Flame-vortex interaction: Effect of residence time and formulation of a new efficiency function

In this study, a combined experimental and numerical investigation of a toroidal vortex interacting with a stagnation premixed flame is carried out with the aim of quantifying the ability of such a vortex to stretch the flame. By scrutinizing the literature, it was found that, although inferred from exactly similar numerical simulations, existing parametric expressions for the efficiency function (the ratio of the flame stretch to vortex strain) do not agree in the way the latter should behave when the ratio of the vortex rotational velocity Uθ to the laminar flame speed SL is increased. These expressions also appear to be unequally accurate when compared to experimental data and do not feature the non monotonic evolution of the efficiency function with Uθ/SL which is observed in both experimental data and numerical simulations of a 'isothermal' propagating interface. In addition, whilst previous studies have focused only on the impact of Uθ/SL and Rv/δL (Rv being the vortex typical size and δL the laminar flame thickness) our study reveals the importance of other parameters, the most important of which being the residence time of the vortex associated with its convection velocity. These results yield a new formulation for the efficiency function which compares favorably well with experimental data.