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3 STATUS OF FIRE HAZARD MODELS AND TEST METHODS I NTRODUCTION A fire hazard model permits calculation of the time available for escape for a given occupant under a given set of conditions. The first step is to specify a detailed fire scenario, which can be selected as a "worst case," a "most probable case," or a combination of the two. A major class of fire scenarios consists of fires that continue to burn, with or without growth, beyond the point where lethal concentrations of fire products (the products of both combustion and pyrolysis) reach occupant locations and escape paths. For escape to be possible, a fire must be detected. Eventually, the escape path will be blocked (by obscuring of vision, by irritants, by toxicants, or by heat). The interval between detection and blockage of escape is the time available for escape (TAE). If TAE is greater than the time needed for escape (TNE), the occupant can escape. A hazard model of such a fire must calculate several entities: the time at which the fire is detected, the fire size and distribution of fire products at that time, the postdetection TAE, and the postdetection THE. The toxicity of the fire products influences mainly the TAE. TAE cannot be calculated until the fire condition at detection is established. For this category of scenarios, TAE might or might not be strongly influenced by the toxicity of the fire products. For example, if the fire is growing and the escape path is effectively blocked because vision is obscured well before lethal conditions are reached at the occupant location or in the escape path, the occupant 45

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46 might live only an additional minute or two if the LC50 is increased by substitution of materials. In this example, TAE depends on the obscuring of vision by fire products, but not on their degree of toxicity. If loss of visibility (or the presence of irritants) in the escape path is not crucial, the LC50 becomes important. For example, the occupant is trapped, and toxic products are building up around him or her; after 10 min. the rescuing firefighter arrives through the window. Or the occupant is willing to grope his or her way through the escape path, in spite of lack of visibil- ity. In such cases, the greater the LC50, the larger the TAE. However, the dependence of TAE on LC50 is less than linear, even for a steady fire, as shown in Chapter 2. For a rapidly growing fire, a doubling of LC50 might increase TAE by only 10 or 20~. For each specific case, a mathematical model must be run to determine the degree of benefit. Of course, some fire scenarios include an extremely rapidly growing fire, perhaps involving flammable liquids, in which TAE is much less than TNE. In such a case, the LC50 is irrelevant to the result. The modeling of such fires will not be considered further here. DETECTION MODELS Assume that a ceiling-mounted detector is a known distance from an initially small, growing fire. In principle, a model can calculate the size of the fire at the time the detector is activated.9 7 2 The effects of walls, doorways, corridors, etc., on the detector response introduce complications. For the simplest case, one may assume a very large, flat-ceilinged room that contains both the fire and the detector. An algorithm has been worked out for this case and presented as a family of curves; 3t it could easily be computerized. The critical fire size (the size when the detector goes off) depends on the following variables: Ceiling height above fire. Distance from fire to detector. Rate of fire growth. Characteristics of detector.

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~7 . assumed). Characteristics of smoke (if a smoke detector is Either a smoke detector (more sensitive) or a heat detector (less prone to false alarm) might be used. To illustrate the magnitudes involved, assume that the ceiling is 10 ft (3 m) above the fire and that a smoke- detector is 20 ft (6.1 m) from the fire axis. Assume that the fire is following a parabolic (t2) growth law, reaching 1 MW in 10 min. that the combustible material produces a type of smoke easily detectable by the detector used, and that the detector is designed to have very little resistance to smoke entry. The design curves then indicate that the detector should respond when the fire reaches about 100 kW. If, instead, the fire is assumed to grow 4 times as rapidly (still following a t2 law), the detector will not respond until the fire is twice as large (200 kW). If it is assumed that the fire grows at the original rate, but that the combustible material produces a less easily detectable type of smoke and that the detector is designed with substantial resistance to smoke entry, then the detector might not respond until ~ he F ; r" ; c ==v ~ times as larae (500 kW). This would occur 3.9 min after it reaches 100 kW. In the original case, if the detector were 40 ft (12.2 m) away from the fire axis, instead of 20 ft (6.1 m), the fire size at detection would be nearly 3 times as great, and detection would occur 2.2 min later. At., .. = _ _ ~ , _ ~ ~ , ~ ~ , ~ If one assumes that a heat detector of known character- istics is used, instead of a smoke detector, similar cal- culations could be performed; the fire size at detection would be substantially greater, and detection would occur several minutes later. The foregoing method of calculation is based on a very large compartment. If the fire compartment is small and the detector is in the fire compartment bather than in an adjacent compartment), response will occur much sooner and while the fire is much smaller. However, the calcula- tion is complicated, because the prefire condition of the compartment will generally involve a vertical temperature gradient, i.e., the temperature will be higher near the ceiling than near the floor. Accordingly, if the fire is small and produces only a weak plume with insufficient buoyancy, the smoke will tend to stratify somewhere below the ceiling (and below the detector). Of the published

