THERMAL RADIATION IN UNWANTED FIRES

R. Viskanta

Following from: Radiative transfer in combustion systems; Combustion phenomena affected by radiation; Radiative transfer in laminar flames; Radiative transfer in turbulent flames; Radiative transfer in combustion chambers; Radiative transfer in two-phase combustion

Unwanted pool, building, urban, wildland, and other large-scale fires present a potential danger to human safety and property loss. Such fires and their mitigation and control have been of concern to mankind since recorded history (Cox, 1995). The phenomenological issues related to different types of unwanted fires and their initiation, spread, and control are very broad topics indeed, and it is beyond the scope of this limited account to discuss the many fundamental and practical concerns related to understanding, modeling, and extinguishing fires. Only a few selected topics with emphasis on radiative transfer are considered and discussed.

Interest in understanding fire is mainly motivated by the need to control and/or prevent accidental fires. Fire dynamics is governed by the interactions of numerous physicochemical processes such as fuel vaporization, air entrainment, chemical reactions, turbulence, soot and pollutant formation, radiation, and others. An early review (Williams, 1982) focused on basic aspects of fire and presented an elementary but unified treatment of the phenomena by considering both urban and wildland fires. Numerous more recent reviews (Joulain, 1998; Karlsson and Quintiere, 2000; Novozhilov, 2001) have treated aspects of flame radiation in fires, and have contributed greatly to the understanding of the phenomena. The reader is referred to these and other (Viskanta, 2005; 2008) accounts for more comprehensive discussions of original works on fire research. The needs for fire safety and mitigation research have been highlighted by Sacadura (2004), and numerous topics needing attention have been identified.

It has now been accepted that radiation is the dominant mode of heat transfer in fires of large scale, whereas convection (or conduction) is the dominant mode of heat transfer of very small-scale fires. Detailed heat transfer measurements have demonstrated that radiant heat transfer from fuel surfaces typically exceeds free convection heat transfer for characteristic fuel lengths greater than 0.2 m (deRis, 1979). Nonluminous and luminous radiation from turbulent diffusion flames has been discussed in THERMOPEDIA, and the importance of turbulence-radiation interaction has been pointed out in a preceding subsection. During the last few decades, there have been numerous contributions to the literature concerning radiative transfer in fires, and it is not possible to do justice to these works in this very short account--and reference is made to reviews for comprehensive discussions of the numerous issues.

During the last two decades, major progress has been made in understanding unwanted fires through scaling and development of CFD models for fire research and transition from zone to more general field models that simulate fire phenomena from first principles. The classification of fire field models is presented schematically in Fig. 1 by identifying groups of models without numerous detailed and less important features in the models and the submodels. The difficulty with scaling is that emission of radiation is a local phenomenon, while absorption is dominated by long length scales. Of vital importance is the absorption of radiation by solid- and liquid-fuel boundaries that subsequently produce the fuel that sustains fire. Within the limited context of this discussion, it is not possible to cite all of the worthwhile contributions to the field, and only three selected topics related to fire modeling that focus on radiative transfer can be covered in this limited account.

Figure 1. Classification of fire field models (Novozhilov, 2001).

Pool Fires

For over 40 years, fire researchers have sought a modeling/scaling scheme that would allow one to infer large-fire behavior from measurements of small-scale model fires. The intent of the smaller model tests has been to reduce costs, increase flexibility, and reduce hazards of large-scale tests. Several modeling criteria have been developed and include Froude, pressure, and radiation scaling. These three types of scaling schemes have their practical advantages as well as disadvantages, and a recent discussion is available (deRis, 1979).

From an energy balance on the burning pool fire, one must have that the rate of energy release due to combustion of the fuel Qc must equal the sum of all the energy flow rates, and we can writet

(1)

where QR represents the rate of radiant energy loss from the combustion products and Qh denotes the rate of sensible enthalpy increase of the products. Energy loss from the system by incompletely oxidized carbon (soot) has been neglected. In pool fires, the feedback heat transfer rate QFB, primarily by convection and radiation, is determined by the burning rate of the fuel through the influence of the burning mechanism on rates of gas-phase heat transfer.

The radiant fraction χR of energy release rate Qc due to combustion that is radiated by the flame can be approximated as (Viskanta, 2005)

(2)

where κ is the mean absorption coefficient of the combustion products, and D is the pool diameter.

