IV
PRESENTED PAPERS CHARACTERIZING FUEL FIRES



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Aviation Fuels with Improved Fire Safety: A Proceedings IV PRESENTED PAPERS CHARACTERIZING FUEL FIRES

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Aviation Fuels with Improved Fire Safety: A Proceedings 12 Combustion Fluid Mechanics: Tools and Methods Gerard M. Faeth Department of Aerospace Engineering University of Michigan ABSTRACT Current understanding and methods of modeling combusting fluid flows are briefly reviewed, emphasizing liquid-fueled buoyant turbulent diffusion flames that are of interest for developing more fire-safe aviation fuels. Liquid fuel/air combustion in both spray flames and pool fires is discussed, considering laminar diffusion flames, buoyant turbulent noncombusting flows, buoyant turbulent diffusion flames, and turbulent sprays and spray flames. INTRODUCTION Post-crash fires caused by the ignition of jet fuel released from damaged fuel systems are an important problem of aircraft fire safety. In particular, fuels with improved fire safety are needed to reduce injuries, loss of life, and the loss of property associated with post-crash aircraft fires. Naturally, a good understanding of the properties of liquid-fueled fires burning in air is a prerequisite for developing fire-safe fuels. Current knowledge about the combustion and fluid-flow phenomena of fires, as well as about available methods of predicting fire properties, are discussed briefly, with emphasis on the burning of liquid fuels both as sprays and pools. The following topics are discussed in turn: laminar diffusion flame structure, buoyant turbulent noncombusting flows, buoyant turbulent diffusion flames, and turbulent sprays and spray flames. LAMINAR DIFFUSION FLAMES Modeling Laminar Diffusion Flames Post-crash aircraft fuel fires are invariably turbulent; nevertheless, an understanding of steady laminar flames is a prerequisite for understanding the complex, unsteady, three-dimensional combusting flow phenomena of turbulent flames. Many contemporary models treat turbulent flames as a collection of distorted laminar flames using laminar flamelet concepts. Thus, consideration of combustion fluid mechanics begins with understanding the properties of laminar flames, examining methods of modeling laminar flames, understanding laminar diffusion flame structure, and conceptualizing laminar diffusion flamelets. Except for a few cases associated with flame ignition and attachment, laminar flames are either nonpremixed (diffusion) flames, where the supplies of fuel and oxidant are separated prior to combustion (e.g., a kerosene lamp flame), or premixed flames, where the fuel and oxidant have been combined before combustion (e.g., a laboratory Bunsen burner flame). Post-crash aircraft fuel fires either involve fuel sprays produced by ruptured fuel lines and fuel tanks to yield spray flames, or liquid fuel spread along aircraft surfaces and the ground to yield pool fires. In both cases, the most representative corresponding laminar flame is a laminar diffusion flame; therefore, this flame configuration will be emphasized, considering both models and experiments. Contemporary methods of modeling laminar diffusion flames emphasize detailed fluid mechanics, transport, and chemical reaction mechanisms. The fluid mechanics and transport aspects of these models are usually based on the CHEMKIN family of computer codes developed by Kee et al. (1986, 1989, 1990, and 1991). These codes allow for effects of multicomponent transport, including thermal diffusion, and variable thermochemical and transport properties under ideal gas approximations that are appropriate for approximating flames at atmospheric pressure. One-dimensional steady calculations are typically based on available detailed chemical reaction mechanisms that provide information about the hundreds of reversible reactions needed to model complex hydrocarbon-fuel/air combustion chemistry (see Chelliah et al., 1992, for typical examples). In spite of relatively uncompromising treatments of fluid mechanics, transport, and chemical reactions, however, these models frequently ignore radiation, which affects temperature distributions in flames, even though radiation can be treated using available technology (Faeth et al., 1989). Other limitations of detailed models of laminar diffusion flames are discussed below.

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Aviation Fuels with Improved Fire Safety: A Proceedings Laminar Diffusion Flame Structure An example of the structure of a heterogeneous liquid-fueled laminar diffusion flame burning in air is illustrated in Figure 12-1. Measured concentrations of major gas species and temperature (Kent and Williams, 1975), along with corresponding predictions (Chelliah et al., 1992), are plotted as a function of distance along the axis of an opposed-jet diffusion flame involving liquid n-heptane and air at a modest strain rate. The results illustrate the main features of laminar diffusion flames proposed by Burke and Schuman nearly 70 years ago: fuel vapor (C7H16) and oxygen (O2) diffuse from opposite sides toward a flame sheet where they react so that the concentrations of saturated combustion products (CO2 and H2O) and the temperature reach maximum values; subsequently, heat flows away from the flame sheet and preheats the fuel and oxygen streams and also provides enough heat to vaporize the fuel at the liquid surface. A more complete chemical reaction mechanism used for the predictions illustrated in Figure 1, however, captures features not considered by Burke and Schuman or other classical models, e.g., the decomposition of the fuel into CO and H2 and the leakage of small concentrations of O2 to the fuel-rich side of the flame. Although the agreement between the predictions and the measurements illustrated in Figure 12-1 is encouraging, there are many problems that must be resolved before the structure of even very simple laminar diffusion flames can be reliably predicted. First of all, fuel-decomposition chemistry is not known very well for the heavy hydrocarbons present in aircraft fuels. More importantly, laminar diffusion flames of hydrocarbon fuels in air generally involve processes of soot chemistry that are not understood well enough to make predictions regarding concentrations of soot precursors and soot of comparable accuracy to those in Figure 12-1. FIGURE 12-1 Measured and predicted structure of a laminar liquid-fueled diffusion flame. Measurements and predictions from Kent and Williams (1975) and Chelliah et al. (1992). This is unfortunate because soot is an obvious feature of hydrocarbon-fueled fires and must be considered for accurate predictions of emissions of toxic materials and flame radiation (Köylü et al., 1991). But, concentrations of soot precursors and soot are relatively small in diffusion flames, which tends to mitigate the penalty of ignoring these properties for some purposes (Sunderland et al., 1995). Finally, full chemical reaction mechanisms are too computationally intensive at the present time for making tractable calculations in more than one independent variable. Various approximate methods have been developed to avoid these difficulties. Laminar Diffusion Flamelet Concepts Numerous reduced chemical reaction mechanisms have been proposed to provide computationally tractable ways of treating the multidimensional time-dependent laminar diffusion flames to be used in developing laminar flamelet concepts for turbulent flames. For present purposes, however, an effective way to model soot-containing hydrocarbon-fueled flames is needed, which is beyond the capabilities of current detailed reaction mechanisms. Fortunately, a reasonably effective alternative has been found. The conserved-scalar formalism, combined with the laminar flamelet concept, has proven to be a reasonably effective way to treat soot-containing hydrocarbon-fueled turbulent diffusion flames (Bilger, 1976; Faeth, 1983, 1987, and 1996; Gore and Faeth, 1988a, 1988b). This approach is based on an extension of Burke and Schuman's ideas about laminar diffusion flames developed by Bilger (1976). In particular, Bilger noticed that scalar properties in soot-containing laminar diffusion flames could be correlated effectively in terms of the extent of mixing (usually represented either by the local mixture fraction, defined as the fraction of mass in a sample that originated in the fuel, or the local fuel-equivalence ratio). This behavior was observed for wide ranges of flame sheet combustion rates, or flame strain rates, in spite of the effects of finite reaction rates associated with fuel decomposition and soot chemistry. These correlations have been termed state relationships, and they are applied to turbulent flames by assuming that turbulent flames correspond to wrinkled laminar flames (Bilger, 1976). Numerous measurements of state relationships for both liquid and gaseous hydrocarbon-fueled laminar diffusion flames have been reported (see Bilger, 1976; Faeth and Samuelsen, 1986; Gore and Faeth, 1988a, 1988b; Sivathanu and Faeth, 1990, for typical examples). Recent predictions using detailed chemical reaction mechanisms for laminar opposed-jet diffusion flames justify this behavior over strain rate ranges extending from near zero up to quenching conditions for nonsoot-containing flames (Lin and Faeth, 1991). This behavior is explained by the strong nonlinearity of reaction rates with temperature so that the flame structure changes