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48 modeling approaches, only the very complex n field model" can deal with this. However, for a small room with an 8-ft (2.4-m) ceiling, a rule of thumb is that, once the fire is larger than a few kilowatts, the plume will be tall enough to reach the ceiling, spread out under it, reach the detector, and activate it within a minute or so. If the detector is in an adjacent compartment, a com- puterized fire model (see the next section) is used. It should calculate the accumulation of hot fire products under the ceiling, the loss of heat from these products to the ceiling, the deepening of the hot layer to below the top of the doorway that leads to the adjacent compart- ment, the mixing and dilution of the hot gases as they flow through the doorway, and the eventual filling of the adjacent compartment. Of course, detection might be by a person, rather than by a device. Any of the five senses can be involved. The location of the person relative to the fire is crucial. For safety purposes, it is common to assume a "credible worst case"--that the people are at a remote part of the structure, relative to the fire. The key element would be the time it takes smoke to move through the building. The modeling of this case is discussed later. MODELS FOR T IME AVAILABLE FOR ESCAPE THE HARVARD MODEL_ The Harvard fire computer code has several variants, two of which, Mark 5.3 and Mark 6 r are discussed here. Mark 5.3 treats one compartment with openings, and Mark 6 treats up to five interconnected compartments, all on one level. Even the simplest version involves some 50 variables and requires a computer larger than the largest microcomputers available in 1984. A standard run on a VAX 11/780 computer takes about 1.5 min of CPU time with the Mark 5.3 version and perhaps 15 min with the Mark 6 version. The necessary inputs consist of routine and nonroutine items. The routine items include dimensions of compart- ments and their openings, whatever forced-ventilation flow is present, thermophysical properties of ceilings

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49 and walls, locations and characteristics of detectors, and locations and ignition characteristics of combustible items present but not originally ignited. The nonroutine items are related to the assumed fire. The model can accommodate either a steady or a growing fire. The modeler must specify the size or growth rate of the fire, in the absence of radiative feedback from the compartment to the burning object. The modeler must also specify the sensitivity of the burning rate to radiative feedback. (The model computes the resulting burning rate). Other needed items are burning efficiency, fraction of energy that leaves the flame as radiation, fuel-air stoichio- metry, and mass fraction of carbon monoxide (CO), smoke, or other important species in the fire products. These nonroutine items, often difficult to obtain, are discussed later. The model combines the inputs with a number of built-in simplifying assumptions and then calculates the history of the fire. One assumption is that each compartment divides into a hot upper zone and a cold lower zone, each uniform (but changing with time) in temperature and composition. Mixing across the horizontal interface between zones is assumed not to take place, except by fire plumes. A second assumption is that each fire plume entrains air in a standard fashion according to a formula that takes no cognizance of small fluid-mechanical disturbances (e.g., eddies and turbulence), which can have substantial effects on entrainment rate. In summary, the fluid-mechanical aspects of the fire are approximated rather roughly. The outputs of the model consist of a number of time- dependent quantities, including the rate of deepening of the hot layer in the compartment, the ignition time of objects after the first object, the rate of gas flow out of the compartment, and the concentration of species in the outflowing gas. Mark 5.3 has been compared with data from several full-scale fire tests, with fairly good agreement for hot-layer temperature, layer height, and gas outflow rate.) 4 7 However, ability to predict CO and optical density is often limited by inadequacies in input data. As for Mark 6 (multiple compartments), no comparison with fire test data has yet been published.

