Abstract
Flame acceleration associated with development of the Landau–Darrieus hydrodynamic instability is studied by means of direct numerical simulation of the Navier–Stokes equations including chemical kinetics in the form of the Arrhenius law. The fractal excess for radially expanding flames in cylindrical geometry is evaluated. Two-dimensional (2-D) simulation of radially expanding flames in cylindrical geometry displays a radial growth with 1.25 power law temporal behavior after some transient time. It is shown that the fractal excess for 2-D geometry obtained in the numerical simulation is in good agreement with theoretical predictions. The difference in fractal dimension between 2-D cylidrical and three-dimensional spherical radially expanding flames is outlined. Extrapolation of the obtained results for the case of spherical expanding flames gives a radial growth power law that is consistent with temporal behavior obtained in the survey of experimental data.
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