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Aviation Fuels with Improved Fire Safety: A Proceedings very little prior to abrupt extinction as strain rates are increased. Nevertheless, corresponding results for soot-containing flames have not been reported. Although the laminar flamelet concept clearly is very helpful, the need for measurements in laminar flames to provide state relationships for soot-containing hydrocarbon-fueled flames is a significant limitation. Fortunately, universal state relationships have been found for hydrocarbon/air diffusion flames that circumvent this difficulty. A universal state relationship for the concentration of CO2 in diffusion flames is illustrated in Figure 12-2, where the universal state relationship function defined by Sivathanu and Faeth (1990), (ψi, is plotted as a function of the local fuel-equivalence ratio based on measurements for a variety of fuels and flame strain rates (see original sources for the details of these flames). The universal functions were motivated by the expectations of chemical equilibrium at fuel lean conditions; clearly, the equilibrium predictions illustrated in Figure 12-2 support this hypothesis. Although finite rate effects cause significant departures from equilibrium at fuel rich conditions, these departures are fortuitously universal. Thus, universal state relationships and laminar flamelet concepts provide a reasonable treatment of scalar properties in soot-containing diffusion flames pending improved understanding of finite-rate effects associated with fuel decomposition and soot chemistry, as well as the development of increased computer capabilities that will make consideration of detailed chemistry in practical calculations computationally tractable. The next problem involves predicting mixing levels (mixture fractions) within the buoyant turbulent flows of interest for post-crash fires. BUOYANT TURBULENT NONCOMBUSTING FLOWS Modeling Buoyant Turbulent Flows Post-crash fires are reasonably represented by liquid-fueled buoyant turbulent diffusion flames. Given state relationships to find scalar properties in diffusion flames, methods of predicting mixing levels in liquid-fueled buoyant turbulent diffusion flames must be addressed. We must first understand noncombusting single-phase buoyant turbulent flows for the present before we address complications due to combustion and multiphase flow. Several methods are commonly used to model noncombusting single-phase buoyant turbulent flows. Integral models are the simplest approach and are often used to treat unit flow processes (e.g., fire plumes, flows along ceilings, etc.) in comprehensive models of fires in structures. This approach is less attractive, however, for the open flames in post-crash fuel fires, and integral models will probably not be widely used to assist the development of fuels with improved fire safety. Thus, integral methods will not be considered here. FIGURE 12-2 Measured universal state relationship for carbon dioxide species concentrations in laminar hydrocarbon-fueled diffusion flames. Source: Sivathanu and Faeth, 1990. Turbulence models and numerical simulations of turbulence, however, should be of interest for fuel development and have already been applied to open liquid-fueled turbulent diffusion flames typical of post-crash fires (Tieszen et al., 1996). The following discussion will begin with consideration of self-preserving flows that can be helpful for evaluating predictions of models of buoyant turbulent flows. The description and the findings of turbulence models and numerical simulations will then be considered. Self-Preserving Buoyant Turbulent Flows Many classical stationary turbulent flows become self-preserving sufficiently far from the source that effects of source disturbances are lost, and properly scaled flow properties become independent of the distance from the source. Such self-preserving flows are fundamentally important because they simplify the interpretation of scaled flow properties even though few flows reach these conditions in the real world. Self-preserving flows also are valuable for testing models of turbulent flows because source disturbances are avoided while modest streamwise development rates (in scaled variables) enhance numerical accuracy. As discussed by Dai and Faeth (1995, 1996) and Dai et al. (1994, 1995a, 1995b), self-preserving buoyant turbulent flows have only been reliably established for round buoyant turbulent plumes. The development of these flows toward self-preserving behavior is illustrated in Figure 12-3 where mean mixture fractions, &fbar;, are plotted as a function of radius, r, normalized by streamwise distance from the virtual origin of the flow, (x-xo), for various values of (x-x o) normalized by the source diameter, d. Self-preserving variables are used for this plot (see Dai et al., 1994) for specification of all notation. Near the source, scaled profiles of &fbar; clearly vary with

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Aviation Fuels with Improved Fire Safety: A Proceedings FIGURE 12-3 Measured mean mixture fraction distributions for round buoyant turbulent plumes plotted in terms of self-preserving variables. Source: Dai et al., 1994. (x-x0)/d, however, once (x-x0)/d > 80, the scaled profiles become universal indicating that self-preserving behavior has been achieved. These results showed that self-preserving plumes were present farther from the source, were narrower in terms of r/(x-x0), and had larger mean scaled property values near the axis than was previously thought (Dai et al., 1994, 1995a, 1995b). This finding has significant implications for modeling flows. Turbulence Model Predictions Various properties of round self-preserving buoyant turbulent plumes have been used to evaluate models of buoyant turbulent flows. An example for the scaled self-preserving mean streamwise velocity, U, is plotted as a function of r/(x-x0) in Figure 12-4. These results involve the turbulence model predictions of Dai and Faeth (1995) and Pivovarov et al. (1993), along with the measurements of Dai et al. (1995a), Shabbir (1987), Ogino et al. (1984), Nakagome et al. (1979), and George et al. (1977). All these measurements were originally thought to represent self-preserving behavior, but this behavior has only been established for the recent findings of Dai et al. (1995a). In order to match the earlier measurements of U with their predictions, Pivovarov et al. (1993) were forced to increase substantially the well-known modeling constant, Cm, from its standard value; in contrast, the new measurements of U by Dai et al. (1995a) were in excellent agreement with predictions using standard turbulence modeling constants—resolving earlier criticism of the use of turbulence models. All other mean properties behaved the same way (Dai and Faeth, 1995). Although the agreement between recent measurements and turbulence model predictions of mean properties in self-preserving round buoyant turbulent plumes is encouraging, corresponding predictions of turbulence properties are less satisfactory. An example of this behavior is illustrated in Figure 12-5, where measurements of the turbulent Prandtl/Schmidt number, σT, for self-preserving conditions are plotted as a function of scaled radial distance. The measurements show that σT progressively decreases from the axis to the edge of the flow rather than remaining constant at σT = 0.7 as prescribed by the most widely used turbulence models. Similar difficulties were encountered with other turbulence model predictions of turbulence quantities, even when using relatively advanced higher-order turbulence models. This raises questions about the capabilities of turbulence models to predict the properties of rapidly developing complex turbulent flows typical of post-crash fires, where good predictions of turbulence properties are necessary for making reasonable predictions of mean properties. Thus, pending FIGURE 12-4 Measured and predicted profiles of mean streamwise velocities for self-preserving round buoyant turbulent plumes. Source: Dai et al., 1994.

