The influence of combustion on the fluid structure in a counter-flow diffusion flame

Abstract

In outlining their experiments on counter-flow diffusion flames in the upstream region of a porous cylinder, Tsuji and Yamaoka [1] used a normal gradient of normal velocity as the single most important parameter in characterising the flow in each experiment. These normal gradients were calculated from ‘cold’ potential flow conditions. More recently, these same normal gradients have been used in attempted simulations of the experiments by way of a similarity solution of the boundary-layer equations. The outer boundary conditions for the fluid were derived from the potential flow solution approximated close to the stagnation point. Such solutions assume a Hiemenz type flow with a constant gradient throughout. The analysis relies on the assumption that the entire combustion and heat conduction region is confined to a thin layer ‘blown off’ a porous cylinder. A comparison with experiment and simple calculation of the order of magnitude of the thickness of the ‘boundary-layer’ shows that it is inappropriate to use this type of analysis. A numerical solution is presented which models the fluid dynamic and chemical characteristics of a counter-flow diffusion flame surrounding a porous cylinder. The model relies on the technique of direct co-ordinate expansions. Closure of the conservation equations is effected by assuming that the chemical heat release gives rise to large normal gradients. It is shown that the fluid mechanics differ radically from those encountered in the ‘cold flow’ calculations. The boundary conditions in the present case are taken from the potential solution of fluid flowing over a cylinder. The existence of a sheart layer is shown separating the combustion zone from the unheated outer flow and this leads to the calculation of a displacement thickness providing an ‘effective radius’ for the cylinder seen by the outer unheated fluid as it approaches the combustion zone. The ‘effective radius’ may be then used as a new boundary condition for the reactive flow. The finite difference equations are solved by a Newton-iteration scheme utilising an adaptive mesh. Profiles are presented for normal and tangential velocities, temperature, chemical species (for a single global reaction mechanism) and mixture density versus radial distance measured from the cyclinder surface. Extension to more complicated kinetics is not a difficulty. It is also proposed that in the light of these results extinction limits be defined at the flame ‘position’ defined with reactive flow parameters rather than using the assumption of undisturbed ‘cold flow’ conditions.