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

Diogo Queiros-Conde (1) , Fabrice Foucher (2) , Christine Mounaïm-Rousselle (2) , H. Kassema (1) , M. Feidt (3)

1 ENSTA Paris - École Nationale Supérieure de Techniques Avancées
2 Ecole Polytechnique de l'Université d'Orléans
3 LEMTA - Laboratoire d'Energétique et Mécanique Théorique et Appliquée

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.

Domaines: Milieux fluides et réactifs

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: Statistical Mechanics and its Applications, 2008, 387 (27), pp.6712-6724. ⟨10.1016/j.physa.2008.09.018⟩. ⟨hal-00618066⟩