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Aviation Fuels with Improved Fire Safety: A Proceedings FIGURE 12-5 Measured turbulent Prandtl/Schmidt numbers for self-preserving round buoyant turbulent plumes. Source: Dai et al., 1995b. well documented improvements in turbulence models for buoyant turbulent flows, measurements should be used as baselines for turbulence model predictions. Numerical Simulations of Turbulence Turbulent flows formally satisfy known three-dimensional time-dependent governing equations; therefore, direct numerical simulations potentially offer a model-free way of predicting the properties of buoyant turbulent flows. Unfortunately, the range of length and time scales of practical turbulent flows will far exceed available computational capabilities for the foreseeable future. Thus, simulations must either involve some level of modeling, typically modeling or approximating the small-scale features to yield a large-eddy simulation (LES), or limiting considerations to low Reynolds number quasi-like turbulence in order to gain insight about the properties of turbulence. Using either approach, these methods are of interest for modeling aspects of post-crash fires and have already been used for this purpose (see Tieszen et al., 1996). Thus, some awareness of this methodology is needed and is addressed in the following based on the computations of large fire plumes in a crossflow due to Baum et al. (1994). The simulations of Baum et al. (1994) begin several fire diameters from the source where temperature variations are modest, where radiation can be ignored, and where the fire can be adequately characterized by release rates of heat and particulate matter. Although the computations involve the complete unsteady equations of conservation of mass, momentum, and energy, they are approximated by a two-dimensional time-dependent flow under the assumption that the component of the fluid velocity in the direction of the ambient wind is constant and equal to the wind speed. The calculations also do not extend to the smallest scales of the actual flow but are truncated by assuming a constant eddy viscosity that is three orders of magnitude larger than the actual viscosity of air. This limits small scale resolution to 5m to 15m, which is acceptable for the very large fire plumes considered in this study. Baum et al. (1994) should be consulted for other details concerning the model and the numerical method; the computer code is an adaptation of an approach used by McGrattan et al. (1994) to model enclosure fires. The numerical simulations of Baum et al. (1994) were evaluated based on experiments of crude oil combustion in a crosswind by Evans et al. (1993). The experiment considered in the calculations involved a 204 MW fire source in a 4 m/s crosswind with an atmospheric lapse rate of -9.2K/km. Some typical results are illustrated in Figure 6 as plots of the measured (symbols) and predicted (solid line) center-line plume trajectory. The comparison between predictions and measurements is quite encouraging in view of the fact that these methods do not require the use of empirical turbulence modeling constants. This highlights the importance of the effects of large scale features on the mixing properties of buoyant turbulent plumes. Other examples of this and similar methodologies can be found in references cited by Baum et al. (1994), McGrattan et al. (1992), and Tieszen et al. (1996). BUOYANT TURBULENT DIFFUSION FLAMES Modeling Buoyant Turbulent Diffusion Flames Modeling buoyant turbulent diffusion flames involves merging methods of finding the scalar properties of flames with methods for predicting the properties of noncombusting flows. Some typical approaches to this problem follow; methods of predicting flame radiation properties will be deferred for the present. The most widely used methods of predicting the structure of buoyant turbulent diffusion flames exploit the k-e or k-e-g families of turbulence models (Bilger, 1976; Lockwood and Naguib, 1975). Bilger (1976) discusses the advantages of mass-weighted (Favre) averaged properties, although the quantitative effect of the averaging procedure is generally

