Orbital instability and prediction of a Bunsen flame tip motion with burner rotation

An orbital instability of the unsteady flame tip motion with burner rotation and the possibility of the prediction of the flame tip motion are investigated from the viewpoint of nonlinear dynamics. A rich methane-air mixture of equivalence ratio 1.43 is used. The mean exit velocity from the burner tube, U, is varied from 0.6 to 1.3 m/s, keeping the swirl number S=1.14 constant. The variation in the flame tip motion is quantitatively evaluated by calculating the mean value of a parallel trajectory value Γ. At U⩽0.7m/s, the value of Γ is estimated to be approximately zero, indicating that periodic motion occurs. As U increases, the trajectory of the attractor becomes complicated and Γ gradually increases. The value of Γ approaches the value of the Fourier-transformed surrogate data with further increase in U. This suggests that the flame tip motion varies from periodic to chaotic due to the influence of phase randomness with increasing U. The short-term forward prediction method, that is based on the orbit of the attractor, first was used. Then the short-term forward prediction method was modified to successfully extend the prediction term. The results suggest that the modified short-term forward prediction method proposed in the present study provides a valid method for predicting the motion of unsteady flames.