Modeling of combustion and turbulent jet diffusion flames in fractal dimensions

Abstract

Turbulent diffusion flames are considered an active field of research used in many engineering applications of combustion theory. The basic properties of jet diffusion flames were obtained in the literature, and their confrontation with observations and experiments support the mathematical aspects of combustion theory founded by famous researchers throughout dozen of years. From the other side, fractal analysis was undertaken effectively in the literature based on recent experimental studies and observations supporting the idea that flame instability results in growth of fractal structures at a flame front. Besides, fractals were used successfully to model the effects of turbulence on flame propagation in heat engines and turbulent flows. In this study, we used the new concept of “product-like fractal measure” introduced recently in the literature by Li and Ostoja-Starzewski in their formulation of anisotropic continuum media to model combustion and turbulent jet diffusion flames in fractal dimensions. The basic equations for flames in fractal dimensions have been derived and applied to study laminar and turbulent non-premixed flame besides flame extinction due to heat volumetric heat loss. Several features have been obtained and discussed in particular the application of the theory at small combustion scales.