An Asymptotic Theory of Heterogeneous Condensed Combustion
Titel:
An Asymptotic Theory of Heterogeneous Condensed Combustion
Auteur:
Margolis, Stephen B.
Verschenen in:
Combustion science and technology
Paginering:
Jaargang 43 (1985) nr. 3-4 pagina's 197-215
Jaar:
1985
Inhoud:
The reaction rate of a heterogeneous, or diffusion-limited, reaction in a solid combustible mixture, sub seq uent to melting of one of the reactants, is proportional to exp[ - m(1- Y)](l- y)-n exp( - e˜/t˜), where Y is the unreacted fraction and r is the temperature. We exploit the largeness of the activation energy Eto derive an asymptotic model for the propagation of a reaction front through such a mixture. The analysis parallels a similar study of homogeneous condensed combustion (Margolis, 1983), in which the reaction rate both before and after melting is proportional to Y exp( - e˜/t˜). We derive formulas for the propagation speed of a steady planar reaction front, as well as present the asymptotic model for nonsteady, non planar combustion. This model is identical in form to that obtained from a special limiting case of the homogeneous problem. Thus, the well-known loss of stability of the stead y planar solution for sufficiently large values of a modified activation energy parameter, and the bifuraction to va rious pulsating and spinningmodes of propagation, is essentially unchanged from that predicted for homogeneous condensed combustion (Margolis et al.,1985). Con sequently, this nonsteady instability is attributable to the more highly nonlinear Arrhenius dependence on temperature for large activation energies, and is independent of the functional dependence of the reaction rate on Y.
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