THEORY OF LAMINAR FLAMES

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. 

The problem of determining the propagation velocity of a deflagration wave was first studied by Mallard and le Chatelier [1], who considered heat loss to be of predominant importance and rates of chemical reactions to be secondary. The essential result that the burning velocity is proportional to the square root of the reaction rate and to the square root of the ratio of the thermal conductivity to the specific heat at constant pressure was first demonstrated by Mikhel son [2], whose work has been discussed in more recent literature [3], [4]. Independent investigations by Mallard s student Taffanel [5] and by Daniell [6] based on simplified models of the combustion wave reached the same conclusion. Subsequently, improved basic equations became available for use in theoretical analyses. 

In more recent years, the idea that the overall activation energy is large in comparison with the thermal enthalpy has led to the development 

FIGURE 5.1. Schematic diagram of a typical laminar-flame experiment. 

FIGURE 5.2. Photograph of a natural gas-air flame on a rectangular burner, with very small magnesium oxide particles introduced into the flow and illuminated stroboscopically in order to make the gas streamlines visible (from [11], courtesy of B. Lewis and of Academic Press). 

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

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

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

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