Solid-flame model

The solid-flame model can be used to overcome the inaccuracy of the point-source model. This model assumes that the fire can be represented by a solid body of a simple geometrical shape, and that all thermal radiation is emitted from its surface. To ensure that fire volume is not neglected, the geometries of the fire and target, as well as their relative positions, must be taken into account because a portion of the fire may be obscured as seen from the target. 

Section 3.5 mentions two approaches, the point-source model and the solid-flame model. In the point-source model, it is assumed that a certain fraction of the heat of combustion is radiated in all directions. This fraction is the unknown parameter of the model. Values for fireballs are presented in Section 3.5.1. The point-source model should not be used for calculating radiation on receptors whose plane intercepts the fireball (see Figure 6.9B). 

The solid-flame model, presented in Section 3.5.2, is more realistic than the point-source model. It addresses the fireball s dimensions, its surface-emissive power, atmospheric attenuation, and view factor. The latter factor includes the object s orientation relative to the fireball and its distance from the fireball s center. This section provides information on emissive power for use in calculations beyond that presented in Section 3.5.2. Furthermore, view factors applicable to fireballs are discussed in more detail. 

For a receptor not normal to the fireball, radiation received can be calculated based on the solid flame model as follows ... 

Ground Distance (m) Solid Flame Model Point Source Model... 

An important parameter for determining the damage caused by a fireball is its specific surface emissive power ( SEP ), at least if the object to be protected is not inside the ball and hence directly exposed. The model used here is the solid flame model. According to [39] the result of the calculation strongly depends on how the SEP is defined and measured. In [2] a low value of 141 kW/m and a maximum value of 450 kW/m are quoted [37] indicates a range from 320 kW/m to 350 kW/m. In view of these values the use of a value of = 350 kW/m for the SEP is recommended. 

TABLE 9.1. Radiation on a (Vertical) Receptor from a 6000-gallon Propane Tank Truck BLEVE Calculated with Solid Flame and Point Source Radiation Models... 

Figure 1. Two-stage granular diffusion flame model for ammonium perchlorate-type composite solid propellants...

Three-dimensioned modeling of solid-flame chaos, Dokl. Phys. Chem., 381... 

We note that burning sometimes occurs throughout the sample, while under other circumstances it occurs only on the surface of the sample, though this is generally due to the effect of limited oxidizer filtration through the sides of the sample, which is not accounted for here. In this chapter we nevertheless restrict consideration to surface burning so that the process can be modeled in two dimensions. Our model thus describes solid flame propagation in a thin cylindrical annulus between two coaxial cylinders, as in the synthesis of hollow... 

A. P. Aldushin, A. Bayliss, B. J. Matkowsky, Dynamics of Layer Models of Solid Flame Propagation, Physica D, 143 (2000), 109. 

Other Types of Fires. For the other types of fires, avaUable models are broadly classified as eifher poinf-source models (simple or with multiple sources) or view-factor models based on either an equivalent radiator or a solid flame approach. They differ in their required input parameters according to the type of fire and the level of detail and complexity inherent in the inputs and submodels needed to describe the physical event. 

Figure 6.5 Schematic of a reaction vessel, (a) Solid model (b) finite element mesh (c) wire flame model and (d) a cross-sectional view of (b).

Aldusihn, A.P., Bayliss, A., and Matkowsky, B.J. (2000) Dynamics in layer models of solid flame propagation. Physica D, 143, 109-137. 

The pool size must be defined, either based on local containment systems or on some model for a flat surface. Burning rates can be obtained from tabulations or may be estimated from fuel physical properties. Surface emitted flux measurements are available for many common fuels or are calculated using empirical radiation fractions or solid flame radiation models. An estimate for atmospheric humidity is necessary for transmissivity. All other parameters can be calculated. 

Fig. 5. Speed of H2/O2/N2 flames doped with 0.04% TMP with different D versus equivalence ratio symbols - experiment, dashed lines - modeling using mechanism (Jayaweera et al., 2005), solid lines - modeling using the updated mechanism.

In order to explain and theoretically prove the phenomenon of solid flames, the model for wide combustion zones was formulated 14,15). According to this model, the degree of chemical conversion in the front was supposed to be insignificant (as opposed to the classic theory by Zel dovich and Frank-Kamenetsky) and the final product formation was assumed to occur in a wide zone behind the front through reactive diffusion. Alternative mechanisms of chemical reactions were not considered. 

Propagation of Gasless Reactions in Solids , Combustion Flame 21, No 1 (1973), 91-97 69) B.E. Douda, Radiative Transfer Model of a Pyrotechnic Flare , NAD-RDTR No 258... 

These studies have indicated that the independent parameters controlling the postulated solid-phase reactions significantly affect the resulting acoustic admittance of the combustion zone, even though these reactions were assumed to be independent of the pressure in the combustion zone. In this combustion model, the pressure oscillations cause the flame zone to move with respect to the solid surface. This effect, in turn, causes oscillations in the rate of heat transfer from the gaseous-combustion zone back to the solid surface, and hence produces oscillations in the temperature of the solid surface. The solid-phase reactions respond to these temperature oscillations, producing significant contributions to the acoustical response of the combustion zone. 

At present there is no small-scale test for predicting whether or how fast a fire will spread on a wall made of flammable or semiflammable (fire-retardant) material. The principal elements of the problem include pyrolysis of solids char-layer buildup buoyant, convective, tmbulent-boundary-layer heat transfer soot formation in the flame radiative emission from the sooty flame and the transient natme of the process (char buildup, fuel burnout, preheating of areas not yet ignited). Efforts are needed to develop computer models for these effects and to develop appropriate small-scale tests. 

Applications The general applications of XRD comprise routine phase identification, quantitative analysis, compositional studies of crystalline solid compounds, texture and residual stress analysis, high-and low-temperature studies, low-angle analysis, films, etc. Single-crystal X-ray diffraction has been used for detailed structural analysis of many pure polymer additives (antioxidants, flame retardants, plasticisers, fillers, pigments and dyes, etc.) and for conformational analysis. A variety of analytical techniques are used to identify and classify different crystal polymorphs, notably XRD, microscopy, DSC, FTIR and NIRS. A comprehensive review of the analytical techniques employed for the analysis of polymorphs has been compiled [324]. The Rietveld method has been used to model a mineral-filled PPS compound [325]. 

We will develop an analytical formulation of the statement in Equation (8.2). This will be done for surface flame spread on solids, but it can be used more generally [1], As with the ignition of solids, it will be useful to consider the limiting cases of thermally thin and thermally thick solids. In practice, these solutions will be adequate for first-order approximations. However, the model will not consider any effects due to... 

---