Stability of planar flames as gasdynamic discontinuities
نویسندگان
چکیده
The stability of a steadily propagating planar premixed flame has been the subject of numerous studies since Darrieus and Landau showed that in their model flames are unstable to perturbations of any wavelength. Moreover, the instability was shown to persist even for very small wavelengths, i.e. there was no high-wavenumber cutoff of the instability. In addition to the Darrieus–Landau instability, which results from thermal expansion, analysis of the diffusional thermal model indicates that premixed flames may exhibit cellular and pulsating instabilities as a consequence of preferential diffusion. However, no previous theory captured all the instabilities including a highwavenumber cutoff for each. In Class, Matkowsky & Klimenko (2003) a unified theory is proposed which, in appropriate limits and under appropriate assumptions, recovers all the relevant previous theories. It also includes additional new terms, not present in previous theories. In the present paper we consider the stability of a uniformly propagating planar flame as a solution of the unified model. The results are then compared to those based on the models of Darrieus–Landau, Sivashinsky and Matalon–Matkowsky. In particular, it is shown that the unified model is the only model to capture the Darrieus–Landau, cellular and pulsating instabilities including a high-wavenumber cutoff for each.
منابع مشابه
On premixed flames as gasdynamic discontinuities: A simple approach to derive their propagation speed
We consider the propagation speed of thin premixed flames disturbed by the fluid flow and suggest a new approach based on using the generalized curvilinear system of coordinates and tensor calculus. The suggested technique is shown to be more simple than the traditional technique used by Sivashinsky (1976), Matalon and Matkowsky (1982a) and also in other publications. The result of Matalon and ...
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