The above relation suggests that the fraction of heat radiated increases with increasing flame diameter for small fires, and decreases for large fires. This is consistent with experimental results (Schönbucher et al., 1985), and an approximate (schematic) representation of the radiant loss fraction χR for different diameter pool fires is shown in Fig. 2, where the shaded area approximates the range of χR values for different fuels and environmental conditions (i.e., crosswind). The explanation of the experimental trends, however, is more complex since the model assumptions are too simplistic, particularly the uniformity of temperature and radiating species composition. More realistic semi-empirical modeling of pool fires is discussed elsewhere (Viskanta, 2005). Detailed 1D and 2D models for laminar pool fires have been developed (Ripoll and Haldenwang, 2002; Prasad et al., 1999).

Figure 2. Approximate representation of the radiant fraction as a function of the tank diameter; the shaded area represents data for different fires.

Numerical simulations of accidental fires resulting from fuel spills or tank explosions can help fire safety personnel to reduce associated hazards. Such fires burn as pool fires, and the fires can be simulated numerically using RANS models, large eddy simulations (LES), and the fire dynamic simulator (FDS) (McGrattan et al., 2001). Large eddy simulations are becoming increasingly useful for investigating turbulent flows, and the method has been extended to include chemically reacting flows (Kang et al., 2001). In LES, the large-scale quantities are directly resolved, and the method is being increasingly used to treat large-scale turbulent pool fires (Kang et al., 2001; Xin et al., 2002). The LES involves solution of spatially filtered equations designed to simulate large-scale structures directly and accurately if appropriate subgrid-scale (SGS) models can be constructed. For example, a laminar flamelet model with subgrid-scale combustion closure in a large eddy simulation has been used to analyze the turbulent structure of medium- and large-scale pool fires.

Radiative transfer has been neglected in some pool fire LES models (Kang et al., 2001), and considered in others (Xin et al., 2002). For example, Xin et al. used a 3D LES to model two buoyant flows with a Smagorisky turbulence model. They accounted for radiative transfer only in a global manner by lowering the heating value of the fuel by 10% to account for the radiant energy loss from the flame. Within a fire, energy is transported from small-scale, high-temperature regions on the rich side of the flames to longer length-scale, lower-temperature regions. Therefore, radiation affects the length scales of gas density gradients, which, in turn, affect the flow field. It appears that this coupling has not been quantitatively studied in terms of flow distribution in fires, but more realistic combustion and radiative transfer models are being used to account for these processes in fire dynamics simulations of pool fires (Xin et al., 2002).

Compartment (Enclosure) Fires

The fundamentals of compartment (enclosure) fire dynamics are discussed in a recently published textbook intended for fire safety engineering students (Karlsson and Quintiere, 2000). Heat transfer in compartment fires, combustion products, and computer modeling of enclosure fires are some of the chapters in the textbook. One of the central issues in compartment fires is the structure of an isolated fire plume and a fire in a compartment. CFD modeling of a fire plume is difficult for two fundamental reasons. First, in a typical laboratory experiment, combustion occurs at the base of the plume in a region that occupies a small fraction (~1-2%) of the overall volume containing the plume and the surrounding source of entrained air. Second, the location of the combustion zone at the base of a plume varies due to the quasi-periodic formation of large-scale, low-frequency toroidal vortices. Therefore, the plume dynamics is inherently time dependent, even at the largest scales, making time-averaging model approaches (e.g., k-ε turbulence model) inappropriate. Hence, a numerical simulation of even small (~10-20 cm diameter) fire plumes (or pool fires) requires resolution of phenomena on length scales covering nearly three orders of magnitude (i.e., the reaction zone is on the order of 1 mm), and clearly understanding and some idealization of the physicochemical phenomena is required to reduce the computational cost.

Discussions of compartment fire growth as well as zone and field models are available (Thomas, 1995; Cox, 1995). More recently, a comprehensive account of CFD modeling of compartment fires has been prepared in which 280 relevant references have been cited (Novozhilov, 2001). The focus of the review is on the field models. Computer programs available for modeling enclosure fires using simple zone and CFD models have been identified (Karlson and Quintiere, 2000). In many physical/numerical simulations of enclosure fires, radiative transfer has been neglected, mainly because of complexities it introduces due to great uncertainties in the dynamic radiation characteristics of gases and particles (soot) of the combustion products, the complexities of treating radiative transfer, and the high computational cost.

