Numerical analysis of tulip flame by dynamic mode decomposition

Inversion of a premixed flame front to the shape of a tulip flower during the last stage of its propagation in a channel or tube of aspect ratio (AR) greater than two has intrigued the scientific community for decades. In the present work, the tulip inversion of hydrogen-air premixed flame is simulated numerically in two dimensional domains of AR 7.32, and 3.66. Dynamic Mode Decomposition is carried out on the two-dimensional pressure distribution obtained from the numerical simulation to understand the reasons behind the flame inversion. A plot of real and imaginary components of the eigenvalues over a unit circle clearly showed the presence of unstable acoustic modes during the tulip inversion for the domain of AR 7.32. The tulip inversion is not observed for the domain of AR 3.66. The distribution of the power and frequency of various modes are also plotted to identify the unstable modes. The present study shows generation of additional pressure waves during the tulip inversion process, which in term creates a velocity field that facilitates the flame inversion process.