Statistical errors in the fractal analysis of flame boundaries

Conference · Mon Oct 01 04:00:00 EDT 1990

OSTI ID:6381826

Shepherd, I G; Cheng, R K

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.

• Research Organization: Lawrence Berkeley Lab., CA (USA)
• Sponsoring Organization: DOE/ER
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 6381826
• Report Number(s): LBL-29666; CONF-9010207--3; ON: DE91001795
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400800* -- Combustion
Pyrolysis
& High-Temperature Chemistry
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
AIR
ALKANES
BOUNDARY CONDITIONS
CHEMICAL REACTIONS
COMBUSTION
CONVERGENCE
DIAGNOSTIC TECHNIQUES
DISTRIBUTION FUNCTIONS
ERRORS
FLAMES
FLUIDS
FRACTALS
FUNCTIONS
GAS LASERS
GASES
HYDROCARBONS
LASERS
MATHEMATICAL MODELS
METHANE
ORGANIC COMPOUNDS
OXIDATION
RESOLUTION
SPATIAL RESOLUTION
STATISTICAL MODELS
THERMOCHEMICAL PROCESSES
TOMOGRAPHY
TURBULENCE