Skip to the content.

KAUST-IAMCS Workshop on Multiscale Modeling, Advanced Discretization Techniques, and Simulation of Wave Propagation

Faisal Al-Malki, Taif University (Saudi Arabia)
Asymptotic and Numerical Study of the Influence of a Poiseuille Flow on Triple Flame Propagation


We present an asymptotic and numerical study of triple flame propagation in a two-dimensional mixing layer in a porous channel against a Poiseuille flow, within a thermo-diffusive model. The problem is solved analytically first in the asymptotic limit of large activation energy of the chemical reaction for flames thin compared with their typical radius of curvature. Explicit expressions are obtained in this limit, describing the influence of the flow on the triple flame. The results are expected to be applicable when the ratio between the flow scale and the flame front radius of curvature (which is mainly dictated by concentration gradients) is of order unity, or larger. When this ratio is large, as in the illustrative case of a Poiseuille flow in a porous channel considered, the flow is found to negligibly affect the flame structure except for a change in its speed by an amount which depends on the stoichiometric conditions of the mixture. This study is complemented by a numerical simulation to assess the analytical predictions and to extend the results to situations where the flame in not strictly thin in order to describe some characteristics of triple flames beyond this range, including the occurrence of extinction fronts, and the dependence of the flame speed on the flow. The numerical results have shown a good agreement with the asymptotic findings, at least in the expected domain of validity of the latter. In addition, several features have been identified such as the influence of the finite values of the Zeldovich number on the qualitative structure of flames and the transition between ignition and extinction fronts.