Extinction of counterflow diffusion flames in counter-rotating finite jets

Extinction of counterflow diffusion flames located between counter-rotating porous disks of large radial extent and finite axial separation distance is theoretically investigated using the method of large activation energy asymptotics. It is shown that slow rotation of the jets modifies the critical minimum values of the Damköhler number at extinction δ_0Eidentified earlier by Liñén for non-rotating, infinite-jet counterflow diffusion flames. In the treatment of the reactive flow, the inviscid limit is considered such that while the diffusion of heat and species concentrations are included, that of momentum is suppressed. The minimum fuel molar concentration at extinction XF_E is found to decrease to a minimum value F_v and increase thereafter with the jet angular velocity ω in qualitative agreement with the experimental observations. Also the envelope of XF_E vs ω curves at different jet velocity V is found to be linear. General aspects of interactions between three randomly moving vectors associated with the linear and angular velocities and the unit normal vector to the instantaneous flame surface are described. The relevance of the findings to the modeling of local flamelet extinction/combustion in turbulent diffusion flames is discussed.