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Aviation Fuels with Improved Fire Safety: A Proceedings FIGURE 12-6 Measured and predicted trajectory of the center-line of a plume for a round 204 MW fire source in a 4 m/s cross-flow with a -9.2 K/km lapse rate. Symbols denote measurements and line denotes predictions. Source: Baum et al., 1994. quite modest for flames. Model constants are usually drawn from classical measurements for turbulent boundary layers and frequently employ gradient diffusion approximations that are known to be questionable for complex turbulent flows (Bilger, 1976; Gore and Faeth, 1988a, 1988b; Holen et al., 1991; Lockwood and Naguib, 1975). Calculations for more complex flows such as KAMELEON typically are based on the SIMPLEC method of Patankar and Spalding (Holen et al., 1991; Tieszen et al., 1996). The two main methods for predicting scalar properties within buoyant turbulent diffusion flames are the conserved-scalar approach, and the eddy-dissipation or eddy-breakup approach. The conserved-scalar approach exploits state relationships for scalar properties, as discussed by Bilger (1976). The studies of Gore and Faeth (1988a, 1988b) represent typical examples of this approach for hydrocarbon-fueled buoyant turbulent diffusion flames. Concentrations of major gas species were found from state relationships obtained from measurements in laminar diffusion flames (discussed in connection with Figure 12-2). A state relationship for temperature was computed from this information while allowing for the relatively large fractions of combustion energy that are radiated from soot-containing flames. State relationships for soot concentrations were also used in these calculations, based on measurements in laminar flames, although later work shows that this procedure is questionable because of fundamental differences between soot processes in laminar and turbulent flames (see Faeth et al., 1989; Sunderland et al., 1995, for discussions of this issue). Finally, prescribed probability density functions of mixture fractions were used to compute mean and fluctuating values of mixture fractions found from solution of the governing equations; the results of Gore and Faeth (1988a, 1988b) used the clipped-Gaussian probability density function although the specific form of the function used does not seem to be very critical as long as it has at least two moments (Lockwood and Naguib, 1975). The other main method for finding scalar properties in buoyant turbulent diffusion flames is based on eddy dissipation or eddy-breakup concepts. The studies of Holen et al. (1991) and Tieszen et al. (1986) represent typical examples of this approach. These methods involve the use of Burke/Schuman-like state relationships in conjunction with various approximations to treat finite-rate reactions, including the production and oxidation of soot. Unfortunately, current understanding of fuel-decomposition and soot reaction processes in diffusion flames is not highly developed, which severely limits capabilities for making reliable predictions of the structure of soot-containing flames. Thus, no method of treating the scalar properties of buoyant turbulent diffusion flames provides reliable estimates of soot concentrations, which are crucial for making accurate estimates of flame radiation properties. Turbulent Diffusion Flame Structure Two examples of turbulent diffusion flames will be considered: a buoyant turbulent round jet diffusion flame, which provides a well-defined and readily reproducible flame configuration, and a pool fire in an enclosure, which is more representative of practical fire environments. The results include measurements and predictions, with the predictions involving both the conserved scalar and eddy-dissipation methods. Representative measurements and predictions of properties along the axis of a soot-containing buoyant turbulent round jet diffusion flame by Gore and Faeth (1988b) are illustrated in Figure 12-7. Predictions of scalar properties are based on the conserved scalar approach and include both mass-weighted (Favre) and conventional time averages. As discussed by Faeth and Samuelsen (1986), the differences between these averages is not very significant for predicting scalar properties. The structure of mean properties in turbulent diffusion flames is only qualitatively similar to the structure of laminar diffusion flames (see Figures 12-1 and 12-7). For the turbulent flame illustrated in Figure 12-7, mean fuel and oxygen concentrations are smallest, and mean combustion product concentrations are largest, in a reaction zone (a flame-containing region) for dimensionless streamwise distances, x/d, in the range 60 to 90. Unlike the laminar diffusion flame in Figure 12-1, however, there is considerable overlap of mean fuel and oxygen concentrations. This overlap is caused by laminar flamelets shifting back and forth along the axis in the flame-containing region, i.e., although fuel and oxygen do not coexist at a point, they both appear because given locations in the flame-containing region have finite residence times in the fuel-lean and fuel-rich portions of laminar flamelets. Measurements and predictions of mean properties shown in Figure 12-7 are in reasonably good agreement, including proper treatment of the overlap between fuel and oxygen and the presence of large concentrations of CO at fuel rich-conditions due to partial oxidation of the fuel. This behavior is typical of the performance of the conserved-scalar formalism

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Aviation Fuels with Improved Fire Safety: A Proceedings FIGURE 12-7 Measured and predicted properties of a round buoyant turbulent acetylene/air diffusion flame. Source: Gore and Faeth, 1988b. when combined with state relationships. The main deficiency of these predictions involves predictions of velocity fluctuations in the plume region of the flow beyond the flame-containing region. This problem is caused by deficiencies of the simple k-e-g turbulence model used by Gore and Faeth (1988b), which does not properly account for buoyancy/turbulence interactions in the plume. Unfortunately, existing advanced turbulence models offer little improvement of this deficiency (Dai and Faeth, 1995). As discussed earlier, relatively poor predictions of turbulence properties are typical of most turbulence models for buoyant turbulent flames and are a concern when these methods are used to treat complex flows where rates of flow development are strongly influenced by turbulence levels. Representative measurements and predictions of the properties of+ a diffusion flame in an enclosure, based on the eddy-dissipation approach of Holen et al. (1991), are illustrated in Figure 12-8. Results shown include measured and predicted mean temperatures at two conditions (averages for the floor and for the enclosure) as a function of time as the fire develops. The agreement between measurements and predictions for this rather complicated fire environment is quite good; predictions of other properties of the enclosure fire were also quite good. Nevertheless, many aspects of the model used for these predictions require additional study and more detailed evaluation than is possible using the comprehensive properties of enclosure fires. Modeling Flame Radiation Flame radiation causes heating of materials in flame environments, which affects fire spread and growth rates. Radiation heat transfer is particularly important for soot-containing hydrocarbon-fueled flames because large fractions (as much as 60 percent) of the chemical energy release are radiated to the surroundings by a continuum of radiation from soot (Faeth et al., 1989). Current methods of modeling flame radiation are described next before representative measurements and predictions of radiation for buoyant turbulent diffusion flames are considered. Reviews of available methods of predicting radiation in turbulent flame environments are presented by Faeth et al. (1989), Gore and Faeth (1988a, 1988b), Gore et al. (1987), and references cited therein. Naturally, information about the scalar structure of flames is a prerequisite for making radiation predictions, and it is assumed in the following description that the necessary properties, based on flame structure predictions that have already been discussed, are known. Issues that must be addressed include consideration of the spectral properties of radiation, the method used to estimate soot concentrations, and the treatment of turbulence/radiation interactions. Practical flames exhibit significant effects of both gasband radiation and continuum radiation from soot. These effects are important because of the wide temperature variations of practical flames and the tendency of the largest soot concentrations to be associated with the highest-temperature regions of the flows. Predictions of soot concentrations in FIGURE 12-8 Measured and predicted temperatures for a rectangular liquid pool fire burning in air within an enclosure. Source: Holen et al., 1991.

