A scale-entropy diffusion equation to describe the multi-scale features of turbulent flames near a wall |
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Authors: | D Queiros-Conde F Foucher H Kassem |
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Institution: | a ENSTA-ParisTech, Unité Chimie et Procédés, 32 Bb Victor, 75015 Paris, France b LME, Polytech’Orléans, Université d’Orléans, 45072 Orléans, France c LEMTA, ENSEM-INPL, 2 Av. de la Forêt de Haye, F-54504 Vandoeuvre lès Nancy, France |
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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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Keywords: | 45 53 +n 47 70 Pq |
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