Flame speed theory

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 chronology of the most remarkable contributions to combustion in the early stages of its development is as follows. In 1815, Sir Humphry Davy developed the miner s safety lamp. In 1826, Michael Faraday gave a series of lectures and wrote The Chemical History of Candle. In 1855, Robert Bunsen developed his premixed gas burner and measured flame temperatures and flame speed. Francois-Ernest Mallard and Emile Le Chatelier studied flame propagation and proposed the first flame structure theory in 1883. At the same time, the first evidence of detonation was discovered in 1879-1881 by Marcellin Berthelot and Paul Vieille this was immediately confirmed in 1881 by Mallard and Le Chatelier. In 1899-1905, David Chapman and Emile Jouguet developed the theory of deflagration and detonation and calculated the speed of detonation. In 1900, Paul Vieille provided the physical explanation of detonation... 

A theory, termed as the back-pressure drive flame propagation theory, has been proposed to account for the measured flame speeds [12]. This theory gives the momentum flux conservation on the axis of rotation in the form of... 

In this simplified situation, can we really consider that the mean flame structure and thickness are steady, after certain delay and distance from initiation, and then the "turbulent flame speed" is a well-defined intrinsic quantity Indeed, with the present state of knowledge, there is no certainty in any answer to this question. Of course, it is hardly possible to build an experiment with nondecaying turbulence without external stirring. In deca)dng turbulence, the independence of the turbulent flame speed on the choice of reference values of progress variable has been verified in neither experiment nor theory. 

The amount of explosion overpressure is determined by the flame speed of the explosion. Flame speed is a function of the turbulence created within the vapor cloud that is released and the level of fuel mixture within the combustible limits. Maximum flame velocities in test conditions are usually obtained in mixtures that contain slightly more fuel than is required for stoichiometric combustion. Turbulence is created by the confinement and congestion within the particular area. Modem open air explosion theories suggest that all onshore hydrocarbon process plants have enough congestion and confinement to produce vapor cloud explosions. Certainly confinement and congestion are available on most offshore production platforms to some degree. 

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. 

A theory, that certain flame retardants vaporize and produce an effect by acting as free-radical chain stoppers to extinguish the flame or to inhibit the flame speed of the burning gases, was proposed. It is based on extensive smdies for 30-40 years [Kuryla and Papa, 1978]. The research efforts devoted to understand the mechanisms of combustion and inhibition for solid materials burning with a diffusion flame in an air environment has multiplied rapidly in the last two decades. 

A transition in the behaviour of the flame is obtained for an equivalence ratio of 0.4. Below this value, the flame becomes unstable correlations of flame speeds and maximum reaction rates along the flame front change sign when the equivalence ratio goes from rich to lean. A similar transition was observed for simple chemistry situations but for a Lewis number of unity. The definition of a Lewis number in a real flame is difficult but in this case, the trend observed in simple chemistry cases (and predicted by asymptotic theories) is confirmed by complex chemistry computations. 

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