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50 Attempts are now being made to improve the Harvard 5.3 model to consider additional effects: radiant heating of the floor, ceiling venting, ignition of the not layer, mixing between layers, wall burning, ceiling burning, and horizontal spread of a hot gas front in a corridor. OTHER IWO-LAYER MODELS The FAST modeling considers essentially the same physical elements as the Harvard model, but formulates equations with a mathematical technique that is claimed to give considerably faster and more "rugged" or "robust" solutions--e.g., those with a lower tendency to give grossly wrong answers or to fail to run to completion--for a wide range of input parameters. Some successful comparisons with data on upper-layer temperatures and interface heights have been made. The ASET model56 is a considerably simplified version of a computer code with many of the same basic features as the codes mentioned above, but requiring less user skill and computer capacity. It is usable only for a single closed compartment with leakage near the floor. It ignores radiative feedback to the burning object and does not accommodate the ignition of more than one object. It allows for energy loss from the hot layer to the compartment in an ad hoc manner. With these restrictions, it computes the time available before the smoke layer deepens to reach the occupant, if burning rate is known. Zukoski and Kubota2 3 3 have developed a model limited to two interconnected compartments, of possibly different ceiling heights and exterior openings, with a specified fire in one compartment. It emphasizes the fluid- mechanical aspects of gas motions. Tanaka, 2 ~ 5 of the Japanese Building Research Institute. has developed a two-layer computer model similar in many ways to those noted above, but differing in that it can be applied to tall buildings with many compartments. , ~ . _ An example Involving bu rooms in a 10-story building has been worked out. There is no forced ventilation, and windows are assumed to be open throughout, which is unrealistic. Wind velocity can be an input. Tanaka stated that the weakest element of his model is the method of calculating gas transport in vertical shafts.

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51 The model gives results for tall buildings that seem reasonable, but has never been compared with multistory- building fire test data. The Dayton Aircraft Cabin Fire model (DACFIR) was developed by MacArthur and Myers specifically for fires in wide-body and standard-width aircraft cabins. This two-layer model accommodates cabin openings and forced ventilation. The flame-spread feature is more detailed than in the other models; the horizontal and vertical surfaces of each seat are divided into 6-in. (15-cm) squares. Each square can undergo transitions from virgin to smoldering to flaming to charred, depending on the instantaneous value of the imposed heat flux. The model handles creeping flame spread if the creeping rate is an input. It may be instructed to produce different toxic gas or smoke concentrations from the smoldering elements and the flaming elements. The model has been compared with a series of seven full-size aircraft cabin test fires. It did not do well at predicting areas of fire spread. It predicted toxic gas concentrations in the hot layer (CO, hydrogen cyanide, hydrogen chloride, and hydrogen fluoride) that were generally accurate to within an order of magnitude, but the prediction of time of first appearance of these gases at potentially toxic concentrations was not accurate. The model was also deficient in predicting hot-layer temperatures at the end of the cabin away from the fire. FIELD. MODELS The models discussed above are all two-layer zone models. Research is also being done on field models, which, instead of dividing a compartment into two uniform zones, divide it into hundreds or even thousands of zones in a three-dimensional array. Such models can predict fluid motions far more realistically, but, needless to say, require extremely powerful computers and do not yet appear to be practical for routine hazard analysis. Two recent examples of field-model studies are those of Cox et al.59 and Baum and Rehm. 2 9

