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 (U0)(U0) only slightly larger than the velocity of a planar flame (UL)(UL), provided this flame is stable. For large values of the velocity ratio U0/ULU0/UL, the tip region becomes slender and the curvature of the reaction sheet at the tip increases proportionally to U0/ULU0/UL. 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 U0/ULU0/UL. 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.