustible vapors, and sooty smoke. Because of the absence of immediate applicability to the mass transit vehicles of interest' and because many recent reviews have been undertaken elsewhere (Quintiere, 1984; Bukowski, 1985; Mitler, 1985b), attention here is concentrated on a nonexhaustive critique of these models. The mathematical fire models are of a number of types requiring different levels of computer capability for the solutions of equations. The deterministic types include field models that divide space into small elements and require greater computational resources to solve the pertinent partial differential equations for the flow of hot buoyant gases derived from the burning of fuels. Zone models, which require less computer resources, divide the space into conceptual zones or control volumes (e.g., upper layer, lower layer, plume or several plumes). The presumption is adopted that within a given zone the temperature, gas composition, smoke concentration, etc., are relatively uniform spatially, but vary with time (Bu~nick and Walton, 1986; Quintiere, 1988~. The generic scenario (Lyons, 1985) is an unwanted ignition within an enclosure that leads to a fire-sustained, turbulent, entraining buoyant plume (Figure 2-2~. This plume transports masse momentum, ant! energy from a lower layer of coo! ambient air to an upper well-mixed (homogeneous) layer of hot, gaseous, sooty fluid. The hot upper layer and plume convey FIGURE 2-2. Conceptualisation of a two layer cone model. Source: Lyons, 1986. heat by radiative transfer to maintain pyrolysis of the already-burning objects and to warm other objects that may be raised to their (prespecified) ignition temperatures. Actually only flat objects (as ZONE-TYPE COMPUTER MODELS -'.':'.,,:.~.'`~2.~.~' I.'' '"'a ~ ; . ~ ;: ..'. UiiER HEATED LAYER , ~ - , ,. I , . ` . ,.; , , ., ~~' ~'2:'2~'';~ ~.e', .'.' .:,: LOWER COOLER LAYER G;:2 ' r I'. ..r it-]

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13 to opposed to vertically distributed objects) are treated satisfactorily. There is also heat transfer by convection and radiation to the ceiling and to the upper walls exposed to the hot upper layer. Despite these losses from the upper layer, it is conceivable that the hot homogeneous contents of the upper layer could ignite, owing to coexistence of oxygen and some unburned fuel vapor. But this consideration is not usually regarded in existing models; rather, a key output is the prediction of the time to ignition of easily ignitable objects on the floor such that multiple plumes arise in the compartment. In the presence of multiple plumes, the height of the interface between the upper and lower layers (another key output of the model) decreases more rapidly in time, and there is enhanced low-level entrainment into the buoyant columns. In flashover, the height of the interface decreases very rapidly to near the floor. Any occupants would be immersed in hot, oxygen-depleted, smoky gases. Escape of occupants after flashover would be an exceptional occurrence. The discussion to this point has ignored the role of forced ventilation and of open windows and/or doors, which may introduce coo} ambient air into the room. More explicitly, once the thickness of the ceiling layer increases to the extent that the interface (or thermocline) between the upper and lower layers lies below the top of a vent in a wall, influx/efflux occurs owing to cross-vent pressure differential. Some exchange between exiting and entering streams also occurs, such that some vitiated air is drawn into the cool lower layer. The solution is largely invariant of the position of the fire plume within the room. It is hardly surprising that, within the broad latitude of the fire event, quite divergent results would be collected from several different experimental apparatuses realizing the event. Furthermore, only spatially averaged information from measurements can be used for comparisons with the output from the computer models for purposes of experimental validation. FIELD-T=E MODELS While a zonal mode! might be pressed into service to discern the time to activation of a fire sensor or of a fire suppression system (e.g., sprinklers), there is motivation to consider so-called field-type models that undertake description of fire spread, smoke transport, convective-column properties, and so forth via a more spatially refined treatment. In practice the alternative to the zonal mode! (which essentially requires that properties of the fire be specified input) is taken to be the solution of coupled nonlinear partial differential equations for conservation of mass, momentum, and energy on a refined mesh (Baum and Rehm, 1984; Ku et al., 1976; Hwang et al., 1976; Yang et al., 19841. While frequent lip service is paid to the possibility of an undertaking of a level of sophistication intermediate to zonal and field models, limited intermediate effort seems to be under way. Special- purpose, often field-type, models have been developed to be used (within or as a comple- ment to a zonal approach) to calculate, for example, the thermal field in the ceiling, but field-type models might also be used to describe the rate of efflux of combustible vapor from a charring solid under a specified radiative flux.

