Insights into non-adiabatic-equilibrium flame temperatures during millimeter-size vortex/flame interactions

Previous experimental and numerical studies have demonstrated that local flame temperatures can significantly increase above or decrease below the adiabatic-equilibrium flame temperature during millimeter-size vortex/flame interactions. Such large excursions in temperature are not observed in centimeter-size vortex/flame interactions. To identify the physical mechanisms responsible for these super- or sub-adiabatic-equilibrium flame temperatures, numerical studies have been conducted for millimeter-size vortex/flame interactions in a hydrogen-air, opposing-jet diffusion flame. Contrary to expectations, preferential diffusion between H2 and O2 and geometrical curvature are not responsible for these variations in local flame temperature. This was demonstrated through simulations made by forcing the diffusion coefficients of H2 and O2 to be equal and thereby eliminating preferential diffusion. Propagation of flame into small (~1 mm) vortices suggested that the amount of reactant carried by such a small vortex is not sufficient to feed the flame with fresh reactant during the entire vortex/flame interaction process. Various numerical experiments showed that the reactant-limiting characteristics associated with the millimeter-size vortices and the local Lewis number (not preferential diffusion) are responsible for the generation of flame temperature that is different from the adiabatic-equilibrium value. The reactant-deficient nature of the millimeter-size vortices forces the combustion products to be entrained into the vortex. While a greater-than-unity Lewis number results in pre-heating of the reactant through the product entrainment, a less-than-unity Lewis number causes cooling of the reactant. Contrary to this behavior, a centimeter-size large vortex wraps and maintains the flame around its outer perimeter by feeding the flame with fresh reactant throughout the interaction process, thereby rendering the flame unaffected by the Lewis number. Since turbulent flames generally involve interactions with small-size vortices, the physical mechanisms described here should be considered when developing mathematical models for turbulent flames.