Aerodynamics of a slender axisymmetric Bunsen flame with large gas expansion

The flow around a stationary axisymmetric premixed flame attached to a plug flow Bunsen burner and propagating with a constant burning velocity relative to the fresh gas is analyzed for large values of the ratio of fresh gas injection velocity to flame burning velocity and small values of the burnt-to-fresh gas density ratio. The shape of the flame is close to a cone of small semiangle, and its presence induces only a small perturbation in the fresh gas. The velocity of the burnt gas is the superposition of a uniform axial velocity and the velocity induced by a line of sources on the axis of the burner. The pressure of the burnt gas on the flame is the sum of a uniform part that does not change the velocity of the fresh gas and a small variable part that causes a vertical acceleration of this gas and a slight deformation of the flame. Only a weak vorticity is generated at the flame. The analysis breaks down in small regions around the tip and the base of the flame where the assumption of a constant burning velocity is not valid.