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Aviation Fuels with Improved Fire Safety: A Proceedings flames have already been discussed. Current methods range from state relationships for soot volume fractions (Gore and Faeth, 1988a, 1988b) to empirical soot reaction expressions (Holen et al., 1991); neither approach is well established so that accurate estimates of soot concentrations in flames are probably the greatest limitation for making accurate estimates of flame radiation. Finally, buoyancy/turbulence interactions increase mean radiation levels as much as two to three times the estimates based on mean scalar properties in flames (Faeth et al., 1989); therefore, accurate treatment of these effects is also important. The radiation treatment by Holen et al. (1991) employs the gray gas approximation and uses mean properties as the basis of predictions while ignoring turbulence/radiation interactions, which is typical of the simplest models of flame radiation. At the other end of the spectrum, the methods used by Gore and Faeth (1988a, 1988b) are reasonably comprehensive and attempt to treat non-gray gas properties and the effects of turbulence radiation interactions; this approach is described next. Predictions of scalar properties for the flames studied by Gore and Faeth (1988a, 1988b) have already been discussed in connection with Figure 12-7. As noted there, state relationships were used for all scalar properties, including soot concentrations, while a k-e-g turbulence model was used to find the distributions of mean and fluctuating mixture fractions. The prescribed clipped-Gaussian mixture fraction probability density function then yielded predictions of scalar property distributions following the conserved-scalar formalism (Lockwood and Naguib, 1975). Radiation predictions were made by first computing spectral radiation intensities for particular paths through the flames and then integrating these results over wavelength and direction in order to estimate radiant heat fluxes. These computations were made ignoring scattering, which is reasonable for typical soot particles and gases in the infrared portion of the spectrum of interest for flame radiation. These predictions involved solving the equation of radiative transfer for given radiation paths, using the Goody statistical narrow-band model with the Curtis-Godson approximation for inhomogeneous gas paths. The computation considered the gas bands of CO2, H2O, CO, the fuel, and continuum radiation from soot (Ludwig et al., 1973). These calculations are straightforward when effects of turbulent fluctuations are ignored, based on mean scalar property predictions along the radiation path. Effects of turbulent fluctuations were also considered based on a stochastic method where distributions of mixture fractions through the flames were numerically simulated using classical statistical time-series methods. Scalar properties along the paths were then found from the state relationships and spectral radiation intensities were predicted as before for each realization of mixture fractions along the path. Sufficient realizations were considered to compute statistically-significant radiation properties (Faeth et al., 1989). Flame Radiation Predictions Methods of predicting the radiation properties of buoyant turbulent flames have been evaluated with reasonably good success for a variety of soot-free and soot-containing flames (Faeth et al., 1989; Gore and Faeth, 1988a, 1988b; Gore et al., 1987). The results of Gore et al. (1987) are of interest for present purposes because they demonstrate capabilities of handling large-scale fires typical of post-crash fires. Present considerations will concentrate on the findings of Gore and Faeth (1988a) instead, however, because they illustrate radiation properties for flames with reasonably large soot concentrations, typical of liquid fuel fires. Typical predictions and measurements of the radiation properties of round soot-containing buoyant turbulent diffusion flames (based on Gore and Faeth, 1988a) are illustrated in Figure 12-9. These conditions involve an ethylene/air flame at atmospheric pressure with a heat release rate of roughly 30 kW and a mean luminous flame height of roughly 500 mm. Spectral radiation intensities are shown as a function of wavelength for horizontal paths through the axis of the flame at various heights above the burner exit. The gas bands of water vapor and carbon dioxide can be seen, but the spectra are clearly dominated by continuum radiation from soot, FIGURE 12-9 Measured and predicted spectral radiation intensities for horizontal paths through the axis of acetylene-fueled round buoyant turbulent diffusion flames burning in air. Source: Gore and Faeth, 1988b.

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Aviation Fuels with Improved Fire Safety: A Proceedings which reaches a maximum intensity near 1500 nm. Not surprisingly, radiation intensities also reach maximum values near the mean luminous flame height, although radiation levels in the plume are still reasonably large. Two predictions are shown, a mean property prediction and a stochastic prediction allowing for turbulence/radiation interactions. As noted earlier, turbulence/radiation interactions significantly increase radiation levels compared to estimates based on mean scalar properties. Nevertheless, differences between the two predictions are comparable to the uncertainties of estimates of soot concentrations and the levels of continuum radiation from soot. Thus, a limited understanding of soot processes in the buoyant turbulent diffusion flames is probably the greatest impediment to making accurate estimates of radiation from practical flames at the present time. TURBULENT SPRAYS AND SPRAY FLAMES Modeling Sprays Sprays and spray flames are an important aspect of post-crash fires. Aircraft fuel is dispersed during crashes by ruptured fuel lines and fuel tanks, by aerodynamic effects due to the motion of the aircraft or wind relative to the aircraft over liquid-fuel streams created by ruptures, and also by splashing or drop formation due to turbulent primary breakup of liquid fuel spilling from ruptured fuel tanks onto aircraft surfaces or the ground. All these effects enhance mixing between the air and the liquid fuel, which creates regions capable of rapid combustion either as premixed flames or as intense spray diffusion flames. Naturally, fuel modifications that would inhibit the formation and mixing of liquid fuels as sprays will tend to enhance resistance to the initiation of post-crash fires. Thus, it is likely that consideration of fuel atomization and spray combustion will be an important aspect of the development of fuels with improved fire safety. Motivated by these considerations, the current understanding of turbulent sprays and spray flames is briefly reviewed beginning with a discussion of contemporary methods of modeling sprays, emphasizing processes in dilute sprays where liquid volume fractions are small, where processes of drop breakup have ended, and where the dispersed phase consists of polydisperse spherical drops. Primary and secondary drop breakup are then considered, prior to a discussion of spray structure and evaluations of predictions with available measurements. The present discussion of the structure and modeling of sprays is brief, but more details can be found in articles by Chen and Davis (1964), Dai et al. (1997), Faeth (1983, 1987, 1996), Grant and Middleman (1966), Hsiang and Faeth (1992, 1993, 1995), Shearer et al. (1979), Ruff et al. (1991), Shuen et al. (1983), Solomon et al. (1985a, 1985b, 1985c), Tseng et al. (1992), Wu and Faeth (1993, 1995), Wu et al. (1992, 1995), and references cited therein. Some of the generic properties of sprays can be considered in a simple way by studying the properties of an ideal spray where spray atomization immediately yields infinitely small gas-and liquid-phase elements (small drops and bubbles). In these circumstances, the assumption that both phases have the same velocity and temperature and are in thermodynamic equilibrium can be adopted so that the flow can be analyzed using the locally-homogeneous flow (LHF) approximation of multiphase flow theory (Faeth, 1983). This implies that the multiphase flow acts like a single-phase flow but with a more complex equation of state. Then the flow can be analyzed using the conserved-scalar formalism combined with state relationships for scalar properties under the laminar flamelet concept. Typical spray state relationships under the LHF approximation, providing scalar properties as a function of mixture fraction, are plotted in Figure 12-10. The results are for an n-pentane spray burning as a diffusion flame in air at normal temperature and pressure (NTP), drawn from Mao et al. (1980, 1981). The state relationships for sprays under the LHF approximation are qualitatively similar to state relationships for gas-fueled hydrocarbon/air diffusion flames, with maximum temperatures and combustion product concentrations at a flame sheet condition where the mixture is stoichiometric. The main difference between the state relationships for sprays and those for gaseous fuels involves the FIGURE 12-10 Predicted state relationships for major gas species for an n-pentane spray burning in air at atmospheric pressure. Source: Mao et al., 1980.

