Effects of fresh gas velocity and thermal expansion on the structure of a Bunsen flame tip

Numerical computations and order-of-magnitude estimates are used to describe the tip region of a Bunsen flame where the flame departs from a planar flame at an angle to the incoming fresh gas flow. A single irreversible Arrhenius reaction with high activation energy is assumed. The well-known linear relation between flame velocity and curvature is recovered in the thermodiffusive limit, when the thermal expansion of the gas is left out, for velocities of the fresh gas ( U 0 ) only slightly larger than the velocity of a planar flame ( U L ) , provided this flame is stable. For large values of the velocity ratio U 0 / U L , the tip region becomes slender and the curvature of the reaction sheet at the tip increases proportionally to U 0 / U L . The thermal expansion of the gas across the flame reduces the aspect ratio of the tip region. A qualitative analysis of the structure of the tip region for very exothermic reactions shows that this region ceases to be slender when the burnt-to-fresh gas temperature ratio becomes of the order of the velocity ratio U 0 / U L . For even larger values of the temperature ratio, the tip region becomes a cap of characteristic size not very different from the thickness of a planar flame.