Fire is a complex phenomenon, and a schematic representation of a typical fire in a compartment is illustrated in Fig. 3. The physical and chemical processes are strongly interactive. Heat released by burning sections of fuel causes nearly virgin fuel to ignite. The hot combustion products ascend in a fire plume, and a smoke layer is formed under the ceiling. Air is entrained into the compartment through the vents. The interaction between the flame, fuel, and the surroundings can be strongly nonlinear, and quantitative estimation of the physicochemical processes is often complex. The processes of interest in an enclosure fire mainly involve mass fluxes and heat fluxes to and from the fuel and the surroundings. Figure 3 shows a schematic representation of these interactions, indicating the processes in an enclosure fire. Detained qualitative descriptions of the different stages of enclosure fire dynamics are available elsewhere (Karlsson and Quintiere, 2000; Novozhilov, 2001).

Figure 3. Schematic model of a compartment fire (Novozhilov, 2001).

Up-to-date physical and mathematical descriptions of compartment fires are available (Novozhilov, 2001), and different levels and sophistication of radiative transfer approaches for compartment fires have been discussed. Probably the most comprehensive radiative transfer model for compartment fires in conjunction with a CFD code has been developed and exercised by Yeoh et al. (2002). Not only gas, but also soot radiation were considered on gray bases, and the soot volume fraction was calculated using a two-equation soot formation and oxidation model.

It must be noted that RANS- and LES-based CFD models have their limitations. They need a far more accurate prediction of turbulence, coupling of chemically reacting flow with chemical kinetics, modeling of soot formation and oxidation, and modeling of the radiation characteristics that are coupled to the radiatively participating species concentrations and their use to calculate local and not just global radiative transfer. Accounting for turbulence-chemistry and turbulence-radiation interactions not only in gases but also in soot may also be required.

Wildland Fires

Wildfires occurring annually in many nations of the world are a threat to people and property. The understanding of the physicochemical mechanisms that control the ignition and the spread of wildland fires constitutes a major objective for the management and protection of forests and agricultural crops. The early statistical, semi-empirical, and physical approaches for simulating spread of forest fires have been reviewed by Weber (1991). Empirical and statistical models have been developed into operational fire management tools; however, there are many questions that cannot be addressed within the framework of such approaches. This is owing to the fact that such models are specific to the experimental conditions on which they are based. The application of simplified empirically based fire spread models for fire spread through fuel beds allows one to gain understanding of the fire rate of spread as a function of the fuel load, the wind speed, and the terrain slope for particular conditions, which are typically close to the experimental conditions carried out in the laboratory used in such models. Unfortunately, use of these models for more general conditions does not always yield satisfactory predictions.

The heat transfer mechanisms that need to be considered in modeling fire spread processes in wildland fuels include: (i) convective heat transfer, (ii) radiation heat transfer, (iii) direct flame contact, and (iv) firebrand contact. Experimental investigations have shown that on flat ground and in the absence of wind, about 60% of the thermal energy required for ignition and received by the fuel comes from burning embers by convective and radiative transfer (Pitts, 1991). This finding seems to confirm the minor part played by the flame to sustain a spreading fire in a forest fuel bed. Although the flames exhibit fully 3D behavior, the major contribution to the energy balance inside a fuel bed and above the litter can be simulated by a 2D configuration, as is shown in Fig. 4. This assumption is justified on the basis of observations that show that widths of many spreading fires in nature are much greater than the fire depth. The fuel to be burned is in a form of particles, and is distributed uniformly throughout the layer of constant thickness on a flat horizontal surface. The unignited fuel bed is treated as a porous medium in which heat transfer is by convection between the gas and the bed, radiation, and conduction. The physicochemical processes in the flame and gas phase (i.e., chemically reacting flow, radiation, gas-particle interaction, heat transfer, etc.) associated with wildfire spread are considered. As a result of the intense heat transfer from the burning zone (flame plus embers), the particles ahead of the fire front break up because of dehydration, pyrolysis (gases and charcoal), and char oxidation.

Figure 4. Schematic representation of a wildland fuel bed flame (Morvan and Dupuy, 2001).