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Aviation Fuels with Improved Fire Safety: A Proceedings Depending on the velocity of the fuel stream hitting the ground, the flowing liquid can be either faster than the gravity wave speed on the free surface, i.e., supercritical, or slower than the gravity wave speed, i.e., subcritical. If it is supercritical, a hydraulic jump will follow, which reduces the velocity to subcritical. The subcritical fluid will continue to spread over the terrain. At this point, the fuel spread rate is governed by several factors, including gravity, the slope of the terrain, inertia of the existing fluid, and viscous drag on the solid surface (Didden and Maxworthy, 1982; Huppert, 1982; Lister, 1992). Soil porosity will also affect the spread rate and size of the spill. Fire can only occur in the presence of fuel, air, and an ignition source. A criterion for ignition can be thought of as the instantaneous overlap of the geometric regions for which ignition energies are present and for which an ignitable spray volume or liquid fuel stream is present. Viewed in this manner, determining ignition requires time-dependent, spatial tracking of energy sources and fuel streams for simultaneous co-location (and accounting for action-at-a-distance mechanisms, such as radiative heating). Determining the ignition of spray requires tracking the concentration and size of drops, which must be sufficient to initiate ignition and propagate flames. The key parameter for the liquid stream is spatial distribution. If ignition sources and fuels can be kept separate for all points in space and for all points in time during the accident transient, then there will be no fire. Figure 14-5 shows the stages of fuel dispersal after ignition of the fuel. Ignition of the mist can result in a fairly sizable fireball that results in radiant heating of nearby fuel surfaces. Fireballs radiate energy for anywhere from a few seconds to tens of seconds, depending on the mass (Dorofeev et al., 1991). Because of the buoyancy induced by combustion, the fireball will rise, and the combusting mist will be elevated with it. In this manner, fireballs quickly consume fuel. However, they also provide a large ignition source for fuel that might not otherwise be ignited. In addition to radiative heat transfer, a fireball can spread flames back along the fuel mist to the fuel source, if the fuel mist has no discontinuous or nonflammable regions. The flame can then anchor onto the spill point on the aircraft. Depending on the amount of damage to the fuel tank and the amount of fuel in the tank at the time of the accident, fuel may continue to drain long after the aircraft comes to rest. If ignition occurs in the fuel on the ground, flame spread can result in the propagation of flames back to the source, if the fuel spill has no discontinuous or nonflammable regions. The flame can then anchor onto the spill point on the aircraft. After the aircraft comes to rest, the flow of liquid from the tanks will primarily be gravity driven. However, fire induced heating of the tanks may produce residual pressures that can contribute to the rate at which the fuel leaks from the tank. The size of the fire will be limited by the balance between the rate of evaporation caused by the fire and the spill rate (Cline and Koenig, 1983). Besides flowing over the ground, fuel can flow into the ground, if the ground is porous and if the pores are not saturated with water. In addition to gravity, fuel is pulled into porous ground by capillary pressure that is a function of pore size. Because of capillary pressure, fuel that has flowed into the ground is not necessarily safe from being evaporated by and contributing to the fire. In this case, evaporation from the fire dries the surface of the soil and fuel under the dry layer is pulled up against the force of gravity by capillary forces to evaporate and feed the fire. Very long duration fires can be sustained this way. Fuel Dispersal Processes in High Velocity Impacts The high velocity impact regime has received less attention than the medium velocity regime. The lack of interest in this regime is not due to a lack of accidents occurring in this regime but to the fact that human survival in this impact regime is problematic. The primary source of data for this regime has been U.S. Department of Defense studies, the most recent of which is the Defense Special Weapons Agency (DSWA) Fuel-Fire Technology Base program, which has sponsored studies of post-crash fuel dispersal (Tieszen, 1995; Tieszen and Attaway, 1996) and fires in post-crash environments (Gritzo et al., 1995, 1996; Nicolette et al., 1995; Tieszen et al., 1996b). The primary goal of these studies is to characterize the post-crash environment to the extent that it affects nuclear weapon safety. Rather than trying to develop preventive engineering measures as the FAA has done, the DSWA program was intended to increase understanding of the crash process so risk-assessment compatible models could be developed. Risk assessments place significant time constraints on models because tens of thousands of scenarios are often run to establish statistical significance. As a result, the models focus only on dominant physical mechanisms. The primary difference between the medium impact velocity regime and the high impact velocity regime is that aircraft tend to slide out in the medium velocity regime and auger in the high velocity regime. The dividing line between the regimes is continuous and therefore somewhat arbitrary. Figure 14-6 shows examples near the boundary between the regimes. On the medium velocity impact side of the regime, damage to the fuel tanks increases as impact velocity increases. For example, a heavily damaged wing may separate from the fuselage and tumble down range, leaking fuel in the process. This type of accident begins to be indistinguishable from the high-speed impact in which the wing is fragmented on impact, and the fuel and fragments are thrown forward from the impact.

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Aviation Fuels with Improved Fire Safety: A Proceedings FIGURE 14-6 Transition from medium-to high-impact velocity regimes. A tumbling wing splashing fuel forward of an impact point becomes indistinguishable from a fragmentation impact. Figure 14-7 shows the stages of fuel dispersal in the high impact velocity regime. In many respects, the flow regimes are not qualitatively different from flow regimes in the medium impact velocity range, although there are quantitative differences. Note that in many cases, the angle of impact, not just the velocity, determines whether or not the impact is of the high normal impact velocity type. The impact of any aircraft at any flight speed against the side of a steel building will result in fragmentation of the aircraft and augering in to the building. Upon initial impact with the ground, the fuel in the tank will be subject to inertial loads caused by the rapid deceleration of the aircraft on impact. The compressibility not only of the fuel mass but also of the surface that is impacted is important. If the surface is sufficiently hard, such as a concrete runway, there may not be craters. If the surface is sufficiently soft, such as a plowed field, then there will certainly be craters. Studies have shown (Tieszen, 1995; Tieszen and Attaway, 1996) that there is a distinct difference in the dispersal characteristics of crashes into cratering and non-cratering surfaces. This difference illustrates the effect of inertial coupling and compressibility on the problem. The next stage of dispersal occurs as the fuel emerges from the ground surface or crater. Just as in the medium impact velocity regime, the fuel stream in the high velocity regime is subject to a free pressure boundary. Because of the destabilizing processes of aerodynamic drag and turbulence within the fuel itself, breakup processes begin, which results in complete atomization of the fuel leaving the surface. Surface tension is the primary force resisting breakup. However, the breakup process occurs in regions of high spatial and temporal gradients, so rate dependent forces, such as viscosity, which retards breakup, can affect the outcome. The fuel that leaves the surface is likely to be completely atomized because of the large scale and high velocity associated with the impact FIGURE 14-7 Stages of fuel dispersal in the high-impact velocity regime.

