Laminar flames theory

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. 

Variations in the initial temperature and pressure should not affect the detonation velocity for a given initial density. A rise in the initial temperature could only cause a much smaller rise in the final temperature. In laminar flame theory, a small rise in final temperature was important since the temperature was in an... 

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. 

Buckmaster, J.D. and Ludford, G.S.S., Theory of Laminar Flames, Gambridge University Press, Cambridge, 1982. 

The initial theoretical analyses for the determination of the laminar flame speed fell into three categories thermal theories, diffusion theories, and comprehensive theories. The historical development followed approximately the same order. 

The simple physical approaches proposed by Mallard and Le Chatelier [3] and Mikhelson [14] offer significant insight into the laminar flame speed and factors affecting it. Modem computational approaches now permit not only the calculation of the flame speed, but also a determination of the temperature profile and composition changes throughout the wave. These computational approaches are only as good as the thermochemical and kinetic rate values that form their database. Since these approaches include simultaneous chemical rate processes and species diffusion, they are referred to as comprehensive theories, which is the topic of Section C3. 

Comprehensive Theory and Laminar Flame Structure Analysis... 

For small-scale, high-intensity turbulence, Damkohler reasoned that the transport properties of the flame are altered from laminar kinetic theory viscosity y0 to the turbulent exchange coefficient e so that... 

Early theoretical treatments of bluff-body stabilized flame spreading have been based, in general, on the assumption that the flame is a discontinuous surface separating gas streams of different densities and temperatures [1, 15-17]. These theories neglect the finite thickness of turbulent flame zone and predict the increase of the spreading rate both with the density ratio across the flame, and with the increase in the laminar flame velocity of fuel-air mixture. This does not correspond to experimental observations (e.g., [8, 10]). 

Buckmaster, J.D., and G.S. S. Ludford. 1982. Theory of laminar flames. Cambridge, UK Cambridge University Press. 

The previous intent has been to use kinetics simply as a tool to describe qualitatively the particular aspect of combustion under study. Numerical values of the kinetic constants were thus assumed for illustrative purposes or approximated from other types of data by making admittedly questionable major assumptions. Approximations include, for example, the extrapolation of low temperature hydrocarbon oxidation rates to high temperature hydrocarbon combustion rates. Other schemes involve application of semiempirical laminar flame speed theories or of flow patterns in the wake of a bluff body immersed in an air stream (43). 

The description of laminar flame structure shows that the burning velocity will be a complex function of both the rate of the initiation process in the preheat zone and the rate of the chemical process in the reaction zone. In the literature, burning velocity is sometimes discussed as if it were purely a chemical phenomenon, but this cannot be the case to date, the only way to get information on the chemical process alone is with the aid of one of the flame-propagation theories that makes assumptions about events in the preheat zone. 

The theoretical questions which are posed and solved in these papers by Ya.B. and by Ya.B. with Yu. A. Zysin (articles 17 and 17a) have developed into an extensive separate branch of science—the theory of chemical reactors. Combustion in a reactor with ideal mixing is an example of the simplest thermal and gasdynamic situation, when the analysis requires only algebraic relations. This allows explicit demonstration of the basic features of exothermic chemical reactions in a flow which are also present in more complicated form in other combustion regimes—a laminar flame, diffusive combustion, detonation wave and others. Critical conditions of ignition and extinction and the existence of several regimes whose occurrence depends on the initial conditions—these are the most remarkable effects of combustion which attract the attention even of laymen. The relative ease of recording them makes them a convenient tool for physico-chemical research. 

The last two sections of this paper will discuss this interplay between detailed modelling and both theory and experiment. The third section describes how a model must be tested in various limits for physical consistency to insure its accuracy. The specific example chosen here is a comparison between an analytic solution and a detailed numerical simulation of a premixed laminar flame. The last section shows how a comparison between model results and experiments can be used to calibrate the model and to guide further experiments. The example chosen is a calculation of flow over an immersed object which is compared to both experimental and theoretical results. 

J. D. Buckmaster and G. S. S. Ludford, Theory of Laminar Flames, Cambridge University Press, 1982. 

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