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14 to LIMITATIONS OF PRESENT COMPUTER MODELING OF FIRES It should be emphasized that even the relatively advanced, single-compartment models are rather crude. They require, as input, quantities that would be outputs from more fundamental treatments. Among such quantities are flame temperature, flame geometry, flame spreading, the ignition process, the fraction of chemically-released heat that appears as radiation, the efficiency of burning (what fraction of pyrolyzed vapor is burned, and, of that fraction what amount of carbon monoxide [CO] relative to carbon dioxide is formed), etc. Other phenomena (e.g., ~hidden" fires within walls and breakage of windows under heating of interior gases) are not included at all. As a consequence, there is little in the way of unanticipated output from these models and more in the way of some quantification within rather preset behavior. In particular, in the absence of detailed chemical kinetics' any yield of toxicants would have to be specified as a predetermined, perhaps time-varying' fraction of the mass of fuel burned. In fact, usually not even this minimum is attempted for any toxicant except CO, and in general the level of CO is particularly poorly predicted by the models (Miller, 1985b). If a candidate theoretical model in the form of a computer code yields any intuitively plausible results, the temptation exists to extend some credibility to other results produced by the code. Often formulation of essential physical processes is compromised because subgridscale phenomena (e.g., turbulent and radiative transfer and smoke production) can be simulated only by adopting parameterizations in terms of gridscale variables. Adequate parameterization may not exist for a given subgridscale phenomenon or may not be known even if it does exist. Typically, the adopted parameterizations are adjusted by the cocle developer or user unfit the computer results are consistent either with the developer's intuitive expectations and/or with experimental data from a limited range of parametric assignments. But such practices amount to mere curve-fitting unless the parameterizations are then held invariant and the code is demonstrated to yield experimentally verified results over a substantially broader range of parameter assignments. Finally, quantification of even gridscale phenomena may be highly approximate (possibly with uncertain error) because of inaccurate input of thermodynamic and/or physicochemical Properties (e.g., of materials comprising the vehicle) and also owing to the complicated character of a mathematical statement of the physics (e.g., three-dimensional flow may be idealized as two-dimensional ~QW, more for reasons of convenience than for reasons of demonstrable justification). To reiterate, most models (e.g., Emmons, 1978) of fires in enclosures seek to estimate only certain features, such as the height of the ceiling layer or the time from ignition to flashover. The production and dispersion of toxicants and smoke often entail chemical details about trace levels of gas species and particulates, details that typically are not undertaken in existing computer models. Thus, existing models of fires in enclosures usually do not attempt to describe the presence of toxicants, other than a limited attempt to characterize CO concentration in the ceiling layer. The increased detail (e.g., of a field-type model) does not necessarily imply increased accuracy, especially since the thermochemical properties of so many materials are so poorly known or documented (Rockett, 1984~. There is no way to establish credibility for one code simply by comparing its output with that of another (perhaps more detailed) code. Consistency establishes nothing more than effective equivalence of two approximation and solution procedures for the particular cases examined. Validation requires comparison of the output of a mode! against the results of a physical experiment or (probably with less complete information) an unplanned accidental fire.

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15 Despite what might appear to be rather severe limitations, proliferation of modeling methodologies, using the parameters of ignition, flame spread, heat release rate, mass burning rate and transport of combustion products, have led to increased application of fire modeling in the assessment of fire hazards. CONCLUSION Fire growth models exist that, although not perfect ire all respects, are perhaps satisfactory for the purpose of estimating the rate of temperature increase, the development of visual obscuration, and the concentration of combustion products as a function of time for a fire scenario. The models may thus be used to provide input for hazard assessment in characterizing the fire safety implications of alternative designs or of changes in materials used. REFERENCES Baum, H. R. and R. G. Rehm. 1984. "Calculation of Three Dimensional Buoyant Plumes in Enclosures." Combustion Science and Technology, Vol. 40, pp. 55-77. Bu~nick, E. K. and W. D. Walton. 1986. "Computer Fire Models, Fire Protection Handbook, 16th Ed., Section 21, Chapter 4, pp. 21-25through 21-30, National Fire Protection Association, Quincy, MA. Bukowski, R. W. 1985. "The Application of Models to the Assessment of Fire Hazard from Consumer Products, Report NBSTR 85-3219. Center for Fire Research, National Institute of Standards and Technology, Gaithersburg, MD. Em mans, H. W. 1978. "The Prediction of Fires in Buildings," Seventeenth SYmDosium (International) on Combustion, Combustion Institute, Pittsburgh, PA, pp. 1101-1111. Hwang, C. C., R. F. Chaiken, I. M. Singer ant! N. H. Chi. 1976. Reverse Stratified Flow in Duct Fires: A Two-dimensional Approach," Sixteenth SYmDosium {Inernationall on Combustion, Combustion Institute, Pittsburgh, PA, pp. 1385-139S. Jones, W. W. 1985. HA Multicompartment Mode! for the Spread of Fire, Smoke and Toxic Gases, Fire Safetv Journal, Vol. 9, pp. 55-79. Ku, A. C., M. L. Doria and I. R. Lloyd. 1976. "Numerical Modeling of Unsteady Buoyant Flows Generated by Fire in a Corridor, Sixteenth Svmoosium (international) on Combustion, Combustion Institute, Pittsburgh, PA' pp. 1373-1384. Lyons, ]. W. 1985. Fire, Scientific American Library, New York, NY. Mitler, H. E. 1985a. "The Harvard Fire Modem, Fire Safety Journal, Vol. 9, pp. 7-16. Mitler, H. E. l985b. Comparison of Several Compartment Fire Models: An Interim Report,. NMSIR 85-3233, Center for Fire Research, National Institute of Standards and Technology, Gaithersburg, MD.

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16 Quintiere, J. 1984. "A Perspective on Compartment Fire Growth, Com Technologv, Yol. 39, pp. 1 1-54. Quintiere, J. l9SX. "Analytic Methods for Firesafety Design, pp. 333-352. Rockett, J. A. 1984. "Data for Room Fire Models, Com Vol. 40, pp. 137-151. On Technologv, Vol. 24 ustion Science Tech nolnov Yang, K. T., I. R. Lloyd, A. M. Kanury, and K. Satok. 1984. "Modeling of Turbulent Buoyant Flows in Aircraft Cabins, Combustion Science and TechnoloeY, Vol. 39, pp. 107-118.