Solid flames

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 ... 

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... 

Ground Distance (m) View Factor Solid Flame Radiation (kW/m ) Point Source Radiation (Hymes) (kW/ni )... 

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

Tantalum-carbon, tantalum-boron, and niobium-boron mixtures may be classified as so-called solid flame systems, where T c is lower than the melting points of both reactants and products. Consequently, the sizes of reactant particles are not expected to change in the combustion wave. The dependence of U on the average metal particle size for these systems is presented in Fig. 47. 

Fig. 47. Effect of metal particle size on combustion velocity in solid flame systems.

Increasing the sample diameter (D) increases the ratio of volumetric heat generation to surface heat loss The dependence of U on D, for different systems, is shown in Fig. 54. By increasing the diameter above a critical value, the combustion temperature approaches the adiabatic value, and U becomes constant. This behavior has been observed for the solid flame Ta-C system (curve 1), the Ti-C system (curve 2) where one reactant melts, and in Ni-Al (curve 3) where both reactants melt. The maximum measured temperature as a function of radial position in a cylindrical pellet with a diameter of 2 cm for the Mo+2Si system is presented in Fig. 55. The data show significant heat losses from the specimen. For this reason, incomplete combustion often occurs for samples with small diameter and may lead to an undesirable product phase composition (Martynenko and Borovinskaya, 1975 Bratchikov et al., 1980). 

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... 

Another family of nonplanar modes of propagation involves pairs of coun-terpropagating (CP) hot spots along the front. Such modes of solid flame propagation have been observed experimentally in [27] and have been described via numerical computations in [11]. It was found in [27] that under low pres-... 

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

A. Bayliss, B.J. Matkowsky, A.P. Aldushin, Solid Flame Waves, Chapter 4 in Perspectives and Problems in Nonlinear Science A Celebratory Volume in Honor of Larry Sirovich, Eds. E. Kaplan, J. Marsden. K. Sreenivasan, Springer Verlag, 2003... 

J.H. Park, A. Bayhss, B.J. Matkowsky, A.A. Nepomnyashchy, Period doubling cascades on the route to extinction in the interfacial motion of a nonadiabatic solid flame, submitted for pubbcation (2005). 

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