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52 EXAMPLE CALCULATIONS FOR MODEL FOR TAE - Fowell~ 2 has used the FAST model to calculate fire development in an apartment in which a loveseat in the living room is assumed to be burning. The burning rate of the loveseat was determined from a measurement in the NBS Furniture Calorimeter. 2 6 The living room is open to a hall 9 m (29.5 ft) long, which in turn is open to an occupied bedroom. Assume that the fire is detected by a smoke detector in the hall and that the occupants must then escape through the hall or be overcome. The model inputs were the following: dimensions of rooms and openings, thermal properties of ceiling and walls, burning rate of the loveseat (grams per second), heat of combustion (18.1 kJ/g), smoke yield (0.03 g/g), and LC50 (32 mg/L). The sequence of calculated events was as follows: Event -40 s Calculation is started (small fire) 0 s Fire actuates smoke detector in hall +73 s Upper temperature in living room is untenable (183C) +91 s Visibility is lost in hall (smoke 1 m--3.3 ft-- above floor) +100 s Upper temperature in hall is untenable (183C) +133 s Lethal concentration is reached in hall +153 s Lethal concentration is reached in bedroom +166 s Upper temperature in bedroom is untenable (183C); fire still developing rapidly For this scenario, the model predicts that the bedroom occupants had 91 s to escape before visibility was lost in the hall and an additional 9 s during which they could grope their way through the hall before the temperature became intolerable. If they failed to escape in this period, but remained in the bedroom, they would be overcome by toxicants 53 s later or by heat 66 s later. (This assumes an instantaneous effect on the victim when the LC50 concentration is reached, whereas a more sophisticated treatment would use the integrated product of concentration and time and would require information on time to loss of consciousness, which, in the case of humans, is not documented.)

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53 Consider the sensitivity of TAE to LC50, assumed to be 32 mg/L. If LC50 were reduced to 16 mg/L (doubled toxicity), the loss of visibility and excessive tempera- ture in the hall would occur at the same times as before, and lethal concentration in the hall would still not be reached at these times, so escape would be unaffected. However, if the occupants had remained in the bedroom., they would now be exposed to lethal concentrations or higher for perhaps 40 s (instead of 13 s) before being overcome by heat. This conceivably would be important only if the occupants were assumed to be rescued--say, by a firefighter who enters through the bedroom window-- between 126 and 153 s after detector actuation. However, if the postulated rescuer arrived sooner or later than that narrow interval, the results would be essentially unaffected by the reduction in LC50. If the LC50 were reduced by a factor of 10, instead of by a factor of 2, lethal conditions would be predicted to occur in the hallway before loss of visibility, and TAE would be reduced from 91 s (based on visibility) to only 20 s (based on instantaneous incapacitation when a concen- tration of 3.2 mg/L is reached). This modeled scenario could also be explored for combustible sensitivity to other properties of the material, namely, burning rate, heat of combustion, and smoke yield. Clearly, each can affect TAE. In par- ticular, the relative order in which smoke, heat, and toxicants reach critical points will change. This example illustrates the possibilities of using a model to explore the sensitivity of TAE to all the relevant properties of the combustible material, not only the LC50. Obviously, it depends heavily on the scenario; under some realistic conditions, it might be very insensitive to LC50. In general, smoke toxicity has a relatively small impact on TAE when the fire (and hence the rate of smoke production) is growing rapidly. In such scenarios, the biggest incremental changes in TAE are caused by manipulating the flame spread rate and the heat of vaporization. When the burning rate (and hence the rate of smoke production) is constant, the impact of toxicity and the impact of burning rate on TAE are the same; e.g., doubling one has the same effect as doubling the other. When TAE is controlled by the buildup of smoke, however, the effect of either is less than one might intuitively expect; e.g., doubling the smoke

