Flame theory

The discussion of laminar diffusion flame theory addresses both the gaseous diffusion flames and the single-drop evaporation and combustion, as there are some similarities between gaseous and Hquid diffusion flame theories (2). A frequentiy used model of diffusion flames has been developed (34), and despite some of the restrictive assumptions of the model, it gives a good description of diffusion flame behavior. 

In addition to the Burke and Schumann model (34) and the Displacement Distance theory, a comprehensive laminar diffusion flame theory can be written using the equations of conservation of species, energy, and momentum, including diffusion, heat transfer, and chemical reaction. 

Note that diffusion flame theory will show the flame temperature is approximately given by 7f Too + Lix,unit mass of oxygen consumed. 

Considering that the temperature difference 9 must be equivalent to (T - T9 in the Zeldovich-Frank-Kamenetskii-Semenov thermal flame theory, the reaction time corresponding to the reaction zone 6 in the flame can also be approximated by... 

See also "Epreuve de propagation dans une gouttiere in Vol 5 of Encycl, p E138-L and also some refs under "Flame Theories )... 

Flame Theories. The following are some refs on this subject ... 

D.B. Spaulding, 6thSympCombstn, Yale Univ 1956, 12-20, 35 refs(Publ 1957) (Ends and means in flame theory, a review)... 

Figure 4. Burning rate data plotted to test validity of granular diffusion flame theory (99)...

If finite chemical reaction times are put into the columnar diffusion flame theory (76), burning rates are predicted to be linearly proportional to pressure at low pressure and independent of pressure (plateau burning) at high pressure. Based on this model, von Elbe et al. (97) proposed the simple equation ... 

Figure 10. Granular diffusion flame theory predictions plotted as (p/r) vs. (p)2/3 for collapsed and distended A/PA flames...

Figure 11. Pressure dependence of burning rate predicted by the granular diffusion flame theory for the case (1) where premixed ammonia/perchloric acid flame is distended and (2) where it is collapsed...

Figure 12. Effect of activation energy of surface reaction on burning rate behavior of granular diffusion flame theory with collapsed A/PA flame zone...

Figure 13. Pressure dependence of flame zone thicknesses predicted by granular diffusion flame theory with distended A/PA flame...

Normal-burning propellants such as PBAA-AP and PB(CT)-AP are in qualitative agreement with the behavior predicted by the granular diffusion flame theory when the NH3/HCIO4 reaction is considered distended. Quantitative comparison between theory and experiment is not... 

Thus, we find a remarkable lack of sensitivity for the calculated burning rates of an adiabatic droplet-burning process in which the reactions go to completion. This observed lack of sensitivity to reaction rates may well be related to the known successes (11,12, 22) of simplified diffusion-flame theories in theoretical predictions of droplet burning rates. 

T. Takeno and S. Ishizuka. A Tubular Flame Theory. Combust. Flame, 64 83-98. 1986. 

A list of substances which have been used or considered to support decomposition flames is shown in Table I. Almost all of these substances have been studied at one time or another to provide fundamental information for the evaluation of the theory of flame propagation. As previously mentioned, the ozone decomposition has proved most useful as the basis of a flame which is amenable to both theoretical and experimental study. The NO decomposition flame provided a situation where a clear-cut prediction was made possible by flame theory (P2). On the basis of a flame calculation it was predicted that a strong preheat would permit the stabilization of this flame at a measurable flame velocity, since it was known that a flame would not propagate into the gas at room temperature. Subsequent experimental work confirmed the prediction by stabilizing a flame with approximately the predicted value. This places a great deal of... 

In full-scale Are modeling, a diffusion flame structure is usually assumed. However, in many fire situations, such as underventilated fires, premixed or partially premixed flame theory may be more appropriate. The Burke-Schumann description of the diffusion flames can be used to conveniently represent the transport of gaseous species by a single scalar quantity called mixture fraction. For a simple one-step reaction ... 

Spalding, D. B., Some Thoughts on Flame Theory, Proc. of the Third AGARD Colloquium, Pergamon, London, 1958, pages 269-296. 

While Gray Yang are not denying the usefulness of such ideas, they consider that too literal an application on the distinction can lead to difficulties. For this reason they tried to unify both theories and this problem is discussed in (heir paper. They also examined the effect of fuel consumption on thermal explosions, definition of critical conditions and the effects of vessel shapes. Finally, the relationship between thermal explosion criteria and flame theory described by Belles (Ref 2), as well as detonability limits were pointed out. Comments on the paper of Gray Yang of Profs R.R. Baldwin R. Ben-Aim are given on p 1061 of Ref 3 Refs 1) N.N. Semenov, "Chemical Kinetics... 

This chapter concerns the structures and propagation velocities of the deflagration waves defined in Chapter 2. Deflagrations, or laminar flames, constitute the central problem of combustion theory in at least two respects. First, the earliest combustion problem to require the simultaneous consideration of transport phenomena and of chemical kinetics was the deflagration problem. Second, knowledge of the concepts developed and results obtained in laminar-flame theory is essential for many other studies in combustion. Attention here is restricted to the steadily propagating, planar laminar flame. Time-dependent and multidimensional effects are considered in Chapter 9. 

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