Landau-Darrieus instability and the fractal dimension of flame frontsстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:Nonlinear dynamics of a slow laminar flame front subject to the Landau-Darrieus instability is investigated by means of numerical simulations of the Frankel equation, when the expansion degree γ=(ρ$_u$-ρ$_b$)/ρ$_u$ is small (here ρ$_u$ and ρ$_b$ are the densities of the unburned and burned “gases,” respectively). Only burning in two-dimensional space is considered in our simulations. The observed acceleration of a front wrinkled by the instability can be ascribed to the development of a fractal structure along the front surface with typical spatial scales being between the maximum and the minimum truly unstable wavelengths. It is found that the fractal excess ΔD=D-1 decreases rapidly with decreasing of γ, to a first approximation as ΔD=D$_0$γ$^2$, where D is the fractal dimension of the front. Our rough estimation of D$_0$ gives D$_0$~=0.3. The low accuracy of the D$_0$ estimation is caused by certain peculiarities of the Frankel equation that lead to extreme difficulties of its simulation even with the aid of supercomputers when γ\lt~0.3-0.4. It is shown, however, that D$_0$ can be calculated also from the statistical properties of the Sivashinsky equation, which is easier to simulate, though the fractal excess for the Sivashinsky equation itself is equal to 0 (in a certain sense). The other important result of our simulations is that the front self-intersections play an extremely weak role when γ is small.