Characteristics of cylindrical flame acceleration in outward expansion

We have studied the outward propagation of a cylindrical flame by means of a flame-tracking numerical method and direct computation of the Sivashinsky equation. The flame speed is modified by the local curvature, via a Markstein length l, that somehow groups the complicated physiochemical effects and can be monotonically relevant to the system pressure. The flame is found to accelerate in a universal profile as a function of time, which is insensitive to initial perturbations after a self-similar regime is reached. The extent of acceleration can be quantified by an exponent of a power law that approximates the dependency of the average flame radius on time. It is shown that the growth exponent is invariant with respect to l while it increases with the density ratio between the unburned and burned gases (q). Furthermore, various fitting approaches are discussed and the proper one is found to satisfy the formal relation according to the fractal analysis. Therefore the diversity of the exponent that was supposed to be invariant as reported in the literature, ranging from 1.25 to 1.5, would be realized via the variation in q as well as the fitting methods, while other factors might also be involved such as the sampling and uncertainty of fitted data. (C) 2008 American Institute of Physics.