A physical model for studying the propagation of a surface fire in a fuel bed based on the multiphase formulation has been proposed to evaluate the rate of spread of a forest fire (Larini et al., 1998; Morvan and Dupuy, 2001). The model considers the composition of a solid forest fuel bed as well as multiple interactions with the gas-phase equations. The processes in the gas phase are coupled to the processes in the solid phase in porous, unignited fuel in the bed. The coupling between the gas and solid phases is accomplished through source terms in the mass, species, momentum, and energy equations. The dehydration, pyrolysis, and char oxidation reaction rates of these contributors to the fire are approximated by Arrhenius laws, whose frequency factors and activation energy are evaluated empirically (Morvan et al., 2001). In addition to the governing conservation equations of mass, momentum, energy, and species for the gas phase, the energy equation for the fuel bed was also included by Morvan and Dupuy (2001). The local energy balance of the solid is expressed in terms of global parameters. The complexity of treating radiative transfer in porous media (even on a gray basis) is recognized, and is discussed by Viskanta (2005). The dehydration and pyrolysis (of gaseous products and of charcoal) reaction rates needed have been provided by Morvan and Dupuy (2001).

Probably the first comprehensive approach in modeling radiative transfer through wildland fuels is due to Albini (1985). He recognized the importance of radiation in fire spread, and formulated a model using the RTE. The emphasis was on the solution of the RTE, and the radiation characteristics used were arbitrary, and the analysis was on a gray basis. The difficulty of modeling gas flow in inhomogeneous porous media and the radiation characteristics of wildland unignited fuel beds consisting of leaves, needles, partially decomposed material particles, etc., is recognized by the fire research community (Morvan and Larini, 2001). Probably the most detailed and physically correct treatment of radiation transfer in wildland fires up to now is that due to Morvan and Dupuy (2001). In the gas phase, the gas plus soot radiation was modeled on a gray basis using the DOM. The formation of soot particles in the flame was considered, and the soot volume fraction was calculated, but the gray soot absorption coefficient was calculated by assuming the carbon spheres have a fixed diameter of 1 μm. In the porous fuel bed, the RTE is modified to account for the fractions in the gas and solid phases in the bed. Emission of radiation by the hot embers is also accounted for.

The most detailed physical/numerical model of fire spread in a forest fuel bed is described by Morvan and Dupuy (2001). A 2D forest fire propagation was simulated using the multiphase formulation. The decomposition of solid fuel constituting a forest fuel bed as well as multiple interactions between the gas and solid in the bed was considered. A comparison of the computed rate of spread results with experimental data made it possible to validate various submodels of the overall multiphase approach for fire propagation of wildland surface fire.

The major challenges in wildland fire simulation include the description of the thermophysical and radiation characteristics of the fuel bed, embers, etc., and modeling of contact heat transfer and convection between the gas and the irregular shape, as well as size, particles. The generalization of the current models (Morvan and Dupuy, 2001) to simulate large-scale fires for conditions that are more representative of the real conditions of propagation of wild fires remains a major task for the future.

Fire Suppression by Water Sprays

Use of water as a method of controlling and quenching compartment, building, and wildland fires has existed since the dawn of time (Williams, 1982). Even though, currently, heat and smoke detectors are being developed and installed to activate automatic sprinklers, water has become the most widely used fire-fighting agent. Physical and chemical suppression mechanisms that act simultaneously during spraying operations have been identified (Grant et al., 2000). However, the fire suppression schemes using water sprays or water mist are not fully understood, and comprehensive models are not routinely available in CFD environment. Use of water sprays in suppression of compartment fires and in protection of buildings and fire-fighting personnel from thermal radiation is an effective and well-established scheme in fire protection and prevention. The blocking of radiation by water spray or mist is an important mechanism of fire extinction and protection. The physical and chemical processes controlling fire dynamics in compartments have already been discussed in the preceding subsection, and introduction of water spray into a compartment to extinguish a fire introduces additional physical phenomena requiring consideration.

A comprehensive account of droplet dynamics and transport is available (Sirignano, 1999), but radiative transfer in the droplet, in the “hot” combustion products, and within the droplet has not been considered, or treated only in a most elementary manner. The complicated effects of radiative transfer on droplet evaporation are shown in Fig 5. The interaction of radiation and the surrounding medium results in a heat source potentially increasing the temperature of the spray, whereas the competing phenomena of vaporization of water droplets, convection, and turbulent transport are expected to cool the medium. The physical and chemical processes controlling fire dynamics, say, in compartments, is reasonably well understood, but use of water sprays in a compartment to extinguish a fire introduces additional physical phenomena that must be considered (Grant et al., 2000; Novozhilov, 2001; Nmira et al., 2007). Absorption and scattering of radiation by the droplets, cooling of the gas in the compartment by evaporation of the droplets, direct cooling of the fuel by an impinging water droplet stream, and interaction of spray with the turbulent gas flow in the compartment need to be accounted for (Dembele et al., 1997). Since water is not opaque but semitransparent to radiation (Hale and Querry, 1973; Pinkley et al., 1977), absorption of radiation by the droplet is not a surface but a volumetric phenomenon, and this complicates greatly the analysis of evaporation of a water droplet situated in hot radiating surroundings.