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54 toxicity does not reduce TAE by 50%, but only by about 30~. Most real fires are characterized by a period of growth followed by a period of relatively constant burning, once the fuel or air supply reaches its limiting value; so calculating TAE in practice must take account of both phases. MODELS FOR TIME NEEDED FOR ESCAPE Once a fire is detected, the time needed for escape is controlled by a combination of psychologic, physiologic, and physical factors. Some models, such as EVACNET+,1 21 deal with physical factors--specifically, the escape paths available, the time needed to traverse each path, the flow capacity of each path, and the initial locations of the occupants. If these inputs are available for a large building with many occupants and multiple escape paths, the computer program can calculate the evacuation status as a function of time. ~ ~ _ However, it is widely recognized that a variety of psychologic and physiologic factors are at least as important as the physical factors represented in models like EVACNET+. For example, response to alarm signals, decision-making, behavioral patterns, male-female dif- ferences, physical capability, knowledge of escape routes, experience with fire, effects of reduced visibility, and panic behavior are important. Stahl has developed BFIRES-II, a behavior-based computer simulation of emer- gency egress during fires. Human behavior during fires has been reviewed by Paulsen 7 4 and by Paul. 7 3 Although chemical components of fire products might influence decision-making or physical ability to escape, no escape models deal with this possibility, presumably because the available data are inadequate. Available TNE models do not use LC50 or other toxicity-related data, so they are not discussed in detail here. However, even a crude estimate of TNE, which might not require a com- puter model, could be sufficient to show whether, in a given scenario, TAE is of the same magnitude as TNE or one is much larger than the other. This comparison will often be enough to show how sensitive the hazard potential of the scenario is to TAE.

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55 TEST METHODS FOR MODEL INPUT DATA BURNING RATE Fire-product calorimeters built at the Factory Mutual Research Corporation, 9 5 at the National Bureau of Standards, 2 S at the University of California, Berkeley, 7 and elsewhere can measure the instantaneous rate of heat release of a fire up to 10 MW in intensity. The principle is to collect the product gases with excess air, to mix them, and to measure their flow rate and instantaneous composition. From the degree of oxygen deficiency or from the total composition, one can calculate the rate of energy release. Simultaneously, the mass loss is mea- sured. When the rate of energy release is divided by the rate of mass loss, the quotient is the heat of combustion per unit mass. (If the combustible material were a pure material that burned completely, the heat of combustion could be obtained from a handbook, but most real com- bustible materials are composites, burn incompletely, or both.) One way of using such a calorimeter (essentially an instrumented fume hood) is to place it above an item to be "realistically" ignited and burned, such as a bed or a sofa. Another way is to start a test fire in a suitably furnished "burn room" with an opening and to collect the fire products as they emerge from the opening. Much useful information for fire models has been obtained with such large calorimeters. But it is a rather expensive way to obtain data, so small-scale tests are highly desirable. Small-scale fire tests are numerous and have been described frequently.98 ~ 6 3 igo Each gives some information on the flammability of the item tested, as each blind man who touches a portion of an elephant obtains some idea of what an elephant is like. However, no standard small-scale tests or any known combination of them is adequate for predicting the full-scale burning rate of an item made from the tested material. One exception to this generalization would be a noncharring combustible material uniformly ignited over a single horizontal surface, for example, a dish of heptane 1 m across or a horizontal slab of polymethyl methacrylate 1.5 m square. In such a case, if one measures the burning

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56 per unit area of a small-scale version--say, 10 cm across--one finds that the burning rate is only 55% (heptane) or 40% (polymethyl methacrylate) or the full- size burning rate.2~9 However, by applying an empirically arrived at radiant heat flux of around 50 kW/m2 to the small-scale sample or by burning the small-scale sample in an atmosphere artificially enriched in oxygen, one can make the small-scale sample burn at about the same rate as the full-scale sample. Then, by using the same small-scale test conditions for other noncharring horizontal materials, one can predict full- scale burning rates. This empirical procedure seems to work reasonably well for a number of materials. Research is in progress to develop such a procedure involving flame radiation characteristics of the combustible material. And means of treating char-forming combustible materials are being studied. Turning from a horizontal to a vertical orientation of the combustible material (for example, a fire-retarded plywood wall), prediction of burning rate, or indeed of whether a fire will propagate or die out, is not yet possible with small-scale tests. The small-scale test that provides the best hope of being useful, when combined with other information, is a rate-of-heat-release test. In this test, a small sample is allowed to burn while being irradiated by an external heater at a specified flux, and burning rate vs. time is measured. Many com- monly used household materials char. The burning rate rises rapidly to a maximum and then Gradually decreases as the char builds up. Toward the end of the test, the burning rate might increase again, because by that time the sample has heated through. One difficulty is in translating a complex curve like this into a single useful number. A second problem is that, in a real fire spreading upward, the largely radiative flux intensity from the burning plume is the input to the not-yet- ignited material just above the burning region. The rate-of-heat-release test gives no measure of the radiative output of the flame, which varies from material to material. No standard test method measures this radiative flux. Finally, no established theory can combine such data into a prediction of whether and how fast the flame will spread. Nonetheless, the rate-of-heat-release data give the best available indication of flammability. ASTM Test