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Aviation Fuels with Improved Fire Safety: A Proceedings (Tieszen and Attaway, 1996). However, not all the fuel in the tank leaves the surface in an accident that involves craters. More than 50 percent of the fuel can remain in the crater, depending on the angle of impact (Tieszen and Attaway, 1996). As a result of the energies involved in impact and the intermixing of aircraft fragments with fuel, ignition is very likely in cratering impacts. In the high velocity regime, it is very difficult to employ any mitigative strategy to prevent ignition by maintaining physical separation of the fuels and ignition sources. Given ignition, the airborne fuel spray causes a large fireball and is consumed. In the medium impact velocity regime, the presence of the fireball significantly increases the probability of ignition and, in this sense, is considered to be detrimental. In the high impact velocity regime, when ignition is virtually guaranteed by intermixing, the fireball is a quick way of burning off the fuel. Often hazardous cargoes are sufficiently hardened so that fireball heat lasting seconds to tens of seconds will not damage the cargo. Long duration fires present a more serious consequence and can be of two types. If the fuel in the crater is in the form of a continuous liquid pool, then the fire will be a pool fire. If the fuel pool is or becomes discontinuous as a result of seepage into porous soil, then the fire can be sustained off the evaporation from the soil and is a dirt fire. The location, intensity, and duration of this fire relative to hazardous cargo containers has been the principal concern in this type of accident. Engineering Tools for Post-Crash Fuel Dispersal Computational and experimental tools that have been applied to fuel dispersal problems are briefly addressed in this section. The purpose is not to be comprehensive but to give the reader a feeling for the types of tools and their uses. As has been discussed, the range of multiphase flow regimes that can result from fuel dispersal is extremely broad. For this reason, space does not permit a discussion of fundamental research tools and results. Tools and issues for four stages of dispersal are briefly covered, tank damage/destruction, fuel atomization, interphase momentum exchange, and ground flows. The initial stage of fuel dispersal involves tracking the fluid out of the tank. Typically, compressibility is important. Computationally, the tool of choice for many years for this type of problem has been the transient, multidimensional hydrocode. An example of the use of the CTH computer code on a fuel dispersal problem is given in Gardner (1990). A new approach has recently been developed that can easily be coupled to standard finite-element based approaches, which are now the norm for structural dynamics (Attaway et al., 1994). The new approach is called "smooth particle hydrodynamics" (SPH). Although SPH has not yet been completely accepted for general fluid mechanics work, it has many advantages for short duration, high strain rate impacts (such as a gridless formulation that allows large mesh deformation without entanglement). Figure 14-8 shows a sample two-dimensional calculation (Tieszen et al., 1996). Shell elements representing the wing FIGURE 14-8 Example of numerical simulation tool for the impact stage of dispersal. Example of two-dimensional SPH calculation. Source: Tieszen et al., 1996a.

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Aviation Fuels with Improved Fire Safety: A Proceedings skin can be used in the same formulation as the gridless integration points. Both the fuel in the wing and the soil in the near impact region employ the smooth particle integration points. Although SPH allows for differing formulations of equation of state, the time step must be very short to take into account the effects of compressibility. For this and other reasons, SPH is not particularly suitable for tracking fluid beyond the impact and breakup of the tank into the atomization regime. Figure 14-9 is a photograph of a small gas gun that was used to test the suitability of the SPH approach for liquid/soil impacts (Tieszen and Attaway, 1996). The facility depicted is representative of the facilities in federal laboratories used to study impacts. Very few of these facilities have been used directly for dispersal studies, but many could be modified to cover the range needed for investigating dispersal. The U.S. Department of Defense (all services), the U.S. Department of Energy, and the U.S. Department of Transportation also have impact facilities, ranging in size from several feet long (Figure 14-9) to large sled tracks that run for miles (for example, at White Sands Missile Range, at Naval Air Warfare Center-China Lake, and at Sandia National Laboratories). Most facilities use high-speed cinematography and can record high-speed digital data, such as data from strain gages. The author knows of no transient measurements of the characteristics of fuel leaving the tanks in any tests. The second stage of fuel dispersal, atomization, is still not understood sufficiently to have been examined computationally at relevant scales and velocities. The principal reason for the lack of an engineering computational tool for this stage (in the author's opinion) has been the differences in length scales. The minimum cross-sectional diameter of a wing, near the wing root, is a significant fraction of a meter. To capture fuel tank breaks and liquid flow from the tank, length scales on this order are required. At the same time, surface tension acts over submillimeter length scales (as evidenced by the distribution of drop sizes from simple pressurized atomization, which range down into the hundreds of micrometers in FIGURE 14-9 Example of impact facility for studying the impact stage showing liquid impact into soil to determine dispersal. Model wing chord is 0.084 m and impact at 45¹ and 64 m/s. Source: Tieszen and Attaway, 1996. diameter). Therefore, to be relevant to the engineering problem and to resolve the range of surface tension forces, a spectrum of at least four orders of magnitude (from submillimeter to meter) for each spatial dimension must be run. In three dimensions, this would require 1012 grid points, a very large number by any standard, particularly for a transient, multiphase flow problem. In many situations the length scale problem can be resolved by placing dense grid points only in regions that require it. This strategy may be used to solve the present problem as well, but as the fuel surface begins to break up, the regions that require high grid density will quickly grow, and the location of break up will change as a function of time. To the author's knowledge, no computational tool directly addresses the problem. Perhaps with the new "teraflop" level of computing hardware, it will be possible to modify existing tools to conduct two-dimensional simulations of the breakup process. It is anticipated that fully transient problems with 108 grid points will be within the capability of the early teraflop level machines. In an experimental sense, substantial progress has been made in the commercialization of hardware that can characterize drop size. Commercial hardware vendors include Malvern, Insitec, Dantec, and Aerometrics. 1 Available instruments can characterize drop size and, in some cases, velocity. Unfortunately, they are most applicable in flow regimes near the end of the primary breakup stage and into the interphase transfer stage. For various reasons, they have increasing trouble in the primary breakup stage. Experimental diagnostics in the primary breakup phase is still being investigated at the laboratory scale, and, in the author's opinion, this situation will continue. Even though engineering scale tests could be conducted in the impact facilities mentioned above, the relevance of the tests would be limited by the level of diagnostics that could be brought to bear. The third stage of fuel dispersal, interphase momentum exchange, has even broader length scale ranges than the breakup stage. However, as the overall density of the fuel phase decreases relative to the gas phase, it is possible to treat the liquid phase as dispersed within the continuous gas phase. Computationally, the drops are treated as subgrid models by size classes, allowing for breakup, coalescence, and interphase momentum exchange, in an engineering sense. Figure 14-10 shows a sample calculation of a dispersal of decane droplets (Glass, 1990). The computational tool is a modification of the KIVA-II code, one of several products of the T-3 group at Los Alamos National Laboratories that can be used for this application. 1   Respectively, Malvern Instruments, Inc., 10 Southville Road, Southborough, MA 01772; Insitec, Inc., 2110 Omega Road, Suite D, San Ramon, CA 94583; Dantec Measurement Technology, Inc., 777 Corporate Drive, Mahwah, NJ. 07430; and Aerometrics, 777 N. Mary Ave., Sunnyvale, CA 94086.