Figure 5. Schematic description of the effects of radiation of water droplet evaporation.

Modeling of fire suppression using water sprays requires knowledge of the radiation characteristics of water droplets. Mie theory has been used to predict absorption and scattering efficiency factors for monodisperse water droplets (Barrett, 1985). It was found that absorption is approximately proportional to the volume of liquid water present, regardless of droplet size. Spectral complex index of refraction data needed by the Mie theory to calculate the efficiency factors are available (Hale and Query, 1973). As discussed elsewhere (Viskanta, 2005), there are three ways of accounting for radiation absorption and enhancing evaporation and cooling of the combustion products: Mie, EM wave, and radiation (geometrical optics) transfer theories. The spectral radiation characteristics of monodisperse and polydispoerse water sprays (needed as input data in the solution of the RTE) have been predicted (Hostikka and McGratton, 2007; Viskanta and Tseng, 2007) based on the Mie theory. Simple semi-empirical correlations based on the mean water droplet diameter were developed for the spectral extinction coefficient and the single scattering albedo by Viskanta and Tseng. The results reported can be used in radiative transfer submodels of CFD codes modeling fire suppression using water sprays/mists (Colin et al., 2005; Hostikka and McGrattan, 2007).

Water spray (mist) in a fire atmosphere provides a heat sink in fire extinguishment, and represents a significant submodel of any CFD scheme in simulating fire suppression (Keramida et al., 2000; Prasad et al., 2002); therefore, it is desirable to discuss heat addition to and removal from a moving droplet in a fire atmosphere. A droplet is heated by convection and absorption of radiation from the “surroundings,” which includes combustion products, fire, and any other sources. Since water droplets are at low temperature (<100°C), emission of radiation can justifiably be neglected in comparison to absorption. Scattering of radiation by the mist is difficult to treat, and no reliable estimates of its significance in fire suppression have been reported. As a consequence of heat addition by convection and radiation, and energy loss by evaporation, the diameter of the water droplet decreases.

In the absence of radiation, droplet vaporization has been extensively studied; the theory is well in hand, and details of the theoretical developments are available in the combustion literature (Turns, 2000). Some recent theoretical analyses, verified by experiments, have shown that absorption of radiation originating from the surroundings (gases and hot walls) by isolated water droplets placed in a quiescent environment can increase the rate of evaporation and shorten the droplet lifetime (Miliauskas, 2003; Tseng and Viskanta, 2006). The greatest impact of radiation is on large-size (~1000 μm diam) droplets. For small (< 10 μm) water droplets, the effect of radiation absorption is negligible because convective heating predominates over radiative heating. Treating a water droplet as opaque to radiation underestimates the deposition of external radiation and increases the droplet lifetime.

Development, use, and validation of CFD models for compartment fires have recently been reviewed by Novozhilov (2001), and several field models for fire suppression in compartments using water sprays have been discussed in this account. The models dealt primarily with sprinkler spray delivery systems, and not with the physicochemical phenomena in the compartment affected as a consequence of water mist introduction into the gas. Recent CFD modeling results indicate that radiation is a primary mechanism in fire extinguishment since it contributes to nearly half of the total heat removal by the droplet (Viskanta, 2005). In a more recent computational study, water mist suppression of large-scale compartment fires was simulated (Prasad et al., 2002). Parametric studies were performed to optimize water mist injection for maximum suppression. Numerical results indicate that for similar injection parameters such as mist injection density, injection velocity, and droplet diameter, the time for suppression was shortest for the top injection configuration. Reference is made to studies by Collin et al. (2008, 2010) for an extensive list of relevant literature citations dealing with water mist and radiation interactions.

Fire suppression using water sprays is an important societal issue in modeling fire and the design of a sprinkler system. Improved understanding and ability to simulate fire extinguishments in turbulent gas flow and cooling of solid fuel is required. The challenge in modeling turbulent two-phase flow and heat transfer (both convective and radiative) is apparent. To improve the treatment of water mist fire suppression systems in the CFD approaches, both fundamental and experimental research is required.

REFERENCES

Albini, F. A., A Model for a Fire Spread in Wildland Fuels by Radiation, Combust. Sci. Technol., vol. 42, pp. 229-258, 1985.