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S7 E906~ 4 has recently been established as a method to measure rate of heat release. Other, more sophisticated small-scale test methods developed by Tewarson et al.2~8 and by Babrauskas25 permit more accurate measurements of rate of heat release, as well as rate of production of smoke and other species of interest. The same methods can be used to measure ignitability under radiative exposure. If a building fire is confined to a single compartment, the fire can be controlled through ventilation, and the burning rate can be estimated from a knowledge of the size of the ventilation opening and the fuel-air stoichio- metry. A model can then be used to predict fire-product movement through the building without further concern with rate of heat release. RATE OF PRODUCTION OF SMOKE AND TOXICANTS As a minimum, the various models require as inputs the burning rate (grams per second) and the heat of combus- tion, which are obtained or estimated as discussed in the previous section. The gross toxic effect of the mixture of products from a gram of burned material, diluted to a given volume, can be determined in animal exposure tests. However, the fire models can predict local concentrations of any species of interest, such as CO or hydrogen chlor- ide (HC1), if test methods can provide the needed inputs, specifically grams of the species of interest yielded per gram of burned material. Some species initially formed in the fire undergo change as the fire products move through the building. For example, soot particles can agglomerate via Brownian motion over time. HC1 can be adsorbed on the walls of ducts or corridors, and acid mist can settle to the floor. Such processes could in principle be included in the computer model, but initial yields must be known. The fire-product calorimeters previously mentioned for measuring burning rate25 7 8 9 5 are easily adaptable for handling any measurable constituent of the fire products. The techniques for these measurements are well known and will not be reviewed here. For each species to be mea- sured, an additional element of cost and complexity is introduced into the fire-product calorimetry procedure;

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58 therefore, unless there is a specific need, the data taken are often limited to an indication of the smoke density by optical transmission through the products and CO and carbon dioxide (CO2) measurements by infrared absorption. The small-scale rate-of-heat-release apparatuses25 2 ~ ~ are also easily adaptable to such measurements. However, the results are very sensitive to ventilation conditions. For example, the molar CO:CO2 ratio in the products of well-ventilated flaming combustion is around 0.002:1 for wood, 0.04:1 for rigid polyurethane foam, and 0.18:1 for benzene.8 3 If the same materials are burned with restricted air flow around the samples, the CO: CO2 ratio can increase progressively toward unity in each case. At the same time, smoke production increases. However, no standard procedure for reducing air supply to the sample nas yet been developed that gives results matching those from a realistic underventilated fire in a room. TOXICITY DATA This subject is reviewed in Chapter 5 and will not be discussed here. One should note, however, that it is widely believed that the lethal condition is expressed more realistically as an integral of concentration and time of exposure than simply as concentration. Models ~ - - ~ ~ Lethality data in concentration-time units are available on CO, as well as on the combined effects of CO and other pure gases, but can be modified to accept such inputs. no standard test method is available for obtaining such data on the fire products of a given composite substance. IGNITABILITY In many fire scenarios, the original ignition is a "given," and the task of a model is to describe the history of the fire after ignition. For example, smoking materials are improperly discarded in a wastebasket, or there is a stove-top accident in the kitchen, or lightning strikes. In each case, a model can assume that a small localized fire appears at time zero and then calculate the development (if any) of the fire. Ignitability of a combustible material exposed to the existing fire can be crucial. This exposure is usually either by direct flame-

