Statistical Errors in the Fractal Analysis of Flame Boundaries
A high speed tomographic technique is used to evaluate the effect of spatial resolution, and requirements for statistical convergence on the fractal analysis of a turbulent, premixed, stoichiometric methane/air flame at high Damkoehler number. The gas velocity at the nozzle exit is 5 m/s, the turbulence intensity is 7%, the integral length scale 3 mm and hence the turbulence Reynolds number is 70. The light source is a copper vapor laser which produces 20ns, 5 mJ pulses at a 4KHz repetition rate. Cylindrical lenses transform the 38mm circular laser beam to a sheet 50 mm high and 0.6 mm thick. A high speed Fastax camera is used to record the tomographic images formed by the scattering of light from oil droplets seeded in the reactant flow. The films are digitized and the flame front extracted from the images by a thresholding technique. Digitization noise, which appears in the fractal plots at approximately twice the pixel resolution, can obscure the inner cutoff. Simple smoothing can remove this problem if the spatial resolution is sufficient. At insufficient resolution smoothing produces plausible resolutes are produced which in fact erroneous. If the inner cutoff is ambiguous the range over which the fractal dimension is determined will be unclear. The wide distribution of fractal dimensions obtained from the individual images indicates the necessity of ensemble averaging the fractal plots if reliable statistical results are to be obtained. 8 refs., 6 figs.
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