Barrett, J. C., The Spectral Properties of Water Droplets in the Infrared, J. Phys. D, vol. 18, pp. 753-764, 1985.

Collin, A., Boulet P., Vetrano, M. R., and Buchlin, J. M., Dynamics of Thermal Behavior of Water Sprays, Int. J. Thermal Sci., vol. 47, pp. 399-407, 2008.

Collin, A., Lechene, S., Boulet, P., and Parent, G., Water Mist and Raadiation Ineractions: Applications to a Water Curtain Used as Radiation Shield, Numer. Heat Transfer, Part A, vol. 57, pp. 537-553, 2010.

Cox, G. (ed.), Combustion Fundamentals of Fire, Academic Press, London, 1995.

deRis, J., Fire Radiation--A Review, Proc. Combust. Inst., vol. 17, pp. 1003-1015, 1979.

Dembele, S., Delmas, A., and Sacadura, J. F., A Method for Modeling the Mitigation of Hazardous Fire Thermal Radiation by Water Curtains, J. Heat Transfer, vol. 119, pp. 746-753, 1997.

Grant, G., Brenton, J., and Drysdale, D., Fire Suppression by Water Sprays, Prog. Energy Combust. Sci., vol. 26, pp. 79-130, 2000.

Hale, G. M. and Querry, M. R., Optical Constants of Water in the 200-nm to 200-μm Wavelength Region, Appl. Opt., vol. 12, pp. 555-563, 1973.

Hostikka, S. and McGrattan, K., Numerical Modeling of Radiative Heat Transfer in Water Sprays, Fire Safety J., vol. 20, pp. 241-255, 2007.

Joulain, P., The Behavior of Pool Fires: Sate of the Art and New Insights, Proc. Combust. Inst., vol. 27, pp. 2691-2706, 1998.

Kang, Y., Wen, J. X., McGrattan, K. B., and Baum, H. R., The Use of a Laminar Flamlet Approach in the Large Eddy Simulation of Flame Structure of the Base of a Pool Fire, Proc. of 9th Interflame Conference, Interscience Communications, London, pp. 743-754, 2001.

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Morvan, D., Portiere, B., Lorand, J. C., and Larini, M., A Numerical Investigation of Cross Wind Effects on a Turbulent Diffusion Flame, Combust. Sci. Technol., vol. 164, pp. 1-35, 2001.

Morvan, D. and Larini, M., Modeling of One-Dimensional Fire Spread in Pine Needles with Opposing Air Flow, Combust. Sci. Technol., vol. 164, pp. 37-64, 2001.

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参考文献

  1. Albini, F. A., A Model for a Fire Spread in Wildland Fuels by Radiation, Combust. Sci. Technol., vol. 42, pp. 229-258, 1985.
  2. Barrett, J. C., The Spectral Properties of Water Droplets in the Infrared, J. Phys. D, vol. 18, pp. 753-764, 1985.
  3. Collin, A., Boulet P., Vetrano, M. R., and Buchlin, J. M., Dynamics of Thermal Behavior of Water Sprays, Int. J. Thermal Sci., vol. 47, pp. 399-407, 2008.
  4. Collin, A., Lechene, S., Boulet, P., and Parent, G., Water Mist and Raadiation Ineractions: Applications to a Water Curtain Used as Radiation Shield, Numer. Heat Transfer, Part A, vol. 57, pp. 537-553, 2010.
  5. Cox, G. (ed.), Combustion Fundamentals of Fire, Academic Press, London, 1995.
  6. deRis, J., Fire Radiation--A Review, Proc. Combust. Inst., vol. 17, pp. 1003-1015, 1979.
  7. Dembele, S., Delmas, A., and Sacadura, J. F., A Method for Modeling the Mitigation of Hazardous Fire Thermal Radiation by Water Curtains, J. Heat Transfer, vol. 119, pp. 746-753, 1997.
  8. Grant, G., Brenton, J., and Drysdale, D., Fire Suppression by Water Sprays, Prog. Energy Combust. Sci., vol. 26, pp. 79-130, 2000.
  9. Hale, G. M. and Querry, M. R., Optical Constants of Water in the 200-nm to 200-μm Wavelength Region, Appl. Opt., vol. 12, pp. 555-563, 1973.
  10. Hostikka, S. and McGrattan, K., Numerical Modeling of Radiative Heat Transfer in Water Sprays, Fire Safety J., vol. 20, pp. 241-255, 2007.
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