A scale-entropy diffusion equation to describe the multi-scale features of turbulent flames near a wall

D. Queiros-Conde, F. Foucher, C. Mounaïm-Rousselle, H. Kassem and M. Feidt

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 27, 6712-6724

Abstract: Multi-scale features of turbulent flames near a wall display two kinds of scale-dependent fractal features. In scale-space, an unique fractal dimension cannot be defined and the fractal dimension of the front is scale-dependent. Moreover, when the front approaches the wall, this dependency changes: fractal dimension also depends on the wall-distance. Our aim here is to propose a general geometrical framework that provides the possibility to integrate these two cases, in order to describe the multi-scale structure of turbulent flames interacting with a wall. Based on the scale-entropy quantity, which is simply linked to the roughness of the front, we thus introduce a general scale-entropy diffusion equation. We define the notion of “scale-evolutivity” which characterises the deviation of a multi-scale system from the pure fractal behaviour. The specific case of a constant “scale-evolutivity” over the scale–range is studied. In this case, called “parabolic scaling”, the fractal dimension is a linear function of the logarithm of scale. The case of a constant scale-evolutivity in the wall-distance space implies that the fractal dimension depends linearly on the logarithm of the wall-distance. We then verified experimentally, that parabolic scaling represents a good approximation of the real multi-scale features of turbulent flames near a wall.

Keywords: Scale-dependent fractal; Flame-wall interaction; Turbulent combustion; Scale-entropy; Entropic-skins geometry (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:27:p:6712-6724

DOI: 10.1016/j.physa.2008.09.018

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