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59 gas impingement or by radiation. In some scenarios, whether ignition occurs can be crucial. For example, a burning cigarette abandoned on upholstered furniture might or might not ignite the furniture. Inasmuch as materials can be chemically modified to make them more resistant to ignition (e.g., by introducing halogens) while increasing the toxicity of the smoke produced when they do burn, a model can in principle provide quanti- tative information on the tradeoff involved. Numerous methods can determine ignitability as a function of heat flux, time of exposure, and sample size and orientation, for both radiative and flame-impingement exposures. The small-scale rate-of-heat-release methods previously mentioned25 2~8 have also been used to measure ignitability in cases of radiative exposure. Ignitability of flammable fabric is measured by a standard test involving a 3-s exposure to a small flame.9~ The Setchkin furnace98 is standardized as ASTM Test D-1929, which measures the furnace temperature at which a small sample will just ignite in an airstream. Either spontane- ous ignition or "piloted" ignition from a small pilot flame can be studied. Test methods have been standardized for specific situations, for example, to determine the resistance of upholstered furniture to ignition by cigarettes. 3 3 Although great masses of data exist on ignitability of various materials by various methods, there is no central source of this information. Furthermore, because material thickness and orientation affect ignitability and an enor- mous variety of materials and combinations of materials are in use, a modeler cannot expect always to be able to consult a reference source for the needed properties. Rather, specific ignition tests might have to be made, if ignitability must be known. SUMMARY A number of available two-layer models represent at least crudely all the physical processes that occur in a fire in a structure. They require such data as burning rate, ventilation, thermophysical properties of and chairs, and critical concentrations of fire that will prevent escape or be lethal. TAE can culated, and the effect on TAE of LCso, burning ceilings products be cal- rates,

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60 compartment sizes, ventilation opening sizes, etc., can be readily explored. The calculated TAE cannot be expected to predict results in an actual fire accurately, for the various reasons cited above, but the relative influences of the various parameters should be more or less correct. None of the available two-layer models can treat the filling of a long corridor with combustion products realistically. Research is being done on this problem. Clearly, the time required to reach a given condition at a given location remote from the fire varies inversely with the burning rate, but, if the flow is buoyancy- driven, this dependence can be expected to be nonlinear. Heskestad9 6 has suggested that the time required to reach a given condition varied inversely with the cube root of the burning rate. No model has attempted to combine the buoyant flow of fire gases in a tall building with all the other factors known to influence air circulation--forced ventilation, the effect of external wind, and the chimney effect that occurs in winter because the air inside the building is warmer and less dense than the outside air. The breaking of windows by heat from a fire has major effects on burning and on hot-gas movement. Models would be able to treat this if the time of window-breaking were known, but no one knows how to handle this. Joneses has made a detailed comparison of most of the two-layer models mentioned above, and Friedman 4 has discussed the components of these models and their interactions, with emphasis on feedback loops and on thermal inertia that causes delays. Computer models now available can, for some cases, calculate the development of a fire within an enclosure, as well as the buildup of smoke at a selected location in the fire environment. If the toxicity of the smoke is known, the fate of an occupant at this location can be predicted. More specifically, TAE can be compared with TNE for a selected scenario. Toxicity data, as expressed by the LC50, are relevant only to TAE. Theoretically, sublethal effects of toxic fire products can affect TNE (e.g., the possible deleterious effect of CO on judgment or ambulation in hindering escape). The calculated

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61 answers depend on material properties in addition to LC50, especially burning rate and its variation with time, and in some cases ignitability. The physical arrangement and ventilation conditions of the enclosure and the means by which the fire is detected are also crucial. The accuracy of the model predictions is limited by the accuracy of the input data. Even if the inputs are all perfectly correct, the models treat the fluid motions and mixing, as well as the energy feedback from the environment to the fire, by a series of approximations, so the model outputs will still be only approximate. However, comparisons with realistic fire tests have shown order-of-magnitude agreement with model predictions in a number of cases. Furthermore, the relative influence of the various parameters should be generally correct. More research is needed for further refinement of models. And improvement is needed in methods of predicting burning rate from small-scale tests. For some scenarios, data on sublethal effects (not generally available) would be more relevant than lethality data.