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Aviation Fuels with Improved Fire Safety: A Proceedings FIGURE 14-10 Example of a numerical simulation tool for the study of the interphase momentum exchange stage using a modified version of the KIV A-II code. Source: Glass, 1990. Experimentally, the interphase momentum exchange can be studied in engineering environments in the impact facilities mentioned above. Figure 14-11 shows a test from a medium-scale study of an impact on a runway in which the fragmentation of the airframe was ignored (Tieszen, 1995). Drop size diagnostics were not used in the study, but the footprint of the spray was determined by mass collection as a function of position from the point of impact. The mass was collected by rapidly deploying absorbent media. All of the commercial drop size measurement devices work well in the interphase momentum exchange regime. Tools are available for the study of ground-based flows in the final stages of dispersal prior to ignition. Computationally, commercial tools like Flow 3D2 can be used to track slow moving free surface flows over terrain. Experimentally, flows can be measured at any number of university hydrology laboratories at the appropriate scales. Post-ignition flows are very difficult to model computationally. The author is not aware of any computational fire models that couple free-surface flow solutions simultaneously with the fire. Computational fire models with fuel spray models are being developed but to the author's knowledge they had not been quantitatively demonstrated at the time of this paper. There are numerous fire test facilities in the U.S. Department of Defense (all services), the U.S. Department of Energy, and the U.S. Department of Transportation. However, the environments are so difficult to work in that the quantitative measurement of fuel dispersal characteristics during fire transients has received very little attention. RISK-BASED DECISION Given the current state of knowledge and the available tools, one may ask how one can design a preventive or mitigative strategy to minimize the consequences of fuel firesin the post-crash environment in a cost-effective manner. The answer involves work in two areas. For a given strategy, such as the strategy pursued by the FAA for antimisting kerosene, one must first develop design criteria and then develop the strategy to meet them. The development of design criteria implies that the post-crash dispersal process is sufficiently understood to permit quantitative assessment. However, from the previous discussion it is obvious that although the dispersal processes in the postcrash environment are qualitatively understood, there is not enough information to predict the effect of a preventive strategy (say a fuel viscosity change) on the dispersal characteristics. This lack of knowledge implies that fundamental work must still be done to characterize the post-crash dispersal environment. The goal of a risk-based decision is to produce design criteria based on risk reduction targets (Bohn, 1992). The methodology is very similar to probabilistic risk assessment (PRA) methodologies. In a PRA the goal is to analyze an existing process to determine the overall risk and the major contributors to that risk. PRA is based on data from three sources, historical data, deterministic subprocess models, and expert elicitation. A risk-based decision differs in that the process to be studied is new. One of the strengths of a risk-based decision is that it can be used (1) to define the physical processes that need to be understood to make changes at the system level, (2) to identify the uncertainties in the process models and sensitivity to uncertainties at a system level, and (3) to conduct cost-benefit analyses to determine the trade-offs for a given preventive or mitigative strategy. For a risk-based decision, historical data, such as accident frequency, can be used as inputs to the process (provided, of course, that the frequency of accidents is not modified by the process modification), but the sequence of events that occurs with a preventive or mitigative strategy in place (say a modified-viscosity fuel) must be specified by one or more deterministic models. The deterministic models must be designed 2   Flow Sciences, Inc., 1325 Trinity Drive, Los Alamos, NM 87544.

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Aviation Fuels with Improved Fire Safety: A Proceedings FIGURE 14-11 Example of impact facility for studying the impact stage showing liquid impact into a runway. Source: Tieszen and Attaway, 1996. so that the effects of the new design strategy can be propagated through the model to the consequence of interest, say passenger deaths from fire. For example, for a modification of fuel viscosity, there might be one model for the effect of viscosity on drop size distribution of the atomized spray, one for the effect of drop size distribution on the size and location of the combustible spray cloud, one for the effect of the cloud size and location on ignitability, and so forth to passenger deaths. The models must be valid over the range of crash parameters for which they will be exercised (medium and high impact regimes). In an ideal world with perfect knowledge of all physical processes, this type of strategy would not be difficult to implement. However, in practice it is very difficult. For example, some of the physical processes may not have been quantified or may be very difficult to quantify. Under these conditions, it is not possible to design deterministic models for physical processes without additional fundamental research to describe the physics, which requires considerable time and resources. Historically, in the absence of a clear physical description of the physical processes involved, engineering judgment has been based on the best available knowledge. The risk-based decision process can be used to focus such expert judgments along the lines of the required models. Engineering judgment from individuals with relevant expertise can also be used to estimate effects, based on the best available knowledge. The initial estimate of the effects could be used to guide the development of experiments and models. This development path, although initially tenuous because of the engineering judgments, would lead to design criteria on a system-wide level. As the process is better understood from the data and models, the estimate of effects would become stronger and more defensible, i.e., less engineering judgment-based and more science-based. The process could be continuously refined to reduce engineering judgment until a satisfactory level of scientific defensibility is reached. At all stages of refinement, uncertainty estimates could be tracked, including uncertainty estimates based on the expert judgment. In the author's opinion, this would be the most cost-effective way of determining the necessary fundamental research to complete a study, and would allow the most resources to be focused on the development of specific preventive or mitigative strategies. Once all processes are known, the risk based decision process can also be used to decide if a preventive or mitigative strategy makes sense on a cost-benefit basis. To make this decision, cost estimates for research, development, and implementation must be generated, as well as estimates of the expected savings based on the number of deaths prevented (from insurance data, for example). Cost-benefit analyses for different strategies can be conducted without insurance data. Using a systems strategy, such as a risk-based decision process, the effect of a preventive measure can be tracked throughout any defined process. For example, if a modification in viscosity could be made to the fuel just before impact, only the postcrash environment would need be considered. If the modification was made as the fuel was pumped onto the aircraft, then the effect of the change would have to be tracked through all processes the fuel is used for, from lubrication to combustion. In this way, the positive effects of the modification in the postcrash environment could be balanced against negative effects in other processes. CONCLUSIONS Much has been learned about post-crash fuel dispersal processes in the last few decades, both from programs directed at understanding this environment and from fun

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Aviation Fuels with Improved Fire Safety: A Proceedings damental research in fluid mechanics. In general terms, the processes of fuel dispersal can be qualitatively described, but in many cases, quantitative predictions of effects are beyond our capabilities. Tools, both experimental and computational, have been developed and applied to the dispersal problem and will continue to be developed and improved with time. In designing a preventive or mitigative strategy, the crash process must be understood well enough to develop quantitative design criteria. Risk-based decisions represent one approach that might achieve this goal. However, quantitative descriptions will not come easily because the postcrash environment involves a myriad of complex, coupled, and nonlinear processes that are, by their very nature, difficult to describe quantitatively. 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Aviation Fuels with Improved Fire Safety: A Proceedings APPENDICES

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