Flame modeling

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... 

In the standard ZFK flame model [6], the chemical reaction rate, Q, is governed by a first-order irreversible one-step Arrhenius law... 

Colin, O., et al., A thickened flame model for large-eddy simulations of turbulent premixed combustion. Phi/s. Fluids, 2000.12(7) 1843-1863. 

Echekki, T., A. R. Kerstein, T. D. Dreeben, and J.-Y. Chen (2001). One-dimensional turbulence simulation of turbulent jet diffusion flames Model formulation and illustrative applications. Combustion and Flame 125, 1083-1105. 

Rogg, B., A. Linan, and F. A. Williams. 1986. Deflagration regimes of laminar flames modeled after the ozone decomposition flame. Combustion Flame 65 79-101. 

Bui, P.-A., D. G. Vlachos, and P. R. Westmoreland. 1997. Self-sustained oscillations in distributed flames modeled with detailed chemistry. Eastern States Section, Chemical and Physical Processes in Combustion Proceedings. Pittsburgh, PA The Combustion Institute. 337-40. 

Generally, the gas-phase reactions in both flame models for premixed gases and the burning of energetic materials are assumed to be bimolecular and hence of second order. Eq. (3.54) can then be expressed as... 

D. R. Dillehay, "Pyrotechnie Flame Modeling for Sodium D-Line Emissions," Proceedings, Fifth International Pyrotech-nies Seminar, Denver Research Institute, Vail, Colorado, July, 1976, p. 123 (available from NTIS as AD A087 513). 

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

Figure 9. Heat supply to propellant surface by A/PA and O/F stages in the granular diffusion flame model...

These calculations were performed for the assumed physical constants listed in the Appendix. The results are shown in Figures 9-14, together with the predictions of the collapsed A/PA granular diffusion flame model of the previous section. 

The work of Mayer and Cams (44) gives a theoretical analysis of flame propagation in a laminar flame model based on simplified reaction kinetics. 

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