OGAWA Toshiyuki    Department   Undergraduate School  , School of Interdisciplinary Mathematical Sciences    Position   Professor
Language	English
Publication Date	2013
Type	Academic Journal
Title	Pattern formation in reverse smouldering combustion: A homogenization approach
Contribution Type	Co-authored (other than first author)
Journal	Combustion Theory and Modelling
Volume, Issue, Page	17(2),pp.185-223
Author and coauthor	E. Ijioma，A.Muntean
Details	The development of fingering char patterns on the surface of porous thin materials has been investigated in the framework of reverse combustion. This macroscopic characteristic feature of combustible media has also been studied experimentally and through the use of phenomenological models. However, not much attention has been given to the behaviour of the emerging patterns based on characteristic material properties. Starting from a microscopic description of the combustion process, macroscopic models of reverse combustion that are derived by the application of the homogenisation technique are presented. Using proper scaling by means of a small scale parameter ϵ, the results of the formal asymptotic procedure are justified by qualitative multiscale numerical simulations at the microscopic and macroscopic levels. We consider two equilibrium models that are based on effective conductivity contrasts, in a simple adiabatic situation, to investigate the formation of unstable fingering patterns on the surface of a charred material. The behaviour of the emerging patterns is analysed using primarily the Péclet and Lewis numbers as control parameters.