Transition from periodic to non-periodic motion of a Bunsen-type premixed flame tip with burner rotation

Unsteady motions of a Bunsen-type premixed flame tip with burner rotation are experimentally investigated from the viewpoint of nonlinear dynamics. The mean velocity from burner tube U is varied from 0.6 to 1.2 m/s, and the rotational speed of the burner tube N is varied from 0 to 2800 rpm. A rich methane/air mixture with the equivalence ratio of ø = 1.43 is used. With the Lewis number Le larger than unity, an axisymmetric oscillating flame is formed between a conical flame and a plateau flame at U = 0.6m/s and swirl number S = 1.14. As U and N increase, but with S constant, the oscillating flame tip motion becomes unstable. This variation in the flame tip motion is shown qualitatively by drawing an attractor and evaluated quantitatively by estimating the correlation dimension. For U ≤ 0.8 m/s, the attractor is a limit cycle and the correlation dimension D_c is estimated at about unity, indicating periodic motion. When U reaches 1.0 m/s, the trajectories of the attractor become rolled up slightly and D_c approaches about 2, indicating quasi-periodic flame tip motion. With a further increase in U, the attractor becomes much more complicated and D_c is estimated as a non-integer value, indicating a deterministic chaos. These results indicate that the flame tip motion with the burner rotation under the condition of Le > 1 varies from periodic to non-periodic (i.e., to chaotic). The present results also show that an analysis based on deterministic chaos theory, such as the correlation dimension, is valid for quantifying the motion of unsteady flames.