Numerical analysis of tulip flame formation in a closed vessel

We have investigated the mechanism of tulip flame formation in a closed vessel by means of numerical analysis. We simulated the unsteady motions of two-dimensional reactive flows using the explicit MacCormack scheme. The numerical model contained compressibility, viscosity, heat conduction, molecular diffusion, reaction, and convection. It was shown in the simulation that the flame is initially convex toward the unburned gas and that a cusp forms at the center of the flame; then the cusp grows and the tulip-shaped flame forms. The history of flame shapes was qualitatively consistent with the experimental results. It is essential to tulip flame formation that the heat release rate is decreased when the semi-elliptic flame reaches the side walls. The cusp on the flame is caused by this and the flame becomes tulip shaped. The growth of the cusp can be explained by the flame close to the wall running faster because of much consumption of the unburned gas and by the hydrodynamic instability of premixed flame fronts.