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

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.
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https://hal.archives-ouvertes.fr/hal-00618066
Contributor : Fabrice Foucher <>
Submitted on : Thursday, February 25, 2021 - 7:11:21 PM
Last modification on : Monday, March 29, 2021 - 4:03:14 PM

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Diogo Queiros-Conde, Fabrice Foucher, Christine Mounaïm-Rousselle, H. Kassema, M. Feidt. A scale-entropy diffusion equation to describe the multi-scale features of turbulent flames near a wall. Physica A, Elsevier, 2008, 387 (27), pp.6712-6724. ⟨10.1016/j.physa.2008.09.018⟩. ⟨hal-00618066⟩

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